Magnetotelluric data analysis using advances in ... - Geomagnetism

. 

Magnetotelluric data analysis using 

advances in signal processing 

techniques 

C. MANOJ 

National Geophysical Research Institute, Hyderabad – 500 007, 

India 

. 

THESIS SUBMITTED TO THE OSMANIA UNIVERSITY FOR THE 

AWARD OF THE DEGREE OF DOCTOR OF PHILOSOPHY IN 

GEOPHYSICS 2003

ii 

Declaration 

I, hereby declare that the thesis submitted for the award of the Degree of Doctor of 

Philosophy in Geophysics of the Osmania University, Hyderabad, India is original in its 

contents and has not been submitted before, either in parts or in full to any University 

for any research degree. 

(C. Manoj) 

Candidate 

Dr. V. P. Dimri 

Dr. Nandini Nagarajan 

Director 

Research Supervisor 

National Geophysical Research Institute Scientist 

Hyderabad 

NGRI 

Hyderabad

iii 

Certificate 

This is to certify that the thesis, entitled ‘Magnetotelluric data analysis using advances 

in signal processing techniques’, which is submitted for the award of the Degree of Doctor 

of Philosophy in Geophysics to the Osmania University, Hyderabad, India, is the bonafide 

research work carried out by Mr. C. Manoj at National Geophysical Research Institute, 

Hyderabad, India during the years 1998 to 2003 under my supervision. The work is 

original and has not been submitted for any Degree at this or any other University 

20-08-2003 

(Nandini Nagarajan) 

Research Supervisor 

Scientist 

NGRI 

Hyderabad 500007 

India

iv 

Acknowledgement 

I sincerely thank Dr. Nandini Nagarajan for the support and guidance she extended 

to my research program as a research supervisor, over the past five years of my work at 

National Geophysical Research Institute. As a mentor and group head of Magnetotellurics 

Division, Dr S. V. S. Sarma gave me moral and institutional support in the early phases 

of my Ph.D program. The present group head Dr. T. Harinarayana also adopted the 

same approach. Dr. H.K. Gupta and Dr. V.P. Dimri, the former and present Directors 

of NGRI, kindly encouraged me to pursue the research work. 

Prof. (late) P.S. Moharir and Mr. G. Virupakshi are profusely thanked for the hours 

of discussion they had with me. Understanding my limitations, they fixed many bugs 

in my computer codes as well as knowledge. The staff of the offices of Dean, Faculty of 

Science and Head, Department of Geophysics, Osmania University is thanked for their 

co-operation throughout the research program. The Senior colleagues of magnetotellurics 

group: Mr. D.N. Murthy, Dr. R.S. Sastry, Dr. M. Someswara Rao, Mr. M.V.C. Sarma, 

Dr. Madhusudan Rao, Dr. K. Veeraswamy and Mr. S. Prabhakar E. Rao are thanked for 

initiating me in magnetotellurics and their help during field campaigns. As immediate 

colleagues, I acknowledge the support of Dr. B.P.K. Patro, Dr. K. Naganjaneyulu, Dr. 

K. Begum, and Mr. K.K. Abdul Azeez for their cooperation and support. Financial 

support from the following agencies is also acknowledged. 

The magnetotelluric data for the present studies were acquired in a project funded by 

Department of Science & Technology, Government of India (No. ESS/16/118/1997). I 

received the Junior Research Fellowship of Council of Scientific and Industrial Research 

(No. 2-31/97(i)-E.U.II) during the initial phase of the research program. Suggestions 

by Dr. Martyn Unsworth, Dr. John Stodt and Dr. Xavier Garcia greatly improved 

a part of the thesis. I take this opportunity to thank my friends Dr. Shyam Chand, 

Dr. Jimmy Stephen, Dr. R. S. Rajesh and Mr. Tomson J.K for their comradeship that 

helped me in different stages of the research program. I thank my wife Mrs Namitha Vaz, 

daughter Meenakshi, father Mr. M.K.C. Nair and mother Mrs. M.N. Sarojini Amma for 

the patience and support they extended to me during my research program.

v 

Magnetotelluric data analysis using 

advances in signal processing techniques 

SYNOPSIS 

Electrical conductivity is one of the most important physical parameters directly indicating 

the Earth’s subsurface nature. Rocks exhibit a wide range (∼ 10 6 ) of conductivity 

and the electrical conductivity of rocks is sensitive to temperature, presence of fluid, 

volatiles, melt as well as its bulk composition. These qualities make electrical conductivity 

an appropriate method to delineate Earth’s subsurface features with a suitable 

measurement at surface. Over the past century a suite of electrical and electromagnetic 

methods was established to probe electrical conductivity structure of the Earth. Among 

them, the natural source electromagnetic method - Magnetotellurics has many advantages 

over all the other methods: with the skin depth relation of EM waves it can virtually 

probe any depth and the natural electromagnetic signals have enough power over a wide 

range of frequencies to penetrate the subsurface (Cagniard [1953]). Thus magnetotelluric 

(MT) method has become a promising technique to probe deep earth structure. The 

magnetotelluric induction, though diffusive in nature like potential fields, is not inherently 

non- unique like potential fields methods. The uniqueness of this method in cases 

where conductivity varies vertically (1-Dimensional) is established (Bailey [1970], Weidelt 

[1972]) in theory. Non-uniqueness in magnetotellurics may results from 1) errors in 

measurement 2) finite frequency range of data and 3) sparse distribution of measurement 

sites. MT practitioners, therefore, strive to obtain more precise data in wider bandwidth 

and with more spatial density. As a result remarkable progress has been made to instrumentation 

(Clarke et al. [1983], Ritter et al. [1998]) and time series processing (Gamble 

et al. [1979], Egbert and Booker [1986], Chave and Thomson [1989]) in the past two 

decades that resulted in better estimation of full tensor (transfer function) elements and 

their variance over a wide band of frequency. Together with the progress of decomposing 

the impedance tensor into regional and residual (Groom and Bailey [1989], McNeice and 

Jones [2001]) and the advances in inversion (Constable et al. [1987], Smith and Booker 

[1991], Siripunvaraporn and Egbert [2000], Rodi and Mackie [2001]), magnetotellurics 

has become a standard tool to determine Earth’s electrical conductivity structure. 

The first step in interpretation of magnetotelluric data is to estimate the MT 

impedance tensor in frequency domain from measured magnetotelluric time series. Magnetotelluric 

time series consist of five simultaneously measured components of earth’s 

electromagnetic field viz. two orthogonal components of horizontal electric fields (Ex, 

Ey in mV/ km) and three orthogonal components of magnetic field (Hx, Hy, Hz in nT). 

Usually the measurements are done in wide bands of overlapping frequency ranges, with 

different sampling intervals. Measured time series are the compounded effect of various 

signal and noise processes in the frequency range of interest to MT. The objective of MT 

processing is to discriminate signal and minimize the effect of noise in the estimation of 

MT transfer function tensor Z . The use of traditional spectral analysis together with 

least squares (LS) estimation is warranted only if the input channels (magnetic fields) 

are noise free, the output channel noise has a Gaussian distribution and the MT time 

series is stationary (Banks [1998]). In reality most data usually show gross departures 

from the above idealistic model. The main causes are geomagnetic phenomena, thunder-

vi 

storms, cultural interference and instrument problems. This results in highly oscillating 

and biased estimates of MT transfer functions. ‘Remote reference’ technique (Gamble 

et al. [1979]) deals with the noise in magnetic fields. Reference magnetic field is recorded 

at a site, which is far outside the coherency range of the noise. Using the cross spectrum 

with the remote site instead of the autopower eliminates the bias in the magnetic field 

power. Problems due to non-stationarity of time series are addressed by subdividing the 

time series (Egbert and Booker [1986], Banks [1998]) into small segments, estimating 

transfer functions for each one and averaging in a way that discriminates against noisy 

data segments. Robust estimation of MT transfer functions (Egbert and Booker [1986], 

Chave et al. [1987], Chave and Thomson [1989]) down weights the data sections with 

such large non Gaussian noise. But this technique still gives erroneous results, if strongly 

correlated noise is present during most of the recording time. To deal with such coherent 

noise, ‘robust multivariate errors-in-variables’ (RMEV) estimate was developed by Egbert 

[1997]. Correlated and uncorrelated noise are separated iteratively, using data from 

multiple stations. Variants of this technique viz. Signal-Noise Separation (SNS) method 

and SNS-remote-reference method are discussed by Larsen et al. [1996] and Oettinger 

et al. [2001]. In a very recent work, Chave and Thomson [2003] proposed a bounded 

influence function to robustly estimate magnetotelluric data contaminated with extreme 

noises. Over the past decade, conventional robust methods have revolutionized the application 

of magnetotellurics in geophysics (Jones et al. [1989], Egbert [1997]) and are now 

applied routinely and automatically producing reliable magnetotelluric responses in most 

instances. The success of robust procedures may be attributed to three factors. First, 

its superiority to other data processing techniques is established (Jones et al. [1989]). 

Second, these procedures can be justified rigorously (Egbert and Livelybrooks [1996]) 

and third it can be easily implemented using iterative-weighted LS procedures and extended 

to remote reference processing (Chave and Thomson [1989]). However at sites 

located near auroral region (Garcia et al. [1997]), major cultural noise centres, electric 

railway lines etc where source field non-stationarity /noise contamination is severe, robust 

methods frequently break down. The possible reasons may be attributed to:- 

1. Failure in identifying noise source for a survey often prompts the processing of all 

sites in a similar fashion. Whereas, stations that were affected with noise should 

undergo special data treatment. 

2. Any MT time series processing algorithm performs better, if presented with a data 

set that is as clean as possible. This is often done by manual inspection of time 

series. A failure/omission at this stage may contribute to break down of robust 

processing. 

3. Conventional robust processing uses an initial estimate of MT transfer functions 

usually derived from an LS estimator. When majority of observations deviate from 

the true one, the initial LS estimate becomes too far (biased) for the robust iterative 

process to improve upon. 

4. The cross and auto spectra between electric and magnetic field elements are usually 

smoothed by a combination of band and section averaging. While effect of outliers 

in section averaging is well known, the same about band averaging is overlooked.

vii 

The present thesis concentrates on these problems of MT time series analysis, with 

an aim to improve the estimation of transfer functions. The wide band magnetotelluric 

data collected over Southern Granulite Terrain, offers scope for development of applications 

that may resist extreme noise contamination. There are two factors that make this 

region important in this context. 1) The majority of upper crustal rocks in SGT belong 

to Archaean and Proterozoic age (Naqvi and Rogers [1987]) and exhibit high electrical 

resistivity as other shield regions in the world (Mareschal et al. [1994]). Highly resistive 

upper crust offers very little attenuation to EM signals and in principle noise can 

propagate over larger distance in SGT as compared to regions where younger rocks are 

exposed. 2) The high population density in the southern states of India, especially in 

Tamil Nadu, where most of the MT sites are located give rise to various cultural noises. 

The industrial belt along the two banks of Cauvery River is another noise source for MT. 

In this context, the objectives of the present thesis are, 

1. To characterize the signal/noise in magnetotelluric data collected over SGT, in 

spatial, temporal and frequency domain and to locate the major sources of noise in 

the data. 

2. To evolve an efficient and automated method to discriminate noisy segments of time 

series. The enrichment of s/n ratio in the data provided by such a process will help 

the robust processing to better estimate MT transfer functions. 

3. To improve the robust processing methods of MT transfer functions particularly 

concentrating on the weak points (reasons stated as (iii) and (iv) earlier) in the 

method, while dealing with noisy data. 

4. Establish the efficacy of the processing methods proposed by application to sufficiently 

large amount of data collected from SGT. 

A suite of advanced signal processing algorithms will be used for achieving the above 

objectives. Typically MT time series is a large volume of multi-channel data (∼10 6 values) 

that are usually stored in compressed, binary format with a header file describing 

location, sensor geometry and filter setting, and the data itself. A variety of MT equipment 

is currently in use, which delivers MT data in wide bands of frequencies. Standards 

have been evolved in industry for the delivery and exchange of electromagnetic data, MT 

in particular, as Electrical Data Interchange (EDI) format by Society of Exploration Geophysicists 

(E. [1988]). Though it can support time series data as well, it is not being used 

so due to a various reasons. As time series is one-step closer to actual data generation 

at the instrument than the MT transfer functions, the variation in MT hardware also 

constraints the adoption of uni-format for MT time series. The major academic software 

for MT time series processing, currently available free of charge are codes from Egbert 

[1997], RRMT by Chave A.D, LiMS by Jones A.G. (available at http://mtnet.info) and 

EMERALD by Ritter et al. [1998]. These codes are written specifically for certain types 

of MT instruments and for use on particular operating systems. The commercial manufacturers 

of MT equipment also give processing software as part of the system (for e.g. 

ProcMT r○ and MAPROS r○ from Metronix GmBH) which optimize user requirements,

viii 

though not as versatile as the academic software. Moreover these software strictly cater 

to the needs of one MT equipment, and mostly their source codes are not open. This 

scenario puts pressure on researchers working on MT time series processing. In order to 

modify processing routines, it is necessary to access the time series, calibrate the data 

etc, which have been specifically evolved for particular equipment. Any new processing 

codes, need to be attached to a time series reading, calibrating and storing utility, which 

also has to be developed. Thus time series processing algorithm should have end to end 

utilities, which involves reading compressed time series data, reading the sensor geometry 

and filter settings, calibrating for system responses, the main processing and finally the 

exporting the results in EDI format. In one way this facilitates easy interchange of data 

and flexibility of applications, compared to a framework, wherein one relies on a set of 

imported utilities to perform the peripheral tasks. For the current thesis, the processing 

codes were written on end to end basis, where it performs all the peripheral processing 

tasks as well. 

As remote reference processing has been increasingly used by MT practitioners, in 

tandem with a robust processing algorithm, a question can be asked ’Why should we be 

concerned with single station processing at all?’. There are several good reasons. First, 

because of instrumental problem (as happened during data acquisition in SGT), it is 

common to have single station recording in many surveys. If the ’reference’ site is very 

noisy and the ’local’ site is not, single station estimation could be better than remote 

reference estimates (Egbert and Livelybrooks [1996]). These factors often necessitate 

single station processing of MT data. However the procedures developed in this thesis 

can easily be extended to remote reference processing as well (an example in this regard is 

discussed in Chapter 6). The thesis spreads in seven chapters. In the following sections, 

an overview of the different chapters in the thesis is given. 

Chapter I 

Maxwell’s equations describe the properties of electromagnetic waves. The relationship 

between electric and magnetic filed within a conductive Earth can be expressed in 

terms of wave equations by combining Maxwell’s equations. A conductive Earth responds 

to the electromagnetic illumination at the surface by allowing the refracted components 

to diffuse according to their frequency content. In consequence the magnetotelluric fields 

contain information regarding conductivity distribution as a function of frequency. Instrumentation 

and field procedures play an important part in the quality of measured 

magnetotelluric data. A discussion on field procedures, sensors and measuring device 

employed to measure magnetotelluric data is given towards the end of Chapter 1. 

Chapter II 

The magnetotelluric transfer functions are obtained by the simultaneous measurement 

of Earth’s time varying electrical and magnetic field. The sources of the natural electromagnetic 

fields in the frequency range 10 −4 to 10 4 Hz have ’quasi-planar’ properties at 

the surface of the Earth. Natural signal sources for MT measurements in the frequency 

range 10 0 to 10 4 Hz are worldwide thunderstorm activity. At frequencies below 1 Hz the 

source signals are generated due to the interaction of magnetosphere with solar wind. 

Observed magnetotelluric fields at the surface of Earth contain additive noises from various 

manmade and natural sources, which do not behave as plane waves. A discussion on 

different signal and noise sources and their effect in MT data is included in Chapter II.

ix 

Chapter III 

This chapter introduces the concepts of random data analysis. Magnetotelluric time 

series like many other natural processes can be considered as wide band random data. 

And thus the estimation of its properties becomes statistical (Bendat and Piersol [1971]). 

A brief review of some of its properties viz. probability distribution functions, autocorrelation 

and power spectral density function are discussed. As magnetotelluric signals 

constitute a multivariate system, the joint properties of individual components like cross 

correlation, cross spectra and coherencies are also important. Reliable estimation of 

magnetotelluric transfer function depends on the amount of noise in the time series measurements 

(Orange, 1989). It is often difficult to obtain noise free measurements as the 

method relies on highly variable natural electromagnetic variation. Severe problems are 

caused by civilization, which produce all kinds of electromagnetic noises. These noises 

manifest themselves in the computed magnetotelluric transfer function as both statistical 

and bias shifts. Sims et al. [1971] proposed the classical least square solution for MT 

transfer functions from noisy measured data. The statistical errors can be minimized by 

averaging large amount of observations, if the noise distribution is Gaussian. As least 

square solutions envisages a noise free input field, noise in input field can severely bias 

such estimates. The bias errors can be tackled to an extent by measuring a remote 

reference (Gamble et al. [1979]). But as shown by Chave et al. [1987], Chave and Thomson 

[1989], Egbert and Booker [1986], violation of the Gaussian assumption for errors 

may lead to severe problems in least square estimation of MT transfer functions. The 

properties of a least square estimator is discussed towards the end of Chapter III. 

Chapter IV 

The data used in the present study were measured over South India, as a part of an 

integrated geological and geophysical study on the Southern Granulite Terrain by NGRI 

under a DST project. The magnetotelluric measurements were carried out in two field 

campaigns from 1998 to 2000. The sites were located in a 300-km long NS corridor. The 

profile traverses major metamorphic and tectonic elements of the region. Harinarayana 

et al. [2003] discusses the result of modeling of the data in terms of subsurface electrical 

conductivity distributions and their importance in local tectonic set up. Five components 

of natural EM variations were measured in the frequency range 0.0001 - 4000 s. The data 

were acquired in four frequency bands. The spatial distribution and quantity of data 

collected is described in detail in Chapter IV. Most of the data were collected in single 

station reference, as the measurement units had time synchronization problems. This 

necessitated use of single station processing techniques (Chapter III) for majority of MT 

sites measured. The measurement corridor passes through many urban areas and one 

industrial belt. Major electrified rail lines passes through some parts of the corridor. More 

over the southern region of India is densely populated. The cultural noises thus generated 

can propagate over large distances, as the upper crust is highly resistive. The indices 

of geomagnetic activity during the measurement time were compared with the averaged 

long period coherence of each site. The agreement of the coherence and the geomagnetic 

indices indicate the validity of such an approach. However a few disagreements were 

also evident. This indicates the possible noise processes contributing to the measured 

data. Spatial relation of the known cultural noise centers and the quality of MT data 

was examined. The strong correlation of the high noise/(signal +noise) ratio to the

x 

major industrial belt indicate that the MT signals may get consistently degraded due 

to presence of an active noise sources, irrespective of the signal activity. However the 

conclusions drawn from this chapter should be treated rather cautiously. The signal 

and noise are defined in this chapter as inline and outline components of a least square 

solution of MT transfer functions. 

Chapter V 

The techniques outlined in Chapter III for estimation of magnetotelluric transfer functions 

from measured imprecise data requires that the time series is presented as clean 

as possible. Cleaning of MT time series is presently done by manual inspection (editing). 

Editing of magnetotelluric time series is subjective in nature and time consuming. 

Artificial neural networks (ANN) are widely used to automate processes, which requires 

human intelligence. In Chapter V Artificial Neural Network is used to discriminate good 

sections of data against noisy ones. Artificial neural networks (ANN) are emerging tools 

that have been applied in many areas of science and engineering where pattern recognition 

is involved, such as speech and character recognition. The learning and adaptive 

capabilities of these models make them attractive for application to some problems in 

geophysics. As ANN based techniques are computationally intensive, a novel approach 

was made to the problem, which involves editing of five simultaneously measured MT 

time series. Neural network training was done at two levels. Signal and noise patterns 

of individual channels were taught first. Training was stopped when both errors were 

below acceptable level. The neural network’s sensitivity to signal to noise ratio and the 

relative significance of it’s inputs were tested to ensure the training was correct. The application 

of ANN based editing to magnetotelluric time series brings out some interesting 

results. In a low noise environment the network editing produces results almost similar 

to blind editing (using all stacks). On such a data, a simple coherency-based estimator 

can do the signal discrimination to a certain level of satisfaction. However the neural 

network’s ability to pick out signal from moderate to high noise environment was evident 

on the other data collected from SGT. In such cases it approximates human intelligence 

- established from the fact that the neural network based editing gives a result similar 

to manual editing. These results satisfy the second objective of the thesis, i.e., to provide 

a robust alternative to manual editing of magnetotelluric time series. The signal 

and noise characteristics in magnetotelluric data are very different in different frequency 

ranges. This is due to the difference in signal and noise source mechanism in different 

part of Earth’s natural electromagnetic spectrum. Sensor geometry and instrumentation 

also affect the pattern of signal on which the neural network is trained. This necessitates 

reformulation of MT signal and noise characteristics for training of ANN, wherever 

necessary. However the extra computational requirement of re-training of ANN may not 

pose a burden on resources, taking into consideration the ever-increasing computational 

power of microprocessors. 

Chapter VI 

In chapter VI, two new approaches are proposed to improve the performance of robust 

statistical procedures on MT time series. Non-parametric estimators such as Jackknife 

(Efron [1982]) were used to robustly compute the variance of MT transfer functions 

(Chave and Thomson [1989]). Its use as an effective initial guess for robust procedures is 

discussed. It is shown that in majority of the cases, the use of Jackknife for initial guess

xi 

resulted in better estimation of MT transfer function as compared to LS estimations. It 

is usual in MT to sub divide the time series, estimate the spectral density matrices for 

each segment individually and then robustly average the spectra or transfer functions 

between the sub segments (section averaging). Within a segment, it is common to use 

a limited number of target frequencies, and obtain smooth spectra by averaging several 

adjacent Fourier harmonics (frequency band averaging). The documented researches on 

robust estimation of MT spectral densities and transfer functions concentrate on section 

averaging. This arises from the assumption that, within a narrow frequency band, the 

distribution of Fourier coefficients are of Gaussian nature and a simple average (LS) 

gives the best estimate. It is shown that this argument often fails, and the problem of 

contamination is applicable to band averaging as well. Robust weighting approach is 

proposed for estimation of cross and auto spectral estimation within a band, without 

making specific model assumptions concerning signal or noise. Both these proposed 

procedures, while applied on a large volume of MT data collected over SGT, South India, 

met with moderate to good improvement of MT transfer functions. 

Chapter VII 

Chapter VII gives an overall summary of the results discussed in chapter IV to VI. 

The main objective of the thesis, i.e. to obtain best estimates of transfer function from 

measured magnetotelluric time series, may require a combination of one or more techniques 

introduced and demonstrated in the chapters IV to VI. Furthermore, Chapter VII 

will take a closer look at the properties of robust processing and neural networks. On 

comparison of individual performances of neural networks and robust processing, it was 

found that their reaction to different types of noise differs in some cases. One reason is 

that the outliers / or coherent noises which are obvious in time domain, failed to produce 

larger outliers and thus were not down weighted by robust procedures. In another 

instance, data sets with noises, which the neural network allowed to pass on, were down 

weighted by robust procedures. This clearly shows the need to combine the two techniques 

in order to discriminate / down weight a majority of noisy data. Further more, 

this points to the necessity of transforming the data more than one domain to discriminate 

noise from signal. In this regard, possible use of wavelet transform in identifying 

transient signals that are the common form of MT signals in for frequencies > 1Hz is 

suggested as a future work.

Contents 

1 Magnetotellurics: Basic Theory, Sensors and Field Procedures 1 

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 

1.1.1 Source fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 

1.1.2 Maxwell’s equations . . . . . . . . . . . . . . . . . . . . . . . . . 3 

1.1.3 Skin depth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 

1.1.4 Impedance tensor: . . . . . . . . . . . . . . . . . . . . . . . . . . 5 

1.1.5 Amplitude and phase of impedance: . . . . . . . . . . . . . . . . . 8 

1.2 Sensors and Field Procedures . . . . . . . . . . . . . . . . . . . . . . . . 8 

1.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 

1.2.2 Electric field sensors . . . . . . . . . . . . . . . . . . . . . . . . . 9 

1.2.3 Magnetic Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 

1.2.4 Recording systems . . . . . . . . . . . . . . . . . . . . . . . . . . 12 

1.3 Field Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 

1.3.1 Survey design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 

1.3.2 Site selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 

1.3.3 Sensor deployment . . . . . . . . . . . . . . . . . . . . . . . . . . 15 

1.3.4 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 

1.3.5 Data acquisition. . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 

2 Signal and Noise Sources for magnetotellurics 18 

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 

2.2 Signal sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 

2.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 

2.2.2 Geomagnetic pulsations . . . . . . . . . . . . . . . . . . . . . . . 21 

2.2.3 Thunder storm activity . . . . . . . . . . . . . . . . . . . . . . . . 23 

2.3 Noise Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 

2.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 

2.3.2 Noises from power line signals . . . . . . . . . . . . . . . . . . . . 25 

2.3.3 Noise from electric traction . . . . . . . . . . . . . . . . . . . . . 26 

2.3.4 Noises from instrument & sensors . . . . . . . . . . . . . . . . . . 27 

2.3.5 Noises from the other sources . . . . . . . . . . . . . . . . . . . . 28 

2.4 Effect of active electrical noise in magnetotelluric data . . . . . . . . . . 29 

xii

xiii 

3 Magnetotelluric time series analysis 31 

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 

3.2 Random data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 

3.2.1 Properties of random data . . . . . . . . . . . . . . . . . . . . . . 33 

3.2.1.1 Probability density function . . . . . . . . . . . . . . . . 33 

3.2.1.2 Mean square and variance . . . . . . . . . . . . . . . . . 34 

3.2.1.3 Median and average absolute deviation. . . . . . . . . . 34 

3.2.1.4 Autocorrelation function . . . . . . . . . . . . . . . . . . 35 

3.2.1.5 Power spectral density function . . . . . . . . . . . . . . 35 

3.2.2 Joint signal properties . . . . . . . . . . . . . . . . . . . . . . . . 36 

3.2.2.1 Cross correlation functions . . . . . . . . . . . . . . . . . 36 

3.2.2.2 Cross-spectral density functions . . . . . . . . . . . . . . 37 

3.2.2.3 Coherence . . . . . . . . . . . . . . . . . . . . . . . . . . 38 

3.2.3 Computational aspects . . . . . . . . . . . . . . . . . . . . . . . . 38 

3.2.3.1 Trend and bias removal . . . . . . . . . . . . . . . . . . 38 

3.2.3.2 Power Spectral Density function . . . . . . . . . . . . . 38 

3.2.3.3 Windowing . . . . . . . . . . . . . . . . . . . . . . . . . 39 

3.2.3.4 Discrete Fourier Transform . . . . . . . . . . . . . . . . 39 

3.2.3.5 Smoothing of spectra by band and section averaging . . 40 

3.3 Magnetotelluric transfer functions . . . . . . . . . . . . . . . . . . . . . . 41 

3.3.1 Least Square Solution . . . . . . . . . . . . . . . . . . . . . . . . 41 

3.3.1.1 Multi input, multi output linear system . . . . . . . . . 41 

3.3.1.2 Solution with noise free data . . . . . . . . . . . . . . . 42 

3.3.1.3 Solution with noise in measurement . . . . . . . . . . . . 43 

3.3.2 Concept of bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 

3.3.2.1 Predicted coherence . . . . . . . . . . . . . . . . . . . . 45 

3.3.3 Coherent and incoherent noises . . . . . . . . . . . . . . . . . . . 45 

3.3.4 Variance & Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 

3.3.5 Coherence and bias of transfer functions . . . . . . . . . . . . . . 46 

3.3.6 Remote reference . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 

4 Signal and Noise Characteristics of MT data measured over the Southern 

Granulite Terrain 49 

4.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 

4.2 Geological objectives of MT investigations in the SGT . . . . . . . . . . 50 

4.3 The Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 

4.3.1 Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 

4.3.2 Typical MT Time series . . . . . . . . . . . . . . . . . . . . . . . 53 

4.3.3 Examples of MT data collected over South India . . . . . . . . . . 55 

4.4 The EEJ effect on MT data . . . . . . . . . . . . . . . . . . . . . . . . . 59 

4.5 Signal Activity during the Field Campaign . . . . . . . . . . . . . . . . . 61 

4.6 Spatial character of coherence . . . . . . . . . . . . . . . . . . . . . . . . 62 

4.7 Geographic relation of noise . . . . . . . . . . . . . . . . . . . . . . . . . 64 

4.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

xiv 

5 The application of the artificial neural networks to magnetotelluric time 

series analysis 67 

5.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 

5.2 Signal and noise in the magnetotelluric time series . . . . . . . . . . . . 68 

5.3 Visual Inspection (editing) of magnetotelluric time series data; why automation 

? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 

5.4 Magnetotelluric noise characterization . . . . . . . . . . . . . . . . . . . . 70 

5.4.1 Patterns of signal & noise : . . . . . . . . . . . . . . . . . . . . . 70 

5.4.2 Amplitude of signals . . . . . . . . . . . . . . . . . . . . . . . . . 71 

5.4.3 Correlation between simultaneously measured channels . . . . . . 71 

5.5 Artificial Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . 71 

5.5.1 Why artificial neural network? . . . . . . . . . . . . . . . . . . . . 71 

5.5.2 ANN theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 

5.6 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 

5.6.1 Network engineering . . . . . . . . . . . . . . . . . . . . . . . . . 74 

5.6.2 Pattern Training . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 

5.6.2.1 Data used: . . . . . . . . . . . . . . . . . . . . . . . . . 75 

5.6.2.2 Pre-processing . . . . . . . . . . . . . . . . . . . . . . . 75 

5.6.2.3 FANN Training . . . . . . . . . . . . . . . . . . . . . . . 76 

5.6.2.4 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . 77 

5.6.3 Inter channel training . . . . . . . . . . . . . . . . . . . . . . . . 78 

5.6.3.1 The data . . . . . . . . . . . . . . . . . . . . . . . . . . 78 

5.6.3.2 FANN training . . . . . . . . . . . . . . . . . . . . . . . 80 

5.6.3.3 Relative significance of input . . . . . . . . . . . . . . . 81 

5.7 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 

5.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 

6 Estimation of Magnetotelluric Transfer Functions: Robust Statistical 

Methods 88 

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 

6.2 Robust estimation of MT transfer functions . . . . . . . . . . . . . . . . 90 

6.2.1 Why robust methods? . . . . . . . . . . . . . . . . . . . . . . . . 90 

6.2.2 Robust M estimators . . . . . . . . . . . . . . . . . . . . . . . . . 91 

6.2.3 Choice of influence functions . . . . . . . . . . . . . . . . . . . . . 93 

6.2.4 Implementation for MT . . . . . . . . . . . . . . . . . . . . . . . 95 

6.2.4.1 Initial guess of transfer function . . . . . . . . . . . . . . 96 

6.2.4.2 Jackknife estimate as initial guess . . . . . . . . . . . . . 96 

6.2.4.3 Scale estimate . . . . . . . . . . . . . . . . . . . . . . . . 100 

6.2.4.4 Robust transfer function estimation . . . . . . . . . . . . 100 

6.2.4.5 Tukey weights . . . . . . . . . . . . . . . . . . . . . . . . 101 

6.2.4.6 Computing the variance . . . . . . . . . . . . . . . . . . 101 

6.2.4.7 Quantile Quantile plots . . . . . . . . . . . . . . . . . . 101 

6.2.5 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 

6.2.5.1 Flowchart . . . . . . . . . . . . . . . . . . . . . . . . . . 102 

6.2.5.2 Comparison of robust processing schemes . . . . . . . . 104

xv 

6.3 Robust Band averaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 

6.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 

6.3.2 Effect of frequency band width . . . . . . . . . . . . . . . . . . . 109 

6.3.3 Robust estimation of spectra . . . . . . . . . . . . . . . . . . . . . 111 

6.3.4 Flow chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 

6.3.5 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 

6.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 

6.4.1 VP14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 

6.4.2 TT08 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 

6.4.3 TT04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 

6.4.4 OK18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 

6.4.5 JN12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 

6.4.6 VP16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 

6.4.7 OK16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 

6.4.8 VP12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 

6.4.9 Comparison of results from the Vellar - Palani profile in SGT . . . 118 

6.4.10 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 

7 Discussion and conclusions 131 

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 

7.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 

7.3 Neural Network and Robust processing . . . . . . . . . . . . . . . . . . . 133 

7.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 

7.5 Suggestions for future work . . . . . . . . . . . . . . . . . . . . . . . . . 137 

Bibliography

List of Figures 

1.1 Quasi planar nature of electromagnteic wave front at great distance from 

source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 

1.2 Behaviour of plane EM wave at the surface of a conducting Earth . . . . 3 

1.3 Diagrammatic representation of 1D, 2D and 3D situations. . . . . . . . 6 

1.4 Planar view. Off diagonal tensor elements become unequal when geology 

has a preferred direction. On rotating the tensor to the strike, diagonal 

elements get minimized. See text for discussion . . . . . . . . . . . . . . 7 

1.5 Implanting of Electrical Field sensor . . . . . . . . . . . . . . . . . . . . 10 

1.6 Installation of induction coil magnetometer . . . . . . . . . . . . . . . . 11 

1.7 Simplified equivalent circuit for induction coil magnetometer . . . . . . . 11 

1.8 Theoretical response function for MFS05 magnetometer (from Pulz and 

Ritter [2001]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 

1.9 Block diagram depicting different signal processing steps in GMS05 

(adapted from Metronix [1997]) . . . . . . . . . . . . . . . . . . . . . . . 14 

1.10 GPU05 (main unit) and HDU05 (display unit) during data acquisition . 14 

1.11 Typical lay out for MT sensors and data acquisition (after Metronix [1997]) 16 

2.1 Earths horizontal magnetic field spectrum (Modified after Macnae et al. 

[1984]) The Black and gray bars indicate the frequency range of measurement 

bands for GMS05. (see 1.1) . . . . . . . . . . . . . . . . . . . . . . 20 

2.2 Plot for MT time series recorded at site VP16 showing geomagnetic pulsations 

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 

2.3 Averaged magnetic amplitude spectra (Hx) at station VP16. Peaks related 

to geomagnetic pulsations are labeled.Thick (gray) line represents 

smoothed spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 

2.4 Plot of MT time series showing impulse signals related to sferics recorded 

at site C12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 

2.5 Electric Field (Ex) spectral amplitude depicting the Schumann resonance 24 

2.6 Distribution of electromagnetic field strength of three phase power transmission 

line in the immediate vicinity of power lines (adopted from Szarka 

[1988]). H total magnetic field, E horizontal electric field. . . . . . . . . 26 

2.7 Amplitude spectra of electric field computed over different data length for 

the site OK14. Thin black line - 1024, Thick gray line 256 and Gray dots 

- 128. See text for discussion . . . . . . . . . . . . . . . . . . . . . . . . 27 

xvi

xvii 

2.8 Current circuit electric railway systems. I is the current in the overhead 

power line I1 is the return current in the rails and I2 is the return current 

in the Earth ( modified after Chaize and Lavergne [1970]). . . . . . . . . 28 

2.9 Near and far field effect of a grounded dipole on MT measurements 

(adapted from Zonge and Hughes [1991]). The two panels on left and 

right describes the apparent resistivity and phase values for far field and 

near field measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 

2.10 Effect of a near field source on MT data, as recorded at the station OK14. 

See text for discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 

3.1 Ordered —Zxy— plotted against number of occurrences observed at station 

C13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 

3.2 Crosscorrelogram of two magnetotelluric time series components. . . . . . 37 

3.3 The Parzen spectral window over the target frequency plotted on background 

of a sample spectra . . . . . . . . . . . . . . . . . . . . . . . . . 40 

3.4 Magnetotelluric linear system with two horizontal magnetic components 

as inputs and horizontal electric components as outputs. Adapted from 

Jones et al. [1989]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 

3.5 MT Transfer function (Z xy ) computed using upward and downward biased 

estimators compared with the coherence functions for station VP20. The 

upper part of the diagram shows real and imaginary components of upward 

and downward biased estimates. The variance of Z xy is shown as solid line. 

The lower part shows the predicted (multiple) and ordinary coherence 

functions. See the text for discussion. . . . . . . . . . . . . . . . . . . . . 47 

4.1 MT stations superimposed over the geology of the measurement corridor 

in South India (Geology adapted from GSI [1995]). See text for discussion 51 

4.2 Typical MT time series measured in the SGT for two frequency ranges a) 

the frequency range 256 Hz to 32kHz (band 1) and b) the period range 8 

Hz to 256 Hz (band2) .See the text for discussion. . . . . . . . . . . . . . 54 

4.3 Typical MT time series measured in the SGT for two frequency ranges c) 

the frequency range 8Hz to 0.25 Hz (band 3) and d) the period range 4 

sec to 128 sec.See the text for discussion. . . . . . . . . . . . . . . . . . 56 

4.4 Plot of apparent resistivity, phase, predicted coherence and degree of freedom 

(DOF) vs frequency for four stations measured over South India. 

Data are computed in their measured direction. See text for discussion . 58 

4.5 Apparent resistivity vs frequency plot for 3 stations tht are near and away 

from the dip equator with day and night curves superimposed (Rao et al. 

[2002]). (a) OK3 - site 300 km north of dip equator, (b) IRA site 100 km 

north of dip equator and (3) KAR - site near the dip equator. . . . . . . 60 

4.6 Averaged Kp indices [Courtesy NGDC], K indices [HYB] during the MT 

measurements are compared with telluric predicted coherence [4 sec 128 

sec]. The mean coherence is drawn as a line. . . . . . . . . . . . . . . . 61

xviii 

4.7 The band averaged telluric predicted coherence plotted as a contoured map 

for all the measured MT sites. (a) Band1 (b) Band2 (c) Band 3 and (d) 

Band4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 

4.8 Contoured map of telluric Noise/(Signal+Noise) ratio, superimposed on 

the major geographical elements of the region. Note N/(S+N) ratio on 

either sides of Cauvery river near Sankari. . . . . . . . . . . . . . . . . . 65 

5.1 Common signal and noise patterns in long period MT time series. Samples 

are collected from different sites. Note the change in amplitudes. (a) Signal 

patterns; Samples of E x and H y shows the geomagnetic pulsations. Other 

channels also show signals but at longer periods. (b) Noise patterns; E y & 

H x shows different types of spikes. A step and its decay is shown in H y . 

Sample of random noise is shown in H z . . . . . . . . . . . . . . . . . . . 69 

5.2 Simple three layer feed forward neural network. The data is processed at 

each neuron in the layers. Each neuron performs a summing of inputs multiplied 

with a weight parameter and outputs the data through its sigmoid 

transfer function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 

5.3 Data flow through the feed forward artificial neural network (FANN) based 

editing scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 

5.4 Stacked amplitude and phase spectra of the training database. The spectra 

of noisy data (class 0.1) clearly different from the signals (class 0.9). . . 76 

5.5 Results from the pattern training. (a) The SSE as a function of epoch. 

The error reached the minimum floor after 400 epochs. Stability of convergence 

is demonstrated up to 1000 epochs. (b) Deviation between manually 

classified and network predicted classes for 500 test time series segments. 

The scattered points shows the major deviations. The correct picking 

constitute 94 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 

5.6 Network output versus signal content. The network was simulated by 

inputs with varying signal content. A narrow region of high variance exists 

when signal content is between 65 . . . . . . . . . . . . . . . . . . . . . . 78 

5.7 Pattern, amplitude ratios and correlation coefficients of 900 stacks which 

form the database for inter channel training and testing . The thick line is 

the running average over 10 points. The broken bar indicates the overall 

stack quality - black good (0.9) and white bad (0.1). (a) E x (squares) and 

E y (triangles) pattern quality predicted as a function of stack number. 

(b) E x - H y (squares) and E y − H x (triangles) amplitude ratio. (c) The 

correlation coefficients of E x to H y (squares) and E y to H x (triangles). . 79 

5.8 Results from inter channel training. (a) The SSE as a function of training 

epoch. (b) Deviation between manually classified stack quality and network 

predicted for 250 stacks. 235 stacks were classified similar to manual 

classification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 

5.9 Relative significance of various inputs to the networks, viz amplitude ratios 

(A1 and A2), correlation coefficients (C1 and C2) and five pattern 

qualities (E x , E y , H x , H y andH z ). The error deviation against each input is 

a measure of its significance to the Neural Network. . . . . . . . . . . . 82

xix 

5.10 Comparison of MT apparent resistivity and phase computed from different 

mode of editing of data from site G12 . Filled circles represent xy and 

diamonds represent yx components. (a) Using all stacks available. (b) By 

neural network editing. (c) By manual editing. . . . . . . . . . . . . . . 83 


mode of editing of data from site VP12 . Filled circles represent xy and 




mode of editing of data from site JN10 . Filled circles represent xy and 




mode of editing of data from site TT08 . Filled circles represent xy and 



5.14 Comparison of manual and neural signal picking for site TT8. The diamonds 

present the neural picking and crosses, the manual. . . . . . . . . 86 

6.1 Examples where robust statistical methods are desirable: (a) A one dimensional 

distribution with heavy tails (b) A distribution in two dimensions 

fitted to straight lines. Adapted from Flannery et al. [1992] . . . . . . . . 92 

6.2 Schematic diagram showing loss, influence and weight functions for Least 

Square (LS or L2) , Least Absolute (L1) Huber and Tukey estimators. 

Values shown in y axis are arbitrary See text for discussion. Adapted from 

Zhang [1996] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 

6.3 Responses of different influence functions to a set of residuals from MT 

data processing. Station VP13 Shows the Ex residuals for 0.1875 Hz for 

all the 105 stacks. (b) Shows the response of three influence functions to 

the residuals. See text for discussion. . . . . . . . . . . . . . . . . . . . . 95 

6.4 Comparison of Least Square and Jackknife estimation of MT transfer functions 

for station VP10 (a) Jackknife difference for the first iteration. (b) 

Variance as a function of iteration number. (c) and (d) comparison of ρ 

and φ values from LS & JK processing . . . . . . . . . . . . . . . . . . . 98 

6.5 Comparison of Least Square and Jackknife estimation of MT transfer functions 

for station VP13 (a) Jackknife difference for the first iteration. (b) 

Variance as a function of iteration number. (c) and (d) comparison of ρ 

and φ values from LS & JK processing . . . . . . . . . . . . . . . . . . . 99 

6.6 Comparison of Least Square and Robust processing of magnetotelluric data 

station TT08 for frequency 0.0791Hz . Triangles represent LS processing, 

and stars represent robust (RB) processing (a) and (b) time series of Ex 

residuals. C) Quantile Quantile plot of Ex residuals d) MT apparent resistivity 

and phase values from LS and robust processing. See text for 

discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

xx 

6.7 Flow chart for robust processing scheme. The gray area represents the proposed 

initialization of the transfer functions using Jackknife. This routine, 

concentrates on the section averaging of MT data. See text for discussion. 103 

6.8 Data flow through the flow chart representing robust processing of MT 

data. The gray area represents the proposed Jackknife initialization. (a) 

Process A uses Jackknife (JK) as initial guess and (b) process B uses Least 

Square (LS) as initial guess. See text for discussion. . . . . . . . . . . . . 104 

6.9 Comparison of robust processing results using Least Square (LS) and Jackknife 

(JK) initialization for stations JN12, VP16, OK16 and VP12. Process 

A refers to robust processing with JK initialization, where as Process 

B refers robust processing with LS initialization See legend for symbol 

identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 

6.10 Comparison of robust processing results using Least Square (LS) and Jackknife 

(JK) initialization for stations VP14,TT08,TT04 and OK18. Process 

A refers to robust processing with JK initialization, where as Process B 

refers robust processing with LS initialization. See legend for symbol identification 

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 

6.11 Spectrum estimation in MT using band averaging. (a) to (d) windows in 

frequency with different radii. Though the window radius seems to increase 

as period increases, effective bandwidth remains the same, as spectrum in 

long period contains fewer Fourier harmonics. (e) Sample E x Ex ∗ spectrum 

in the band 4, with target frequencies projected as dotted lines. It is 

common to have 10 12 target frequencies per band. . . . . . . . . . . . . 110 

6.12 Apparent resistivities as a function of frequency window length. Triangles 

represent ρ xy and circles ρ yx . Error bars represents 95% confidence interval. 

See text for discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 

6.13 Concepts of robust band averaging. (a) Magnitude of cross spectrum between 

H x and H y for station VP13, around a target frequency 6 Hz. The 

spectra are multiplied by a Parzen window. LS least square, RB Robust. 

(b) Quantile Quantile plot for real part of the same cross spectrum. 

Inverted triangles unweighted, Circles robust weighted. See text for discussion. 

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 

6.14 Comparison of robust and least square band averaging for different frequencies 

and band (Parzen) radius for station VP13. Magnitude of H x Hy 

∗ 

(nT 2 /Hz) cross spectra are plotted for all the cases. X-axis show the frequency 

bins. Solid line represents robust average and broken line represents 

Least Square average.The left column represent the the band averaging for 

different target frequencies, where as the right column represents the band 

averaging with different radius length for the same target frequency. See 

text for discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 

6.15 Flow chart representing robust band averaging. Gray area represents the 

proposed processing routine (a) Shows the different steps in robustly estimating 

the spectral matrix from raw time series Schematic diagrams (b) to 

(e) shows four processing schemes defined. SS single station, RR remote 

reference, RB robust band averaging, LS Least square . . . . . . . . . 122

xxi 

6.16 Results of single station (SS) and remote reference (RR) processing for 

station VP10. Process C (SS) and E (RR) use least squares band averaging, 

whereas process D (SS) and F (RR) use robust band averaging. The 

MT transfer functions were derived from a robust section averaging §6.2.4 

from the spectra sets produced by Process C to F. See text for discussion. 123 

6.17 Comparison of upward and downward biased estimates of apparent resistivities 

for JN12 for processes C and D (a) XY component and (b) YX 

component. UP - up biased (E- reference) and DN down biased (Hreferences). 

Symbols are same for both plots. See text for discussion. 

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 


for VP16 for processes C and D (a) XY component and (b) YX 



. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 


for KG02 for processes C and D (a) XY component and (b) YX 



. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 


for OK18 for processes C and D (a) XY component and (b) YX 



. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 

6.21 Comparison of telluric predicted coherency, apparent resistivity and phase 

values from robust processing with and without robust band averaging for 

stations VP14 and TT08. The explanation for symbols are given in legend. 




stations TT04 and OK18. The explanation for symbols are given in legend. 




stations JN12 and VP16. The explanation for symbols are given in legend. 




stations OK16 and VP12. The explanation for symbols are given in legend. 


6.25 Comparison of results from two different processing scheme for MT data: 

Left panel shows the results from ProcMT and the right panel shows the 

results from the robust processing and ANN editing. . . . . . . . . . . . 130

xxii 

7.1 Comparison of robust processing (RB) with and without neural network 

(NN) editing for Station JN12. (a) Apparent resistivity and phase values 

from both processing schemes. (b) Comparison of robust and neural 

network weights. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 

7.2 Comparison of robust processing (RB) with and without neural network 

(NN) editing for Station OK18. (a) Apparent resistivity and phase values 

from both processing schemes. (b) Comparison of robust and neural 

network weights. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

List of Tables 

1.1 Frequency bands for measurements, GMS05 (after Metronix [1997]). . . . 14 

2.1 Classification of noise sources that affect MT measurements. . . . . . . . 25 

4.1 The locations and measurement details for the MT stations . . . . . . . 53 

6.1 Few commonly used influence functions. Adapted from Zhang [1996]. . . 93 

xxiii

Chapter 1 

Magnetotellurics: Basic Theory, 

Sensors and Field Procedures 

1

2 

1.1 Introduction 

Magnetotelluric signals originate in Earth’s magnetosphere and atmosphere from different 

phenomena. The constant bombardment of solar wind on Earth’s magnetosphere leads 

to its deformation and which in turn disturb the terrestrial magnetic field. This time 

varying phenomena constitutes MT signals, which have periods usually above 1 second. 

The worldwide thunderstorm activity generates high frequency ( > 1 Hz) electromagnetic 

signals, which propagate around the globe in the Earth-ionosphere waveguide and constitute 

the higher frequency part of magnetotelluric signals. These electromagnetic waves 

reach Earth’s surface as quasi-homogeneous waves and a small part of it penetrates the 

conductive Earth as quasi-planar waves. The induced electromagnetic response of Earth, 

both amplitude and phase, depends on the subsurface electrical conductivity structure. 

The relation between electric and magnetic fields at the surface of Earth forms frequency 

domain transfer functions, which can be interpreted in terms of the subsurface structure. 

Magnetotellurics is a method of electromagnetic exploration that uses natural electromagnetic 

waves as source field (Vozoff [1972]). In the following sections the basic ideas 

of magnetotellurics viz, planar assumption for source field, properties of EM field in 

conductive earth, estimation of magnetotelluric transfer functions/impedances and their 

behavior over different type of media are discussed. Accurate and simultaneous measurement 

of the time varying electromagnetic fields is the preliminary requirement to 

obtain MT transfer functions. A brief discussion about sensors, recording devices and 

field procedures commonly adapted for MT data acquisition is given in § 1.2 and § 1.3. 

1.1.1 Source fields 

Magnetotelluric methods evolved out of the observation of similar variation in Earth 

current and magnetic fields. Telluric methods were already in use as an exploration 

tool. Tikhonov [1950] and Cagniard [1953] examined the relationship between horizontal 

orthogonal electromagnetic components and developed formulae to estimate impedance 

of subsurface from the simultaneous measurement of these electromagnetic field components. 

In essence, the formulae between the two components are valid only if the fields 

do not have a lateral gradient over scale lengths that varies with frequency. For example 

for an electromagnetic wave, with a frequency 10 −3 Hz and in a media of resistivity 10 3 

ohm.m, the scale length = ∼350 km (Wait [1954]). The scale length and uniformity of 

harmonic source field (with frequencies < 1 Hz) in the Earth’s ionosphere and magnetosphere 

has been established by Dungey [1955]. Monitoring and study of atmospheric 

electricity / lightning generation, propagation of sub-ionospheric waves provide adequate 

characterization of audio-frequency variations in electromagnetic waves. 

At a distance from the source, the electromagnetic wave front becomes locally planar, 

in the sense the oscillation of the wave is only in a plane that is perpendicular to the 

propagation direction. Such waves are called plane waves or plane polarized waves (Figure 

1.1). Magnetotellurics envisages its inducing electromagnetic fields as plane polarized. 

When such waves are incident on Earth’s surface, maximum energy is reflected. In the 

context of MT, it was shown by Cagniard [1953] that the refracted wave propagates down 

nearly vertically, due to the large contrast in the speed of electromagnetic waves in the

3 

Figure 1.1: Quasi planar nature of electromagnteic wave front at great distance from 

source 

Figure 1.2: Behaviour of plane EM wave at the surface of a conducting Earth 

atmosphere and in the Earth. (or the large contrast of conductivities between the two 

media). It follows that the direction of propagation of electromagnetic fields within the 

Earth does not depend on the angle at which it hit the Earth’s surface. Figure 1.2 depicts 

this situation. 

1.1.2 Maxwell’s equations 

Once refracted the electromagnetic fields propagate through the Earth. The electromagnetic 

fields in isotropic and homogeneous media (of constant electric conductivity σ 

[S/m]) of uniform electric permitivity ɛ [As/Vm] and magnetic permeability µ [Vs/Am] 

are described by the Maxwell’s equations. Considering the fields with harmonic temporal

4 

variation (e iwt ) these equations are; 

∇ × E = iωµH 

∇ × H = iωɛE + σE ≈ σE 

∇.H = 0 

∇.E = q/ɛ ∼ = 0 

(1.1) 

The electric current density j [A/m 2 ] is proportional to the electric field according to 

Ohm’s law; 

j = σE (1.2) 

where q [As/m 3 ] is the volume density of charge, H the magnetic field [Vs/m 2 ], 

E [V/m] the electric field and ω=2πf, the angular frequency. Both permittivity and 

permeability in the earth are assumed to have approximately constant values. 

In the Cartesian system of coordinates, the first two equations of system 1.1 can be 

written as 

∣ i j k ∣∣∣∣∣ 

iωµH = 

∂ ∂ ∂ 

∂x ∂y ∂x 

∣ E x E y H x 

and 

∣ 

(1.3) 

i j k ∣∣∣∣∣ 

σE = 

∂ ∂ ∂ 

∂x ∂y ∂x 

∣ H x H y H x 

It follows that 

∂E x 

∂z 

= iωµH y 

∂H y 

∂z 

= −σE x 

(1.4) 

By taking partial derivative of each equations and making appropriate substitutions, 

∂ 2 F 

∂z 2 + k2 F = 0 (1.5) 

Where F = E or H and with the assumption that in a homogeneous Earth σ is a 

constant. The constant k describes the complex penetration depth 1/k [m] of the EM 

field. 

1.1.3 Skin depth. 

In terms of the diffusion factor describing the penetration in depth of the fields, the 

so called skin depth (δ(ω) [m]) in a homogeneous earth is defined as 

√ √ 

2 2 

δ(ω) = 

|k 2 | = (1.6) 

ωµσ

5 

which represents the exponential decay of the EM field amplitude with depth. At 

depth δ(ω) the EM-field amplitude will drop by 1/e with respect to its value at the 

surface. The penetration in depth of the EM field for a stratified Earth is defined as a 

response function C(ω) = E x /iωH y . In case of a homogeneous Earth C(ω) = 1/k. 

Case 1, σ varies along z. 

For a 1D stratified Earth of N layers, the penetration in depth of the EM fields 

measured at the surface is solved iteratively, with a recursive formula described by the 

EM – response function C i (ω). This index refers to the EM-response measured at the 

top of the layer I (Weaver [1994]); 

where I = N-1,N-2,. . . .1, and 

C i (ω) = 

1 − r ie −2k it i 

k i [1 + r i e −2k i t i ] 

(1.7) 

r i = 1 − k iC i+1 (ω) 

1 + k i C i+1 (ω) 

(1.8) 

and t i is the thickness of the layer i and k i = ρ i (iωµ) −1 , the diffusion factor in the 

layer and ρ i is the resistivity of the layer i (See Figure 1.3). The bottom most layer has 

the response function 1/k N . 

Case 2, σ varies along z and either x or y. 

In a 2D earth with strike along the horizontal x-axis and conductivity σ as a function 

of z and y, the Maxwell’s equations are de-coupled into two polarization modes. The 

decoupling is valid since the EM fields are treated as plane waves. In this context, the 

so called TE- polarization mode refers to the tangential electrical field and the TMpolarization 

mode to the tangential magnetic field; both components are tangential with 

respect to the strike (x axis) of the conductivity structure. 

TE – polarization : (E x H y ); 

TM – polarization: (E y H x ); 

∂H z 

∂y 

− ∂Hy 

∂z 

= σE x 

−∂E x 

∂z 

= iωµH y 

−∂E x 

∂y 

= iωµH z 

(1.9) 

− ∂Ez 

∂y 

1.1.4 Impedance tensor: 

+ ∂Ey 

∂z 

= iωµH x 

−∂H x 

∂z 

= σE y 

−∂H x 

∂y 

= σE z 

(1.10) 

The electrical impedance Z [mV/T] is the ratio between the electric and magnetic 

field components, which can be represented as 

E=Z H (1.11)

6 

Figure 1.3: Diagrammatic representation of 1D, 2D and 3D situations. 

In a homogeneous media the ratio of the orthogonal components is 

Z = iω/k (1.12) 

However, earth cannot be approximated to perfect homogeneous media and it is usual 

to assume structural inhomogeneity for subsurface. Figure 1.3 depicts the 1D, 2D and 

3D inhomogeneity in conductivity within earth. 

In a general 3D earth, the impedance (transfer function of Earth) is expressed in

7 

Figure 1.4: Planar view. Off diagonal tensor elements become unequal when geology 

has a preferred direction. On rotating the tensor to the strike, diagonal elements get 

minimized. See text for discussion 

matrix form in Cartesian coordinates, 

[ ] [ ] 

Ex Zxx Z 

= 

xy 

∗ 

E y Z yx Z yy 

[ 

Hx 

H y 

] 

(1.13) 

Thus each tensor element is Z ij = E i /H j (i,j = x,y). 

For a 1-D layered Earth, besides having diagonal elements of Z ≈0, the off diagonal 

elements are related in the form, 

Z xy = −Z yx orZ 1D = Z xy = −Z yx . (1.14) 

In a 2D earth the diagonal elements of Z vanish (in the 2D-strike coordinate system). 

And the off diagonal elements become unequal. 

[ ] [ ] [ ] 

Ex 0 Zxy Hx 

= 

∗ 

(1.15) 

Ey Z yx 0 Hy 

However, if the measurement axes are not in alignment with the geological strike, the 

diagonal elements may not vanish. The simplest case one can imagine is a geological 

fabric in a preferred direction, or a structural orientation such as a fold or fault system 

(Figure 1.4). 

In such cases the tensor can be rotated to an angle θ with the rotation matrix R to align 

it with geological strike. 

[ ] 

cos θ sin θ 

Zm = RZR T , where R = 

(1.16) 

− sin θ cos θ 

with positive θ.

8 

Once rotated optimally, the tensor may be written as, 

[ ] 0 ZT 

Z m = 

E 

Z T M 0 

(1.17) 

Where Z T E (transverse electric) is the impedance tensor element parallel to the strike 

and Z T M (transverse magnetic) is impedance element perpendicular to the strike direction. 

1.1.5 Amplitude and phase of impedance: 

The complex impedance (transfer function) Z is usually represented by its amplitude and 

phase. The electrical resistivity (inverse of σ) as a function of depth can be inferred 

by the EM field of the corresponding penetration depths. Resistivity obtained from the 

ratio of the measured electric and magnetic fields is called “apparent” resistivity, which 

is frequency dependent. The apparent resistivity ρ aij [Ohm.m] (i,j = x,y) is defined in 

terms of the transfer function element by the form: 

ρ aij = µjZ ij j 2 /ω (1.18) 

In case of a homogeneous Earth, the apparent resistivity reflects the true value of 

the Earth’s resistivity. Apparent resistivity is what we sense at the surface; the true 

resistivity of objects at some depth is masked by intervening material. The phase of 

the transfer function element describes the phase shift between the electric and magnetic 

field components. 

( ) 

φ = tan −1 im(Zij ) 

(1.19) 

re(Z ij ) 

In a homogeneous Earth the impedance phase is π/4 (45 0 ). In a 1D layered Earth, 

the phase increases over 45 0 when the EM response penetrates into higher conductivity 

media. By the same convention, phase decays below 45 0 for the EM response penetrating 

into a less conductive media. 

1.2 Sensors and Field Procedures 

MT parameters such as apparent resistivity and phase values are derived from simultaneously 

measured time varying components of electric and magnetic fields. Magnetotelluric 

time series consist of five components of the Earth’s electromagnetic field i.e., two orthogonal 

components of horizontal electric fields (E x , E y ) and three orthogonal components of 

magnetic field (H x , H y , H z ). The measurements are usually made in wide bands of overlapping 

frequency ranges, with different sampling intervals. In the following section, an 

overview of magnetotelluric field sensors, data acquisition equipment and field procedures 

given.

9 

1.2.1 Introduction 

A variety of instruments are used to measure the time varying components of Earth’s 

natural electromagnetic fields. Primary requirement of any measuring device is that the 

electric and magnetic field measurements must cover a frequency range that is appropriate 

to the exploration problem and with sensitivity and accuracy, which is required for the 

computation of magnetotelluric transfer functions (Kaufman and Keller [1981]). The 

strength and frequency characteristics of natural electromagnetic waves are statistically 

known but cannot be predicted in advance. The field equipment should have the sufficient 

dynamic range and sensitivity to adequately measure the fields, even though, its strength 

may vary from hour to hour at a site. For getting long period (>10 sec) information, 

recordings must be carried out for time ranging from hours to days. This necessitates 

the recording equipment to be stable and resistant to adverse weather conditions. The 

procedure of acquiring magnetotelluric data can be divided into two parts : 1) that of 

sensors, which are capable of converting the electric and magnetic field variations to 

voltages and 2) recording of these voltages in a way that is suitable for recovery later on. 

The modern recording devices are even capable of in site data processing and preliminary 

inversion of observed data. This facilitates redefining of acquisition plans in the field itself, 

which may save lot of money and time. The following sections are devoted to 1) sensors 

2) recording equipment and 3) field procedures. 

1.2.2 Electric field sensors 

At frequencies that are measured in magnetotelluric sounding, the electric field is detected 

by measuring the voltage drop between pairs of electrode that are in contact with 

Earth. The electric field can be thought as the limit of voltage drop when electrode 

spacing tends to zero. In this way, it may be advantageous to have short electrode separation 

if one wants to measure electric field correctly. But in practice there are two 

drawbacks for this. The current density may change at contact of rocks with different 

conductivity. A large separation of electrode will average out such small gradients to 

obtain a regional picture. More over, there is a chance that the voltage measured over 

small electrode spacing may be below the noise level (∼ 1µV/Hz) of the sensor. Typical 

separation between electrode contact ranges from 50 to 200 m. The electrodes that are 

commonly used are non-polarizing electrodes. Such electrodes consist of a metal immersed 

in saturated solution of one of its salts. The advantage of using non-polarizing 

electrodes is that the voltage difference between a pair of electrodes is relatively stable. 

If metal electrodes such as copper or steel are used, relatively large potential difference 

resulting from electrochemical reactions at the metal surface can be present and these can 

vary with time in an unpredictable manner. Several types of electrodes are now in use 

(Petiau and Dupis [1980]) the data analysed in the thesis was collected with Cd-CdCl 4 

cell. One disadvantage of this cell is the high toxicity of CdCl 4 solution. The Electric 

Field Probe (EPF05 from M/s Metronix) showed good stability even during long period 

measurements (1-2 days). 

The electrical field sensors are planted in small pits (∼0.2 m) at least few hours before 

they are used. The pits need to be water saturated and covered to retard evaporation

10 

Figure 1.5: Implanting of Electrical Field sensor 

temperature changes. In some types of soil, a few milli-Amperes of current can quickly 

cause a significant polarization of the ground around the electrodes, leading to long 

exponential decay of this potential. Contact resistance of the telluric electrodes should 

be as low as possible; a typical value measured between two electrodes spaced at 100 m 

in the highly resistive Southern Granulite Terrain (§ 4.2) was between 200 - 1,000 and 

10,000Ohm.m. Field photograph in Figure 1.5 shows a typical implant of electrical field 

sensor. 

1.2.3 Magnetic Sensors 

The problem of detecting magnetic field variations with the required accuracy is much 

more difficult than that of detecting electric field variations (Kaufman and Keller [1981]). 

The magnetic sensors are required to detect variation in magnetic field for the frequency 

range 10 −4 Hz to 10 4 Hz. The dynamic range of magnetic field varies from as low as few 

tenths of a nano-Tesla for micro-pulsations to as high as few nTs for diurnal variations. 

Also the magnetometers should ideally have same response over such a wide range of 

frequency and amplitude as well as it should be robust to the severe fluctuations in 

temperature. These requirements make designing of magnetometers difficult. Some of 

the commonly used magnetometers are Super Conducting Quantum Interference Devices 

(SQUID see Clarke et al. [1983], Fluxgate and induction coil (Karmann [1977]). A short 

description is given on the induction coil magnetometers, which were used to collect the 

data analysed in this thesis. 

1.2.3.1 Induction coil magnetometers 

At its simplest, the induction coil is a loop of wire which produces a voltage proportional 

to its area multiplied by the time derivative of B across the cross sectional area 

of the loop. For the low field strength and low frequencies of interest in magnetotelluric 

surveys, the induction coils are fabricated with a high permeability µ metal core about 

which the coil is wound. A very large number of turns must be used to provide a measurable 

voltage output from a coil. For example, an induction coil with 50,000 turns of

11 

Figure 1.6: Installation of induction coil magnetometer 

Figure 1.7: Simplified equivalent circuit for induction coil magnetometer 

1m 2 area produces 31.41 nV at 1000 sec (Kaufman & Keller, 1981). A further problem 

in the design of sensitive induction coil is that if a very fine wire gauge is used, the total 

resistance is very high. On the other hand a heavier gauge wire with lower resistivity will 

make the induction coil heavier, limiting its mobility. One such type of magnetometer 

namely MFS05 (M/s Metronix) was used to measure magnetic field in the present study 

(Field photograph given in Figure 1.6). In addition to having a large resistance, an induction 

coil will also have an appreciable inductance and capacitance between windings. A 

simplified equivalent circuit is shown in the Figure 1.7. This circuit will have a resonant 

frequency above which voltage output decreases with increasing frequency. 

The frequency dependence of induction coil response is ideally suited to the measurement 

of natural field, where the 1/f dependence of natural field strength (Figure 2.1)

12 

Figure 1.8: Theoretical response function for MFS05 magnetometer (from Pulz and Ritter 

[2001]) 

compensate for the low output from the induction coil for the longer periods (Figure 1.8, 

adapted from Pulz and Ritter [2001]). In higher frequencies frequency- independent magnetometer 

response is obtained by feeding back into coil, a magnetic field proportional to 

the current. These techniques effectively extend the dynamic range of the magnetometers. 

1.2.4 Recording systems 

Historically, MT studies have been concerned with the determination of the electrical 

resistivity of the Earth’s crust or upper mantle on a regional scale. For that purpose, 

signals in the period range between 10 s and 10000 s have been recorded with data 

sampling rates in the order of several seconds to minutes. Accordingly, the recording 

times for long period MT (LMT) data have been in the order of weeks to months at a site. 

The amount of data that could be collected dependents on the progress in data storage 

technology. In the 1950’s and 1960’s, analogue data were recorded on photographic 

film or paper chart recorders and digitised manually at a later stage (For eg. See Vozoff 

[1972]). From the 1970’s digital data were stored directly, However, on modified analogue 

audiocassette recorders (Allsopp et al. [1973]). In the 1980’s, with the arrival of digital 

tape and floppy disks, a new era of digital recording systems began and the most advanced 

MT systems today use rugged hard drives (Ritter et al. [1998]). Robustness, compactness 

and low weight are desirable features for all geophysical instruments. Because of their long 

deployment times, data loggers must have good long-term stability; they must operate 

very reliably and have low power consumption. The invention of the microprocessor in the 

1980’s opened the field to the in field data processing and modelling (Clarke et al. [1983]). 

This also facilitated the measurement of high frequency magnetotelluric data (audiomagnetotelluric, 

AMT). AMT (Hoover et al. [1976]) data are natural electromagnetic 

variation signals, typically in the frequency range 20,000 Hz - 0.01 Hz. Because a large 

volume of data is produced in a relatively short time, most AMT instruments are designed 

as real-time systems. Short, non-continuous segments of time series data are processed 

simultaneously, enabling on-line quality control of the stacked results. The corresponding 

electromagnetic fields penetrate only the first hundred meters or first few kilometres of the 

Earth’s crust, which are economically important (Egbert and Livelybrooks [1996], Garcia

13 

and Jones [2002]). The signal strength in the high frequency range varies enormously over 

the spectrum shown in Figure 2.1. Artificially generated signals from the main power 

supplies or electric railways exceed the natural signals by several magnitudes in narrow 

frequency ranges. To eliminate these narrow band noises, MT instruments are equipped 

with special hardware filters (notches). In the frequency range of the dead band around 

1 Hz, the natural signal activity is at a minimum. Hence, recording in narrow frequency 

bands is necessary to ensure optimum dynamic range of the signals, while LMT (>10 sec) 

data are usually recorded in one broad frequency band. The remote reference technique 

(Gamble et al. [1979], also see § 3.3.6) that brought major improvement in the MT 

impedance estimates requires synchronized recording in two MT data acquisition devices. 

Clarke et al. [1983] describes a radio telemetry system for simultaneous recording of data 

from two stations. Hard wiring and synchronized recording using a crystal clock are the 

other options. With the advent of global positioning system (GPS), it is now possible to 

have both the measuring devices synchronized to a very high precision. The two sets of 

MT equipment should follow a common recording timetable, so as to facilitate remote 

reference processing. Very recently the concept of computer networking is being adopted 

for MT measuring devices, with each MT unit is envisaged as a node in a network, 

connected by cheap coaxial network cables/telephone cables. 

In the present study, the data were collected using Geophysical Measuring System 

(GMS05) manufactured by M/s Metronix GmBH, Germany. On standard, the GMS 05 

is equipped for the 5 channel MT and AMT method. GMS05 consists of following components. 

1. Geophysical Processing Unit – GPU 05 

2. Sensor Connection Box – SDB 05 

3. Display Unit – HDU06 

4. 3 Magnetic Field Sensors MFS 06 

5. 4 Electric field components 

The sensors used by this system is already been discussed in § 1.2. The first two 

components are described below. 

The Geophysical Processing Unit(GPU) houses the major electronic circuitry for conditioning, 

digitising and storing of magnetotelluric data. It can receive up to 8 channels 

of data and digitises it using 16-bit A/D converter, with a dynamic range of 132 dB. 

Data are stored in hard drive of 1GB capacity. The intel 486-driven mother board works 

on DOS platform and performs infield data processing and storage. This also allows the 

operator to inspect the time series and computed MT parameters (§ 3) online. Communication 

is provided through serial or parallel connectors with a maximum data transfer at 

115 k B/s. External power supply required by the system (12 V DC) is usually provided 

with standard car batteries (100 Ah or better). For remote reference applications a highly 

stable precision real time clock (PRC) synchronizes the GMS05. The clocks synchronize 

automatically as soon as the signals from the GPS satellites are received. The accuracy 

of the PRC is better than 10 −12 seconds in long term as it runs synchronously with the

14 

Figure 1.9: Block diagram depicting different signal processing steps in GMS05 (adapted 

from Metronix [1997]) 

Figure 1.10: GPU05 (main unit) and HDU05 (display unit) during data acquisition 

Caesium clocks on board of the satellites. Figure 1.9 shows a schematic diagram of the 

digital processing steps in GMS05. Figure 1.10 shows a field photograph of GMS05, in 

operation. 

The GMS05’s total frequency range from (4096 sec) −1 to 8192 Hz is split into a total 

of 5 bands. The factor between lowest and highest frequency for one band is always 32. 

In the table 1.1, an overview of the channel-sampling rates is given. 

The SDB 05 is used for interconnection of different sensors with the GPU 05. The 

sensor connection box has three inputs for the magnetometers and inputs to connect the 

Band Lower freq. Hz Upper freq. Hz Sampling rate Hz 

1 256 Hz 8,192 Hz 32,768 Hz 

1 8 Hz 256 Hz 1024 Hz 

3 1/4s 8 Hz 32 Hz 

4 1/128s 1/4s 1 Hz 

5 1/4096s 1/128s 1/32s 

Table 1.1: Frequency bands for measurements, GMS05 (after Metronix [1997]).

15 

electric field probes for E x and E y measurement. The small waterproof box also contains 

the preamplifiers for the electric fields. 

1.3 Field Procedures 

1.3.1 Survey design 

As any modern geophysical survey, magnetotelluric surveys are also planned before fieldwork 

starts. Though the survey must accommodate changes due certain unforseen circumstances, 

the overall plan remains the same. Two major decisions to be made before 

start of survey are station spacing and minimum recording time. Minimum recording 

time depends on the depth of interest and the geological condition. Forward modelling 

of an assumed model can provide minimum safe recording time. For deep crustal studies, 

minimum recording of 2 to 3 days are required over a resistive terrain. For basement 

configuration in hydrocarbon exploration, a recording times range from 1 day to 2 days. 

2 

Minimum site spacing also depends on the conductivity structure and required lateral 

resolution. Spacing of 5 – 10 km is required for a regional survey, where as a spacing of 1 

km or less is required for geothermal exploration (for eg. Harinarayana et al. [2002]). In 

the current survey, the stations were spaced 8-10 km (§ 4.3.1) and more densely spaced 

measurements were carried out over suspected geological contacts. 

1.3.2 Site selection 

Site selection is one of the major factors governing the data quality. A good site can 

yield quality data within a short duration of record compared to a noisy site. Cultural 

noises arising from various sources such as power lines, electric railways, irrigation pumps, 

vehicular traffic, radar transmitters etc may act as non planar source (§ 1.1.1) field and 

corrupt the computed transfer function (see § 2.4 for more details). An overview of noise 

sources affecting MT measurements is given in § 2.3. The scenario becomes complicated 

in areas like south India, where such noises travel great distances as the upper crust 

is highly resistive (Harinarayana et al. [2003]). It is a practice to avoid high-tension 

power lines and electric rail lines by at least 2 km and vehicular traffic by 200 m. It is 

advisable to avoid any natural feature that might affect the electric field such as abrupt 

topographical relief, water bodies and rock outcrops. In most surveys carried out in 

India, dry and ploughed fields provide an ideal site. 

1.3.3 Sensor deployment 

Proper deployment of sensors is also essential for good quality MT data. Once a site is 

selected, a pattern for sensor alignment is planned by surveying. Most preferable is a cross 

pattern aligned with geomagnetic directions. The directions are marked with the help of 

a compass and sensors are laid in alignment with the geomagnetic directions. Geography 

and topography some times prevent the array from being aligned to the geomagnetic axes 

or the spread for electrodes being exactly equal. These factors are taken into consideration

16 

Figure 1.11: Typical lay out for MT sensors and data acquisition (after Metronix [1997]) 

while computing system transfer functions. A typical set-up followed for data collection 

is shown in Figure 1.11. 

Electrode pits are prepared few hours ahead of data acquisition to allow for stabilization. 

The dipole wires and connecting cables are weighted/covered with soil so as to 

minimize wind caused movement. According to Clarke et al. [1983], a 1 m length of wire 

vibrating at 1 Hz with amplitude of only 1 mm generates about 0.5 µV, a voltage that 

is comparable to the electric field signals at that frequency. Magnetometers are leveled 

using a spirit level and buried in pit (∼30 cm depth) with a cover of plastic sheet and soil 

to protect it from wind, animals and temperature transients. Induction coil H z , requires 

a vertical hole of about 1 m depth. The data acquisition crew consisting of six people, 

select and prepare the site during daytime. The recording usually starts once the sensors 

are stabilized and connections are properly made. More crewmembers are needed under 

difficult field conditions; for example if the area inaccessible by vehicles. 

1.3.4 Calibration 

The natural electromagnetic fields, measured with a suite of sensors and recording 

devices (system), are modified by the properties of the system itself. A proper knowledge 

of the measurement system’s response over the entire frequency range of interest is 

essential in obtaining accurate magnetotelluric transfer functions. Any modern MT data 

acquisition system employs a suite of analogue filters to precondition the signal prior 

to digitisation. The sensors, particularly the magnetometers, also respond differently

17 

in different frequency ranges. Even the cables that carry the signals have appreciable 

responses at higher frequencies. All these factors make the MT system’s response a 

complex non-linear function. The GMS05 system may be calibrated in two ways: 1) A 

theoretical calibration table could be computed with the knowledge of different data acquisition 

parameters, filter setting etc and 2) By sending a Pseudo Random Binary Signal 

(PRBS – basically white noise) to the magnetometers and electric field preamplifiers and 

by obtaining the ratio between the calibration signal and the system output in frequency 

domain. In the first mode fine effects caused by tolerances in the components are not 

accomodated. The accuracy that can be achieved with the model function is about ±10% 

or better for band 1 and ± 2% for band 2 to 5, whereas in the second mode accuracy 

better than +/- 0.5% in magnitude and +/- 1 ◦ in phase can be achieved. The procedures 

given by Ellinghaus [1997] were used to calibrate the measured MT time series, for the 

present study. 

1.3.5 Data acquisition. 

Prior to data recording, a thorough check of sensors and instruments is a good practice. 

At each site parameters such as noise levels, amplifier gain and filter performance are 

checked usually using short calibration runs (§ 4.3.1). During data acquisition in South 

India, the electric field amplitudes were so high in the frequency range 8 Hz to 256 Hz 

(band 2) for few sites that the measurement were made with lowest gain settings. As 

many modern digital MT equipment, GMS05 also allows the storage of time series data 

in addition to the computed MT parameters. The storage of time series was crucial in 

obtaining better estimates of magnetotelluric impedance, as will be shown in the following 

chapters. The quantity of data to be collected at each site depends on the requirements of 

the exploration program (§ 1.3.1). However, time required in collecting the data depends 

on the prevailing natural signal strength as well. Once the recording begins, data quality 

is monitored continuously. Monitoring consists of 

1)Manual Editing: Inspection of magnetic and electric time series for obvious outliers 

(See § 5.2 for more details regarding noise patterns of time series). A continuous 

disturbance in one or more channels and dead / muted traces may be due to equipment 

malfunctioning (Figure 5.1). 

2)Coherency: This is a measure of the correlation between the E and H fields and 

predictability of the E fields from the H fields (§ 3.3.5). Coherency less than about 0.8 

generally indicates problems associated with local noise sources associated with instrumentation 

or cultural effects (for e.g. see Figure 6.19). It can also indicate localized 

natural sources such as lightning that do not conform to the MT assumption of spatially 

uniform source fields. 

3)Smoothness: Well-behaved MT curves will show smooth variations between estimated 

magnetotelluric transfer functions. Sudden offsets, rapid changes in curvature 

such as slope reversals across less than 0.5 log cycle of frequency and curve slopes greater 

than 45-degrees on log-frequency versus log-apparent resistivity are physically implausible 

and indicate a “near field” source (§ 2.4). It is desirable to have low scatter, moderate 

curvature and well-joined frequency-band curve segments.

Chapter 2 

Signal and Noise Sources for 

magnetotellurics 

18

19 


The definition for signal and noise vary from one geophysical method to another. In 

the context of magnetotellurics, Stodt (1983) defined signals as those components of 

measured electric and magnetic fields, which are deterministically related through the 

transfer functions of a multi-input multi-output linear system (§ 3.3.1.1). Noise in MT 

may be then defined as the additive components in the measured fields that are not 

related in such a way. This definition carries over to the frequency domain as well as 

the Fourier transform is a linear operator (Stodt [1983]). From a different point of view 

Madden [1964] termed all unpredictable part of MT data as noise. One consequence of 

this definition is that, deterministic noises such as 50 Hz (power line) harmonics will not 

be treated as noise, even though they will not qualify by Stodt [1983] criteria for signal. 

However, any unpredictable changes in amplitude and /or phase of a deterministic noise 

will be treated as noise. A third way of defining signal and noise in MT would be checking 

the source field morphology. However, if the signal and noise components have overlaps in 

time, frequency or spatial domains, their separation is im-perfect. MT signal processing 

algorithms try to differentiate the signal and noise parts by transforming the measured 

data to a suitable domain and or with the help of additional independent measurements. 

The derivations made in § 1.1.4 for MT transfer functions assumes a planar source field. 

Any process (natural or man-made) that makes the source field inhomogeneous may thus 

be treated as noise source and its effect in MT records as noise. One way to better 

understand the signal and noise in MT data is to study their sources. Many signal and 

noise sources have its own characteristics, which may be used to separate their effects 

on measured MT data. The first section of this chapter deals with the signal sources for 

MT. A discussion on various noise sources is given in the second part. 

2.2 Signal sources 


Magnetotelluric method uses naturally occurring electromagnetic field as source signal. 

The advantage of using natural field is to have unlimited power available throughout the 

frequency range of interest (∼ 10– 4 to 10 4 [Hz]). This is particularly important, in the 

low frequencies (< 0.01 [Hz]), where a large power source and equipment set up would be 

needed otherwise to generate signals. This ensures the probing range of MT to 100s of 

kilometers. But to depend on natural source means spending sufficient time in the field 

to measure enough data. This is necessary as the signal level of natural electromagnetic 

waves is unpredictable and interfered with man-made and other noises (§ 2.3) especially 

near the frequency range 10 −1 to 1 [Hz]. 

Natural electromagnetic waves come from a variety of processes and from sources 

ranging from Earth’s core to distant galaxies (Vozoff [1991]). Within the frequency range 

of interest to magnetotellurics, only two sources are important. These are the atmosphere 

and magnetosphere. World wide lightning activities in the lower atmosphere are causes 

for MT signals from 1 Hz to 10 4 Hz, whereas below 1 Hz the fields originate mainly in 

the magnetosphere due to its interaction with solar wind and energy exchange between

20 

Figure 2.1: Earths horizontal magnetic field spectrum (Modified after Macnae et al. 

[1984]) The Black and gray bars indicate the frequency range of measurement bands for 

GMS05. (see 1.1) 

particles and waves. Figure 2.1illustrates the components in the natural electromagnetic 

spectrum (modified after Macnae et al. [1984]) the amplitude and shape shown in the 

plot may vary with location and time. The bars indicate the measurement bands used 

for the study (see also table 1.1). 

As can be seen from the Figure2.1, the amplitude of natural magnetic fields spectra 

varies by almost 5 decades within the frequency range ∼10 −2 to 10 5 Hz. The relatively 

higher amplitude in the lower frequency ranges are due to geomagnetic pulsations. The 

signals from world wide thunder storm activity (sferics) is the main source of natural 

signal for frequency > 1 Hz. These two phenomena do not overlap in frequency and there 

exists ‘dead band’ around 1 Hz, with very low signal amplitude. We may define another 

dead band around 1KHz as well. However, in magnetotelluric context, the effect of first 

‘dead band’ has been recognized widely and in the present thesis, the term ‘dead band’ 

refers to the low energy frequency band around 1 Hz. The sharp peaks in the spectra 

between 10 to 1000 Hz are due to power line interference. This clearly shows how narrow 

band noise can override the natural signals. In the following sections, an overview of the 

two sources for magnetotelluric signals are given.

21 

2.2.2 Geomagnetic pulsations 

Geomagnetic pulsations are temporal variations in the Earth’s magnetic field that have 

a quasi-periodic structure with frequencies ranging from 10 −3 [Hz] to 2 [Hz] (Kaufman 

and Keller [1981]). The magnetosphere is the region around the Earth in which the main 

magnetic field is confined by solar wind. Solar wind consists of charged particles, mostly 

hydrogen and helium nuclei, ejected from sun and it take four days to reach Earth. Earth’s 

magnetosphere contains ionised oxygen and nitrogen, which make the magnetosphere 

conductive. The conductive part (100 to 250 km) of magnetosphere is called ionosphere 

and the resistive lower part is called atmosphere. This very complex system of Earth’s 

magnetosphere is constantly bombarded by solar wind. The magnetosphere responds to 

magnetic pressure of solar wind plasma by generating waves. The EM hydrodynamic 

waves thus set up travels towards the Earth. To reach Earth’s surface these waves 

must cross the ionosphere and resistive atmosphere. Ionosphere, with its anisotropy does 

not allow the vertical components of E and H . This not only modifies the horizontal 

components of the EM field, but set up horizontal currents in the ionosphere. It is believed 

that geomagnetic pulsation observed on surface of the Earth is mainly due to this current 

system in ionosphere. The time behavior of magnetic pulsations is episodic but includes 

features localized in frequency / space as a result of local conditions (Vozoff [1991]). 

Geomagnetic pulsations are divided into two classes; continuous (Pc) and irregular (Pi). 

The continuous pulsations are subdivided into six classes (2 – 0.001 [Hz]). They are Pc1 

(2 – 0.2 [Hz]), Pc2 (0.2 – 0.1[Hz]), Pc3 (0.1 to 0.022 [Hz] ), Pc4 (0.022 – 0.0066 [Hz]), 

Pc5 (0.0066 – 0.00166 [Hz]) and Pc6 with frequency less than 0.00166 [Hz]. The second 

class of pulsations, Pi, which have an irregular from, is divided into three types: Pi-1 (1 

– 0.025 [Hz]), Pi-2 (0.025 – 0.0066 [Hz]) and Pi-3 with frequency less than 0.0066 [Hz] 

(Kaufman and Keller [1981]). As discussed earlier, due to the unpredictable occurrence 

character of the geomagnetic pulsation, long time of measurement is required to obtain 

a rich spectrum of the signals in full bandwidth. 

To obtain signals up to 0.001 [Hz] it is usual to record for more than one day at a site. 

A suite of statistical methods is then employed to obtain smooth spectra in the frequency 

range of geomagnetic pulsations. Such an example from MT data collected at site VP16 

is presented here. The data was collected in period range 4sec to 128 sec, with a sampling 

rate 1 Hz. All the 5 MT components were measured for approximately 34 hours (25 - 27 

Feb.2000). Signal activity was strong in the range of Pc3 to Pc5 during last half of the 

recording session. Figure 2.2 shows a record for 4096 seconds of the measurement. The 

transient sinusoids, apparent in the records are geomagnetic pulsation and can easily be 

identified (see §5 ). The data was subjected to spectral analysis (§ 3.2.3). The total 

record was divided into 30 segments of 4096 samples each. Each of the segments were 

Fourier transformed and an average spectral amplitude for H x is given in Figure 2.3. As 

a whole, the spectral power decreases monotonically with increasing frequency, much in 

agreement with the natural EM spectra as given in Figure 2.1. Superimposed on the 

main trends, at least three lobes associated with Pc3, Pc4 and Pc5 are prominent.

22 

Figure 2.2: Plot for MT time series recorded at site VP16 showing geomagnetic pulsations 

Figure 2.3: Averaged magnetic amplitude spectra (Hx) at station VP16. Peaks related 

to geomagnetic pulsations are labeled.Thick (gray) line represents smoothed spectra

23 

Figure 2.4: Plot of MT time series showing impulse signals related to sferics recorded at 

site C12. 

2.2.3 Thunder storm activity 

Magnetotelluric signals with frequency above 1 Hz mainly originate from worldwide thunderstorms. 

About 100 to 1000 lightning storms happen at any given moment worldwide. 

The fields as seen by the MT system depend on the strengths, path lengths (cloud heights) 

occurring frequencies etc (Vozoff [1991]). These signals, which are called Atmospherics 

or sferics, die off with distance. Most of these storms are located in the tropical region. 

Each lightning produces a current flow in the atmosphere with a peak intensity of 300 

[Am]. The lightning excites the electric field in the resistive atmosphere that is sandwiched 

between relatively conductive ionosphere and Earth. While propagating from 

the lighting source, electromagnetic waves get reflected at lower and upper boundaries 

due to the high resistivity contrasts. They effectively travel round the glob 7.75 times a 

second (A circumference of 38,400 [km] with a speed of 297600 [km/s]). The atmosphere 

acts as a resonator and filters the lightning spike to multiples of resonant frequencies. 

These resonance frequencies are called ‘Schumann resonance’. In 1952 W.O. Schumann 

predicted (Meloy, scientific report available at http://space.tin.it/scienza/rromero) the 

existence of electromagnetic resonance in the Earth - Ionosphere cavity as, 

f n = 7.49 [n(n + 1)] 1 2 

for n = 1, 2, 3... (2.1) 

The equation yields f1 = 10.6 Hz, f2 = 18.4 Hz and so on. However, the first observational 

evidence of resonance came after the studies of Balser and Wagner [1960], when 

they measured the resonance of electromagnetic pulse generated from nuclear explosions. 

They found the resonance at f1 = 7.8 Hz, f2 = 14.2 Hz etc. The difference in values

24 

Figure 2.5: Electric Field (Ex) spectral amplitude depicting the Schumann resonance 

between prediction and observation was attributed to the ionospheric loses. Sufficiently 

far from the lighting source, the electromagnetic fields behave like a plane wave - a requirement 

for MT (see § 1.1.1). A plot of MT time series measured at a sampling rate 

1024 Hz (Band 2) is given in Figure 2.4. An impulsive source and its decay are evident 

between data samples 100 – 150. When signal activity is strong, the observed MT 

data contains superposition of individual sferics originating from different thunderstorm, 

throughout the world. Schumann resonance frequencies become prominent in such cases 

and an example is given in Figure 2.5. The amplitude spectra plot for E x component 

of electric field clearly shows the resonance frequencies related to thunder storm activity 

especially at frequencies 8 Hz and 16 Hz. 

As discussed in § 2.2.1, the typical natural electromagnetic signals with frequencies 

around 1 kHz have very low signal strength (Figure 2.1) and are below the background 

noise from the measuring instruments. After analyzing the seasonal and diurnal behavior 

of a large set of high frequency MT data collected from Canada and northern Germany, 

Garcia and Jones [2002] conclude that, to better estimate high frequency MT transfer 

functions, the measurements should be made in the nighttime. During daytime, the 

atmospheric conductivity is larger, compared to night, as direct sun light ionizes the 

atmosphere. The increased conductivity results in strong attenuation of sferics. The 

highest observable signal occurs when the whole propagation path from the lightning to 

the site is unlit.

25 

Active Passive Natural Instrument 

Electric power Conductors: Magnetic storms, Failure in electronics, 

transmission, power lines, Lightning, Microseisms, 

Sensor 

Electrified Rail Pipelines, Fences, 

Wind, malfunctioning, 

lines, Electric Large iron structures 

Equatorial elec- 

Dropped bits, sen- 

switching, Factories,Vehicle 

Resistors: trojet. 

sor misalignment, 

Roads, ditches, 

muted traces. 

movement. culverts 

Table 2.1: Classification of noise sources that affect MT measurements. 

2.3 Noise Sources 


Compared to signal sources, the number of mechanisms that produce noise in the measured 

magnetotelluric data are numerous. This make it difficult to review the various 

noise sources for MT. Further the classifications of the noise sources are different in 

different research documents. An attempt is made here to classify the noise sources for 

magnetotellurics, within the limit of the scope of the thesis. Thus the terms ‘geologic’ and 

‘terrain’ noises are not described in detail. Ward [1967] divided noise in measured electromagnetic 

data into instrumental, terrain & disturbance field. McCraken and Hohman 

[1986] classified EM noises into ‘geologic’ and ‘electromagnetic’. While reviewing man 

made electromagnetic noises in geophysics, Szarka [1988] classified them into passive, 

active and other effects. Hatting [1989] classified them into mechanical equipment and 

electromagnetic. A compilation of the noise sources is given in the table 2.1. 

The various sources listed in the table above describes the major noises that affect 

electromagnetic methods and magnetotelluric in particular. The list is by no means 

comprehensive. For a detailed review on noise sources see Szarka [1988], Junge [1996]. 

2.3.2 Noises from power line signals 

Man made noise, in the EM spectrum (Figure 2.1) comes mainly from the electric power. 

Figure 2.6 shows the distribution of electromagnetic field strength of three phase power 

transmission line in the immediate vicinity of power lines (Szarka [1988]). The interference 

from power line exponentially decreases with distance from it. Several authors studied 

EM harmonics in the vicinity of 50 Hz power lines (Szarka [1988]). This interference is 

inductive in nature and will not harm MT data, if the site is sufficiently far. However, 

there are other types of interference that causes a current flow in the Earth. An ideal and 

perfectly balanced AC power transmission system does not cause any active EM noise in 

the earth. In the case of unbalanced networks (ie in practice) a current component appears 

having equal amplitudes and directions in each conductor. This is the so-called zerosequence 

current (Szarka [1988]) which usually flows through soil. The noisy interference 

from this current may travel a great distance and affect MT data, depending on the 

resistivity of the soil. Motor loads operate non-synchronously and can also produce

26 

Figure 2.6: Distribution of electromagnetic field strength of three phase power transmission 

line in the immediate vicinity of power lines (adopted from Szarka [1988]). H total 

magnetic field, E horizontal electric field. 

side bands and sub-harmonics of the main frequencies. Added to this are the problems 

arising from finite observations. This results in ‘spectral leakage’ and can corrupt the 

transfer function estimate in the vicinity of power line harmonics as well. Results of 

such an analysis is shown in Figure 2.7. The data were acquired at OK14, in band 2 

(sampling rate 1024) and was affected by noise from nearby power lines. Power spectrum 

of electric field computed from three sets of data length viz. 128, 256 and 1024 are plotted. 

The distinctive peaks of the spectrum are related to main power line frequency and its 

harmonics. Leakage of power from main lobe is visible for spectrum calculated from 

128 and 256 data samples compared to the spectrum computed from 1024 data samples. 

This shows how the narrow band noise can leak into their vicinity. The transfer function 

estimations near to 50 Hz and its harmonic can get affected, if they are computed from 

a low-resolution spectrum. 

2.3.3 Noise from electric traction 

Electrified railways are another noise source for magnetotellurics. The Indian Railways 

adopted 25,000 V as standard for its electric traction in 1957. The electric traction is 

powered by AC power lines, which hang above the tracks. The current loop is completed 

through the electric motors which are in turn connected to the wheels and thus to the 

rail tracks. Rail tracks are grounded at regular intervals for safety reasons. A part of the 

current will travel through the ground to the electric substation. In this way, rail related 

noises have two components. While the induction effect from the power lines can be felt 

at distances less than few hundred meters, the electric impulse through ground can travel 

a great distance. In the context of South India, where the upper crust is highly resistive 

these noises can carry great distances from the source. Chaize and Lavergne [1970] give

27 

Figure 2.7: Amplitude spectra of electric field computed over different data length for 

the site OK14. Thin black line - 1024, Thick gray line 256 and Gray dots - 128. See text 

for discussion 

a brief description of source mechanism for noise interference. As described in the Figure 

2.8 current I 2 having an impulse like character due to the power entering the Earth 

where the rail track is grounded and it is this erroneous current that causes distant EM 

disturbances. Power for underground railways is usually supplied at the voltage of 1000 

v and its loading may result in an impulse with an amplitude 7000 A (Szarka [1988]). 

2.3.4 Noises from instrument & sensors 

Noises from failure in electronics in equipment, quantization errors at A/D converter 

(Hatting [1989]), malfunctioning of sensors and errors in aligning the sensors are common 

in magnetotelluric data. In addition to this the sensors and the circuitry has its own 

background noise, which may vary with time as the electronic component develop fatigue. 

One way to identify such a problem is to calibrate the system (§ 1.3.5). Another way is to 

set up electric and magnetic sensors in parallel (Pedersen [1988]). The sensors should be 

placed sufficiently far away from each other that they do not interact but sufficiently close 

that the signals are same. Then by averaging over a number of frequency components we 

may define the coherence γ 2 between two sensor outputs. A corresponding expression for 

the signal to noise ratio is obtained as S/N = γ 2 /(1-γ 2 ). A very low coherence indicates 

malfunctioning of one of the sensors/circuitry. Disorientation of sensors can also induce 

noise to the transfer function estimation. Pedersen [1988] showed that a 5 0 deviation in 

magnetic sensor alignment would correspond to a skew of 0.1.

28 

Figure 2.8: Current circuit electric railway systems. I is the current in the overhead 

power line I1 is the return current in the rails and I2 is the return current in the Earth ( 

modified after Chaize and Lavergne [1970]). 

2.3.5 Noises from the other sources 

Switching of submersible pumps causes disturbances in measured fields and is observed in 

farm areas and villages. Electric channels are more prone to this type of noise. Movements 

of ferrous metals or other magnetic material in the vicinity of the magnetic field sensor can 

introduce noise into the magnetic channels. Vehicular traffic generates both magnetic and 

seismic noise. In most cases, the magnetic effects are negligible, when the magnetometers 

are more than 200 m from the road (Clarke et al. [1983]). Seismic noise transforms into 

magnetic noise through the movement of magnetometer in the Earth’s field. Clarke et al. 

[1983] reports that for the worst case, when the sensor is aligned perpendicular to earth’s 

main magnetic field, a rotation of 0.002 0 produced by seismic vibration produces a field 

change of 1 nT. 

Passive noise sources of EM measurement generally mean superficial resistivity inhomogeneities 

of man made origin. Conductive constructions (Pipelines, metal fences 

etc.) may cause a redistribution of extreme natural electromagnetic phenomena such as 

magnetic storms, lightning etc. Passive distortion effects of man made construction can 

surely be avoided by choosing the MT site away from them (§ 1.3.2). But this may not 

be possible always, especially in industrial areas (as discussed in § 4). The largest and 

most common source of natural noise is wind, which can either move the magnetometer 

directly or induce seismic noise by blowing on trees or bushes whose roots then move the 

ground. Thus ideally the magnetometers should be in a flat area and buried away from 

trees. The cable connecting the sensors to the data acquisition system should be secured 

to ground, to protect it from moving in wind. A 1 meter length of wire vibrating at 1 z 

with an amplitude of only 1 mm generates about 0.5 µ V, a voltage that is comparable 

to the telluric signal at that frequency.

29 

Figure 2.9: Near and far field effect of a grounded dipole on MT measurements (adapted 

from Zonge and Hughes [1991]). The two panels on left and right describes the apparent 

resistivity and phase values for far field and near field measurements 

2.4 Effect of active electrical noise in magnetotelluric 

data 

Most of the active noise sources discussed above manifest in MT measurements as correlated 

and un-correlated noise that can be attributed to the near field of a grounded 

dipole (Oettinger et al. [2001]). Zonge and Hughes [1991] describe the electromagnetic 

field grounded in a homogeneous half space. Figure 2.9 gives a diagrammatic sketch of 

such a setup. Consider the near field and far field case. The near field case applies when 

the dipole – measurement site distance is far smaller than the skin depth of the EM wave 

(r A

30 

Figure 2.10: Effect of a near field source on MT data, as recorded at the station OK14. 

See text for discussion 

One such example from the data collected at station OK14 is presented here. The 

station is located 80 km south of Erode in the measurement corridor (Figure 4.1). The 

data was collected in a visibly excellent site, but was found to be affected noise from 

unknown source. Time series collected in band 2 (sample rate 1024 Hz) were sub segmented 

into stacks of 1024 data samples and were processed using least square technique 

(Sims et al. [1971]). The magnetotelluric transfer functions, especially the xy component 

showed the near source effect. The apparent resistivity and phase are plotted in Figure 

2.10 follows the exact description of Zonge and Hughes [1991] of near source effect. The 

error bars computed have dimension less than the symbols in the plot. In the far field 

(r C >> δ) the electric and magnetic field decay as 1/r 3 and the apparent resistivity and 

phase depends on frequency and resistivity (Figure 2.9). The ratio E/H is independent 

of the dipole – site distance r. The phase difference between E and H is 45 0 and apparent 

resistivity equals the resistivity of the homogeneous half space. 

The effect of near source noise in MT is one such example of how noise affects the 

computed MT parameters. In the presence of noise, it becomes necessary to apply statistical 

signal processing tools to minimize its effect on computed MT parameters. Many 

of the standard spectrum analysis techniques on random data have been applied to MT 

for this purpose. In the next chapter, an overview of various signal processing methods 

that are commonly employed in magnetotelluric time series analysis is given.

Chapter 3 

Magnetotelluric time series analysis 

31

32 


Various natural and anthropogenic processes contributing to magnetotelluric signal observed 

at Earth’s surface were described in the previous chapter. Assuming a quasiuniform 

source field, the linear relation between measured electric and magnetic data may 

yield usable information about the distribution of electrical conductivity of earth. Unfortunately 

not all electromagnetic signals that are measured at Earth’s surface comprise 

the induction process or include the information we seek. Data reduction and processing 

techniques are necessary to convert the measured time series to an interpretable form. 

Generally interpretation of magnetotelluric data is done in frequency domain. Therefore, 

the first step in interpreting magnetotelluric data involves evaluating time series 

to identify and reject variations that seem to be of non-inductive sources. The next is 

to estimate 10 1 – 10 2 frequency domain complex transfer functions Z( ω) from the raw 

electric and magnetic field time series E(t) and H(t) with approximately 10 6 real numbers 

/ site (Egbert and Livelybrooks [1996]). MT data processing is straight forward when 

there is no noise present in the measurements and the equations relating inducing and 

induced variations through the impedance tensor (§ 2) are directly applicable. When 

noise is present a large number of processing methods have been proposed (Sims et al. 

[1971], Goubau et al. [1978], Gamble et al. [1979], Stodt [1983]); Formerly MT time series 

analysis was done as an extension of classical random data analysis (Bendat and 

Piersol [1971]). Much of the same data reduction and transformation techniques are still 

followed. However, the last two decades have seen considerable improvement in the procedural 

and computational aspects of magnetotelluric method (Park and Chave [1984], 

Egbert and Booker [1986], Chave and Thomson [1989], Larsen [1989], Sutarno and Vozoff 

[1991], Egbert [1997], Banks [1998], Ritter et al. [1998], Oettinger et al. [2001], Smirnov 

[2003], Chave and Thomson [2003], Manoj and Nagarajan [2003]). 

In this chapter an introduction to various signal processing steps that are used in 

MT data analysis are described. Natural signals like magnetotelluric fields are usually 

treated as random process and statistical methods are applied to derive their properties. 

Basic concepts of random data and its properties are discussed in § 3.2.1. In the context 

of magnetotellurics it is also desirable to describe certain joint properties of data from 

two or more random processes, namely components of horizontal electric and magnetic 

fields. The concept of joint probability distribution functions, cross correlation functions 

and cross-spectral density functions are described in § 3.2.2. Computational aspects of 

these functions from real data are described in § 3.2.3. Perhaps the dual input – dual 

output linear system with additive noise in all components is the best way to describe the 

relation between magnetotelluric fields. The classical least square method of solving for 

the magnetotelluric transfer functions, its properties and associated errors are described 

towards the end of the chapter (§ 3.3). Violations to the assumption of noise free input 

signals may bias the LS estimation. A brief discussion on certain disadvantages of LS 

estimators is also included in § 3.3.

33 

3.2 Random data analysis 

When considered individually, both signal and noise processes in magnetotelluric field 

components can be considered as independent random processes. All deterministic parts 

are noise and can easily be removed. Random process may be categorized as stationary 

and non stationary. Statistical properties of stationary random processes do not vary 

with time, where as these properties will change with time for non-stationary processes. 

3.2.1 Properties of random data 

The main types of statistical functions used to represent a random process are (1) probability 

distribution function (2) mean square value and median (3) auto-correlation function 

and (4) power spectral density function. 

3.2.1.1 Probability density function 

Probability density function or pdf describes the probability that the data will assume 

certain amplitude within some defined range at any instant of sampling. The probability 

that sample r(n) assumes a value between r and r+∆r may be obtained by taking the 

ratio N r /N where N r is the total number of occurrences that r(n) had in the range (r, 

r+∆r) from N independent field observations. In equation form, 

Pr ob[r < r(n) ≤ ∆r] = 

lim 

(3.1) 

N → ∞ N 

The probability that the current sample r(n) is less than or equal to some value r is 

defined by P(r), which is equal to the integral of the probability density function from 

minus infinity to r. A typical plot of probability density versus instantaneous values for 

magnetotelluric transfer function is presented in Figure 3.1 to demonstrate the property. 

The data recorded in band 3 (table 1.1) were sub-segmented to 174 blocks of 512 data 

samples each. Transfer functions were estimated for each segments using least square 

technique (equation 3.37) , with minimum 5 adjacent Fourier coefficients used for each 

estimate. The derived estimates were sorted into 10 bins of ranges. The main peak (near 

27.5 mV/(km.nT)) is flanked both sides by near symmetric decay. 

The bell shaped probability density plots indicated in the Figure 3.1 are typical of 

either narrow or wide band random processes. These probability density plots would 

ideally be of the classical Gaussian form as given by the equation for variable x, 

N r 

p(x) = e−x2 /2σ x 2 

σ x 

√ 

2π 

(3.2) 

Where σ is the standard deviation of x (§ 3.2.1.2). Gaussian or normal density function 

is most common in natural processes as is evident from MT measurements. Central limit 

theorem postulates that when a large number of processes contribute to single random 

process, its pdf will tend to be a Gaussian, irrespective of probability density functions 

of individual process (Menke [1984]).

34 

Figure 3.1: Ordered —Zxy— plotted against number of occurrences observed at station 

C13 

3.2.1.2 Mean square and variance 

The mean square value is simply the average of squared values in the time series. Consider 

the horizontal magnetic field h x (t), the mean square value ψ 2 of the time series is given 

as, 

Ψ 2 = 

lim 1 

T → ∞ T 

∫ T 

0 

h 2 x(t)dt (3.3) 

Many random processes have a static time invariant component and a dynamic or 

fluctuating component. The static component mean (µ) is the simple average of all the 

values and the fluctuating component variance is the mean square value about mean. 

Variance is given as, 

σ 2 = 

lim 1 

T → ∞ T 

∫ T 

0 

[h x (t) − µ] 2 dt (3.4) 

The positive square root of the variance is called standard deviation. 

3.2.1.3 Median and average absolute deviation. 

If a set of N observations are sorted into the ascending order, h(1)≤h(2) ≤h(3) 

≤. . . .≤h(N), where h(j) is called j th order statistic. Median x is the middle sample

35 

is T is odd. The sample median is ambiguous for N even but it is typically chosen as 

(h [N/2] +h [N/2+1] )/2. Another class for the estimation of dynamic fluctuation is average 

absolute deviation and is given by 

σ = 

lim 1 

T → ∞ T 

∫ T 

0 

|h(t) − x|dt (3.5) 

Mean and median are various types of averages. It is less commonly realized that 

such averages are the result of minimizing various norms. The mean µ is obtained by 

minimizing the L 2 (or LS) norm or least squares norm (§ 3.3) of the samples. Whereas 

the median is obtained by minimizing the L 1 norm of samples (Chave et al. [1987]). 

3.2.1.4 Autocorrelation function 

The autocorrelation functions of random data describes the dependence of the values of 

data at one instance on the values at another time. In equation form, 

R x (τ) = 

lim 1 

N → ∞ N 

∫ T 

n=0 

h(n)h(n + τ)dn (3.6) 

where τ is the time lag. Autocorrelograms for a random process like magnetotelluric 

will be sharply peaked at lag τ = 0 and rapidly diminishes to zero on either side of the 

correlogram. In the limiting case of hypothetical white noise, the autocorrelogram is a 

dirac delta function at zero lag (Bendat and Piersol [1971]). 

3.2.1.5 Power spectral density function 

Frequency analysis of random data essentially involves the implementation of the Fourier 

transform. If F( ω) and f(t) are frequency and time domain expression of a random data 

its relation given by Fourier transform are, 

and 

f(t) = 1 

2π 

∫ ∞ 

−∞ 

F (ω)e iωt dω (3.7) 

F (ω) = 

∫ ∞ 

f(t)e −iωt dt. (3.8) 

−∞ 

The transform defined in the equations 3.7 & 3.8 are only valid for functions with 

finite energy and a different treatment is necessary for data which exist for all the time so 

that the total energy (Σf 2 (t) , t = -∞. . . .∞) is not finite. In such cases one must consider 

the spectral properties of the energy density rather than the spectral properties of the 

amplitude fluctuations. Power spectral density function of a random data describes the 

frequency composition of the data in terms of the spectral density of its mean square

36 

value. Its concept is well understood by considering a narrow band analog filter. The 

mean squared out put of the filter will converge on average over a long period of time. 

In equation form, 

Ψ 2 x(f, ∆f) = 

lim 1 

T → ∞ T 

∫ T 

0 

h 2 (t, f, ∆f)dt (3.9) 

where T is the length of the record, H(t)(Bendat and Piersol [1971]). For small ∆f a 

power spectral density function S xx (f) can be defined such that, 

Ψ 2 x(f, ∆f) ≈ Sxx(f)∆f (3.10) 

According to so-called Wiener-Khinchin theorem (Ghil et al. [2002]) the power spectral 

density is equal to the Fourier transform of the autocorrelation function. Hence power 

spectrum of H(t) can be estimated by the Fourier transform S hh (f) of an estimate of 

autocorrelation function R x ( τ). 

S x (f) = 2 

∫ ∞ 

R x (τ)e −j2πfτ dτ (3.11) 

The random part of the error in the estimation of S xx 

error, 

−∞ 

is given by the normalized 

ɛ = √ 2/dof, (3.12) 

where, dof is the numbers of degree of freedom. As dof = 2 for each Fourier harmonics, 

ɛ >1 implying that the standard deviation of the estimate S xx is greater than the estimate 

itself. There for the need of spectral smoothing is seen. Spectral smoothing is discussed 

while addressing the computational aspects of power spectral density in § 3.2.3. 

3.2.2 Joint signal properties 

In many applications such as magnetotellurics, it is desirable to study the joint signal 

properties of two or more random processes. Cross-spectral density between Earth’s 

natural electric and magnetic field gives the relation between the fields in amplitude and 

phase, which in turn is useful to understand the subsurface conductivity distribution (§ 

1.1). The joint statistical properties like joint probability distribution, cross correlation, 

cross-spectral density etc are essentially the extensions of § 3.2.1. 

3.2.2.1 Cross correlation functions 

Cross correlation function of two sets of random data describes the general dependence 

of the values of one set of data on the other (Bendat and Piersol [1971]). Consider two

37 

Figure 3.2: Crosscorrelogram of two magnetotelluric time series components. 

random series H(t) and E(t), their cross correlation is given as 

R hy (τ) = 

lim 1 

T → ∞ T 

∫ T 

0 

h(t)y(t + τ)dt (3.13) 

The function R hy (τ) is always a real valued function which is symmetrical about the 

ordinate when h and y are interchanged. That is, 

R hy (−τ) = R yh (τ) (3.14) 

A Typical plot of the cross correlation versus time lag plot for two random processes 

(Ex and Hy) is given in Figure 3.2. Note the sharp peak at lag = 0 second and few other 

less defined peaks which shows the existence of correlation between two series Ex(t) and 

Hy(t) at specific displacements. The value of cross correlogram at lag=0 may be used 

to measure the similarity between two processes. For example, in § 5, correlation of 

orthogonal electric and magnetic field components were used to as a quality parameter 

of that section of time series. 

3.2.2.2 Cross-spectral density functions 

The cross spectral density (csd) function of two time series can be defined as the Fourier 

transform of their cross correlation function, in the same manner we defined power spectral 

density of a random process. As the cross correlation is an odd function, csd is a 

complex valued function unlike psd.

38 

3.2.2.3 Coherence 

When considering physical measurement of two random processes, it is often desirable 

to compute a real valued function γ 2 (f ), called ordinary coherence function, which is a 

measure of linear relation between the processes as a function of frequency and frequency 

domain equivalent of cross correlation. It may defined from the psd and csd of the 

processes as, 

S 

γhy(f) 2 = 

hy 2 (f) 

∣S hh (f)S yy (f) ∣ (3.15) 

The coherence function satisfies the limit 0

39 

3.2.3.3 Windowing 

Finite observation of an infinite process can be viewed as multiplying the infinite process 

with a boxcar function. Boxcar function has a value one within the observation period and 

zero outside the observation period. Then the estimated power spectral density function 

S xx (f ) is the convolution of the true power spectral density with the frequency domain 

transform of the boxcar function. Thus convolution causes spectral energy to leak from 

the original frequency to adjacent frequencies by adding infinite number of smaller side 

lobes. Near power line frequency and its harmonics as observed in magnetotelluric time 

series, the leakage may totally corrupt the adjacent frequencies as discussed in § 2.3.2 

(see Figure 2.7). Many alternate window functions were introduced to obtain smooth 

spectra (Bendat and Piersol [1971]). A simple ‘Hanning’ window can be realized as, 

W (i) = 0.5 

( 

1 + cos 

( πi 

N 

)) 

(3.17) 

Where I = 0,1,2,3. . . ..N samples of time series. 

As the window function effectively suppresses the time series data at both ends, 

windowing results in loss of information. In order to retrieve the data that are lost due to 

windowing, it is a common practice to overlap, adjacent windows. In the magnetotelluric 

time series analysis carried out in this thesis Hanning window with 50 % overlap was 

used. However, the overlapping will decrease the effective degrees of freedom (dof) and 

corrections are given as, 

( 1 

dof = dof · 

2 + 1 ) 

(3.18) 

π 

3.2.3.4 Discrete Fourier Transform 

Discrete Fourier Transform (DFT) is obtained by frequency domain sampling of the 

continuous Fourier Transform presented in equations 3.7 and 3.8. DFT realized on N 

discrete samples of data H(t) is given by, 

F DF T (f k ) = 1 T 

∑T −1 

kn 

−2πi 

W (t)h(t)e T (3.19) 

t=0 

With a spectral resolution ∆f=f s /N. Here k = 1,2,. . . T-1 and f s, is the sampling 

frequency. W(t) is the windowing function given in equation 3.17. This summarization 

does not change the units the raw DFT should be divided by the sampling frequency, 

F (ω) ⇔ F DF T (ω k )/f s (3.20) 

to obtain the same result as in equation 3.8. Thus H(t) measured in the unit V will 

get the V/Hz after the transformation. To remove the effects of windowing, the DFT 

has to be multiplied with inverse of the integral of the windowing function, here Hanning 

windows with an integral value 2. Power spectral density S xx (f k ) of time series H(t) is

40 

Figure 3.3: The Parzen spectral window over the target frequency plotted on background 

of a sample spectra 

thus computed by, 

S xx (f k ) = 2 

T f s 

|F DF T (f k )| 2 (3.21) 

with the units V 2 /Hz. With the same reason, the amplitude spectrum get the unit 

V/ √ Hz. 

3.2.3.5 Smoothing of spectra by band and section averaging 

The estimate S xx (f) itself is a random function and from a loose definition of central limit 

theorem, it can be said that the S xx (f) will have a Gaussian distribution even though 

the time series may have different distribution. It is thus usual to attribute 2 degrees 

of freedom to each spectral density values (except for first (mean) and last (nyquist) 

harmonics, which have only 1 dof each). From equation 3.12 it is seen that the power 

spectrum estimate is inconsistent, as the estimate is less than its standard deviation. In 

order to reduce bias and variance in estimated power spectrum, a number of techniques 

are proposed (Jenkins and Watts [1968], Ghil et al. [2002]). A combination of frequency 

band smoothing and segment averaging is generally followed in magnetotellurics to reduce 

variance in psd estimations (Sims et al. [1971], Chave et al. [1987]). As the MT transfer 

functions are slowly varying functions of frequency, the frequency band smoothing is 

performed over a window in frequency domain, here the Parzen (Jenkins and Watts 

[1968]) window, 

⎧ 

⎨ 

W (f) = 

⎩ 

1 if f z − f = 0 

( sin(u) ) 4 if 0 < f 

u z − f < f r 

(3.22) 

0 if f z − f ≥ f r 

where f z is the target frequency and f r is the radius of the Parzen window. A 

schematic diagram is presented in Figure 3.3 showing band averaging over Parzen window.

41 

Jenkins and Watts [1968] discuss the use of other types of ‘spectral windows’ to reduce 

the variance in spectral estimation. They have shown that given a particular radius M, 

Parzen window achieves the smallest variance among other types of windows. 

However, frequency smoothing reduces spectral resolution. A trade off between frequency 

resolution and estimated variance dictates the choice of Parzen radius. Another 

problem with band averaging is the bias error. Parzen window like other spectral windows, 

may result in biased estimates of cross and auto spectrum and can affect the 

computed MT transfer functions. As will be shown in § 6.3, robust weighting of spectra 

within a band can vastly improve the estimates of auto and cross spectra and thereby 

yield less biased MT transfer functions. Section averaging, which is defined as averaging 

of spectra computed from the sub- segments of time series, may be applied to further 

smooth the spectra. Also called Bartlett’s smoothing procedure, this will also result in 

decrease in variances associated with the estimate of spectra (Jenkins and Watts [1968]). 

Cross-spectral densities are also computed in the same fashion as for psd as described 

above. Frequency band averaging assumes the individual spectral values have a Gaussian 

distribution (§ 3.2.1.1). Whereas the problem with non-Gaussian distribution in section 

averaging is well recognized, the same for band averaging has been overlooked. It will be 

shown in § 6.3 that a better estimate of cross and auto spectral densities can be obtained 

by robust band averaging. 

3.3 Magnetotelluric transfer functions 

3.3.1 Least Square Solution 

3.3.1.1 Multi input, multi output linear system 

Magnetotelluric data can be considered as a result of a system of random process, with 

the signal components deterministically related between the inputs and outputs. Under 

the assumption of a plane source field, concepts appropriate for multiple-input / multiple 

out put linear system can be applied (Jones et al. [1989]). The estimation of weighting 

response functions, or their frequency domain equivalent transfer functions for such a system 

is described in this section. Conventionally, the horizontal components of magnetic 

field Hx(t) and Hy(y) [nT] are treated as the inputs, and the horizontal components of 

electric field Ex(t) and Ey(t) [mV/km] are treated as outputs (Figure 3.4. The inputs 

and outputs are related by a convolution operation to the four time domain weighting 

functions Z( τ). The magnetotelluric data can be interpreted in terms of its weighting 

response functions Z( τ) (Kunetz [1972], Yee et al. [1988]) or its frequency domain 

representation, Z( ω) (see Vozoff [1991]). Many authors questioned the time domain approach 

due to unstable statistical properties of the weighting response functions (Jenkins 

and Watts [1968], Egbert [1992]). With some exceptions the transfer functions are now 

computed in the frequency domain.

42 

Figure 3.4: Magnetotelluric linear system with two horizontal magnetic components as 

inputs and horizontal electric components as outputs. Adapted from Jones et al. [1989]. 

3.3.1.2 Solution with noise free data 

In frequency domain the complex frequency dependent relation between the horizontal 

MT fields can be written as given by Swift [1986], 

[ ] [ ] [ ] 

Ex Zxx Z 

= 

xy Hx 

(3.23) 

E y Z yy H y 

Z yx 

Where Z is the MT transfer function tensor (impedance tensor) [mV.km −1 .nT −1 ], 

E [mV.km −1 .Hz − 1 2 ] and H [nT.Hz − 1 2 ] are Fourier transforms ( of electric and magnetic 

fields E(t) and H(t) respectively at a particular frequency ω in radian. The relationship 

between vertical (H z ) and horizontal magnetic field can also be expressed in the same 

way as, 

H z = [ ] [ ] 

H 

T x T x 

y , (3.24) 

H y 

Where T x and T y are called tipper functions (Vozoff [1991]). As the solution for 

tipper functions are similar to that of impedance functions, they are not separately dealt 

with in the following sections. When the measurements are noise-free, two independent 

observations of field components E and H are enough to estimate the transfer functions 

(Sims et al. [1971]). For example a solution for one tensor element is obtained as, 

∣ H ∣ 

x1 E x1 ∣∣∣ 

H x2 E x2 

Z xy = 

∣ H ∣ 

x1 H y1 ∣∣∣ 

(3.25) 

H x2 H y2 

where the subscript 1 and 2 indicate data from two measurements. An additional

43 

requirement is that H x1 H y2 ≠ H x2 H y1 , which physically mean the two field measurements 

must have different source polarization (Kaufman and Keller [1981]). 

3.3.1.3 Solution with noise in measurement 

In the measured magnetotelluric data, we have no knowledge of the true signal components 

in Ex, Ey, Hx, Hy or Hz and it is desirable to make more than two independent 

observations for each components. With more than two measurements equation 3.23 is 

over determined and a solution for transfer functions is sought which minimizes the errors 

in observations. An equivalent matrix form replaces a component of the tensor equation 

3.22 as, 

E = ZH + r (3.26) 

where there are N observations so that E and r are N vectors, H is an N X 2 matrix 

and Z is a two vector. The last variable in equation (3.26), r is the difference between 

measured and predicted output field (here, Electric) and is the residual parameter to be 

minimized. Classical way of solving MT equation is by the least squares technique (Swift 

[1986], Sims et al. [1971]) where in the square of the residual power in equation (3.26) is 

minimized to yield a solution for Z. Writing one component of equation (3.26), 

E xi = Z xx H xi + Z xy H yi + r i (3.27) 

Squaring this equation and summing for all the N records sets we obtain, 

r 2 = 

N∑ 

(E xi − Z xx H xi − Z xy H yi ).(Exi ∗ − ZxxH ∗ xi ∗ − ZxyH ∗ yi) ∗ (3.28) 

i=1 

(Asterisk indicates complex conjugate). Setting the derivative of r 2 with respect to 

Z xx and Z xy in turn to zero yield two independent equations, 

< E x H ∗ y > = Z xx < H x H ∗ y > + Z xy < H y H ∗ y > (3.29) 

< E x H ∗ y > = Z xx < H x H ∗ y > + Z xy < H y H ∗ y > (3.30) 

If we minimize noise in magnetic field in equation (3.27) two more equations arise. 

They are, 

< E x Ex ∗ > = Z xx < H x Ex ∗ > +Z xy < H y Ex ∗ > 

< E x Ey ∗ > = Z xx < H x Ey ∗ > +Z xy < H y Ey ∗ > 

(3.31) 

where the quantities like H x H x and H y H y are power spectral densities (or auto 

spectra) and quantities E x H x and H x H y are cross-spectral densities (or cross spectra 

- § 3.2.2.2) between different field components. The bars indicate segment averaging 

and braces () indicate an average over a small frequency band (§ 3.2.3.5). From now 

onwards the use of these symbols are omitted for simplicity. Any of the two equations 

(3.28 through 3.29) must be solved simultaneously for Z xx and Z xy . Thus there are six

44 

possible estimates for each of the tensor elements. For example, estimates of Z xy 

obtained as, 

are 

Ẑ xy = H xE ∗ xE x E ∗ y − H x E ∗ yE x E ∗ x 

H x E ∗ xH y E ∗ y − H x E ∗ yH y E ∗ x 

Ẑ xy = H xE ∗ xE x H ∗ x − H x H ∗ xE x E ∗ x 

H x E ∗ xH y H ∗ x − H x H ∗ xH y E ∗ x 

Ẑ xy = H xE ∗ xE x H ∗ y − H x H ∗ yE x E ∗ x 

H x E ∗ xH y H ∗ y − H x H ∗ yH y E ∗ x 

Ẑ xy = H xE ∗ yE x H ∗ x − H x H ∗ xE x E ∗ y 

H x E ∗ yH y H ∗ x − H x H ∗ xH y E ∗ y 

Ẑ xy = H xE ∗ yE x H ∗ y − H x H ∗ yE x E ∗ y 

H x E ∗ yH y H ∗ y − H x H ∗ yH y E ∗ y 

Ẑ xy = H xH ∗ xE x H ∗ y − H x H ∗ yE x H ∗ x 

H x H ∗ xH y H ∗ y − H x H ∗ yH y H ∗ x 

(3.32) 

(3.33) 

(3.34) 

(3.35) 

(3.36) 

(3.37) 

Where the hat corresponds to an estimate. Equation (3.32) is the solution for Z xy 

in the equations 3.31, which assumes that all noise is in magnetic fields. Two of the 

equations (3.34 and 3.35) are relatively unstable in the 1-D case where the fields are 

unpolarized. Any noise in the electrical field will cause the estimate for Z xy to bias 

upward. Equation 3.37 is the solution to set of equations 3.29 & 3.30, which treat the 

electrical field as output, (as in Figure 3.1). Noises in magnetic field components will 

down bias this estimate. However, MT transfer functions are rarely estimated using 

equation (3.32), as i) The magnetic measurements are made with better accuracy than 

electric field and ii) Electric fields can get polarized due to electrical resistivity anisotropy 

and denominator of equation 3.32 can become very small or zero. 

3.3.2 Concept of bias 

A crucial factor in the Least Square method described above is the assumption of noise 

– free data in either the electric or magnetic data. In the equations for the estimations 

Z xy (eq 3.30), this assumption is implicit in use of auto spectra. Under the assumption 

that noise is uncorrelated with signal, A S B N ∗ =0, where A, B ∈ {E x , E y , H x , H y }, A S 

is the signal in component A and A N is the noise component in A, one can write, 

{ 

AB ∗ = (A S + A N )(B S∗ + B N∗ ) = 

A S B S∗ when A ≠ B 

A S B S∗ + A N B N ∗ when A = B 

(3.38) 

While estimates for the cross spectra are statistically distributed and yield a good 

approximation to the true value, the estimates of the auto spectra are systematically too 

large (Müller [2000]). Thus noise in E x E ∗ x cause Z xy in equation (3.32) to bias upwards, 

where as noise in H x H ∗ x and H y H ∗ y in the denominator of equation 3.37 biases Z xy

45 

downwards. The downward and upward biased estimates give an envelope within which 

true transfer functions should lie (Jones et al. [1989]). To reduce the bias effect Sims et al. 

[1971] proposed to take averages over four stable estimates, the argument being that the 

negative and positive bias would cancel each other. Kao and Rankin [1977] devised an 

iterative approach to remove the biasing effects. Goubau et al. [1978] and Gamble et al. 

[1979] used magnetic data from a remote station (§ 3.3.6) in order to avoid the use of 

auto powers in solutions such as equations 3.32 to 3.37. 

3.3.2.1 Predicted coherence 

The coherence between measured and predicted output data describes the optimality of 

LS estimate such as given in equations 3.32 to 3.37. For example, squared predicted 

coherence, when consider Ex as output according to equation (3.37) is given by, 

∣ ∣∣∣∣ 

γ 2 E pEx p = |E x Ex| p 2 

(E x Ex)(E ∗ xE p p∗ 

(3.39) 

∣ 

where, 

x ) 

E p x = ẐxxH x + ẐxyH y (3.40) 

(modified after Swift [1986]). Predicted coherence (or multiple coherence) functions 

will strongly indicate the presence or absence of linear relationship between input and 

output. This should be differentiated from the ordinary coherency defined in equation 

3.15 (§ 3.2.2.3). A value of 1.0 indicates the derived impedances are in perfect line with 

the observations of E and H. Presence of uncorrelated noise in the fields reduces the 

predicted coherence from unity. The three conditions under which the coherences can 

have non-unity values (Jones [1981]) are, when,: 

1. noise is present in both electric and magnetic fields 

2. the system relating the magnetic and electric field are non linear 

3. processes other than electromagnetic induction are involved 

Many approaches were made to weight MT spectra sets from different observations, 

according to predicted coherence (Stodt [1983], Egbert and Livelybrooks [1996], Larsen 

et al. [1996]). However, as pointed out by Dekker and Hastie [1981], the multiple coherence 

functions can get biased upwards when computed from fewer number of observations 

and/or in the presence of correlated noise between measured fields. Correction to bias 

error in coherence is discussed in § 4.6. 

3.3.3 Coherent and incoherent noises 

Noises in MT data can be classified into coherent and in-coherent. Noises in electric or 

magnetic channels (or both) that cannot be related via transfer functions (out of line) 

are termed incoherent. An example is the thermal noises in sensors. Predictive coherence

46 

may be used to detect them. Coherent noises are noises that affect both the input (say 

magnetic) and out put (say electrical) channels in line with the linear model (impedance). 

An example is a correlated spike. It may be detected by examining the time variations 

of the impedance functions (§6.2). 

A rigid coherency gate may not be useful in dead band as the signal-to-noise ratio is 

least here. Coherency Weighted Estimate (Stodt [1983]) or Coherency sorting will give 

better results. However as shown by Egbert and Livelybrooks [1996], a combination of 

these schemes with robust processing may significantly improves the results (§6.2). 

With no coherent noises, coherency gate is arguably the best choice. However, coherence 

cannot always be relied for the discrimination, when the measured data contains 

coherent noises (Banks [1998]). Windows that are contaminated with coherent noises 

can generate transfer functions significantly different from the normal ones. A realistic 

approach would be a combination of the coherence and robust schemes ( Egbert and 

Livelybrooks [1996]). As shown in §6, with a proper initialization, robust processing can 

remove the noisy data (see §6.2.4.2). 

3.3.4 Variance & Errors 

Estimates of error in computed transfer function are important, as they are required at 

the modeling or inversion stage to assess the adequacy of fit of a derived model to the 

measured data (Eisel and Egbert [2001]) Statistical variance for each component of the 

transfer function tensor (equation 3.1) may be as, 

(∆Z xy ) 2 = k F (k, 2N − 4, δ = 0.05)[1 − γ2 ExExp ]E xE ∗ x 

(2N − 4) [1 − γ 2 HxHy ]H yH ∗ y 

(3.41) 

Where δ = 0.05 is the significance level corresponding to a 0.95 or 95 per cent confidence 

limit, N is the number of Fourier coefficients used, 2N-4 is the degree of freedom, 

F(m,n,δ) is the factor for F distribution (Bendat and Piersol [1971]) and k is 4 for confidence 

limit of |Z xy | 2 (Schmucker [1978]). The errors for apparent resistivity and phase are 

∆ρ xy = 2µ |Z ω xy| 2 ∆Z xy and 

∆ϕ xy = 

∆Z xy 

|Z xy| 

(3.42) 

The estimate of variance in equation (3.41) is exact under the assumption that the 

noise in output channel (r in equation 3.25) are normally distributed and statistically 

independent while at the same time the inputs are error free. Chave and Thomson [1989] 

describe many instances wherein these assumptions can break down resulting in biased 

estimation of confidence limit. 

3.3.5 Coherence and bias of transfer functions 

Figure 3.5 shows MT transfer function (Z xy ) computed using equations 3.32 (up biased) 

and 3.37 ( down biased) respectively, compared to their associated coherence and variance 

for station VP20 (see section § 4.3.3). The upward and downward biased estimates

47 

Figure 3.5: MT Transfer function (Z xy ) computed using upward and downward biased 

estimators compared with the coherence functions for station VP20. The upper part 

of the diagram shows real and imaginary components of upward and downward biased 

estimates. The variance of Z xy is shown as solid line. The lower part shows the predicted 

(multiple) and ordinary coherence functions. See the text for discussion. 

behave identically over most of the period range except near 8 seconds and periods > 

200 sec. In these ranges, the two different estimates deviate from each other. The up 

biased estimates show considerable bias from the common trend. Though the apparent 

magnitude of bias seems to be less, the down biased estimates show reduced values in 

these period ranges. On inspection on the coherence plots, it can be seen that these 

period- ranges are associated with low predicted coherence. The ordinary coherence 

function E x H y decreases with increase in period whereas coherence E x H x behaves in 

exactly opposite way. The increased dependency of E x on H x in the longer period might 

be caused by the polarization of electric fields by geological structures at depth. However, 

the predicted coherence function is undisturbed by the polarization. This is due to the 

fact that predicted coherence takes into consideration, the transfer function between 

collinear fields as well (in this case Z xx ). 

The iterative scheme proposed by Kao and Rankin [1977] averages the up and down 

biased estimates to obtain bias free transfer functions. But this assumes that both electrical 

and magnetic channels are equal in noise content. Any deviation from this (as 

practically seen, electric channels are more noisy than magnetic channels Travassos and 

Beamish [1988]) will results in inferior estimate than that of conventional ones. This was 

agreed by the authors while replying to a question by Hernandez and Jacobs [1979].

48 

3.3.6 Remote reference 

In § 3.3.6, we have seen the bias error in estimated transfer functions due to auto-power 

terms in equations such as 3.32 and 3.37. One effective way to reduce bias errors has been 

the remote reference (RR, it is usual to denote single station processing as SS) method 

(Gamble et al. [1979]), in which two independent signal channels are recorded for use as 

the complex conjugate part of cross and auto powers in equation such as 3.37. 

Ẑ xy = H xR ∗ xE x R ∗ y − H x R ∗ yE x R ∗ x 

H x R ∗ xH y R ∗ y − H x R ∗ yH y R ∗ x 

(3.43) 

Equation 3.43 gives the RR estimate of Z xy . By providing a kind of synchronous 

detection, the method helps compensate for noise, both internal and external to the measuring 

device (Vozoff [1991]). The remote channels usually designated R x and R y are 

the most commonly H x and H y components measured at a remote, noise free site. In 

principle the electric field also can be used as a remote reference. However, as shown by 

Travassos and Beamish [1988], this may not result in better transfer function estimate, as 

the electric fields are more affected (polarized) by local geology and the spatial coherence 

between electric field components are often small. Combined with robust (§ 6.2) estimations, 

this technique is widely used at present. Jones et al. [1989] proved its superiority 

in a comparison of different processing techniques on MT time series. In a recent work 

by Shalivahan and Bhattacharya [2002] the question of ‘how remote can the far remote 

reference site be?’ is addressed. They processed MT data from one permanent site with 

remote fields collected at distances 80, 115 and 215 kilometers away from it. Only by 

using the farthest station data, they could improve quality of MT data in all frequency 

ranges. However, the data used for the thesis were collected in single station mode, 

though more than one systems were used in the field. Instrument problems prevented 

the synchronization data acquisition system’s internal clock with that of GPS (Global 

Positioning System) satellite. For this reason, the various approaches made in the thesis 

are for single station processing, though it can easily be extended to dual station processing. 

In some cases there is scope to improve remote reference processing as shown in 

the § 6.3.

Chapter 4 

Signal and Noise Characteristics of 

MT data measured over the 

Southern Granulite Terrain 

49

50 

4.1 Introduction. 

Magnetotelluric studies were carried out as part of an integrated geophysical study of 

the Southern Granulite Terrain (SGT) during 1998-2000. The region south of the 13 o 

N latitude marking the high-grade granulite zone was traversed by a N-S corridor of 

geophysical observations (Figure 4.1). Of these, MT studies were conducted along 2 N-S 

profiles extending from Kuppam, near Bangalore in the north to Palani and Kodaikanal 

in the south. The Magnetotelluric measurements carried out over the Southern Granulite 

Terrain (SGT) in two field campaigns during September 1998 – December 1998 and 

January 2000 - March 2000 form the basic data used in the thesis. These MT studies 

form part of a major geophysical and geological study on the SGT initiated by the Deep 

Continental Studies programme of the Department of Science and Technology. There are 

three factors that make this region important in terms of MT signal analysis. 1) The 

majority of the upper crustal rocks in the SGT belong to the Archaean and the Proterozoic 

age (Naqvi and Rogers [1987]) and exhibit high electrical resistivity as other shield 

regions in the world (Mareschal et al. [1994]). Highly resistive upper crust offers very little 

attenuation to EM signals and in principle noise can propagate larger distance on the 

SGT as compared to regions where younger rocks are exposed. 2) The high population 

density in the southern states of India, especially in Tamil Nadu, where most of the MT 

sites are located give rise to various cultural noises (§ 2.3). The industrial belt along the 

two banks of Cauvery River is another noise source for MT. And 3) while studying the 

effect of Equatorial Electrojet (EEJ) on magnetotelluric data, measured further south 

of the main measurement corridor, Rao et al. [2002] reports perceptible decrease in daytime 

apparent resistivity curves compared to night-time estimates in periods excess of 

100 Sec. The analysis of MT data, in context of its signal and noise characteristics in 

time, frequency and space domain is discussed in this chapter. Harinarayana et al. [2003] 

discusses preliminary interpretation based on 2D MT modeling along three NS profiles. 

4.2 Geological objectives of MT investigations in the 

SGT 

Deep structure of South Indian Shield Region (SISR) (Figure 4.1) has warranted the 

attention of earth scientists owing to its association with various tectonic features. It is 

characterized by expanses of high-grade crystalline provinces south of 13 o N. Regional geology 

has been well mapped and studied, resulting in the identification of gradual increase 

in high-grade metamorphic assemblages. It comprises of Archaean and Proterozoic terrain 

and exposes major crustal scale thrust faults and tectonic lineaments. The geology of 

the South Indian Peninsula could be envisaged as a northward plunging structure that exposes 

the Archaean craton and adjacent shallow green stone belts to the north and deeper 

high grade granulites to the South in an oblique section (Naqvi and Rogers [1987]. These 

features seem to have played a major role in the evolution of the continental lithosphere 

of the region. Several models of tectonic evolution of the region, based on metamorphic, 

structural and geophysical data have been proposed (Drury et al. [1984], Radhakrishna 

[1989]). Earlier geophysical studies include regional gravity (Mishra [1988]), MAGSAT

Figure 4.1: MT stations superimposed over the geology of the measurement corridor in 

South India (Geology adapted from GSI [1995]). See text for discussion 

51

52 

(Mishra and Venkatarayudu [1985]), aeromagnetic studies (Reddi et al. [1988]), seismic 

tomographic studies (Rai et al. [1993]) and electromagnetic induction studies (Nityananda 

et al. [1977], Nityananda and Jayakumar [1981]). During a magnetometer array study in 

South India, no large scale electrical conductivity anomaly was observed in Kuppam – 

Salem area, in contrast to crustal electrical anomalies observed along coastal margins in 

the Southern granulite block ( Thakur et al. [1986]). A detailed discussion of the more 

recent insights into crustal evolution of South Indian shield has been compiled by Mahadevan 

[1994]. In order to obtain more information about the deep crust of south India 

and its evolution, integrated geophysical studies in the Southern Granulite Terrain (SGT) 

were initiated under Deep Continental Studies program of Department of Science and 

Technology, Government of India. Studies involving coincident seismic refraction and 

reflection profiling, magnetotellurics, gravity and deep resistivity soundings have been 

completed (For a detailed report, see Memoir of Geol. Soc. Ind. No 50, 2003). 

4.3 The Data 

4.3.1 Acquisition 

Figure 4.1 shows the locations of the selected MT stations superimposed on the geology 

of the measurement corridor. The corridor, which roughly trends NS, lies in the southern 

peninsula of India, with an approximate dimension of 300 X 100 km. The MT data were 

acquired mainly along three profiles, viz. Kuppam-Bommidi (KB), Omalur- Kodaikanal 

(OK) and Kolattur-Palani (KP), all being roughly oriented NS, with a station spacing of 

around 10 km. The corridor cuts across major geologic and tectonic elements of the region 

– highly resistive high grade granulite gniess, ultra-basics, granite –gniesses and low-grade 

amphibolite granulite facies in the south (Naqvi and Rogers [1987]). For the MT survey, 

a wide-band digital MT system (GMS05 from Metronix GmbH) was used to measure 

the five electromagnetic field components in single station mode. The electric fields were 

measured using porous pots with Cd-CdCl 2 electrodes. Four electrodes were laid in a 

cross arrangement with 90m distance between the pairs. Induction coil magnetometers 

with ∼30,000 turns were used to measure the natural magnetic fields (§ 1.2.3). MT time 

series were measured in four overlapping frequency bands (§ 1.2.4) for a period of 24-48 

hours per site, with a maximum possible frequency range, (4096 sec) −1 to 8192 [Hz]. 

At most of the sites the data were recorded in three sessions. Out of three, one of the 

session would carry out relatively longer period of measurements than other sessions. 

It was typical to have around 100 stacks (1 stack = 1024 data points) for band 1 to 3 

and 80 to 100 stacks for band 4. This effectively means a total recording time of more 

than 24 hours. In the other sessions, the quantity of data collected would be less. As the 

signal and noise in MT are time variant processes, the chief session need not always result 

in best estimate of MT transfer functions. However, the present thesis concentrate on 

processing the data from the chief session of each site, as this contains the largest volume 

of continuous data. A selected subset of about 24 MT stations is used to demonstrate 

the methodologies developed for MT time series processing. MT data from sites with 

differing signal/noise distribution and geology were included in this set of 24 stations. 

Table 4.1 shows location, Village names and stations codes, recording date etc.

53 

4.3.2 Typical MT Time series 

The observed MT time series exhibit varying amplitude, pattern and frequency content 

based on the signal as well as noise sources, which in turn are time variant processes. 

It is important to inspect the time series to identify obvious outliers in time series and 

remove those segments from further processing (Manoj and Nagarajan [2003]). Time 

series samples measured in the four frequency bands in South India are displayed, as 

representative examples in Figures 4.2 and 4.3 . 

Figure 4.2(a) shows a snapshot of MT time series (1024 points) measured in the band 

1 (sampling rate was 32 kHz). Here the natural signal is superimposed on power line 

frequency and its harmonics. The pattern of the signal in this frequency range is pseudosinusoids. 

Superimposed on such a background, a burst of signal activity is observed 

at 0.015 sec. This activity is correlated well over four of the five measured channels. 

The obvious source for this transient signal is lightning (§ 2.2.2). Since the transient 

envelope is rich in high frequency content, the lightning might have occurred near to the 

site. But the term ’near’ has to treated cautiously. If the lighting were occurred so near 

MT Station Village Latitude Longitude Day Start Day End 

JN02 Venkatapalli 12.900917 78.3894167 12-Jan-00 14-Jan-00 

JN07 Kochchakallur 12.402861 78.3060556 22-Jan-00 24-Jan-00 

JN10 Puliampatti 12.152708 78.3267083 28-Jan-00 29-Jan-00 

JN12 Regadahalli 12.031389 78.2559722 29-Jan-00 01-Feb-00 

EW01 Vellicahndi 12.335361 78.0815833 03-Feb-00 05-Feb-00 

VP01 Vellar 11.892528 77.9628056 07-Feb-00 09-Feb-00 

VP03 Ellakutaur 11.779278 77.9203889 11-Feb-00 12-Feb-00 

TT06 Ramudaiyanur 11.156917 78.1988889 12-Feb-00 14-Feb-00 

KG01 Tottikinaru 11.795417 77.7229722 14-Feb-00 16-Feb-00 

KG02 Pakapudur 11.718194 77.6813056 16-Feb-00 17-Feb-00 

TT08 Valasiramani 11.123028 78.3431944 16-Feb-00 18-Feb-00 

KG03 Kottur 11.636722 77.6697222 17-Feb-00 18-Feb-00 

TT09 Venkatachalapuram 11.244278 78.5219722 17-Feb-00 19-Feb-00 

TT10 Viralipatti 11.12175 78.7151389 19-Feb-00 20-Feb-00 

VP11 Pudupalayam 11.16875 77.6191111 22-Feb-00 23-Feb-00 

VP10 Siliamaptti 11.300222 77.5708611 23-Feb-00 23-Feb-00 

VP13 Muttukkalivalasu 10.968222 77.5275556 23-Feb-00 25-Feb-00 

VP12 Rasipalayam 11.072722 77.5706389 24-Feb-00 26-Feb-00 

VP16 Talakkarai 0.796778 77.5331111 25-Feb-00 27-Feb-00 

VP15 Gollipatti 10.703222 77.5446944 26-Feb-00 27-Feb-00 

VP17 Kuppanavalasu 10.635556 77.52925 27-Feb-00 28-Feb-00 

OK15 Kuthilabbai 10.601583 77.7785556 28-Feb-00 29-Feb-00 

VP19 Karadikuttam 10.452778 77.4468889 28-Feb-00 29-Feb-00 

OK18 Viralipatty 10.140778 77.7341389 01-Mar-00 03-Mar-00 

Table 4.1: The locations and measurement details for the MT stations

Figure 4.2: Typical MT time series measured in the SGT for two frequency ranges a) 

the frequency range 256 Hz to 32kHz (band 1) and b) the period range 8 Hz to 256 Hz 

(band2) .See the text for discussion. 

54

55 

that the em fields due to lighting behaved non planar at the site (§ 1.1.1), this burst 

would be treated as noise. By constructing MT transfer function between the channels 

and verifying its consistency between segments, one can easily check this. The telluric 

signals fluctuates within ∼100mV/km and magnetic fields within 0.2 nT. But in certain 

instances the telluric fields can have even higher amplitudes. MT time series measured at 

site TT08 in band 2 (sampling rate 1024 Hz) is presented in Figure 4.2(b). The narrow 

band noise present in all the channels is noticeable. They are power line signals (50 Hz), 

perfectly manifested in MT time series as sinusoids. The time series data were filtered 

with analogue notch filters (50 & 150 Hz) before being digitized. The high power of the 

50 Hz signals even after notch filtering shows the level of 50 Hz signals prevalent in the 

area. Consider the higher amplitude for telluric and magnetic fields compared to band 1. 

The visual inspection of this time series will not yield any first hand information about 

the signal content, its distribution over frequency etc. It is common practice to look for 

large spikes or discontinuity in the time series, to exclude such segments from further 

processing. The large spike seen at 0.3 sec and is reflected in all the channels is one of 

such examples. The magnetic fields show a sharp decreasing trend at the beginning of 

each channel. It repeats in all the segments and could most probably be an artefact from 

measurement system. 

MT time series measured in Band3 (Figure 4.3(a) includes the well-known MT ’dead’ 

band around 1 sec (§ 2.2.1). The natural electromagnetic signal energy (Figure 2.1) is low 

in this band and the time series usually look like a random process. The data displayed 

in Figure 4.3(a) were measured at VP12, which is relatively a noise free site (see §4.3.3 in 

this chapter). The data were measured with a sampling rate 32 Hz and the duration of 

the displayed time series is 128 sec( 4096 samples). The time series fluctuates randomly 

from a common mean, with some large spike activity in between. Spike activity is more 

in Ex, Hy and Hz channels and is less in Ey and Hx channels. But the major spikes, for 

example the one occurs at 95 sec is well correlated between the channels. This indicates 

an inductive source for the noise and was probably due to switching of large power loads. 

The amplitude of telluric signals are in the order of ∼4 mV/Km and for magnetic fields 

it is ∼0.01 nT/s. 

Visual inspection of time series (§ 5) is more appropriate in the measurement band 4 

(sampling rate 1 Hz). The time series measured at JN10 are presented in Figure 4.3(b), 

contains 4096 samples. The main signal source for long period MT measurements are 

geomagnetic pulsations. Envelopes of pulsation activity (Pc4 and Pc5 - see §2.2.2) are 

observed near 1500, 1900, 2500 and 3500 seconds and is best observed in Hx. The spike 

activity with much larger magnitude made the pulsation activity less obvious in other 

channels. In addition to the short period pulsations, fluctuations with longer period 

were also observed (and correlated) in all the channels. The magnitudes of the signals 

displayed were largely controlled by the spike activity. 

4.3.3 Examples of MT data collected over South India 

Station VP12 (western part) and TT08 (eastern part) lie in the centre of the measurement 

corridor (Figure 4.1) and are near to a major EW trending shear zone in the

Figure 4.3: Typical MT time series measured in the SGT for two frequency ranges c) the 

frequency range 8Hz to 0.25 Hz (band 3) and d) the period range 4 sec to 128 sec.See 

the text for discussion. 

56

57 

region. JN10 and VP20 are from northern and southern part of the corridor, respectively. 

All of the sites are on exposed crystalline gneisses of Archaean / Proterozoic age. The 

time series in each station were processed in the following manner: 

1. For each measurement band, the total available time series were sliced into sub 

segments with the constraints of lowest frequency of interest and required degree 

of freedom for each estimate. 

2. The bias and trend of the time series were eliminated by procedures outlined in § 

3.2.3.1. 

3. To reduce the bias of the spectra due to finite measurements, a hanning window 

was applied to each time segments, followed by FFT and calibration. 

4. Smooth cross and auto spectra of MT field components were estimated for each 

time series segment by frequency band averaging (§ 3.2.3.5). 

5. Robust processing (§ 6.2) was applied to obtain global spectral matrices from all 

the segments. 

Apparent resistivity, phase, coherence between predicted observed electrical field (§ 

3.3.5) and degree of freedom for each estimates are presented for sites VP12 in the Figure 

4.4(a). Data are presented in their measured co-ordinates. The xy and yx components 

of apparent resistivity show split that becomes appreciable for frequencies below 0.01Hz. 

As the phase components also behave differently from each other, it could be the result of 

lateral resistivity contrast. Predicted coherence are above 0.8 for most of the frequency 

range, but with a low in the dead band (5 Hz to 10 Sec). The degrees of freedom 

(dof ) exponentially decrease with frequency in each band. Fourier transform results in 

equally spaced harmonics in linear scale, where as the target frequency to compute MT 

parameters are equally spaced in logarithmic scale. Due to this, the number of spectral 

lines available for target frequencies exponentially reduces with decrease in frequency. 

In addition to this the selective stacking processes modify the dof. But the effect of 

degree of freedom seems to be minimal on the predicted coherence. In fact, near 0.1 Hz 

the even with an effective dof of 2000, both the coherences are low. The steep rise in 

apparent resistivity and low values for phase observed between 10,000 Hz to1,000 Hz is 

clearly the effect of a near field signal. Computed error bars (xy) shows large values in 

the dead band and frequency less than 0.01 Hz. Whereas the large errors for dead band 

result from the poor signal strength, for lower frequency range, where the coherences 

are relatively high, low dof are the reason for large error bars. Station JN10 lies in the 

northern part of the measurement corridor and is relatively noisy compared to VP12. 

The apparent resistivity values (Figure 4.4(b)) monotonously decrease with increase in 

frequency. Phase smoothly varies except in the dead band. The coherences assume low 

values between 10 Hz to 0.01 Hz. Quantity of observed data is less compared to VP12, as 

seen on dof plot. TT08 lies in the eastern part of the measurement corridor and is heavily 

affected with noise especially in band 3 & band 4 (frequencies below 8 Hz). Apparent 

resistivity and phase values of xy (Figure 4.4(c)) component are scattered and have larger 

associated errors. Though the quantity of measured data is relatively high (see the dof

Figure 4.4: Plot of apparent resistivity, phase, predicted coherence and degree of freedom 

(DOF) vs frequency for four stations measured over South India. Data are computed in 

their measured direction. See text for discussion 

58

59 

plot), the predicted coherences (E xp E x ) are less than 0.6 for majority of the frequency 

range. Apparent resistivity observed in frequencies less than 10 Hz is much lower than 

one would expect on a crystalline terrain. The MT transfer functions are evidently biased 

in the frequency range 10 Hz to 0.01 Hz by noise. VP20 is located in the southern part 

and Figure 4.4(d) presents the MT data from this station. The site was relatively noise 

free and the apparent resistivity and phase values vary smoothly and are self-consistent. 

Still there is a clear evidence for bias error in the ρ xy values for frequency less than 0.01 

Hz. The coherence plot also shows low values (E xp E x ) for corresponding frequencies. To 

conclude, bias and random errors due to noise are evident in many of the sites and it is 

not always reflected in the associated coherences and errors. 

4.4 The EEJ effect on MT data 

Equatorial Electrojet (EEJ) is a non-uniform east flowing current in the ionosphere, 

within 5 0 each side of the magnetic equator. The direct incidence of sun’s radiation at 

equatorial regions, ionizes the upper atmosphere, where geomagnetic field is essentially 

horizontal. This current amplifies the northward component of slower magnetic variations. 

The EEJ will also affect the geomagnetic pulsation (§ 2.2.2) amplitude (Sarma 

et al. [1982], Sastry et al. [1983]) of MT signal below 3 Hz. The two reported studies on 

the effect of equatorial electrojet on measured MT transfer functions at sites close to dip 

equators are by Padilha et al. [1997] and by Rao et al. [2002]. MT data were collected 

along 1000-km profile in Brazil, with the dip equator passing through the center of the 

profile. The time series were measured in day and night were processed separately using 

conventional as well as robust processing, to obtain apparent resistivity and phase for 

the un-rotated diurnal and nocturnal tensor elements (Padilha et al. [1997]). However, 

the comparison between daytime and nighttime results did not show any significant difference 

in the entire period band. The MT curves were nearly identical, within very low 

error bars. This was true for all the measured sites along the profile, indicating that EEJ 

currents did not affect the MT data. The theoretical modeling of EEJ, approximated 

as a conductive layer at 110 km, the authors found EEJ may affect MT responses at 

periods greater than 1000s. But they did not have enough observed data at comparable 

period range. They concluded that the theoretically anticipated EEJ distortions are 

probably overestimated and the plane wave assumption of MT signals at equatorial regions 

is valid at least in the frequency range 1000 to 0.0005 [Hz]. But recent studies by 

Rao [2000] and Rao et al. [2002], on analyzing MT data collected near and away from 

Indian magnetic dip equator showed the effect of EEJ is appreciable above 100 sec. The 

data were collected during the same field campaign in South India, the stations being 

south of the main measurement corridor. The data collected at three sites viz OK3, IRA 

and KAR, which lie in a NS profile, with KAR being southern most and at the center 

of dip equator. MT time series measured at each site were separated into daytime and 

nighttime segments. After omitting the sub-segments with obvious outliers, independent 

daytime and nighttime estimates of MT impedance were made. It was observed (Figure 

4.5(a) to (c) that the ρ yx component is very similar between day and night estimates at 

OK3 as well as IRA. But at station KAR, which is at the center of EEJ, the daytime

60 

Figure 4.5: Apparent resistivity vs frequency plot for 3 stations tht are near and away 

from the dip equator with day and night curves superimposed (Rao et al. [2002]). (a) 

OK3 - site 300 km north of dip equator, (b) IRA site 100 km north of dip equator and 

(3) KAR - site near the dip equator. 

estimates were biased down at frequencies less than 0.01 [Hz]. This corroborate the idea 

that, increased signal amplitude for H x as a result of the eastward current flow associated 

with EEJ might bias the MT transfer functions. 

The effect of EEJ on MT transfer functions seem to be decreasing fast as one goes 

away from the dip equator, as evidenced by the similarity in daytime and nighttime curves 

of IRA and OK3, which lies to the north of dip equator and KAR. As the measurement

61 

Figure 4.6: Averaged Kp indices [Courtesy NGDC], K indices [HYB] during the MT 

measurements are compared with telluric predicted coherence [4 sec 128 sec]. The mean 

coherence is drawn as a line. 

corridor for the present study is located ∼300 km north of the dip equator, the effect 

of EEJ on MT transfer functions may be treated as negligible, at least in the frequency 

range of measurement. 

4.5 Signal Activity during the Field Campaign 

MT data were collected in two field campaigns in September - December 1998 and January 

– March 2000. In order to study the ability of different processing methods to estimate 

MT transfer functions (> 1 sec) in the presence of both low and high noise levels, compared 

to signal levels, the geomagnetic activity during the measurement were examined. Shown 

in Figure 4.6 as histograms are the averaged daily global Kp and Hyderabad K indices, 

with long period average coherence (§ 4.5). K indices are a local quasi-logarithmic 

measure of geomagnetic activity (Jones et al. [1989]) and have 10 classes between K =0 

and K =9 (magnetic storm). K =9 correspond to a range of 300 nT for Hyderabad 

observatory. Where as Kp indices are global indicators of geomagnetic activity and 

are weighted average of a selection of local K indices and with weights reflecting the 

geomagnetic latitude and longitude. Note that some stations are omitted. The stations 

are plotted in sequential order from Jan 12 to Mar 3, 2000. The K and Kp indices 

shows almost same magnitude and variation through out the measurements time, with 

a maximum at VP3 on 12 th February 2000. The low geomagnetic activity (indices less 

than 2) is observed between station KG01 and VP11 (16-23 rd February) which in turn is 

flanked by two well defined highs (indices > 3). Predicted coherence functions are good 

measure of the quality of MT data (§ 3.3.5), within the statistical limit of the least square 

solution of MT transfer functions. Procedures used to compute the average bias-corrected 

coherence function are discussed in § 4.6. The averaged predicted coherence values for 

all the station varies with a mean of ∼0.7 for the measurement duration. They are 

generally high in the region of K > 0.3 and low at stations whose period of measurement 

coincided with low geomagnetic activity. But stations KG03 and TT08 whose period of 

measurement have low geomagnetic indices, show relatively high coherence values and 

station VP13 with K indices > 0.3 shows low coherence. These deviation from the general

62 

trend, indicate the presence of other factors which might have also contributed to the 

coherence distribution. 

4.6 Spatial character of coherence 

Predicted coherence function defines optimality of the least square solution for MT transfer 

functions (§ 3.3.5). It has widely been used to examine the quality of the measured 

MT data (Vozoff [1972]). Though it is possible to compute predicted coherence functions 

for all the measured MT fields, telluric coherence functions are more frequently used 

for two obvious reasons i.e., 1) The magnetic fields are usually measured at a greater 

level of accuracy than the electric fields, 2) Electric fields are more prone to noise from 

man-made sources. Due to reasons 1 & 2, the least square estimation of MT transfer 

functions usually consider magnetic fields as noise-free inputs and minimize the noise in 

electric fields (Sims et al. [1971]). In this section, the distribution of averaged predicted 

coherence of E x and E y components for all the stations in the measurement corridor are 

described. The averaged predicted coherence is defined as, 

γ 2 = 1 2 

( 

γ 

2 

Ex−HxHy + γ 2 Ey−HxHy) 

(4.1) 

The individual coherence functions within the bracket are defined in § 3.3.5. However, 

it is relatively well known that the predicted coherence functions get biased due to noise. 

Jones [1981] and Jones et al. [1983] describe a simple way to reduce the bias in coherence 

functions. For predicted coherence it is defined as, 

( ) 4 (1 

γb 2 = γ 2 − 

) ) 

− γ 

2 2 

(1 + 4γ2 

(4.2) 

v − 2 

v 

Where γ b is the bias reduced estimate of γ and v is the degree of freedom for the 

estimate. In order to estimate the MT transfer functions, all the time segments available 

at the stations were processed and averaged the coherence without using any preferential 

stacking algorithms. The idea here is to represent the noise contributions at each site 

and time segments with obvious outliers were also kept to estimate impedance tensor and 

their associated coherence functions. Considering the bias in coherence estimation in the 

presence of noise either correlated between the input and output fields or un-correlated 

noise in the input field, the coherence function over respective frequency bandwidth of 

measurements were averaged. At each site we have four estimates of predicted coherence 

functions in four bands of measurements. The coherence estimates at all the sites are 

gridded (with grid surface always going through the data points) and presented as a 

contour map for the measurement corridor for each band in Figure 4.7. 

A total of 69 sites were used to prepare the map out of 80 stations. The predicted 

coherence functions of the telluric fields vary between 0.3 and 0.9 for most of the sites and 

over bands of measurements. The spatial distribution of coherence is however not similar 

for all the bands. The distribution patterns are similar for band 1 and band 2 (Figure 

4.7(a)&(b)) with coherence assuming high values for most of the sites. Except for the NE 

apart and a site in the center of the measurement corridor, the coherence values are very

63 

Figure 4.7: The band averaged telluric predicted coherence plotted as a contoured map 

for all the measured MT sites. (a) Band1 (b) Band2 (c) Band 3 and (d) Band4. 

high (>0.8). As band1 and band2 covers the noise contributions from power lines, there 

could be two reasons for high coherence for MT data in this range. If the noise source 

can be considered as ‘near field’ (§ 2.4) for that measurement site, the MT coherence may 

still be very high, but the apparent resistivity will just be a function of frequency, with 

least amount of information of subsurface resistivity. On the other hand, if measured 

sufficiently far from the noise source, so that the plane wave conditions for MT are met, 

then the power line signals can be an ideal source for the high frequency MT. However, it 

is impossible to distinguish these two possibilities by analyzing the coherences. The MT 

data in the middle frequency range (Band3 – 0.25 – 6 Hz) exhibits comparatively low 

values for coherence (Figure 4.7(c). As the natural signal strength in this frequency band 

are very low compared to other bands, it is not surprising to observe the low coherence 

for band3. However, the southern part of the measurement corridor (south of 11 0 Lat) 

has higher coherence values than the northern part. The low coherence for the NE part 

observed in Band1 and Band2 (Figure 4.7(a)&(b)) also is repeated in band3. Except for a 

site in the north and for an EW (11.5 0 Latitude) belt in the center, the MT measurements 

show fairly high coherence values in the long period measurements (Figure 4.7(d)). On 

a closer look at all the four plots it is apparent that a EW belt in the center of the 

measurement corridor shows low values throughout the frequency bands.

64 

4.7 Geographic relation of noise 

As we have seen in § 4.5 the geomagnetic indices varied during the measurement period. 

However, its direct implication on coherence of longer period data was not clear. One 

reason could be the varying effect of man-made noise in the MT data. The spatial 

distribution in predicted coherence (§ 4.6) consistently showed as EW belt of low values 

for all the measurement bands. In order to understand the relation of noises in MT 

data measured over South India to the major geographical elements of the region, the 

contoured plot for noise/(signal+noise) ratio for all the stations was superimposed on the 

geography map for the measurement corridor (Figure 4.8.The noise/ (signal+noise) ratio 

is defined as , 

n 

s + n = (1 − γ2 ) (4.3) 

Where γ is the averaged predicted coherence defined in equation 4.1 & 4.2. The 

ratio is bounded by values 0 and 1. Major roads (thick black lines) and rail tracks 

crisscross the measurement corridor. Major rail/road links between two state capitals viz 

Bangalore and Chennai passes through the northern part of the corridor. Cauvery river 

flows through the center of the corridor, with major towns like Erode and Sankaridurg on 

its banks. In addition to the rail and road clusters, this area hosts a number of cement 

factories. Limestone is present all along the fringes of an exposed granite (Sankari) 

dome. Availability of limestone and water from Cauvery made this region suitable for 

such factories. The measurement corridor is relatively free of anthropogenic disturbance 

sources further south (ie south of 11 0 Latitude). The contour plot for N/(S+N) ratio 

shows an interesting relation to the distribution of man made electromagnetic disturbance 

sources. The northern region of the corridor shows three isolated highs at stations JN08, 

JN03 and JN05. Though it is spatially correlated well with the Chennai – Bangalore 

rail lines and roads, the other three stations in the area viz. JN01, JN02 and EW02 

do not show high N/(S+N) ratios. In the middle of the measurement corridor, 8 MT 

stations distributed in and around the towns Erode and Sankaridurg shows very high 

N/(S+N) ratio. This cluster of highs in noise ratio clearly shows their affinity towards 

the industrial belt mentioned above. Though one expects the effect of the industrial zone 

to extend all along the banks of the river Cauvery, except for station TT08, the effect 

of noise is not perceptible further West. In line with the observation that the southern 

part of the corridor is devoid of major anthropogenic disturbance source, the N/(S+N) 

ratios of southern MT sites have relatively low values. In conclusion, in the northern and 

central part of the measurement corridor, the noise distribution is related to the known 

man-made electromagnetic disturbance sources. 

4.8 Discussion 

An attempt has been made in this chapter to characterize the signal and noise in the 

measured MT data over the Southern Granulite Terrain. Processing of MT data start 

with visual inspection of the measured time series. As seen in Figure 4.2 and 4.3, the 

time series collected over the SGT shows effects of noise from various sources. Moreover

Figure 4.8: Contoured map of telluric Noise/(Signal+Noise) ratio, superimposed on the 

major geographical elements of the region. Note N/(S+N) ratio on either sides of Cauvery 

river near Sankari. 

65

66 

the noise is manifested in the time series with patterns different from the natural signals. 

However, visual inspection of time series will not remove all the noise in the measured 

data, as many noise processes have temporal characteristics similar to the signals. A more 

quantitative definition of signal and noise is required to separate them in MT data. One 

straightforward way to do this is to construct a transfer function between the measured 

electric and magnetic field. Now the portion of electric and magnetic fields that cannot 

be explained by such a relation may be treated as noise. As we have seen in § 4.3.3, 

criteria for separating signal and noise based on the coherence and errors may not work 

always. This necessitated looking at some other properties of the data, specifically, two 

independent observations on the processes contributing to signal and noise. In this respect 

the indices of geomagnetic activity during the measurement time were compared with 

the averaged long period coherence of each site. The agreement of the coherence and the 

geomagnetic indices indicate the validity of such an approach (Figure 4.6). However, a few 

disagreements are also evident. This indicates the possible noise processes contributing 

to the measured data. Spatial relation of the known cultural noise centers and the quality 

of MT data was examined. The strong correlation of the high noise/(signal +noise) ratio 

to the major industrial belt indicate that the MT signals may get consistently degraded 

due to presence of an active noise sources, irrespective of the signal activity. However, 

the conclusions drawn from this chapter should be treated rather cautiously in instances 

where the underlying noise processes deviate from a Gaussian distribution. The signal 

and noise are defined in this chapter as inline and outline components of a least square 

solution of MT transfer functions. In the next chapter, we will take a closer look at 

the temporal properties of MT data and propose a new signal discrimination method, 

without the definition signal and noise from a least square solution.

Chapter 5 

The application of the artificial 

neural networks to magnetotelluric 

time series analysis 

67

68 

5.1 Introduction. 

In the previous chapter the signal and noise characteristics of MT data acquired from 

SGT were analyzed. The noises from various sources manifest in MT data in different 

forms. A part of noise is obvious in the time series itself. The manual inspection of the 

time series is often the first step in MT data processing, which selects a subset of time 

segments, followed by statistical transfer function estimation such as robust processing. 

However, manual inspection has its own limitations. Firstly, it is a time consuming process, 

which constitutes ∼ 80 % time used in MT time series analysis. Secondly, like other 

human decision making processes, MT time series editing is also a subjective process, 

wherein the same person may output differently, in a long session of editing. Considering 

the large volume of MT data collected over SGT, a need to develop a procedure 

to automate the manual editing of MT time series was felt. An approach was made to 

this problem from pattern recognition angle demonstrating the efficacy of artificial neural 

networks in discriminating noisy sections of time series against the signals. In first 

instance, characteristics of long period (4-128sec, band 4). MT time series were used to 

build training / testing data base for artificial neural networks. 

5.2 Signal and noise in the magnetotelluric time series 

An exact classification of signal and noise characteristics in magnetotelluric time series 

is difficult as their sources may have similar spectral content. Unfortunately there are 

often more noise sources than signal sources. Still, a generalized classification is possible 

according to the origins of both signal and noise. At periods longer than 1 sec, the natural 

electromagnetic field originates in the upper ionosphere and magnetosphere. Random 

bursts of energy originate in charged particles from the Sun and induce sinusoidal electromagnetic 

waves in the magnetosphere and ionosphere (see § 2.2.1 for more details). 

The signal amplitude and frequency may vary with the energy and type of activity and 

there may be a long gap between the arrival of two trains of signal. Figure 5.1(a) shows 

some typical magnetotelluric signal patterns. Magnetotelluric noise sources have been 

listed in table 2.1. Any or all the these noise sources may be present together with MT 

signal resulting in compounded responses in the recorded time series. Some of the most 

common MT noise patterns are presented in Figure 5.1(b). 

5.3 Visual Inspection (editing) of magnetotelluric 

time series data; why automation ? 

Manual editing is often the first step in magnetotelluric data processing. The editor 

examines each stack of time series and labels it as either good or bad according to 

its signal/noise character. The bad stacks are removed from further processing. The 

task involves an intensive amount of pattern recognition. Experience provides a judicial 

balancing of signal characteristics such as shape, amplitude, frequency and correlation.

69 

Figure 5.1: Common signal and noise patterns in long period MT time series. Samples 

are collected from different sites. Note the change in amplitudes. (a) Signal patterns; 

Samples of E x and H y shows the geomagnetic pulsations. Other channels also show 

signals but at longer periods. (b) Noise patterns; E y & H x shows different types of 

spikes. A step and its decay is shown in H y . Sample of random noise is shown in H z . 

This process is subjective in nature and the same editor may output differently in long 

sequences of editing. A rule of thumb is that ‘if in doubt throw it out’. If questioned 

about a particular decision, however, the editor may offer a few rules for guidance but 

can give no obvious systematic reasoning. This constitutes the major time and human 

resource used in MT data processing. The number of stacks of time series recorded 

sometimes runs into hundreds. With several such sessions of recordings from a station 

and many such MT stations occupied in each survey, there is a pressing need to provide 

a more robust alternative, which is less time consuming and more objective.

70 

5.4 Magnetotelluric noise characterization 

Automation of MT time series editing requires a systematic evaluation of the task performed 

by the editor. What parameters influence an editing decision? How much importance 

does the editor give to each parameter? Can it be quantified? As there is 

no information available in this regard, an editing evaluation exercise was undertaken. 

It involved discussion with different editors and re – analysis of previously edited data 

and identification of the influence of different parameters in magnetotelluric time series 

editing. From the study, it was found that the following factors reasonably represent the 

criteria applied in editing: 

1. Signal pattern 

2. Signal amplitude 

3. Correlation of different field components 

4. General noise level 

5. Quantity of MT data available. 

When the general noise level is very high and/or the quantity of data available for 

editing is limited, compromises are made in editing. As these are exceptional cases, they 

were excluded from the present analysis. The first three factors were analyzed and each 

was given a percentage of influence. The percentage of influence for a particular factor 

was found by preferential editing using that criterion and comparing results with the 

regular mode of editing. 

5.4.1 Patterns of signal & noise : 

Pattern controls a major part of decision making. The signal pattern is transient overlapped 

sinusoids. The noise patterns can be classified as follows. 

1. Spikes : High amplitude, maximum duration for few data samples. Sometimes a 

spike is followed by a transient decay. These are commonly power related. 

2. Noise bursts: Plateau or step-like appearance spanning hundreds of data samples. 

3. Noisy trace: Random fluctuations due to wind, seismic effects and or low signal. 

4. Muted or dead trace: Instrument problem such as broken cable or failure in electronics. 

In most cases, the quality of signal can be deduced from the signal waveform. This, 

according to our study influences 60% of editing decisions.

71 

5.4.2 Amplitude of signals 

Although naturally varying electromagnetic fields exhibit a large variation in their 

strength, a broad range can be specified. In most cases, the amplitude ratio of orthogonal 

electric and magnetic signals was found to be a good discriminator. In long 

period time series, the electric field fluctuates within +/-100 mV/km and the magnetic 

field fluctuates within +/-0.5 nT in a noiseless environment. The channel amplitude may 

be increased many times in the presence of certain types of noise. Amplitude criterion 

often gives the most reliable information if the contaminated signal has the same pattern 

as noise- free signals but enhanced amplitude. This was found to influence 20% of the 

decisions. 

5.4.3 Correlation between simultaneously measured channels 

The electric and magnetic fields are related by a transfer function defined in § 3.3.1.2 In 

the ideal case the MT signals should be highly correlated and random noise will reduce 

the correlation. However, noise can be highly correlated between E and H channels. 

Noise from power lines especially near 60/50 Hz is an example. In longer period data, 

it was found that the correlation coefficients between orthogonal electric and magnetic 

fields (E x - H y and E y - H x ) could be a signal discriminator. Correlation was found to 

influence another 20% of editing decisions. 

As the above-described parameters influence the bulk of editing decisions, they were 

selected as the basis for automation. An automation scheme was developed using an 

artificial neural network for classification/editing of time series data. 

5.5 Artificial Neural Networks 

5.5.1 Why artificial neural network? 

Optimal conventional automation requires statistical characterization of the noise. This 

means estimation of certain statistical parameters from the data. In other words the 

likelihood ratio of signal/noise is replaced by sufficient statistics of data. The method is 

simple and appealing. It works very well when the target signal is known and the noise 

has a normal distribution. But in most cases noise does not have a normal distribution 

and the likelihood ratio is a complicated nonlinear function of input data. Garth and 

Poor [1994] classifies geophysical signals as non-Gaussian, unstructured signals as they 

involve least amount of detail. Classification of such signals is best done by labeling 

them according to their signal content and then presenting them to a pattern recognition 

scheme. Artificial neural networks (ANN) are an emerging tool that have been applied 

in many areas of science and engineering where pattern recognition is involved, such as 

speech and character recognition. The learning and adaptive capabilities of these models 

make them attractive for application to some problems in geophysics (Calderon-Macias 

et al. [2000]). The most documented application of ANN in geophysics has been for the 

automation of seismic data processing and interpretation (Murat and Rudman [1992], 

McCormack et al. [1993], Fish and Kusuma [1994], Dai and MacBeth [1995]). ANN also

72 

Figure 5.2: Simple three layer feed forward neural network. The data is processed at 

each neuron in the layers. Each neuron performs a summing of inputs multiplied with a 

weight parameter and outputs the data through its sigmoid transfer function. 

have found other applications in geophysics; such as in interpretation of well log data 

(Winer et al. [1991]) , locating subsurface targets from electromagnetic field data (Poulton 

et al. [1992]) prediction of upper atmospheric and ionospheric activities (Lundstedt [1996], 

Altinay et al. [1997], Koons and Gorney [1991]). More recently, artificial neural networks 

have been used in magnetotelluric inversion (Zhang and Paulson [1997], Spichak and 

Popova [2000]). 

5.5.2 ANN theory 

An artificial neural network is an information processing system composed of a large 

number of processing elements called neurons, which are modeled on the functions of 

neurons in the human brain. ANN differ from conventional pattern recognition techniques 

in their ability to adaptively discriminate or learn through repeated exposure to examples 

and in their robustness in the presence of high noise levels. ANN do not require a priori 

knowledge about the noise distribution of the process under study, as do its statistical 

counterparts. Unlike conventional methods, which incorporate a fixed algorithm to solve 

a particular problem, ANN perform a mapping, usually non-linear, between the input 

and output data, which allows the network to acquire important information on the 

problem being solved. It is these characteristics of neural networks that motivated us to 

investigate their use in MT data processing.

73 

One of the most widely used types of ANN, the feed forward artificial neural network 

(FANN) was used in the present study. Its architecture is outlined in Figure 5.2. It 

consists of a layer of neurons that accept various inputs (input layer). These inputs are 

fed to further layers of neurons (hidden layers) and ultimately to the output layer, which 

produces a response. The aim of the technique is to train the network such that its 

response to a given set of inputs is as close as possible to a desired output. A number 

of algorithms are available for training a neural network. Back propagation is the most 

popular training algorithm (Werbos [1990]) and was used in the current study. During 

FANN training, each hidden and output neuron process inputs by multiplying each input 

by its weights. The products are summed and processed using an activation function, 

here, a sigmoid function, 

f(x) = 1/(1 − e −x ), (5.1) 

to produce an output with reasonable discriminating power. The neural network 

learns by modifying the weights of the neurons in response to the errors between the 

actual and targeted output values. For a given set or vector of N inputs (x 1 , x 2 ,....,x n ), 

the output of node j is computed as 

(∑ ) 

y j = f Wji x i (5.2) 

where W ji is the weight of the connection between the ith and j th neurons. The 

learning rule for the adjustments in the weight between neurons i and j is expressed as 

∆W ji = ηδ j o i (5.3) 

where o i is either the output of node i or an input, η is a positive constant named 

the learning rate and δ j is the error term of node j. Thus, 

where 

and, 

δ j = δE 

δ netj 

(5.4) 

E = 0.5 ∑ (y j − o j ) 2 (5.5) 

net j = ∑ W ji o i . (5.6) 

Here, y j is the target value for the j th node and o j is the output for the j th node. 

The value δ j is computed as, 

δ j = o j (1 − o j ) ∑ δ k W kj , (5.7) 

if the node is not an output unit. To improve the convergence characteristics, a 

momentum gain β is added to the weight correction term which stabilizes oscillations 

during the learning process ( Boadu [1998]), i.e., 

∆W ji (n + 1) = ηδ j o i + β∆W ji (n), (5.8)

74 

where n is the iteration index. The training of the network is complete if the convergence 

of weighting coefficients has been achieved. The convergence criterion requires 

that the sum square error at the output must be less than a desired tolerable error (Luo 

and Unbehauen [1997]). 

While training a network, we may start with arbitrary values for the weights W ji . It 

is usual to choose the random numbers in the range -1 to 1. Next, the outputs (O) and 

errors (E) for that set of weights are calculated, followed by the derivatives of E with 

respect to all of the weight (equation 5.7). If increasing a given weight would lead to 

more error, the weights are adjusted downwards. If increasing a weight leads to reduced 

error, it is adjusted it upwards. After adjusting all the weights up or down, start all over 

again and keep going through this process until the error is close to zero. The sequence of 

presenting the entire training database, calculating the network response, comparing the 

result with the assigned class, propagating the error backwards and adjusting the weights 

is called an epoch. Few thousands of such epochs of training are usually required by a 

neural network to reach zero error. However, if the number of training patterns exceed 

the number of weights in the network it may not be possible for the sum squared error 

(SSE) to reach zero. 

5.6 Data analysis 

5.6.1 Network engineering 

As a neural network’s massive interconnectivity and inherent non-linearity requires significant 

computing resources, dedicated mainframe computers and workstations were 

traditionally used for neural network training. Most of the applications utilizing ANN 

in geophysics deal with single-channel data using a small sliding window moving along 

the time series. The current application, where 5 channels of data, each containing 256 

points, were to be classified simultaneously, posed a major challenge. A novel approach 

was made to accommodate multi-channel data so that all the computing could be done 

on a PC. Figure 5.3 gives a schematic representation of the data flow. This method can 

be used for any multivariate signal detection scheme. 

As the signal shape and pattern controls a major part of the editing decisions, attention 

was focused on this part of the analysis. The inter-channel parameters, such 

as amplitude ratios and correlation coefficients were also included for neural network 

training. The signal detection scheme was divided into two steps. 

a) Detection of the patterns of individual channels: Patterns of individual channels 

were evaluated using a neural network. Within each stack (256 points) of 5 channels, 

each channel’s pattern successively were classified. Thus pattern detection of a single 

stack resulted in 5 values corresponding to the 5 channels. 

b) Detection of inter-channel parameters: Amplitude ratios (E x /H y , E y /H x ) and correlation 

coefficients between channels were computed. These parameters, along with the 

pattern quality data from step (a), formed the inputs for another neural network. Output 

from this network indicates the overall quality of that data stack. 

This separation provided us with the flexibility and ease of operating on a small 

computer, without having to compromise on network performance.

75 

Figure 5.3: Data flow through the feed forward artificial neural network (FANN) based 

editing scheme. 

5.6.2 Pattern Training 

5.6.2.1 Data used: 

Selecting an appropriate training data set is one of the most critical steps in successful 

training. How many patterns are required in training? How many patterns should be 

dominated by signal and how many by noise? A rule of thumb is that the patterns in 

the training set should cover the main categories of signal and noise. The signal pattern 

should represent the typical features of a signal with different frequency characteristics. 

Obviously there are more noise patterns than signal patterns (Zhao and Takano [1999]). 

With an input data space of 256, the number of exemplars required to train a neural 

network was large (> 1000 sets). This required us to search for and select a large number 

of time series segments. 1200 sets of MT long period time series data stacks (256 s. 

length, each stack) were collected from different data sets giving 6000 traces. 

5.6.2.2 Pre-processing 

Each channel was corrected for trend and bias and normalized between 1 and 0. The 

data segments were then manually classified and assigned a value between 0.9 and 0.1, 

depending on quality. The label varied between 0.1 (bad) and 0.9 (good) depending on 

the pattern quality of the data. There is no fixed generic relationship between the label 

and quality ( one can as well have labels in the reverse order). 

Out of the classified time series segments, 5000 extreme cases were selected for training. 

This set contained 2500 very good and 2500 very bad data samples. Care was taken 

to include all categories of signal and noise patterns generally found in MT time series. 

The database was shuffled to have a random distribution of good and bad data for training. 

From this data base 3000 exemplars (training vectors) were kept for training and

76 

Figure 5.4: Stacked amplitude and phase spectra of the training database. The spectra 

of noisy data (class 0.1) clearly different from the signals (class 0.9). 

the rest, for testing. 

5.6.2.3 FANN Training 

The network was presented with the training database of 3000 time series segments. 

Training was done with different values of learning rate (η) and momentum gain (β) for 

different epochs (defined in §5.5.2). Training typically took 60 minutes to complete 1000 

epochs on a 500 MHz PC. The longer time for training hampered effective interaction 

with the process and limited an exhaustive search for the optimum network configuration 

( i.e.; optimize η, β and the number of hidden neurons). A transform of the input data 

was sought which would preserve the essential information about the signal while reducing 

the dimensionality of the input space. For this, the time series was Fourier transformed, 

after applying a cosine taper to both ends. To test whether the amplitude spectra alone 

could be used as a discriminator, the spectra of good and bad signals in the entire training 

database were stacked separately. As seen in Figure 5.4, there is a clear difference between 

the two types. Noise generally raises the spectral power at higher frequencies, where as 

signal has more power at lower frequencies. Amplitude spectra were used for further 

training. FFT enabled us to reduce the number of input data from 256 to 128. Training 

was attempted with different subsets of spectral harmonics by removing the highest 

frequency elements successively. The first 100 harmonics were found to be sufficient 

and the training time was considerably reduced (20 minutes). The sum squared error 

(SSE ) as a function of epoch for the last training is plotted in Figure 5.5(a). The SSE 

reached a minimum of 33.73 for 2000 training samples. In neural network training, more

77 

Figure 5.5: Results from the pattern training. (a) The SSE as a function of epoch. The 

error reached the minimum floor after 400 epochs. Stability of convergence is demonstrated 

up to 1000 epochs. (b) Deviation between manually classified and network predicted 

classes for 500 test time series segments. The scattered points shows the major 

deviations. The correct picking constitute 94 

importance is given to how the network performs on novel (non training) data than the 

SSE of training itself. FANN on test samples (samples which were not used for training) 

gave 94 % (472/500) correct classification (Figure 5.5(b) with η = 0.09, β = 0.1 and 10 

hidden neurons. As observed by Dai and MacBeth [1995], although this solution was 

considered optimal for the current application, further architecture optimization could 

undoubtedly be achieved by a more exhaustive search procedure on a more powerful 

computer. 

5.6.2.4 Sensitivity analysis 

The neural network’s sensitivity to the signal to noise ratio was examined using the 

following analysis. A time series of 256 points with high signal content was mixed with 

a normally distributed random noise series. The trained neura1 network was assigned to 

classify the signal. In each run the signal content was changed with a small increment 

so that it covered the range 0% to 100%. The network steadily gave values near to 0 

(Figure 5.6) until the signal content reached 60%. The output changes to higher values 

as signal content exceeds 60% and asymptotes to 1 after it is 80%. It is now evident that 

the network is able to detect signals if the signal content is more than 70%. Another 

interesting aspect is the narrow region of high variance (when signal content is between 

65% and 75%) in the output. A thorough analysis with noise of other distributions was 

beyond the scope of the present study.

78 

Figure 5.6: Network output versus signal content. The network was simulated by inputs 

with varying signal content. A narrow region of high variance exists when signal content 

is between 65 

5.6.3 Inter channel training 

Here, a separate neural network was trained with the inter channel parameters (explained 

in §5.6.3). To keep this as the final step in determining the overall quality of the stack, 

the 5 pattern quality values predicted by the first step also as input were also included. 

The inputs to the network were, 

1. 5 pattern quality values from earlier network 

2. 2 amplitude ratios (E x /H y & E y /H x ) 

3. 2 correlation parameters (E x - H y & E y - H x ) 

5.6.3.1 The data 

To train the network, 900 stacks were selected from different data sets ( 5 channels, 

256 data points each). Care was taken to include an equal number of signal and noise 

segments. Each stack was manually inspected to assign a class vector 0.1 or 0.9 depending 

on its overall signal quality, as explained previously. A training database was made as 

follows. 

1. The trained FANN was used to classify the patterns of the 5 simultaneously measured 

channels within each stack. Output of this processing varied between 0.0 

(bad) and 1.0 (good). Figure 5.7(a) shows the pattern classes for E x and E y channels 

versus the stack numbers. The broken bar below the graph indicates the 

manually assigned stack class (Black-good; White-bad). An excellent correlation

79 

Figure 5.7: Pattern, amplitude ratios and correlation coefficients of 900 stacks which 

form the database for inter channel training and testing . The thick line is the running 

average over 10 points. The broken bar indicates the overall stack quality - black good 

(0.9) and white bad (0.1). (a) E x (squares) and E y (triangles) pattern quality predicted 

as a function of stack number. (b) E x - H y (squares) and E y − H x (triangles) amplitude 

ratio. (c) The correlation coefficients of E x to H y (squares) and E y to H x (triangles). 

between the manually assigned stack class and the pattern class of individual channels 

computed from FANN processing is evident. This justifies our earlier comment 

that signal discrimination largely depends on the pattern of time series signals. 

2. As the amplitude ratios between the orthogonal electric and magnetic field were 

found to be another signal discriminator, the two ratios were included in the training 

database. Further, in order to keep the values within 0 and 1.0 (as necessitated by 

the sigmoid function) they were normalized as 

A ExHy = 

E x 

H y 

A EyHx = 

E x 

H y 

+ Ey 

H x 

and (5.9) 

E x 

H y 

E y 

H x 

+ Ey 

H x 

(5.10)

80 

where, E x , E y , H x and H y are simple ranges of amplitude (maximum - minimum) of 

respective channels for a stack. As plotted in the Figure 5.7(b) the ratios vary considerably 

and a direct correlation with the signal class is impossible. This parameter 

was retained for training, as it adds another dimension to the input data. 

3. Correlation coefficients between orthogonal electric and magnetic fields (E x - H y 

and E y - H x ) were calculated for each stack. The correlation coefficient r(τ) ( 

Molyneux and Schmitt [1999]) between two vectors X and Y ( t = 0,1,2.....n) is 

given by 

r(τ) = 

√ 

n t=n ∑ 

t=0 

∑ 

X(t) 2 − 

n t=n 

t=0 

X(t)Y (t + τ) − t=n ∑ 

( t=n ∑ 

t=0 

) 

√ 

2 

X(t) 

t=0 

n t=n 

X(t) t=n ∑ 

t=0 

∑ 

Y (t + τ) 2 − 

t=0 

Y (t + τ) 

( t=n ∑ 

t=0 

) 

(5.11) 

2 

Y (t + τ) 

A value of r =1 indicates perfect positive correlation between two vectors; r = 0 

indicates no correlation, meaning the vectors are not similar; r = -1 indicates anticorrelation 

(meaning two vectors are of same shape but of opposite polarity). The 

correlation coefficients for all the 900 windows are plotted in Figure 5.7(c). The 

squares represent E x -H y correlations and diamonds represent the E y -H x correlations. 

Most of the E x -H y coefficients are distributed between 0.2 and 0.6 whereas 

the E y -H x distribution is between -0.2 and -0.6. It can be clearly seen that the 

signal class is = 0.9 (good quality signal) when E x -H y and E y -H x coefficients are 

well separated (when they are closer to ± 1). 

5.6.3.2 FANN training 

The training database thus prepared was a 9 x 900 matrix. The rows were shuffled to 

produce a random distribution. Around 70% of the database was used for training the 

neural network and the remaining 30% was used for testing. As the input vector is only 

of length 9, the training procedure was rather simple compared to the pattern training. A 

three layer feed forward network was trained with 9 neurons in the input layer, 2 nodes in 

the hidden layer and one node in the output layer. The momentum gain β was set to 0.1 

and the values of learning rate (η) and number of hidden layer nodes were changed. Each 

training consisted of 5000 epochs and took 7-10 minutes to complete. As the training 

progressed, the number of hidden layer nodes was reduced to one. The training stopped 

when sum squared error (SSE) was 7.9 for 650 samples with η = 0.09. Figure 5.8(a) 

shows SSE as a function of epoch for the final training. On simulating the network using 

the test data, SSE was 3.72 (i.e. 0.1222 per vector ). Figure 5.8((b) shows the deviation 

of network-predicted signal class values from the manually classified values. It can be 

seen that the network classification was successful.

81 

Figure 5.8: Results from inter channel training. (a) The SSE as a function of training 

epoch. (b) Deviation between manually classified stack quality and network predicted 

for 250 stacks. 235 stacks were classified similar to manual classification. 

5.6.3.3 Relative significance of input 

The network was fully trained to classify MT signals. To find out the relative importance 

of the nine inputs (5 pattern classes, 2 correlations & 2 amplitude ratios) to the FANN, a 

validation training was carried out. At each run, the particular input of interest was set to 

nil all through the run. This resulted in a greater error compared to the original training 

using non-zero inputs. The extent of departure from the previous error is considered 

as the relative significance (Altinay et al. [1997]) of that particular point for the neural 

network. As can be seen in Figure 5.9, patterns of E x , H y , E y and H x are dominant 

in the neural network response, followed by the correlation parameters. Pattern of H z 

and amplitude ratios have the least influence on the neural network. This roughly agrees 

with our earlier classification of the factors influencing editing decisions, but with two 

surprises. First is the relative insignificance of E y as compared to E x . As the database 

for training was equally biased to all the 5 channels, it was not the result of faulty 

training. The excellent performance of the neural network on test data also proves this. 

Second is the low influence of amplitude parameters. While formulating the problem, 

the amplitude and correlation were given equal weight, but the training results disprove 

it. As the testing sessions proved the discrimination capability of ANN, the training was 

stopped.

82 

Figure 5.9: Relative significance of various inputs to the networks, viz amplitude 

ratios (A1 and A2), correlation coefficients (C1 and C2) and five pattern qualities 

(E x , E y , H x , H y andH z ). The error deviation against each input is a measure of its significance 

to the Neural Network. 

5.7 Application 

The artificial neural network based signal detection scheme was applied to the MT data 

collected from SGT. The neural network approach was successful in discriminating bad 

time series segments against the good segments in majority of the cases. Here the result 

of neural network processing from four sites viz, G12, VP12, JN10 and TT8 are presented. 

The selections were made to demonstrate the performance of neural network in the presence 

of varying degree of noise contamination. Station TT8 situated in the industrial belt 

(§ 4.7) is most affected by noise, followed by JN10 and VP12. G12 is a station occupied 

in the Western India, with very high signal-to-noise ratio in the longer period. This was 

included to demonstrate neural network’s performance on a very good site as well. The 

long period data collected in the chief session (§ 4.3.1) of each site were subjected to three 

type of editing viz 1) Blind editing - selected all the stacks, 2) ANN based editing scheme 

and 3) Manual editing by a third person. Once edited, the data were subjected to a 

common processing procedure as detailed below. Auto and cross spectra were computed 

for each target frequencies (Figure 3.3) from all the available time segments, after the 

editing. Transfer functions were estimated (§ 3.3.1.3) for each time segments, for all the 

target frequencies. Average telluric predicted coherence (equation 4.1) functions were 

used to sort the auto and cross spectra. A subset consists of 70% of the highest coherent 

spectra sets were the selected and used for estimating the final transfer functions. Note 

that this method differs from ’Coherency Threshold’ methods, wherein data sets with 

predicted coherence below a preset value are rejected for final transfer function estimation. 

This choice of somewhat old-fashioned algorithm is justified as it allowed to show 

the efficacy of neural network based editing. Moreover, the algorithm does not interfere 

too much with the data selected. Variance of the MT transfer function was computed 

according to equation 3.41 in § 3.3.4. General descriptions of results from each site are 

given below.

83 

Figure 5.10: Comparison of MT apparent resistivity and phase computed from different 

mode of editing of data from site G12 . Filled circles represent xy and diamonds represent 

yx components. (a) Using all stacks available. (b) By neural network editing. (c) By 

manual editing. 

1. G12: The station was located over basaltic province of western India. 192 stacks 

were available for processing. The time series was generally noise free with long 

period geomagnetic pulsations (sinusoids). The occasional spikes were smaller than 

the waveforms within which they occur. Figure 5.10(a) shows MT apparent resistivity 

and phase computed from all available stacks (192). The curve is quite smooth 

and without deviation, suggesting that the time series were relatively noise free. 

Neither FANN based editing (selected 157 stacks) nor manual editing (selected 150 

stacks) improved the curve significantly. Results are given in Figures 5.10(b) and 

(c). A small number of noisy segments were easily rejected by the coherency-based 

estimator, without any need of editing. 

2. VP12: This station was located in the granulite province of South India. A total 

of 352 stacks were recorded. Almost half of the stacks carried spikes and step 

like features originated from submersible electric pumps and switching of power 

supplies. The MT apparent resistivity and phase computed from all the stacks are 

given in Figure 5.11(a). The resistivity (ρ) values, especially between 1.0 and 0.1 Hz 

are scattered and phase (φ) is poorly resolved, with both xy and yx modes being 

equally affected. Figure 5.11(b) shows the results of FANN-based editing ( 140 

stacks selected ), where, both apparent resistivity and phase are better resolved. 

Improvement is clearly evident in the 1.0 to 0.1 Hz range. Manual editing resulted 

in selecting 127 stacks and the computed apparent resistivity and phase are similar 

to FANN editing (Figure 5.11(c)). 

3. JN10: This site was also located in the same region as VP12, but with more noise 

in the data. The effect of the noise is evident in the apparent resistivity curves

84 


mode of editing of data from site VP12 . Filled circles represent xy and diamonds 

represent yx components. (a) Using all stacks available. (b) By neural network editing. 

(c) By manual editing. 


mode of editing of data from site JN10 . Filled circles represent xy and diamonds represent 

yx components. (a) Using all stacks available. (b) By neural network editing. (c) By 

manual editing.

85 


mode of editing of data from site TT08 . Filled circles represent xy and diamonds 

represent yx components. (a) Using all stacks available. (b) By neural network editing. 

(c) By manual editing. 

computed from all the stacks (Figure 5.12(a)). The phase is also affected in the 

range 1- 0.1 Hz. The neural editing picked 80 stacks out of 256 available and gave a 

better estimate, as shown in Figure 5.12(b). A less rigorous manual editing picked 

107 stacks and gave a similar result (Figure 5.12(c)). 

4. TT8: This station was the most affected by noise. Both electric channels, especially 

E x , were affected by noise originating from an industrial belt nearby. Increased 

spike activity was observed in all channels. The MT apparent resistivity and phase 

computed (Figure 5.13(a)) from all the 256 stacks available gave a very distorted 

picture. Both xy and yx components were poorly resolved. Significant improvement 

was made by FANN editing (Figure 5.13(b)) which selected 67 stacks out of 256. 

The yx component is now smooth and relatively error free. The xy component is 

also improved except near 0.1 Hz. Almost the same result is produced by manual 

editing (69/256) as shown in Figure 5.13(c). The stacks picked by neural network 

and manual editing are compared in the Figure 5.14. Overall the pickings match 

quite well. Deviation between the two editing schemes is evident for a few picks 

between stack numbers 150 - 180. Between these there are stacks with moderate to 

low signal content, which were accepted by manual editing but rejected by neural 

editing.

86 

Figure 5.14: Comparison of manual and neural signal picking for site TT8. The diamonds 

present the neural picking and crosses, the manual. 

5.8 Discussion 

The application of ANN based editing to magnetotelluric time series brings out some 

interesting results. The ANN based noise rejection predicts an overall quality of each 

subsection of time series (0 to 1). While this value cannot be treated as errors of the corresponding 

impedances, the response is a measure of quality of the time series/ impedances 

and help improve the process of editing of data more objectively as compared to manual/ 

visual editing. In a low noise environment such as station G12, the network editing 

produces results almost similar to blind editing (using all stacks). On such a data, a 

simple coherency-based estimator can do the signal discrimination to a certain level of 

satisfaction. However, the neural network’s ability to pick out signal from moderate to 

high noise environment was evident on the data collected from SGT. In such cases it approximates 

human intelligence - established from the fact that the neural network based 

editing gives a result similar to manual editing. These results satisfy the objective of the 

present chapter, ie, to provide a robust alternative to manual editing of magnetotelluric 

time series. This experiment, brought out ANN’s potential to automate MT time series 

editing, efficiently and reliably. The scheme could be adapted into routine processing to 

save human time and increase reliability in editing. The current scheme performs about 

70,000 floating point operations (flops) per stack for classification. FFT of five channels 

alone uses 40,000 flops. If the further computation uses the same spectra, some of 

the computational redundancy can be removed. It points to the possibility of integrating 

ANN based editing into real time processing of MT data. The signal and noise characteristics 

in magnetotelluric data are very different in different frequency ranges. This is due 

to the difference in signal and noise source mechanism in different part of Earth’s natural 

electromagnetic spectrum. Sensor geometry and instrumentation also affect pattern of 

signal, which the neural network depends on. This necessitates reformulation of MT signal 

and noise characteristics for training of ANN, wherever necessary. However, the extra 

computational requirement by re-training of ANN may not pose a burden on resources, 

taking into consideration the ever-increasing computational power of microprocessors. 

The neural network based approach described in this chapter see the time varying

87 

processes for a finite duration as a whole. It does not assume a transfer function relation 

between the different channels under preview. Noise processes, which will not affect the 

pattern, amplitude and correlation parameters of the time series, but have potential to 

badly affect the estimation of MT transfer functions, may still escape from the screening 

of the neural network based editing. Secondly, once the time series has been selected, 

the signal content at all the frequencies from that time segment may not be the same. 

This provides for and necessitates a second screening of MT data, now in the domain 

of frequency, after an initial data screening by ANN. One advantage of working in the 

frequency domain is that estimation is done independently at many frequencies. For 

stationary processes, the data at different frequencies are strictly uncorrelated (Chave 

and Thomson [2003]). The robust processing techniques effectively search the frequency 

space to estimate MT transfer functions and its superiority above other comparable 

methods in frequency domain is established (Jones et al. [1989]). However, as stated in 

the introduction, in certain cases of noises, robust processing fails. The next chapter 

critically analyze and propose improvements to the robust processing techniques for MT 

transfer function estimation.

Chapter 6 

Estimation of Magnetotelluric 

Transfer Functions: Robust 

Statistical Methods 

88

89 


After the raw time series have been inspected by manual or automated noise rejection 

methods, the selected segments are used for estimating MT transfer functions. This involves 

estimating 10 1 -10 2 complex frequency domain transfer function elements Z(ω) 

from electric and magnetic field time series E(t) and H(t) (approximately 10 6 real numbers 

per site) (Egbert and Livelybrooks [1996]). This data reduction, though superficially 

simple, can result in useless MT transfer functions, in the presence of noise in measurements. 

The classical least-square method of computing MT transfer functions, allowing 

for noise distributed in the simplest manner was discussed in § 3.3.1. However, the drawbacks 

of least-square (LS) method has been widely recognized and documented in the 

past three decades (Sims et al. [1971], Gamble et al. [1979], Egbert and Booker [1986], 

Egbert and Livelybrooks [1996]). The failure of the LS method has been attributed to 1) 

presence of noise in the ‘input’ channel and 2) violations of Gaussian noise assumptions. 

In the first instance, the linear statistical model, (equation 3.26) through which the 

natural electromagnetic fields are related to each other, considers the input as noise free 

and the noise is restricted to the output or ‘predicted’ data. In MT it is usual to assume 

the magnetic fields as input and electrical fields as output. It follows that the noise in 

magnetic fields can down bias the transfer function estimates ( see § 3.3.2). To avoid these 

bias errors, Gamble et al. [1979] proposed the measurement of two remote magnetic field 

components as references and remote reference processing substantially improved (Jones 

et al. [1989], Shalivahan and Bhattacharya [2002]) MT transfer functions, over the single 

station least squares approach. In the second case, Gaussian distribution of errors is 

assumed by the LS estimator. The observed errors in magnetotelluric data often have a 

Gaussian distribution, but with heavier tails due to the presence of outliers (abnormal 

data). These non-Gaussian noise produces scatter (or low point to point continuity) in 

the processed data. If ignored, these outliers can corrupt the estimated magnetotelluric 

transfer functions, making them useless for geologic interpretation. A number of processing 

methods have been proposed which adaptively weights or screen the data. Stodt 

[1983] showed the usefulness of weighting the subsections of MT data according to their 

predicated coherence (see § 3.3.4). However, such approaches may fail in the presence of 

correlated noise in the data. Substantial improvements were bought out by the application 

of robust – M (Hampel et al. [1986]) statistical procedures to MT and geomagnetic 

time series analysis (Egbert and Booker [1986], Chave and Thomson [1989], Chave et al. 

[1987], Larsen [1989], Sutarno and Vozoff [1991], Egbert and Livelybrooks [1996], Egbert 

[1997], Ritter et al. [1998], Nagarajan [1998], Smirnov [2003], Chave and Thomson 

[2003]). The success of robust procedures may be attributed to three factors. First, its 

superiority to other data processing techniques is established (Jones et al. [1989]). Second, 

these procedures can be justified rigorously (Egbert and Livelybrooks [1996]) and 

third it can be easily implemented using iterative-weighted LS procedures and extended 

to remote reference processing (Chave and Thomson [1989]). 

In this chapter, two new approaches are proposed to improve the performance of 

robust statistical procedures on MT time series. The basics of the robust M procedures are 

discussed in § 6.2 and more stress is given to the computational aspects. Non-parametric 

estimators such as Jackknife (Efron [1982]) were used to robustly compute the variance

90 

of MT transfer functions (Chave and Thomson [1989]). Its use as an effective initial guess 

for robust procedures is discussed in § 6.2. It is shown that in majority of the cases, the 

use of Jackknife for initial guess resulted in better estimation of MT transfer function as 

compared to LS estimations. It is usual in MT to sub divide the time series, estimate 

the spectral density matrices for each segment individually and then robustly average 

the spectra or transfer functions between the sub segments (section averaging). Within a 

segment, it is common to use a limited number of target frequencies and obtain smooth 

spectra by averaging several adjacent Fourier harmonics (frequency band averaging). 

The documented researches on robust estimation of MT spectral densities and transfer 

functions concentrate on section averaging. This arises from the assumption that, within a 

narrow frequency band, the distribution of Fourier coefficients are of Gaussian nature and 

a simple average (LS) gives the best estimate. In § 6.3 it is shown that this argument often 

fails and the problem of contamination is applicable to band averaging as well. A robust 

weighting approach is proposed for estimation of cross and auto spectral estimation within 

a band, without making specific model assumptions concerning signal or noise. Both these 

proposed procedures, while applied on a large volume of MT data collected over SGT, 

South India, met with moderate to good improvement of MT transfer functions. Majority 

of these data were collected in single station mode, except for few stations, where remote 

reference data were available. A synchronization problem of MT equipment and GPS was 

the reason for single station recording during the study (§ 4.3.1). However, the robust 

processing procedures outlined in this thesis can easily be extended to remote reference 

processing and such an example is shown for station VP10 (§ 6.3.5). The application of 

the proposed robust processing methods are discussed in § 6.2.5 and § 6.4. 

6.2 Robust estimation of MT transfer functions 

The term ‘robust’ was coined in statistics by G.E.P. Box in 1953 (Hampel et al. [1986], 

Flannery et al. [1992]). Various definitions are possible for a robust procedure. But 

in general referring to a statistical estimation like MT transfer function, it means ‘one 

which is relatively insensitive to the presence of a moderate amount of bad data or to 

inadequacies in the statistical model and that reacts gradually rather than abruptly to 

perturbations of either’ (Jones et al. [1989]). 

6.2.1 Why robust methods? 

LS estimators are best on a data with Gaussian (normal) distribution of errors. It is well 

known that the break down point of least square (LS, or L2) estimates is zero. Break down 

point describes the smallest percentage of bad data that can corrupt an estimate. This in 

turn means that the presence of few outliers can corrupt an LS estimate. The resistance 

of median and other L1 estimates (L1 – minimizing the first power of residuals) to the 

presence of outliers is well - documented in the geophysical context (for e.g. Claerbout 

and Muir [1973]). Simple median has a break down point of 50 %. This led to the 

suggestion that L1 norm can replace L2 norm in many geophysical estimation problems. 

However, Chave et al. [1987] pointed out major drawbacks with L1 estimator on practical

91 

data sets. It was shown that L1 estimator requires about 60% more data to achieve the 

same parameter uncertainties as L2 estimator. Also, the natural probability distribution 

function for L1 is double exponential (Laplace) which make statistical inferences difficult. 

This suggests that it is desirable to treat the outliers within the framework of a Gaussian 

model, rather than outright abandonment of that model (Chave et al. [1987]). One 

way to achieve this is to identify the outliers and process the remaining segments of 

data with usual LS procedures, one such example is the ANN editing discussed in §5. 

However, in many situations like time series analysis, detection of outliers itself becomes 

extremely difficult and it may result in rejection of all the data as well. As a consequence, 

robust methods are developed, which can accommodate outliers and still minimize their 

influence. Without going into detail, the situation in which robust methods are desirable 

is shown in Figure 6.1. The probability distribution function shown in Figure 6.1(a) has 

heavier tails than expected for Gaussian distribution. Any fluctuation in these tails may 

lead to inaccurate estimate of the location of central peak (Flannery et al. [1992]). The 

simple line-fitting problem, given in Figure 6.1(b) shows the influence of few outliers on 

the estimation of the slope of the line, constrained to go through the origin. An estimate 

that is robust to the presence of the outliers should instead produce a fit, which satisfies 

majority of observations. Thus the need for robust estimates is seen. 

6.2.2 Robust M estimators 

Statisticians have developed various robust statistical estimators. For MT transfer function 

estimation, M – estimators are more relevant (M – stands for maximum likelihood) 

and are discussed in detail here. A brief discussion of development of robust estimation 

in MT follows. Let us reproduce the MT transfer function equation 3.26, 

E = Z H + r (6.1) 

where there are N observations so that E and r are N vectors, H is an N X 2 matrix 

and Z is a rank two vector. The last variable in equation 6.1, r is the difference between 

measured and predicted output field (here, Electric) and is the residual parameter to 

be minimized. The classical way of solving MT equation is the least squares technique 

(Swift [1986], Sims et al. [1971]), where the square of the residual power in equation 

6.1 is minimized to yield a solution for Z. Let r i be the residual of the i th observation, 

the difference between observation and prediction. The standard L2 method tries to 

minimize Σ r 2 i . The M estimators try to reduce the effect of outliers by replacing the 

squared residual r 2 i by another function of residuals, yielding, min Σ ρ(r i ), where ρ is a 

symmetric, positive defined function, called loss function with a unique minimum at zero. 

For standard L2, ρ( r i ) = r 2 i /2, while for the L1 estimator ρ( r i ) = | r i |. In general, if 

ρ(r) is chosen to be –log f(r), where f(r) is the true probability density function (pdf), of 

the residuals, then the M estimator is maximum likelihood (Chave and Thomson [1989]). 

However, as it is difficult to obtain a pdf from finite observations, the loss function is 

chosen in theoretical ground. Performing minimization, 

∑ 

ψ(r i )z ij = 0, for j = 1, 2. (6.2) 

i

Figure 6.1: Examples where robust statistical methods are desirable: (a) A one dimensional 

distribution with heavy tails (b) A distribution in two dimensions fitted to straight 

lines. Adapted from Flannery et al. [1992] 

92

93 

Type Loss- ρ(r) Influence ψ(r) Weight w(r) 

L2 

r 2 2 

R 1 

L1 |r| sign(r) 

1 

|r| 

Huber 1) if |r| < k 

x 2 

2 

R 1 

Huber 2) if |r| ≥ k k = (|r| − k 2 

sign(r) 

k 

|r| 

Tukey 1) if |r| < k 

k 2 

6 (1 − [1 − ( r k )2 ] 3 ) r[1 − ( r k )2 ] 2 [1 − ( r k )2 ] 2 

Tukey 2) if |r| ≥ k 

k 2 

6 

0 0 

Table 6.1: Few commonly used influence functions. Adapted from Zhang [1996]. 

Where ψ(r )= ∂ρ( r)/ ∂(r), is called the influence function and z ij is one component 

of the 2 X 2 tensor Z. The equations will reduce to least squares, when ρ( r) = r 2 /2, 

ψ(r )=r or to least absolute deviations when ρ( r) =|r|, ψ(r) = sign(r). To normalize 

the equations such as 6.2, it is common to divide the equation with a robust estimate of 

scale for which median absolute deviation (MAD) is a good choice (Sutarno and Vozoff 

[1991]). 

d = med|r i − med(r i )| 

σ MAD (6.3) 

Where σ MAD is the theoretical counter part of an appropriate pdf. Now equation 6.2 

becomes, 

∑ 

i 

ψ( r i 

d )z ij = 0. (6.4) 

To solve this equation, it is easiest to write it as a weighted least square, by defining 

a weighting function, w i = ψ(r i /d)/r i and rewriting, equation 6.4, 

∑ 

w i r i z ij = 0, for j = 1, 2. (6.5) 

i 

The weights are computed based on the residual r and scale parameter d, from the previous 

iteration and they are initialized using a least square solution (Chave and Thomson 

[1989]). The major difference between the solution given above and a normal weighted 

LS procedure is that, in the first case the weights are computed based on the residuals 

and scale estimate from previous iteration, where as in later case, weights are computed 

based on the data itself. 

6.2.3 Choice of influence functions 

The influence function ψ(r) measures the influence of a datum on the value of the parameter 

estimate. We have already seen the influence function for L1 and L2 estimates. Given 

in the table 6.1 are four different influence functions. (Zhang [1996]). Their graphical 

representation is given in Figure 6.2. 

From the table 6.1 and plot (6.2) it may be deduced that,

94 

Figure 6.2: Schematic diagram showing loss, influence and weight functions for Least 

Square (LS or L2) , Least Absolute (L1) Huber and Tukey estimators. Values shown in 

y axis are arbitrary See text for discussion. Adapted from Zhang [1996] 

1. L2 (least-squares) estimators are not robust because their influence function is not 

bounded. The larger the residual, the heavier weight it gets. 

2. L1 (absolute values) estimators are not stable and their weight function at r=0 is 

unbounded and solution may become undetermined. 

3. Huber function is a parabola in the vicinity of zero (like L2) and increases linearly 

at a given level |r| >k (like L1). Where k = 1.5d gives 95% efficiency with Gaussian 

data. This is most widely used and suitable to residuals drawn from a probability 

distribution that is Gaussian in the center and Laplacian in the tails. This blend 

of L2 and L1, is more suitable for the distribution presented in Figure 6.1. 

4. Tukey’s function is very severe for outliers (Figure 6.2) 

However, use of either Huber or Tukey function alone is not advisable. The Huber 

weights fall off slowly for large residuals and never descend to zero and thus do not 

provide adequate protection against large outliers (Chave and Thomson [1989]). Tukey’s 

influence function outputs near zero values for slightly higher residuals. Used alone, it 

may result in rejection of all data, or acceptance of very few. Hence it is advisable to 

use a Huber function for the first few iterations and then use Tukey’s function as a final 

weighting to protect against large outliers (Egbert and Booker [1986]). 

The response of influence functions to a set of MT data is presented in Figure 6.3. 

The data (VP13) were collected in the period range 4 sec to 128 sec at a sampling rate 

1Hz. The time series were sub segmented into sections of 2048 data points each and 105 

such overlapped sections were available for processing. Figure 6.3(a) shows the E x -E xp 

(defined in § 3.3) residuals at frequency 0.1875 Hz for each stack. Majority of the residuals 

assumes small and similar values with a small amount of scatter. However, there are 

large outliers present (∼16), especially near stacks 20, 40 and 100. The weight functions 

computed according to Huber, L1 and Tukey functions for these residuals are presented 

in Figure 6.3(b). L2 weights are always 1. L1 weights (inverted triangles) show low values 

for the outliers. However, their weights become very large for very small residuals. Huber 

weights (stars) are combinations of L1 and L2 weights, with a cut off at k = 1.5d. They

95 

Figure 6.3: Responses of different influence functions to a set of residuals from MT data 

processing. Station VP13 Shows the Ex residuals for 0.1875 Hz for all the 105 stacks. (b) 

Shows the response of three influence functions to the residuals. See text for discussion. 

are less influenced by the large outliers (as L1) and can accommodate the fluctuations 

within small residuals (near the Gaussian peak, like L2). As seen for values between 

stacks 50 and 60, Huber function down weights the large residuals, where the influence is 

same as L1. The steady response of Huber weights is more clearly demonstrated between 

stacks 60 and 80. Tukey weights show very low weights (< 10 −4 ) for large outliers. If 

used alone, it may result in deselecting most of the data sets. Severity of Tukey’s weight 

dominate everything else, as demonstrated at stacks 50-60, 100 to 105. However, it also 

rejects usable data especially at stacks 10, 40-50 and 70. 

6.2.4 Implementation for MT 

The application of robust processing developed for the estimation of magnetotelluric 

transfer functions is presented in this section. A MATLAB [2001] code ‘robspm.m’ was 

realized by integrating the algorithms discussed by Egbert and Booker [1986], Chave 

and Thomson [1989], Ritter et al. [1998], with the two new approaches introduced in this 

chapter. All the computations are performed in frequency domain. It is assumed that the 

time series were collected for sufficient duration of time. It is then divided into segments 

(subsets / stacks) of fixed length. Size of subset is chosen based on the lowest frequency of 

interest and a target value for degrees of freedom. Each segment was tapered by a Hanning 

window. The segments may be overlapped, provided corrections to dof are made. After 

Fourier transform, each channel was divided by calibration transfer function (§ 1.3.4) 

to remove the effect of instrument and sensors. A matrix of auto and cross spectra 

between channels (5 x 5 for single station set up), was made for a particular frequency 

by band averaging the adjacent frequency points respecting a narrow frequency window

96 

(this averaging is critically analyzed in § 6.3). The preprocessing results in generation of 

a 4 dimensional matrix for a site, with size L segments, N frequency and 5 x 5 channels. 

This forms the basic data for robust estimation. A flow chart for the robust processing 

implemented in this thesis is shown in Figure 6.8(a) and discussed towards end of this 

section 

6.2.4.1 Initial guess of transfer function 

One component of equation 6.1 may be written as, 

E l x = Z x x l H l x + Z x y l H l y + r l x (6.6) 

Where E and H are frequency domain components of electromagnetic field recorded 

in l = 1,2,. . . .L time segments. Z xx and Z xy are components of Z (equation 6.1). The 

algorithm described here will use the above equations. However, the same steps can be 

used to estimate the other components of the tensor and also magnetic transfer functions 

(equation 3.24). Estimations are done independently for all the N frequencies, so that 

the frequency terms have been omitted. To get an initial guess for transfer functions, 

’global’ spectral matrix is obtained by averaging all the L cross and auto spectra sets for 

a particular frequency, in the least square sense. For example one element of the global 

5 x 5 matrix is obtained by, 

〈 

Ex H ∗ y〉 

= 

1 

L 

L∑ 〈 

Ex Hy〉 

∗ 

l=1 

l 

(6.7) 

Conventional way of getting an initial estimate for Z is by solving the equation 6.1 

in least square sense (see § 3.3.1.3), with the global cross and auto spectra as obtained 

above. 

6.2.4.2 Jackknife estimate as initial guess 

The idea of using LS as an initial guess is to keep the solution somewhere in the convergence 

path and then to iterate to a solution with robust re-weighting. If one can keep 

the initial solution nearer to the actual/desired one, the convergence can be fast. Here 

the use of a simple nonparametric estimator called Jackknife (Efron [1982], Chave and 

Thomson [1989], Eisel and Egbert [2001]) as a better replacement for LS as initial guess is 

demonstrated. Chave and Thomson [1989] demonstrated its ability to estimate variances 

of the MT transfer functions robustly, alleviating the need to accurately compute the dof 

as needed by conventional variance estimate (such as given in 6.16). However, Eisel and 

Egbert [2001], while discussing the results from processing of 2 years of continuous MT 

data, commented that they are systematically too large for most of the periods. The 

jackknife estimator was used to compute an initial MT transfer function (not variance) 

in the robust processing routine. This is shown to be resistant to outliers and thus may 

produce an initial guess, nearer to the true one. One advantage of Jackknife method is 

its computational simplicity. This is important, as these routines will be regularly called 

in robust processing. Consider Z as any one component of the transfer function derived

97 

by locally solving the equation (6.1). From all the time segments we have L number of 

estimates of Z. Let Z mean be the mean based on all the data. The data are then divided 

into L groups of size L-1 each by deleting an entry in turn from the whole set. Let the 

estimate of Z based on i th subset, when the i th datum has been removed be Z −i (Chave 

and Thomson [1989]). The jackknife mean is given as, 

Z jackknife = LZ mean − L − 1 

L 

L∑ 

Z −i (6.8) 

The quantity in the above equation was originally introduced as a low bias replacement 

for regular mean (Chave & Thomson, 1989, Effron, 1982). We may construct a difference 

vector, 

∣ 

Z diff 

−i = 

∣ Z −i − 

The Jackknife variance is then given by, 

Z var = L − 1 

L 

i=1 

∣ 

L∑ ∣∣∣∣ 

Z −i . (6.9) 

i=1 

L∑ ( 

i=1 

Z diff 

−i 

) 2 

. (6.10) 

Note that jackknife variance is entirely different from the conventional variance which 

are ‘parametric’ estimations. (In the sense they depend on number of dof, value of 

coherence etc). Advantages and disadvantages of this variance are thoroughly discussed 

by Chave and Thomson [1989], Eisel and Egbert [2001]. The aim here is to investigate 

the use of jackknife estimate as an initial guess for robust processing. Iterations can be 

performed by successively deleting data rows (stacks) which gives maximum difference 

as in equation 6.9. After each iteration, the variance of current iteration is compared 

with the previous one. Iterations are stopped when there is no more improvement to the 

variance, or the data get exhausted. 

An example of the application of Jackknife estimation of MT transfer function is 

plotted in the Figure 6.4. From the station VP10, a total of 103 overlapped sections 

(length 1024) of time series data were available. An equal number of transfer functions (Z) 

were generated from these data sets. The jackknife difference as calculated by equation 

6.9 for the first iteration is shown in Figure 6.4(a). The plot shows large differences 

especially at the beginning and end of the stacks. To proceed data row (stack) with 

highest difference will be deleted. Figure 6.4(b) shows the progressive decrease of variance 

as the iteration progresses. In this case, iteration was stopped at 28. Figure 6.4(c) and 

(d) compares the output of a least square and jackknife estimations of MT apparent 

resistivity and phase values (YX). Figures 6.5(a) to (d) depict the jackknife estimation 

of MT transfer functions for site VP13. As can be seen from the plots, the jackknife 

gives better estimate of the parameters as compared to the LS. The LS estimations were 

distorted by few and large unusual data elements. However, the jackknife estimations 

are not advised as the final ones, as the variability of jackknife estimate can be large 

for some statistical distributions (Chave and Thomson [1989]). It may be concluded 

that jackknife can be good start for robust processing, considering its computational

Figure 6.4: Comparison of Least Square and Jackknife estimation of MT transfer functions 

for station VP10 (a) Jackknife difference for the first iteration. (b) Variance as a 

function of iteration number. (c) and (d) comparison of ρ and φ values from LS & JK 

processing 

98

99 

Figure 6.5: Comparison of Least Square and Jackknife estimation of MT transfer functions 

for station VP13 (a) Jackknife difference for the first iteration. (b) Variance as a 

function of iteration number. (c) and (d) comparison of ρ and φ values from LS & JK 

processing 

simplicity, non-parametric nature and superior performance over LS.

100 

6.2.4.3 Scale estimate 

Once the initial guess for transfer function is made, we derive the residuals r l , for all the 

time segments for a particular frequency as, 

r l2 

x 

= ∣ E 

l 

x − Z xx Hx l − Z xy Hy 

l ∣ 2 (6.11) 

Equation 6.11 describes one way of assessing the quality of a least square solution 

to the observations in E and H. There are also other possibilities like variance ∆Z, 

coherence γ 2 etc to be used as quality parameters (Ernst et al. [2001]). However, the 

residuals between predicted and observed fields are popularly used to assess the quality 

of LS solution of MT transfer function and are used in this thesis as well. 

An initial MAD scale estimate for the robust weighting procedures is obtained as, 

d M = 1.483med.(|r l − med.(r l )|). (6.12) 

For MT data the residuals in the above equations are complex in nature. One way 

of measuring the residual size is by its magnitude and it is preferred, as it is rotationally 

invariant (Chave and Thomson [1989]). In a simple way, the weight assigned to a complex 

value changes both real and imaginary parts in the same way such that its phase remains 

the same. 

An upper limit to the scale estimate may be given as k M = 1.5d M (see §6.2.3 case 3). 

6.2.4.4 Robust transfer function estimation 

The Huber weights w l for each stack l is calculated according to k M . 

{ 1 for r 

w l = 

l ≤ k M 

k Mr 

l for r l (6.13) 

> k M 

Now using the weights, new auto and cross-spectral estimates are given by, 

〈 1 

Ex Hy〉 ∗ = 

L∑ 

L 

∑ 

w l l=1 

l=1 

w l 〈 E x H ∗ y〉 l 

(6.14) 

From the modified spectra sets, new estimates (robust) of transfer function Z are 

obtained. To estimate the new MAD scale estimate, we must take into account the 

weighting process. 

d 2 H = L L 2 c 

L∑ 

w l (r l ) 2 (6.15) 

l=1 

where, L c is the number of weighted events with w l = 1 in step 6.13. Now by using 

the new upper limit k H = 1.5 d H , the steps 6.11 and 6.15 are repeated, resulting another 

estimation of Z xx & Z xy . Though, it is advised in the literature to iterate equations 6.11 

to 6.15, to our experience the transfer functions hardly changes after second iteration.

101 

6.2.4.5 Tukey weights 

The extreme outliers in the data are removed by again weighting the spectral matrices 

with Tukey’s biweight criterion. In order to compute a new scale estimate. Following 

Ritter et al. [1998], 

d 2 T = 

1 

L 

L∑ 

1 

( 

1 − 

( 

1 

L 

L∑ 

(w l r l ) 2 

l=1 

) ) 2 

r l 

k H 

(1 − 5 

( 

) ) (6.16) 

2 

r l 

k H 

With an upper limit k T = 6d T , we obtain Tukey weights w l as (reproducing from 

Table 6.1), 

{ ( ) 

w l r 

1 − 

= 

k T 

for r l ≤ k T 

0 for r l > k T 

(6.17) 

Spectral matrices are weighted again with this new weight. This forms the final step 

in robust processing. The transfer functions are computed from the weighted spectral 

matrices. 

6.2.4.6 Computing the variance 

The robust processing procedure modifies the degree of freedom of individual estimates. 

While computing the variance, this also must be taken into consideration. In the processing 

code, it was realized for each weighting step as, 

dof new = dof (∑ 

old w 

l) 

. (6.18) 

L 

Now the variance for one element of the transfer function is given by, 

(∆Z xy ) 2 = k F (k, 2dof − 4, δ = 0.05)[1 − Coh2 (E x E p x)]E x E ∗ x 

2dof − 4 [1 − Coh 2 (H x H y )]H x H ∗ y 

(6.19) 

Müller [2000]. Where F is the Fischer distribution, with k = 4 (See Bendat and 

Piersol [1971]). An indirect estimate of the degree of noise level can be obtained from 

the misfit of the final model (impedances) with the weighted data sets (cross and auto 

powers) of the final iteration. However this assumes that, once the outliers are removed, 

the residuals (model predictions observations) gets a Gaussian distribution 

6.2.4.7 Quantile Quantile plots 

In Figure 6.6, comparison of Least Square and the robust processing method (described 

above) is demonstrated for station TT08. The E x -E xp residuals from LS estimates of 

transfer functions for all the stacks of frequency 0.0791 Hz are plotted in Figure 6.6(a) and 

b (zoomed version). Inverted triangle represents the un-weighted (LS) residuals and stars 

represent the weighted (Robust) residuals. In general, the residuals follow a Gaussian 

distribution, but superimposed by few outliers. The Quantile – Quantile (QQ) plot in

102 

Figure 6.6: Comparison of Least Square and Robust processing of magnetotelluric data 

station TT08 for frequency 0.0791Hz . Triangles represent LS processing, and stars 

represent robust (RB) processing (a) and (b) time series of Ex residuals. C) Quantile 

Quantile plot of Ex residuals d) MT apparent resistivity and phase values from LS and 

robust processing. See text for discussion. 

Figure 6.6(c) better explains this statement. QQ plot describes the departure of observed 

data set from a particular distribution, here Gaussian distribution (§ 3.2.1.1). If the 

residuals are drawn from a Gaussian distribution, the QQ plot will be an approximately 

straight line (Chave et al. [1987]). As can be seen from the Figure 6.6(c), up to 1.5σ 

(standard normal quantile) the residuals (LS – inverted triangles) follow a straight line. 

However, the departure from Gaussian distribution is evident above 1.5σ. The weighted 

residuals (Robust – stars) closely follow the straight line, indicating the effectiveness of 

robust processing methods to eliminate non-Gaussian errors. The effect of these outliers 

on computed MT apparent resistivity (ρ xy ) and phases (φ xy ) are shown in Figure 6.6(d). 

The highly irregular nature of the LS estimate (triangles) are the results of a few outliers 

in the data influencing the transfer function estimate. The robust processing resulted in 

better estimation of both ρ xy and φ xy for all the frequencies. 

6.2.5 Application 

6.2.5.1 Flowchart 

A flow chart for the robust processing scheme developed in line with the discussions in 

the above sections is given in Figure 6.7(a). Robust processing scheme receives a spectral

103 

Figure 6.7: Flow chart for robust processing scheme. The gray area represents the proposed 

initialization of the transfer functions using Jackknife. This routine, concentrates 

on the section averaging of MT data. See text for discussion.

104 

Figure 6.8: Data flow through the flow chart representing robust processing of MT data. 

The gray area represents the proposed Jackknife initialization. (a) Process A uses Jackknife 

(JK) as initial guess and (b) process B uses Least Square (LS) as initial guess. See 

text for discussion. 

matrix (4 dimensional) as input. The process starts with an option of least square (LS) 

or Jackknife (JK) solution as initial guess. Then the data successively go through the 

weighting procedures. In majority of cases, more than two iterations may not be needed 

and one can apply the Tukey’s weights for final estimation of spectra sets. Finally the 4D 

(L stacks, N frequencies n x n channel) spectral matrix gets reduced to 3D (N frequencies 

n x n channel), which is the final output of the robust algorithm. This routine, written 

in MATLAB [2001] takes 10-20 seconds on a 500 MHz PC, with a typical 5 channel MT 

time series with a total of ∼10 6 values. Two processes are defined to demonstrate the 

superiority of robust processing with Jackknife as initial guess. The data flow for the two 

processes are plotted on the flow chart in Figure 6.8(a) & (b). Process A uses robust 

processing with Jackknife (JK) as initial guess, where as Process B uses least square 

(LS) for the same. The two processing schemes are compared in the following section, 

according to their performance on application to 8 MT stations from SGT. 

6.2.5.2 Comparison of robust processing schemes 

The eight stations chosen for the demonstration are evenly distributed in the measurement 

corridor (Figure 4.1) and the results are presented in Figures 6.9 and 6.10. In all 

the plots, the solid symbols represent Process A and open symbols represent Process B. 

The station JN12 (Figure 6.9(a)) located in the northern half of the corridor was affected 

by a large number of spikes in the longer periods and by power line harmonics in the 

range 10 to 100 Hz. This is evident as the ρ xy in this frequency range exhibits grossly 

different values from Process B. Robust processing with Jackknife (Process A) improved

105 

the estimates of ρ xy in the frequency range 10 to 100 Hz. In the longer period, Process A 

resulted in smoother ρ and φ values. In station VP16 (Figure 6.9(b)), no major change 

is observed between results of processes A and B. Perhaps as the station is relatively less 

affected with noise, the initial LS solution itself is comparable to that of Jackknife (A). 

Even then Process A resulted in better estimation of φ values in the frequency range 10 

Hz to 1Hz. The results from OK16 (Figure 6.9(c)) show that process A (JK) initialization 

created a down bias in ρ xy values as compared to process ‘B’. However, the process 

A resulted in smoother φ values as compared to process B. In a later discussion it will 

be shown that how this bias may be removed from Process A. The Process A resulted 

in smoother estimates of φ values for station VP12 (Figure 6.9(d)) as compared to the 

output of process B. However, the sharp drop of ρ values computed through Process A 

near 6 seconds seems to be unreal. 

The dramatic improvement of φ values (especially for periods > 1 Sec) at station 

VP14 (Figure 6.10(a)) by Process A as compared to Process B gives another evidence 

that robust processing results in better estimation, if started with a good initialisation. 

It is also seen from the Figure 6.10(c) that the ρ values from process A are less scattered 

in the same range of period. Station TT08 is located near the industrial zone, along 

the Cauvery river (Figure 4.1, see § 4 for discussion on this). It was written earlier 

that the long period time series from this station is affected with high magnitude spike 

activity. The Jackknife estimates (A) resulted in better estimates of φ yx values especially 

by defining a smooth curve between 1 and 10 sec (Figure 6.10(b)). Though Process A, 

could not produce better results for φ xy , it failed gracefully by predicting a trend for 

the φ xy , in the period range 1 to 10 sec, which was absent from the Process B. The E x 

channel of station TT04 was severely affected by near source noise (§ 2.4) in the frequency 

range 0.1 Hz to 10Hz, as manifested in a 45 0 raise in ρ xy values and small values for φ xy 

values. The conventional robust processing, which was biased by the LS initialisation, 

failed in the presence of majority of noisy data. Jackknife produced a better initial guess 

and when followed by the main robust scheme, dramatically improved the ρ xy and φ xy 

values as shown in Figure 6.10(c). However, in the longer period the ρ yx values seem to 

be biased down compared to conventional processing (Process B). At station OK18, the 

ρ values from both processing do not differ much. Still, the φ xy values from Process B, 

seems to be scattered for periods > 10 sec. Also the steep decrease in φ xy values with 

increase in frequency from1 Hz to 10 Hz seem to be unreal and inconsistent with ρ xy 

values. In both the frequency ranges Process A produced a better estimates as shown in 

Figure 6.10(d). 

6.3 Robust Band averaging 


Role of section and band averaging of auto and cross spectra in the context of magnetotelluric 

signals was discussed in § 3.2.3.4. It was shown by Jenkins and Watts [1968] 

that subdividing a time series into sections of length M and forming smoothed spectra 

is equivalent to smoothing the spectrum of undivided time series by a sinc (sin(x)/x)

106 

Figure 6.9: Comparison of robust processing results using Least Square (LS) and Jackknife 

(JK) initialization for stations JN12, VP16, OK16 and VP12. Process A refers to 

robust processing with JK initialization, where as Process B refers robust processing with 

LS initialization See legend for symbol identification

107 

Figure 6.10: Comparison of robust processing results using Least Square (LS) and Jackknife 

(JK) initialization for stations VP14,TT08,TT04 and OK18. Process A refers to 

robust processing with JK initialization, where as Process B refers robust processing with 

LS initialization. See legend for symbol identification

108 

function. In magnetotellurics, it is a common practice to use the combination of section 

and band smoothing, due to various reasons. 

1. With magnetotelluric data, one seeks to estimate a time stationary quantity (transfer 

functions), which varies smoothly over frequency – Band averaging over a spectral 

window facilitates this. 

2. The measured time series may not be a contiguous sequence as there may be gaps 

in time series recording due to instrumental reasons – This necessitates the use of 

section averaging in addition to band averaging 

3. A short duration noise with high power, may corrupt larger number of FC’s if band 

averaging only used, than the case where spectra is estimated from sub-segmented 

time series sections (section averaging) (Egbert and Booker [1986]) - This make it 

necessary to reject parts of time series affected by noise. 

The robust statistical procedures, as the one presented in § 6.2, concentrates only 

the section averaging. Sims et al. [1971] commented that the average over adjacent 

frequencies would facilitate the estimation of spectra and might give sufficient dof to 

reduce noise powers in cross spectra. The mention of band averaging can also be found 

elsewhere in context of magnetotelluric time series processing (Swift [1986], Gamble et al. 

[1979]). While applying the robust procedures on MT transfer function estimates, Chave 

et al. [1987], Chave and Thomson [1989] opined that the same approach might not be 

amenable to band averaging. Egbert [1997] discussed robust estimation of spectral density 

matrices (SDM) for multi-station MT processing. However, he limited himself to the 

problem of estimating SDMs from a set of sections, which are individually averaged 

over a frequency band. Recognizing the need for better estimation of cross and auto 

spectra before the actual estimation of transfer functions, Ritter et al. [1998] suggested 

procedures to predict single event spectra by comparing with a global (estimate from all 

the stacks/sections) average. While comparing two processing techniques for synthetic 

MT time series processing, Ernst et al. [2001], commented that the use of lesser number 

of frequency points in the vicinity of target frequency to average the spectra might help 

to prevent over smoothing of long period estimates. Recently Smirnov [2003] computed 

MT transfer functions for all the Fourier coefficient pairs and used a repeated median 

estimator to arrive at a better estimate of MT transfer function. However, such an 

approach may fail at the instance of strongly polarized fields (either due to the Geology or 

to coherent noise), as it may not give enough degree of freedom for a practical estimation. 

The effect of few outliers on MT data processing is well recognized and it is demonstrated 

in the previous section. However, effect of outliers in band averaging in the vicinity of 

a target frequency has not been estimated. It is usual in MT, to apply a small window 

over the target frequency (f ) (Figure 3.3) and average the cross and auto spectra with 

respect to this window. For example the cross spectra between E x and H y at the target 

frequency f from a single event spectra is obtained by, 

E x H ∗ y(f) = 1 M 

M/2 

∑ 

k=−M/2 

E x (f + k)H ∗ y(f + k).win(k) (6.20)

109 

To give lesser weights to the harmonics farther from the central frequency, it is usual 

to average over a window function. The number of harmonics to be averaged depends 

upon the position of target frequency within the spectrum and the length of the time 

series segment. If the time series were segmented into smaller sections, the number of 

harmonics to be averaged over a particular frequency reduces. However, this will be 

compensated by the increased amount of data due to larger number of sections. The 

robust processing methods thus advocated the need for shorter time windows (Egbert 

and Booker [1986]) . Even if the time series does not arise from a Gaussian process, it 

is assumed that the Fourier coefficients (FC) that result from the summarization of time 

series, follow a Gaussian distribution, (from Central Limit Theorem) (Chave et al. [1987], 

Menke [1984]). So within a band it was felt reasonable to assume a complex Gaussian 

distribution for the FCs and LS averages were used to estimate auto and cross spectra. 

However, it will be shown in the next section that this assumption often fails due to the 

presence of some unusual data. A weighted robust averaging is essential to remove the 

outliers within a frequency band well. 

6.3.2 Effect of frequency band width 

In Figure 6.11 the concept of frequency band averaging is presented for varying window 

lengths, effectively using more FCs in each window in Figure 6.11 (a) to (d). The term 

‘frequency band’ refers to the narrow band around a target frequency, whereas the term 

band 1, band 2, etc represents the measurement band. ’Parzen’ window (§3.2.3.5; also see 

Jenkins and Watts [1968]) is applied in frequency domain, whereas ’Hanning’ window is 

applied in time domain (Bendat and Piersol [1971]). The upper four plots (a to d) show 

the Parzen window with different sizes. Parzen window is preferable over a boxcar, as 1) 

it gives less and less importance to farther harmonics from the target frequency and 2) 

Boxcar (§ 3.2.3.3) in frequency domain has a sinc (sin(x)/x) ‘impulse response’, which 

is not desirable in spectrum estimation. The vertical broken lines are drawn through 

each target frequency at which MT transfer functions are to be computed. The bottom 

plot show a sample E x E x spectra for data collected in the frequency range 8 Hz to 0.25 

Hz, with a sampling interval 32 Hz. The spectrum at each target frequency is usually 

estimated by averaging the adjacent harmonics with respect to the window. Though 

the window width seems to increase as the frequency decreases, the effective bandwidth 

remains the same, considering the distribution of FC on a logscale (Wight and Bostick 

[1980]). 

In order to study the effect of frequency band averaging on MT transfer functions, the 

ρ xy and ρ yx for a particular frequency were computed using different frequency window 

lengths. Figure 6.12 show ρ xy and ρ yx values at 6Hz plotted as a function of number of harmonics 

used for the station VP13. The time series were subdivided into sections of 2048 

length and robust procedure described in § 6.2 is used to estimate the transfer functions. 

Variance of each was estimated according to equation 6.17, taking into consideration the 

modification to dof by the robust procedures. Two results from this computation are: 1) 

As the estimate is made over longer window sizes, the expected variance decreases. This 

can be seen in the form of reduced error bars for the estimates with larger number of 

harmonics. 2) However, the reduction in variance comes at the cost of bias error. As the

110 

Figure 6.11: Spectrum estimation in MT using band averaging. (a) to (d) windows in 

frequency with different radii. Though the window radius seems to increase as period 

increases, effective bandwidth remains the same, as spectrum in long period contains fewer 

Fourier harmonics. (e) Sample E x E ∗ x spectrum in the band 4, with target frequencies 

projected as dotted lines. It is common to have 10 12 target frequencies per band.

111 

Figure 6.12: Apparent resistivities as a function of frequency window length. Triangles 

represent ρ xy and circles ρ yx . Error bars represents 95% confidence interval. See text for 

discussion. 

window size increases the computed ρ xy and ρ yx values get biased down. The ρ xy values, 

which are around 7000 Ohm m at a frequency window with less than 100 harmonics, get 

biased to ∼5000 Ohm m with number of harmonics > 250. This dependence of resistivity 

values on frequency bandwidth has nothing to do with the geology and are clearly due to 

noise. To be more specific, the noise power in the magnetic field auto spectra may not get 

averaged out as the number of data point increase as they are squared and positive and 

any outliers may worsen the situation. It is worthwhile to examine the distribution of 

these residuals to check the assumption of Gaussian distribution for the spectra within a 

band. Figure 6.13(a). shows the magnitude of a cross spectrum obtained by multiplying 

H x with H y ∗ respecting the Parzen window in frequency domain, at frequency 6 Hz for 

station VP13. Few frequency points with grossly different spectral amplitude than the 

majority are seen. A Quantile-Quantile plot of spectra of real part of the cross spectrum 

(Figure 6.13(b)) shows (inverted triangles - unweighted) large deviation from linear function 

at the higher quintiles, indicating the departure from a Gaussian distribution. This 

shows that the individual spectral coefficients within a frequency band might not follow 

a Gaussian distribution and an LS average is not desirable in such cases. 

6.3.3 Robust estimation of spectra 

Here, a robust weighting procedure is proposed to minimize the effect of outliers in the 

estimation of cross and auto-spectra from a frequency band. Once spectra are estimated 

in a robust sense, any type of section averaging procedures may be adopted for the estimation 

of MT transfer functions. Though theoretically possible, computation of transfer 

functions using a pair of spectra sets from two adjacent FC’s (Smirnov [2003]) is unstable

112 

Figure 6.13: Concepts of robust band averaging. (a) Magnitude of cross spectrum between 

H x and H y for station VP13, around a target frequency 6 Hz. The spectra are 

multiplied by a Parzen window. LS least square, RB Robust. (b) Quantile Quantile 

plot for real part of the same cross spectrum. Inverted triangles unweighted, Circles 

robust weighted. See text for discussion.

113 

because of the chances of having same polarization. So minimization of residual noise 

from an LS transfer function estimate is undesirable within a frequency band. Without 

assuming any signal & noise components, a Huber weighting procedure was used, assuming 

that the spectra are random variables. For complex data, we used the magnitude to 

define the weights (a discussion in this regard is given by Chave and Thomson [1989]. The 

algorithm devised for robust spectrum estimation is as follows. At each target frequency 

we have M number of FC’s from two channels, in the vicinity of the target frequency, f. 

We would like to compute the cross spectra between two channels, say Ex and H y from 

M realizations of E x H y *, equally distributed around the target frequency, f. 

S f ExHy = 〈〉 

E x Hy 

∗k 

M 

∗ win(k), where k = − 

2 ...f...M (6.21) 

2 

Where function win is a Parzen window (§ 3.2.3.5) and equation 3.22) with radius 

M/2. Residuals r k were calculated by subtracting median (|S|) from each value in |S|. A 

MAD scale estimate σ is obtained as in equation 6.12 as, 

σ = med. (∣ ∣ r 

k ∣ ∣ − med. 

∣ ∣r k ∣ ∣ ) (6.22) 

Then the Huber weights w k are used to down weight the data that exceeds r i 

{ 1 if rk ≤ σ 

w k = σ 

r k 

if r k > σ 

σ . 

(6.23) 

If the outliers have been eliminated the spectra are the sum of almost normally distributed 

cross products. The robust estimate of spectra (here the cross spectra between 

E x and H y ) are obtained as, 

E x H ∗ y(f) = 1 M 

M/2 

∑ 

k=−M/2 

E x (f + k)H ∗ y(f + k).w k .W in(k) (6.24) 

It may be followed by iteration with Tukey’s weighting (§ 6.2.4.4) to reduce the 

influence of large outliers. However, the experience shows that this may not be required 

in majority of the cases. Figure 6.13 shows results of robust band averaging. Figure 

6.13(b) shows Q-Q plot of robust weighted H x H y cross spectrum. Represented with 

circles, the robust weighting clearly reduced the outliers at higher quantiles compared 

to un-weighted (or LS) spectra (triangles). The LS estimate gave a value of 2.1563e-010 

-3.9535e-011i nT 2 /Hz for the cross spectrum, while the robust estimate gave 1.4426e-010 

-2.4245e-011i nT 2 /Hz, both at 6 Hz. This means the LS estimate gave a value ∼60% 

higher than that of robust weighted estimate of spectrum at 6Hz. This reduction in 

spectral amplitude (solid horizontal line, Figure 6.13(a)) by robust weighting could be 

attributed to the elimination of few large outliers, which biased the LS estimate (broken 

line, Figure 6.13(a)) up. Figure 6.14 shows a series of band averaging instances from the 

MT data at station VP13. All the eight plots show cross spectrum estimation of between 

H x and H y , for different target frequencies and different Parzen (Figure 3.3) radius sizes. 

Note that X axis do not represent the frequency itself, but the wave number from FFT. 

Y axis shows the magnitude of the cross spectrum in nT 2 /(Hz). The two horizontal bars

114 

show the averages from LS (broken) and robust (solid) weighting scheme. Column (a) 

band averaging for four target frequencies and column (b) shows the band averaging at 

single target frequency (6Hz) with different radius sizes. From these results it can be 

seen that there exists a consistent bias error in spectrum estimation, which in turn may 

corrupt the transfer function computed out of it as well. As the magnitude of the spectra 

is a positive function, outlier contamination can only bias it upwards and that is exactly 

seen in these plots, where robust weighting procedures always resulted in smaller values 

as compared to LS. The robust band average always resulted in smaller magnitudes for 

spectra. Therefore the need for robust band averaging is seen. 

6.3.4 Flow chart 

Flow chart for the proposed robust band averaging to estimate cross and auto spectral 

matrices from time series is presented in Figure 6.15(a). The entire codes were written 

in MATLAB [2001]. The input to the routine can be either standard 5 Channel single 

station MT time series or 7 channel with remote reference channels. Pre-processing of 

data involve removal of trend and bias (§ 3.2.3.1) , sub-segmentation, Fourier transform 

(§ 3.2.1.5) and calibration (§ 1.3.4. There are two options for band averaging, viz. least 

square (LS) and robust (RB). While LS perform conventional frequency band averaging 

respecting a window around target frequency (§ 3.2.3.5), RB will perform a weighted 

averaging approach as presented in the above section (equation 6.24). The averaging 

routines are called in confined loops (L, N and n x n). With a 5 channel MT time series 

of 80 stacks of 1024 data points each, the averaging routine will be called 24,000 times 

to estimate spectra at 12 target frequencies. This necessitates the optimization of the 

processes within the averaging routine. For this reason, the robust weighting procedure 

was designed as simple as possible and the final iteration by Tukey’s weights was avoided. 

As a result, the processing of a time series of comparable dimension as earlier stated, takes 

∼1 minute on a 500 MHz Pentium PC. Further reduction in processing speed is possible 

by rewriting the codes in C or C++. The routine will deliver a 4 dimensional spectral 

matrix as output, which will form input to any section average processing, including 

robust processing. 

6.3.5 Validation 

Four more processing schemes are defined based on this flow chart to validate the results 

of robust band averaging. These are 1) single station LS band averaging (Process C), 

2) single station robust band averaging, (Process D) 3) remote reference and LS band 

averaging (Process E) and 4) remote reference and robust band averaging (Process F). 

They are represented in the Figure 6.15(b) to (e) respectively. These processes deliver 

the 4D spectral matrix, from the MT time series data. The process A, defined in § 6.2.5, 

which is a robust section averaging method employing a Jackknife initial guess will be 

used to estimate MT transfer functions for all the four processes defined above. In order 

to demonstrate the efficacy of the robust band averaging methods, station VP10 was 

chosen, where, in addition to the single station data for all the bands, one session of 

remote reference data were also available from station VP13. This enabled us to exam-

115 

ine the performance of the proposed robust processing procedure with remote reference 

processing as well. The results from four processing methods on the data set are presented 

in Figure 6.16. Figure 6.16(a) shows the ρ xy component, where as ρ yx component 

is plotted in Figure 6.16(b). The φ values are not shown, as they are not much varied 

by the processes described above. However, the φ values are included at a later stage 

when the applications of the procedure is discussed. The quantity of remote reference 

data for period range 4 sec to 128 sec (band 4) was insufficient for a through estimation. 

However, this was included to get a complete evaluation. It can be seen from the figures 

that the best and unbiased estimate for ρ values are derived from process F (stars). The 

ρ values are clearly higher and less smoother than the other estimates, except for a few 

data point between 10 and 100 Hz. The conventional robust remote reference processing 

(E -solid line) , are similar to the results from process F, except for few data points 

in ‘dead’ band, where they are biased down compared to process F. The usefulness of 

robust band averaging results are more evident in single station estimates (Process C & 

D). Clearly both these process output ρ values that are down biased compared to remote 

reference data. However, the robust band averaging (Process D) improves the situation, 

with the ρ values that are nearer the their remote reference counter parts. This clearly 

shows the effect of robustly averaging the spectra sets within a band. On single station 

estimates, the robust band averaging reduces the down bias as compared to LS band 

average. Even remote reference processing can benefit from robust band averaging, as 

evidenced from the improved RR estimate of ρ xy and ρ yx values by robust band average 

in the ‘dead’ band range (1 to 10 seconds). This analysis could not be extended to all 

other data sets, as reference data sets were not recorded at majority of stations due to 

instrument problems. 

In the second approach to validate the results of robust band averaging, the estimates 

of ρ values from robust band averaging were compared with E-referenced and H-referenced 

estimators on spectra generated from conventional robust processing. Standard LS estimators 

have the property that E-reference (transfer function from admittance analysis) 

are biased upward by un-correlated noise on the electric field components and the H- 

reference estimates are biased downwards by the noise in un-correlated noise in magnetic 

field. (See § 3 for more discussion). Obviously downward and upward biased estimates 

give an envelope within which the true transfer function should lie (Jones et al. [1989]). 

The ’up’ and ’down’ (§ 3.3.1.3) biased estimates were computed from process C and 

compared it with the result of Process D. Both these processes are done in single station 

mode and the results from four stations are plotted in the figures 6.17 to 6.20. Figure 

6.17 shows the data from station JN12. The up biased estimates from Process C shows 

larger deviation near the dead band. This is common, as the s/n ratio at this frequency 

range is low compared to other ranges. As clearly seen from Figure 6.17, the ρ xy and 

ρ yx components are less biased from Process D. This is more pronounce near the ’dead’ 

band (between 1 and 10 seconds). Near the period of 100 seconds, the ρ xy (top panel) 

values from Process C seems to be heavily biased, which to an extend restored by Process 

D. Station VP16 is relatively noise free and ρ xy and ρ yx values are well defined over the 

full bandwidth by conventional processing. Processing D results in an ’inner envelop’ of 

’up’ and ’down’ biased estimate within the same estimates by Process C (Figure 6.18). 

The results from station KG02 (Figure 6.19) shows large deviations between the biased

116 

estimates for periods > 1 seconds. Here also the robust band average results in reduced 

split between both estimations. Perhaps the use of robust band averaging (Process D) is 

well explained by the results from the processing of long period data from station OK18 

(Figure 6.20). The ρ xy values at the periods > 4 seconds are obviously affected by poor 

s/n ratio as evidenced by the large split between the ’up’ and ’down’ biased estimates 

of Process C, especially for periods > 10 seconds. The ρ yx vales in the same period 

range are not that affected with noise, as the up and down biased estimates follow same 

curve. However, is evident in ρ yx values between 0.1 to 10 Hz. Here again, the robust 

band averaging (Process D) resulted in reduced split between the up and down biased 

estimate. 

6.4 Results and discussion 

From the validation experiments carried out in the earlier section, it is established that 

the robust band averaging reduces bias in the estimation of ρ values and may even improve 

the remote referenced solution for transfer functions. In this section a combination 

of robust band averaging (to produce robust spectral matrix) and robust section averaging 

(to estimate transfer functions) (Process D) were used to the same set of sites 

used for validation. For discussion the ρ and φ values and their associated telluric predicted 

coherencies (positive square root of coherence function, γ 2 ) derived from the above 

combination were compared with that of conventional spectrum estimation with robust 

transfer function estimation (Process C). The long period MT data were subjected to 

ANN editing as detailed in § 5. The results are shown in Figures 6.21 to 6.24. The top 

panel in each Figure compares the coherencies, the middle panel compares the apparent 

resistivities and the bottom panel compares the phase values. 

6.4.1 VP14 

This site was occupied in the southern part of the measurement area where the main 

rock type exposed is gneiss ( see § 4.2). The predicated coherencies from process D are 

consistently higher than that process C. The increase in predicted coherencies are more 

clear in the frequency range 0.1 Hz to 10 Hz. This is also attested in the form of improved 

estimates of ρ and φ values in the bottom panels. However, in the xy coherencies from 

process D for periods > 1 seconds are less than compared to Process C. (Figure 6.21(a)) 

6.4.2 TT08 

The noise environment for the station TT08 was described in §5, in the context of application 

of ANN. The improvement in the estimation of ρ and φ values by Process D 

are evident in the middle and bottom panel of Figure 6.21(b). Frequency to frequency 

variability of φ values were remarkably reduced for the periods > 1 sec. The Process 

D also increased the values of predicted coherencies as shown in the top panel. The 

improvement in φ values indicate a better estimate of cross spectra sets, where as the 

reduction in bias may be attributed to the better estimation of auto spectra. This is

117 

stated to emphasize that robust band average give cleaner spectral matrices, from which 

the robust section average can further, improve upon. 

6.4.3 TT04 

This station, also falls in the industrial belt near the Cauvery river. The xy components 

(ρ and φ) between 0.1 second and 10 seconds were seriously affected by a coherent noise 

source, which distorted these curves as shown in Figure 6.22(a). While discussing the 

results of robust processing with jackknife initialization (Process A) (§ 6.7), it was seen 

that Process A resulted in recovering the heavily distorted ρ values of this station. However, 

Process A induced a bias in long period ρ yx values. The robust processing with 

robust band averaging and jackknife initial guess substantially reduced this bias as seen 

in the middle panel of Figure 6.22(a). The improvement in predicted coherencies are 

evident, perhaps the difference is less compared to TT08 or VP14 

6.4.4 OK18 

The station lies in the south end of the measurement corridor (see Figure 4.1). Electric 

water pumps for domestic and small scale agricultural purposes were operational in the 

area, during the measurements. This resulted in increased noise activity in the electric 

fields, mainly for long period data. The high frequency data were influenced by power 

line related noise. It can be seen from the plot (Figure 6.22(b)) that the xy component of 

the data are more affected than yx components. The heavy bias for ρ xy values at periods 

> 1 second are associated by a low in predicted coherency values confirm this. Process 

D gave reduced bias in ρ values and smoother φ values, which are consistent with their 

orthogonal counterparts. The increase in predicted coherencies brought by Process D is 

also evident in Figure 6.22(b). 

6.4.5 JN12 

The MT station JN12, lies in the northern part of the measurement corridor, near the 

town Dharmapuri. The area has as average long period noise/(signal + noise) ratio of 

0.35 (Figure 4.8) and relatively less noisy. The resistivity values monotonously reduce 

with increase in period (Figure 6.23(a)). The Process C poorly estimated the ρ xy values 

especially in the frequency range 100 Hz and 10Hz. This resulted from power related 

noise that biased up the ρ xy values near 50 Hz. The robust band and section averaging 

with jackknife initial guess (process D) gave a better estimation of all but two ρ xy values 

in the band. However, there was not much improvement obtained for long period φ values 

from robust processing. For ρ xy values at periods > 4 seconds, there small but perceptible 

reduction in bias by Process D. This is also attested by the increased predicted coherencies 

values as shown in the top panel of Figure 6.23(a).

118 

6.4.6 VP16 

The site falls in the southern portion of the measurement corridor, over exposed gneisses 

(Figure 4.1). The moderate geomagnetic indices (Figure 4.6) for the period of survey 

were favorable for the occurance of MT signals in the long period. Average noise ratio 

(Figure 4.8) of 0.4 for the long period data also indicate that the site is relatively noise 

free. The Process C resulted in almost same estimate as Process D as shown in the middle 

and bottom panel of Figure 6.23(b). The predicated coherencies for the estimates from 

process D do have higher values as compared to the that of process D. However, near 

10 seconds, the robust band averaging resulted in a small kink (upward) which was not 

there in the estimates from Process C. 

6.4.7 OK16 

This station lies in the southern end of the measurement corridor. The site is away from 

the major cultural noise sources as shown in Figure 4.8. However, the effect of noise 

from other sources are evident in the ρ and φ values (Figure 6.24(a)) from Process C. 

Remarkable improvement in the smoothness of φ values resulted from the application 

of process D. The improvement is also evident in ρ xy values , as Process D resulted in 

smoother and less biased estimates especially in the frequency range 1 Hz to 10 Hz. This 

is also attested by the increased telluric predicted coherencies as shown in the top panel 

of Figure 6.24(a). 

6.4.8 VP12 

Situated far south of the major industrial zone along the Cauvery river, the station VP12 

is relatively free from cultural noise sources. The ρ and φ values from Process C and 

D are almost same, except for four frequencies in ’dead’ band (period 1 second and 10 

seconds) as shown in Figure 6.24(b). In this frequency range, the Process D produced 

ρ values that are higher than that of Process C. However, as there are no appreciable 

increase in predicted coherencies from Process D in this period range, increased estimates 

in ρ values cannot be confirmed as an improvement. Between 10 and 100 Hz, the Process 

D resulted in better estimation of ρ xy values as compared to that of Process C. The 

predicted coherencies from Process D are slightly higher than that of Process D in the 

frequency range 10 Hz to 0.1 Hz. 

6.4.9 Comparison of results from the Vellar - Palani profile in 

SGT 

The results presented in Figure 6.25 compare the MT data sections along the Vellar - 

Palani profile (the broken line in the Figure 4.1) over the Southern Granulite Terrain. 

The left panels show the ρ xy and φ xy sections from ”ProcMT”, the MT data processing 

software of Metronix (Ellinghaus [1997]) and the right panels show the results from the 

proposed approach. The data are not smoothed or contoured to better represent the 

reality. The data that are missing/ out of range are represented as white patches. The

119 

length of the FFT and parzen windows were kept identical for both schemes. For ProcMT, 

the available time series were manually edited and the MT impedances were estimated 

by Robust-M processing. While using the scheme proposed here, the time series were 

not manually edited. The long period data were subjected to ANN editing. The cross 

and auto spectra were computed by robust band averaging. The MT impedance were 

estimated by robust processing with jackknife initialization. 

The resistivity data ranges from 10 1 to 10 5 Ohm-m, typical of the highly resistive crust. 

The high frequency data (>1 Hz) shows a relatively resistive crust in the northern part 

of the profile (especially north of station VP10). However, point to point discontinuities 

are evident along majority of the stations for the data processed by ProcMT (Figure 

6.25a). Figure 6.25b shows the ρ xy section derived from the scheme proposed. A greater 

smoothness for data are now evident between stations, and the two major resistivity 

blocks are clearly visible. In addition, the smaller resistive structures within the high 

frequency data below the southern part of the profile are more evident. The improvements 

are not so evident for the low frequency data (

120 

to be accounted in frequency band averaging as well. The bias effect in ρ values caused 

by ignoring this factor is demonstrated on MT data collected from SGT. The robust 

weighting approach proposed in this chapter can alleviate this problem to an extent as 

demonstrated by its application to the field data. The robust weighting procedures for 

spectral estimation may easily extended to robust processing as well. 

In summary, the Robust band averaging deals with the averaging of the adjacent 

Fourier coefficients around a target frequency while estimating the auto and cross powers 

(or power spectral densities PSD). As shown in Figure 6.12, the apparent resistivity 

value has a systematic dependency on the number of harmonics averaged. This means 

the conventional way of computing PSD by band averaging leads to biased estimates 

of apparent resistivity values. Robust band averaging, proposed , here accounts for the 

abnormal Fourier coefficients while averaging around a target frequency. This clearly 

results in 

1. Minimizing the effect due to non Gaussian distribution of Fourier coefficients. Once 

the spectral coefficients are robustly weighted, they are more appropriate for a LS 

averaging (Figure 6.13) 

2. The robust band averaging results in improved (bias less) estimates of power spectra 

(Figure 6.14) 

3. Finally the MT transfer functions computed from the above PSDs have low bias 

compared to the conventional processing (Figure 6.16 and §6.3.5) 

It may be concluded that the two new approaches made in the robust processing of 

magnetotelluric data clearly showed it effectiveness while applied to a large volume of 

data collected from SGT and are easily adaptable to the conventional MT time series 

processing routine.

121 

Figure 6.14: Comparison of robust and least square band averaging for different frequencies 

and band (Parzen) radius for station VP13. Magnitude of H x Hy 

∗ (nT 2 /Hz) cross 

spectra are plotted for all the cases. X-axis show the frequency bins. Solid line represents 

robust average and broken line represents Least Square average.The left column represent 

the the band averaging for different target frequencies, where as the right column 

represents the band averaging with different radius length for the same target frequency. 

See text for discussion

122 

Figure 6.15: Flow chart representing robust band averaging. Gray area represents the 

proposed processing routine (a) Shows the different steps in robustly estimating the 

spectral matrix from raw time series Schematic diagrams (b) to (e) shows four processing 

schemes defined. SS single station, RR remote reference, RB robust band averaging, 

LS Least square

123 

Figure 6.16: Results of single station (SS) and remote reference (RR) processing for 

station VP10. Process C (SS) and E (RR) use least squares band averaging, whereas 

process D (SS) and F (RR) use robust band averaging. The MT transfer functions were 

derived from a robust section averaging §6.2.4 from the spectra sets produced by Process 

C to F. See text for discussion. 

Figure 6.17: Comparison of upward and downward biased estimates of apparent resistivities 

for JN12 for processes C and D (a) XY component and (b) YX component. UP - up 

biased (E- reference) and DN down biased (H-references). Symbols are same for both 

plots. See text for discussion.

124 


for VP16 for processes C and D (a) XY component and (b) YX component. UP 

- up biased (E- reference) and DN down biased (H-references). Symbols are same for 

both plots. See text for discussion. 


for KG02 for processes C and D (a) XY component and (b) YX component. UP 


both plots. See text for discussion.

125 


for OK18 for processes C and D (a) XY component and (b) YX component. UP 


both plots. See text for discussion.

126 

Figure 6.21: Comparison of telluric predicted coherency, apparent resistivity and phase 

values from robust processing with and without robust band averaging for stations VP14 

and TT08. The explanation for symbols are given in legend. See text for discussion.

127 


values from robust processing with and without robust band averaging for stations TT04 

and OK18. The explanation for symbols are given in legend. See text for discussion.

128 


values from robust processing with and without robust band averaging for stations JN12 

and VP16. The explanation for symbols are given in legend. See text for discussion.

129 


values from robust processing with and without robust band averaging for stations OK16 

and VP12. The explanation for symbols are given in legend. See text for discussion.

130 

a) b) 

c) d) 

Figure 6.25: Comparison of results from two different processing scheme for MT data: 

Left panel shows the results from ProcMT and the right panel shows the results from the 

robust processing and ANN editing.

Chapter 7 

Discussion and conclusions 

131

132 


Magnetotellurics has been established as a versatile exploration tool, serving the needs 

of shallow – resource exploration as well as deeper crustal and lithospheric studies (Vozoff 

[1991], Jones [1992]) Continuing improvements in instrumentation, data acquisition 

procedures, data processing and modelling of MT measurements provide a fertile environment 

for experimentation and application. In order to determine the sub-surface 

electrical conductivity, it would be necessary to obtain the ‘best’ possible transfer functions 

from the data collected. Developments in this aspect of MT have been outlined in 

Chapters 3, 4, 5 and 6. Just as in the preparations for a MT experiment it is possible 

to consider several scenarios, models and contingencies and attempt to plan the optimal 

survey. Similarly it is observed in this work that while processing the time series, it is 

necessary to study all the characteristics possible, in space, time and frequency domain 

and attempt through a suite of processing routines to obtain the ‘best’ or optimal curves. 

It is concluded here that the study of data characteristics after the survey also shed light 

on the most suitable methods of processing. It is clearly demonstrated in Chapters 5 and 

6 that the same routine may not be optimal for different data sets with different noise 

characterization (Egbert and Livelybrooks [1996]). Further, for the same measurement, 

one process would eliminate some types of noise and another process the other. 

Significant developments for MT transfer function estimation in magnetotellurics, in 

the past three decades were the introduction of remote reference processing (Gamble et al. 

[1979]) and robust processing (Egbert and Booker [1986]). This was complementary to the 

requirement of more precise MT estimates by the new and sophisticated data modeling 

algorithms developed simultaneously. Advances in both these fields accelerated in 1980’s 

with the availability of cheap and fast microprocessors. Thus the tremendous development 

in MT methodologies in the past three decades, greatly owe to the advances in digital 

computing. The effective depth of MT probing ranges from few hundred meters typical 

for geo-technical investigation (Garcia and Jones [2002]) to more that hundred kilometers 

for deep crustal studies (Chen et al. [1996]). This greater range of depths demands wider 

bandwidth of measurements, which in turn demands better instruments/sensors. To 

estimate the transfer function for full bandwidth, as precisely as possible, data processing 

algorithms need to be improved as well. 

7.2 Summary 

The time series processing steps introduced in this thesis were applied to the following: 

1. Identifying the noise sources in space domain (§ 4), 

2. Discrimination of bad segments of time series data against good segments in time 

domain (§ 5) and 

3. Effectively down weighting the unusual data in a robust sense in time - frequency 

domain (§ 6).

133 

In the first instance, an attempt was made to characterize the signal and noise components 

in the MT data collected from SGT. The MT data were analyzed in time, frequency 

and space domain in this regard. The comparison of indices of geomagnetic activity with 

the long period coherence showed their general agreement. The effect of noise from an industrial 

zone was evident in the long period data, while analyzing the noise/(signal+noise) 

for all the sites in relation with the known cultural noise sources. 

The second approach was made, in response to another requirement of MT exploration 

- an automated method of processing. For example, the data acquired in SGT, amounted 

to ∼10 6 real numbers of data per site, and with 80 such stations, the magnitude of data 

reduction in MT is a major task. In such scenario, the editing of MT time series becomes 

challenging and may consume more that 80 % of the time spent on time series analysis. 

The artificial neural network approach introduced in § 5, is a very promising solution to 

this. It not only proved to be a good replacement to manual inspection of time series, 

but turns out to be a stable and objective decision-maker as well. 

In the third approach made in this thesis, the robust processing algorithm was critically 

reviewed and two steps were introduced to further improve this type of estimators 

in the presence of severe noise contamination as found in SGT. The two approaches 

namely Jackknife and Robust band averaging were used to replace simple Least Square 

procedures, that were still in use in two steps of robust processing. The effects of a few 

outliers on MT data are well recognized and robust processing was essentially introduced 

to tackle this (Eiesel & Egbert, 2001, Chave et al 1987, Chave & Thomson, 1989). Some 

of the computational steps retained LS averaging, overlooking its effect. The effect of 

unusual data at the frequency band averaging level has been evaluated in this thesis and 

a robust band averaging technique suggested to alleviate this problem. In the same manner, 

Jackknife estimates were used to find an initial guess for robust processing, replacing 

the commonly employed Least Squares. 

Holistically, the last two approaches may be considered as a natural outgrowth of 

MT time series processing procedures, against the back drop of increasing computational 

power and improving instrumentation. Neural networks, with their computational complexity, 

were rarely used in geophysics in 1980’s. With the availability of fast and cheap 

microprocessors, neural networks are widely used in a variety of applications in geophysics 

today. When introduced, robust processing (in MT) concentrated on the averaging of 

transfer functions. Later, by going back one step in the processing algorithm, Egbert 

[1997] proposed robust estimation of global spectral density matrix (SDM) from all the 

available SDMs. The approach made in this chapter may treated as one more step back 

in the processing level, wherein, the individual SDMs from a single time section is also 

estimated in robust sense. 

7.3 Neural Network and Robust processing 

Neural network approach introduced in Chapter 5 and the robust processing techniques 

(Chapter 6) discriminate signal against noise. The fundamental differences between these 

two methods are 

1. ANN based editing is performed in time domain alone, where as robust processing

134 

is done on spectra sets frequency domain, generated from short time segments. 

2. ANN based editing is used to discriminate signal patterns, correlation structure 

and amplitude ratio to search for and select signal elements from the subdivided 

time series. Robust processing attempts to down weight data that deviate from the 

fit with the transfer function (large residuals). 

3. Decision of ANN editing is binary, i.e. it either accepts or rejects the time segment. 

Robust processing algorithm tries to minimize the effect of larger residuals, with 

proportional weights and the decision is analog. Tukey weighs at the final iteration 

in robust processing may be considered binary. However, it affects only a part of 

the data. 

4. ANN requires previously saved ’intelligence’ (weights) to perform processing, where 

as robust processing requires none. 

In the figure 7.1 & 7.2, the results of processing MT data from two sites are given. The 

MT time series collected were subjected to the robust processing algorithm described in 

§ 6 (Process D), with and without prior ANN editing. The derived apparent resistivity & 

phase for stations JN10 and OK18 are plotted in Figure 7.1(a) &7.2(a). In Figure 7.1(b) 

& 7.2(b), the comparison of neural network picking and robust weights are compared 

for all the stacks. The upper panel in Fig Figure 7.1(b) & 7.2(b) shows the neural 

network decision as a function of stacks. In the lower panels, the robust weights from 

the final step in robust processing (§ 6) are presented as a function of frequency and 

stacks. Dark areas indicates good data, white indicates bad data and the gray levels 

in between indicate intermediate data. As can be deduced from these plots, the robust 

processing with and without NN editing at station JN10 seems to yield the same results. 

On closer inspection of the network picking and robust weights in same figure(Figure 

7.1(b) & 7.2(b)), it is seen that from stacks 1 to 15, the neural network consistently 

gave zero and the corresponding robust weights also gave smallest values, throughout 

time and frequency scale with the exception of stack 3 & 4. In the same way stacks 

around 30 also gave similar results for robust and NN processing. It may be concluded 

that the similar results from robust processing with and without neural network editing 

is due to fact that the signal discrimination were similar, though the approaches were 

made in different domains. In the second example the processing results from stations 

OK18 is presented. The robust processing alone resulted in biased estimate of ρ xy values 

and scattered φ xy values (open circles) with large error bars. However robust processing 

after neural network editing resulted in better estimation of ρ xy and φ xy (stars). (Figure 

7.2(a)). On verifying the neural network output and robust weights as a function of stacks 

(Fig 7.2(b)), it is observed that the two considerably vary especially between stacks 20 

and 60. The neural network rejected around 12 stacks in this interval, whereas the robust 

weights are near the value 1 for all frequencies. However between stacks 60 and 80, the 

robust procedures down weight around 5 stacks, where as the neural network did not 

reject any. The reason is that the outliers and/or coherent noises which are obvious in 

time domain between stacks 20 and 60, failed to produce larger outliers and thus were 

not down weighted by robust procedures.

135 

a) 

b) 

Figure 7.1: Comparison of robust processing (RB) with and without neural network (NN) 

editing for Station JN12. (a) Apparent resistivity and phase values from both processing 

schemes. (b) Comparison of robust and neural network weights. 

Those data, which the neural network passed on to robust processing between stacks 

60 an 80 with noise that was not evident in time domain, were down weighted by robust 

procedures. This clearly shows the need to combine the two techniques in order to 

discriminate / down weight a majority of noisy data.

136 

a) 

b) 

Figure 7.2: Comparison of robust processing (RB) with and without neural network (NN) 

editing for Station OK18. (a) Apparent resistivity and phase values from both processing 

schemes. (b) Comparison of robust and neural network weights. 

7.4 Conclusions 

Major conclusions that can be drawn from the thesis are 

1. The magnetotelluric data collected from SGT encountered severe interference from 

cultural noise sources, and their effects are fully understood only if analyzed in a

137 

multi- domain approach. Routine application of any one of the data processing 

methods is bound to give inferior results in such cases. 

2. In time domain, the application of artificial neural networks clearly demonstrated 

its usefulness as an effective signal discriminator, even in the presence of large noise 

contamination. 

3. The prominent weak points in robust processing of MT data are the uses of least 

square estimators in two of the steps, namely estimation of spectra and transfer 

function initialization. 

4. The application of a non-parametric estimator called Jackknife to initialize MT 

transfer functions, resulted in improved robust estimation of MT transfer functions. 

Robust band averaging reduces the uncertainties in estimating the spectra of 

magnetic and electric field components. Robustly estimated spectra always result 

in better MT transfer functions. 

5. On applying these methods to a large numbers MT stations in SGT, the effectiveness 

of a combined use of neural network and robust processing, in eliminating 

severe noise was established and demonstrated. 

7.5 Suggestions for future work 

The natural signal sources for MT data >1Hz (AMT) are the world wide thunderstorms 

(§ 2). These signals are manifested in high frequency MT time series (band1 of table 

2.1) as transient bursts. It is well known that the MT apparent resistivity values are 

systematically biased down at frequencies > 10 3 Hz. The frequency range 10 3 to 10 4 Hz 

contains the ‘dead band’ of AMT (Garcia and Jones [2002]), where the natural signal 

energy is very low compared to the higher and lower frequencies (Figure 2.1). The 

transient signal such as we found in Fig 2.4, has enough spectral energy in the AMT 

dead band. However, there are two reasons, why they fail to improve the MT estimates 

in the ‘dead band’: 1) The MT signals appear as transient envelopes of signals, on the 

background of power transmission harmonic noise (and 50 and 150Hz, in this case) and 

their occurrences are random. 2) It is widely recognized that FFT fail to perform spectral 

analysis on transient signals, as the amplitude spectra thus derived do not give any 

temporal information. Due to these reasons, the sparse signal activity in this frequency 

range gets down weighted in spectral estimation as well as in robust processing. It would 

be worthwhile to explore the use of the wavelet transform (Kumar and Foufoula-Georgiou 

[1997] to discriminate transient signals in the high frequency MT time series against the 

majority of background noise. Wavelet transforms have the unique ability to retain 

temporal characteristics, while giving the spectral information. It is thus important to 

estimate MT transfer function in dilatation – translation domain of wavelet transform 

(somewhat equivalent to frequency-time domain), as it allows us to effectively isolate 

energetic signal events both in frequency and time domain. 

Thus it may be seen that continuing improvement in MT data acquisition, processing 

and modeling complement each other with the need for ever-more accurate imaging of the

138 

Earth’s sub-surface structure. In the case of MT data processing, novel applications of 

computational and statistical advances in signal processing, continue to be implemented 

as in the work outlined above. Multi-domain analysis of signal discrimination would be 

favored as the benefits of such approaches are validated by more data analysis.

Bibliography 

D. Allsopp, M. Burke, D. Rankin, and I. Reddy. A wide band magnetotelluric recording 

system. Geophys. Prosp., 22:272–278, 1973. 

O. Altinay, E. Tulunay, and Y. Tulunay. Forecasting ionospheric critical frequency using 

neural networks. Geophys. Res. Lett., 24:1467 – 1470, 1997. 

R. Bailey. Inversion of the geomagnetic induction problem. Proc. Roy. Soc. Lond., 315: 

185–194, 1970. 

M. Balser and C. Wagner. Observations of earth-ionosphere cavity resonance. Nature, 

188:638 – 641, 1960. 

R. J. Banks. The effects of non-stationary noise on electromagnetic response estimates. 

Geophys. J. Int., 135:553–563., 1998. 

J. S. Bendat and A. G. Piersol. Random data: Analysis and measurement procedures. 

John Wiley & Sons, New York., 1971. 

F. K. Boadu. Inversion of fracture density from field seismic velocities using artificial 

neural networks. Geophysics, 63:534–545., 1998. 

L. Cagniard. Basic theory of the magneto-telluric methods of geophysical prospecting. 

Geophysics, 18:605–635., 1953. 

C. Calderon-Macias, M. K. Sen, and P. Stoffa. Artificial neural networks for parameter 

estimation in geophysics. Geophys. Prosp., 48:21–47., 2000. 

L. Chaize and M. Lavergne. Signal et bruit en magnetotellurique. Geophys. Prosp, 18: 

64–87., 1970. 

A. D. Chave and D. J. Thomson. Some comments on magnetotelluric response function 

estimation. J. Geophys. Res., 94:1421514225., 1989. 

A. D. Chave and D. J. Thomson. A bounded influence regression estimator based on the 

statistics of the hat matrix. Appl. Statist., 52(3):307 – 322., 2003. 

A. D. Chave, D. J. Thomson, and M. Ander. On the robust estimation of power spectra, 

coherences and transfer functions. J. Geophys. Res., 92:633–648, 1987. 

139

140 

L. Chen, J. Booker, A. Jones, N. Wu, M. Unsworth, W. Wei, and H. Tan. Electrically 

conductive crust in southern tibet from indepth magnetotelluric surveying. Science, 

274:1694–1696., 1996. 

J. F. Claerbout and F. Muir. Robust modeling with erratic data. Geophysics, 38(5): 

826–844., 1973. 

J. Clarke, G. T. D., W. M. Goubau, R. Koch, and R. Miracky. Remote-reference magnetotellurics 

equipment and procedures. Geophys. Prosp., 31:149–170., 1983. 

S. C. Constable, R. L. Parker, and C. G. Constable. Occam’s inversion: A practical algorithm 

for generating smooth models from electromagnetic sounding data. Geophysics, 

52(3):289–300., 1987. 

H. Dai and C. MacBeth. Automatic picking of seismic arrivals in local earthquake data 

using an artificial neural network. Geophys. J. Int., 120:758 – 774., 1995. 

D. L. Dekker and L. M. Hastie. Sources of error and bias in magnetotelluric depth 

sounding of the Bown Basin. PEPI, 25:219–225., 1981. 

S. A. Drury, N. B. W. Harris, R. W. Holt, G. F. Reeves-Smith, and R. T. Wightman. 

Precambrian tectonics and the evolution of South India. J. Geol., 92:3–20., 1984. 

J. Dungey. Electrodynamics of the outer atmosphere in the physics of the ionosphere. 

The physics of the Ionosphere, The Physical Society (London), page 229, 1955. 

W. D. E. Mt/emap Data Interchange Standards, Revision. Society of Exploration Geophysicists, 

USA., Revision 1.0, 1988. 

B. Efron. The jackknife, the bootstrap and other resampling plans. Society for Industrial 

and Applied Mathematics, Philadelphia, 1982. 

G. D. Egbert. Noncausality of the discrete-time magnetotelluric impulse response. Geophysics, 

57:1354–1358., 1992. 

G. D. Egbert. Robust multiple station magnetotelluric data processing. Geophys. J. Int., 

130:475–496., 1997. 

G. D. Egbert and J. R. Booker. Robust estimation of geomagnetic transfer function. 

Geophys. J. Roy. astr. Soc., 87:173–194., 1986. 

G. D. Egbert and D. W. Livelybrooks. Single station magnetotelluric impedance estimation: 

Coherence weighting and the regression M-estimate. Geophysics, 61:964–970, 

1996. 

M. Eisel and G. D. Egbert. On the stability of magnetotelluric transfer function estimates 

and the reliability of their variances. Geophys. J. Int., 144(1):65–82., 2001. 

A. Ellinghaus. PROCMT - Users guide, Revision 2. Metronix GmbH, Braunschweig, 

Germany, 1997.

141 

T. Ernst, E. Y. Sokolva, I. M. Varentsov, and N. G. Golubev. Comparison of two techniques 

for magnetotelluric data processing using synthetic data sets. Acta Geophysica 

Polonica, XLIX (2):213–243., 2001. 

B. C. Fish and T. Kusuma. A neural network approach to automate velocity picking. 

in Society of Exploration Geophysicists 64th annual international meeting; Technical 

program, expanded abstracts with authors’ biographies, 64:185–188., 1994. 

B. P. Flannery, W. H. Press, S. A. Teukolsky, and W. T. Vetterling. Numerical recipes in 

c. The art of scientific computing, Cambridge University Press, UK, page 1020, 1992. 

T. D. Gamble, W. M. Goubau, and J. Clarke. Magnetotellurics with a remote reference. 

Geophysics, 44:53–68, 1979. 

X. Garcia, A. Chave, and A. Jones. Robust processing of magnetotelluric data from the 

auroral zone. J. Geomag. Geoelectr, 49:1451–1468., 1997. 

X. Garcia and A. Jones. Atmospheric sources for audio-magetotelluric sounding. Geophysics, 

67 (2):448 – 458., 2002. 

L. Garth and H. Poor. Detection of non - gaussian signals: a paradigm for modern 

statistical signal processing. Proc. IEEE, 82:1060 – 1095., 1994. 

M. Ghil, M. R. Allen, M. D. Dettinger, K. Ide, D. Kondrashov, M. E. Mann, A. W. 

Robertson, A. Saunders, Y. Iian, F. Varadi, and P. Yiou. Advanced spectral methods 

for climatic time series. Rev. in Geophysics, 40(1):1–41, 2002. 

W. M. Goubau, T. D. Gamble, and J. Clarke. Magnetotelluric data analysis: Removal 

of bias. Geophysics, 43:1157–1166., 1978. 

R. W. Groom and R. C. Bailey. Decomposition of magnetotelluric impedance tensors in 

the presence of local three-dimensional galvanic distortion. J. Geophys. Res., 94(B2): 

1913–1925., 1989. 

GSI. Geological and Mineral map of Tamil Nadu and Pondicherry (scale 1:0.5 million). 

Geological Survey of India, Calcutta, India, 1995. 

F. Hampel, E. M. Ronchetti, P. J. Rousseeuw, and W. Stahel. Robust statistics: The 

approach based on influence functions. John Wiley & Sons Inc. , New York, USA., 

1986. 

T. Harinarayana, D. N. Murty, S. P. E. Rao, C. Manoj, K. Veeraswamy, K. Naganjaneyulu, 

K. K. A. Azeez, R. S. Sastry, and G. Virupakshi. Magnetotelluric Field 

Investigations in Puga Geothermal Region, Jammu and Kashmir, India: 1-D Modeling. 

Geothermal Resources Council Transactions, 122:393–397, 2002. 

T. Harinarayana, K. Naganjaneyulu, C. Manoj, B. P. K. Patro, S. K. Begum, D. N. 

Murthy, Madhusudana-Rao, V. T. C. Kumaraswamy, and G. Virupakshi. Magnetotelluric 

investigation along Kuppam - Palani geotransect, South India - 2-D modeling 

results. Memoir Geological Society of India, 50:107–124, 2003.

142 

M. Hatting. The use of data-adaptive filtering for noise removal on magnetotelluric data. 

PEPI, 53:239–254., 1989. 

W. Hernandez and J. Jacobs. Discussion on ” enhancement of signal-to-noise ratios in 

magnetotelluric data”, by kao dw and rankin d. Geophysics, 44:1594 – 1596, 1979. 

D. B. Hoover, F. Frischknecht, and C. L. Tippens. Audiomagnetotelluric sounding as a 

reconnaissance exploration technique. J. of Geophys. Res., 81:801–809., 1976. 

G. M. Jenkins and D. G. Watts. Spectral analysis and its applications. Holden-Day, San 

Francisco, California., 1968. 

A. Jones. Electrical conductivity of the continental lower crust. in D.M Fountain et al. 

(eds). The continental lower crust, Elsevier:81–143., 1992. 

A. Jones, A. D. Chave, G. D. Egbert, D. Auld, and K. Bahr. Comparison of techniques for 

magnetotelluric response function estimation. J. Geophys. Res., 94(B10):14201–14213., 

1989. 

A. G. Jones. Transformed coherence functions for mutivariate studies. IEEE trans. ASSP, 

29 (2):317–319., 1981. 

A. G. Jones, B. Olafsdottir, and J. Tikkainen. Geomagnetic induction studies in Scandinavia 

III : Magnetotelluric observations. Jour. Geophys., 54:35–50., 1983. 

A. Junge. Characterization of and correction for cultural noise. Surv. Geophys., 17:361 

– 391., 1996. 

D. W. Kao and D. Rankin. Enhancement of signal to noise ratio in magnetotelluric data. 

Geophysics, 42:103–110., 1977. 

R. Karmann. Search coil magnetometers with optimum signal-to-noise ratio. in Vozoff, 

K. (ed) Magnetotelluric methods: SEG Geophysics Reprint Series 5, pages 215–218, 

1977. 

A. A. Kaufman and G. V. Keller. The magnetotelluric sounding method. Elsevier Scientific 

Publishing Company, Amsterdam, 1981. 

H. C. Koons and D. J. Gorney. A neural network model of the relativistic electron flux 

at geosynchronous orbit. J. Geophys. Res., 96(A4):5549–5556., 1991. 

P. Kumar and E. Foufoula-Georgiou. Wavelet analysis for geophysical applications. Reviews 

in Geophysics, 35(4):385–412., 1997. 

G. Kunetz. Processing and interpretation of magnetotelluric soundings. Geophysics, 37: 

1005–1021., 1972. 

J. C. Larsen. Transfer functions: Smooth robust estimates by least squares and remote 

reference methods. Geophys. J. Int., 99:645–663, 1989.

143 

J. C. Larsen, R. L. Mackie, A. Manzella, A. Fiordelisi, and S. Rieven. Robust smooth 

MT transfer functions. Geophys. J. Int., 124:801–819., 1996. 

H. Lundstedt. Solar origin of geomagnetic storms and prediction of storms with the use 

of neural networks. Surv. Geophys., 17:561–573., 1996. 

F. Luo and R. Unbehauen. Applied neural networks for signal processing. Cambridge 

University press, Cambridge, UK., page 123, 1997. 

J. Macnae, Y. Lamontagne, and W. G. F. Noise processing technique for time domain 

electromagnetic systems. Geophysics, 49:934–948., 1984. 

T. Madden. Spectral, cross spectral and bispectral analysis of low frequency electromagnetic 

data. ed. Bleil D.F., Pentium Press, New York., 1964. 

T. Mahadevan. Deep Continental Structure of India: A Review. Geol. Soc. India Memoir, 

28:569, 1994. 

C. Manoj and N. Nagarajan. The application of artificial neural networks to magnetotelluric 

time series analysis. Geophys. J. Int., 153:409–423., 2003. 

M. Mareschal, R. D. Kurtz, and R. C. Bailey. A review of electromagnetic investigations 

in the Kapuskasing Uplift and surrounding regions; electrical properties of key rocks. 

Canadian Journal of Earth Sciences, 31(7):1042–1051., 1994. 

MATLAB. User’s manual, version 6, mathworks inc. MathWorks Inc., Natick, USA., 

2001. 

M. D. McCormack, Z. D. E., and D. D. W. First-break refraction event picking and 

seismic data trace editing using neural networks. Geophysics, 58:67–78., 1993. 

M. L. McCraken, K. G. Oristaglio and G. W. Hohman. Minimization of noise in electromagnetic 

exploration systems. Geophysics, 51:819–832., 1986. 

G. W. McNeice and A. G. Jones. Multi-site, multi-frequency tensor decomposition of 

magnetotelluric data. Geophysics, 66:158–173, 2001. 

W. Menke. Geophysical data analysis, discrete inverse theory. Academic Press Inc, 

Orlando, Florida, USA., 58:67–78, 1984. 

Metronix. Geophysical Measurement System (GMS05). Operating Manual, Revision 3.1, 

Metronix GmbH, Germany, page 112, 1997. 

D. C. Mishra. Geophysical evidence for a thick crust south of Palghat-Tiruchi gap in the 

high grade terrains of South India. Jour. Geol. Soc. India, 33:79–81., 1988. 

D. C. Mishra and M. Venkatarayudu. Magsat scalar anomaly map of India and part 

of Indian ocean - Magnetic crust and tectonic correlation. Geophys. Res. Lett., 12: 

781–784., 1985.

144 

J. B. Molyneux and D. R. Schmitt. First-break timing: Arrival onset times by direct 

correlation. Geophysics, 64:1492 – 1501., 1999. 

A. Müller. A new method to compensate for bias in magnetotellurics. Geophy. J. Int., 

142:257–269., 2000. 

M. E. Murat and A. J. Rudman. Automated first arrival picking; a neural network 

approach. Geophys. Prosp., 40:587–604., 1992. 

N. Nagarajan. Application of robust estimation of transfer function for a magnetovariational 

array in Eastern India. in Deep Electromagnetic Exploration ed. KK. Roy et al, 

Narosa Publishing House, India, page New Delhi, 1998. 

S. M. Naqvi and J. J. W. Rogers. Precambrian Geology of India. Oxford Monographs in 

Geology and Geophysics No 6, Oxford University press, Oxford., page 223, 1987. 

N. Nityananda, A. K. Agarwal, and B. P. Singh. Induction at short period on the 

horizontal field variation in the Indian Peninsula. PEPI, 15:5–9., 1977. 

N. Nityananda and D. Jayakumar. Proposed relation between anomalous geomagnetic 

variations and tectonic history of South India. PEPI, 27:223–228., 1981. 

G. Oettinger, V. Haak, , and J. C. Larsen. Noise reduction in magnetotelluric time-series 

with a new siganl-noise separation method and its application to a field experiment in 

the Saxonian Granulite Massif. Geophys. J. Int., 146:659 – 669, 2001. 

A. L. Padilha, I. Vitorello, , and L. Rijo. Effects of the Equatorial Electrojet on magnetotelluric 

surveys: Field results from Northwest Brazil. Geophys. Res. Lett., 24(1): 

89–92., 1997. 

J. Park and A. D. Chave. On the estimation of magnetotelluric response functions using 

the singular value decomposition. Geophys. Jour. of Roy. astr. Soc., 77:683–709., 1984. 

L. Pedersen. Some aspects of magnetotelluric field procedures. Surveys in Geophysics, 9: 

245–257., 1988. 

G. Petiau and A. Dupis. Noise, temperature coefficient and long time stability of electrodes 

for telluric observations. Geophys. Prosp., 28:792–804, 1980. 

M. Poulton, B. Stenberg, and C. Glass. Location of subsurface targets in geophysical 

data using neural networks. Geophysics, 57:1534 – 1544., 1992. 

E. Pulz and O. Ritter. Entwicklung einer kalibriereinrichtung fuer induktionsspulenmagnetometer 

(search coils) am GeoForschungsZentrum Potsdam. Scientific Technical 

Report, GeoForschungsZentrum - Potsdam 10/01., 2001. 

B. Radhakrishna. Suspect tectono-stratigraphic terrain elements in the Indian subcontinent. 

Jour. Geo. Soc.India, 34:1–24., 1989.

145 

S. S. Rai, D. Srinagesh, and V. K. Gaur. Granulite evolution in south India - a seismic 

tomographic perspective. Mem. Geol.Soc. of India, 25:235 – 265., 1993. 

M. Rao. Study of geomagnetic pulsation characteristics and their solar cycle dependence 

in the equatorial region India? Ph.D. thesis, Osmania University., 2000. 

M. Rao, S. V. S. Sarma, N. Nagarajan, T. Harinarayana, C. Manoj, K. Naganjaneyulu, 

and V. T. C. Kumaraswamy. On the magnetotelluric source field effects in the Indian 

equatorial region - an experimental study. Presented at 16th EM induction workshop 

held at Santa Fe, USA:12–22nd June, 2002. 

A. B. Reddi, M. P. Mathew, B. Singh, and P. S. Naidu. Aeromagnetic evidence of crustal 

structure in the granulite terrane of Tamilnadu - Kerala. Jour. Geol. Soc. India, 32: 

368 – 381., 1988. 

O. A. Ritter, , and G. J. K. Dawes. New equipment and processing for magnetotelluric 

remote refernce observations. Geophys. Jour. Int., 132:535–548., 1998. 

W. Rodi and R. L. Mackie. Nonlinear conjugate gradients algorithm for 2-d magnetotelluric 

inversions. Geophysics, 66:174–187., 2001. 

Y. Sarma, T. Sastry, and S. Sarma. Equatorial effects on nighttime Pc3 puslation. Ind. 

J. Radio & Space. Phys., 11:29–32, 1982. 

T. S. Sastry, Y. S. Sarma, S. V. S. Sarma, and P. V. S. Narayan. Daytime Pi pulsations 

at equatorial latitudes. J. Atmos. Terr. Phys., 45:733–741, 1983. 

U. Schmucker. Auswerteverfahren gottingen, in protokoll 7 kolloquium ’elekromagnetische 

tiefenforschung. Niedersachsisches Landesamt, Hannover., pages 163–188, 1978. 

Shalivahan and B. B. Bhattacharya. How remote can the far remote reference site for 

magnetotelluric measurements be? Jour. Geophys. Res, 107(B6):ETG 1–1, 2002. 

W. E. Sims, F. Bostick, and H. W. Smith. The estimation of the magnetotelluric 

impedance tensor elements from the measured data. Geophysics, 36:938–942., 1971. 

W. Siripunvaraporn and G. Egbert. An efficient data-subspace inversion method for 

two-dimensional magnetotelluric data. Geophysics, 65(3):791–803., 2000. 

M. Y. Smirnov. Magnetotelluric data processing with a robust statistical procedure 

having a high breakdown point. Geophys. J. Int., 152:1–7., 2003. 

J. T. Smith and J. R. Booker. Rapid Inversion of Two - and Three-Dimensional Magnetotelluric 

data. J. Geophys. Res., 96(B3):3905–3922., 1991. 

V. Spichak and I. Popova. Artificial neural network inversion for magnetotelluric data in 

terms of three-dimensional earth macroparameters. Geophys. J. Int., 142:15–26., 2000. 

J. A. Stodt. Noise analysis for conventional and remote reference magnetotellurics. PhD. 

dissertation, Univ of Utah, Logan, 1983.

146 

D. Sutarno and K. Vozoff. Phase-smoothed robust m-estimation of magnetotelluric 

impedance functions. Geophysics, 36:938–942., 1991. 

C. M. J. Swift. A magnetotelluric investigation of an electrical conductivity anomaly in 

Southwestern US. in Magnetotelluric methods, Geophys reprint series vol 5 ed. Vozoff, 

K., Soc. Explor. Geophys. Tulsa, Okla, pages 156–166, 1986. 

L. Szarka. Geophysical aspects of man-made magnetic noise in the earth - a review. 

Surveys in Geophysics, 9:287 – 318., 1988. 

N. K. Thakur, M. V. Mahashabde, B. R. Arora, B. P. Singh, B. J. Srivastava, and S. N. 

Prasad. Geomagnetic variation anomalies in Peninsular India. Geophys. Jour. Res. 

astr. Soc., 86:838–854., 1986. 

A. Tikhonov. On determining electrical characteristics of the deep layers of the Earth’s 

crust. Dokl. Akad. Nauk S.S.S.R., 73:295–297., 1950. 

J. M. Travassos and D. Beamish. Magnetotelluric data processing: A case study. Geophys. 

J. Int., 93:377–391., 1988. 

K. Vozoff. The magnetotelluric method in electromagnetic methods in applied geophysics. 

ed by M.N. Nabighian, Society of Exploration Geophysics, Tulsa, USA., 1991. 

K. A. Vozoff. Magnetotelluric method in the exploration of sedimentary basins. Geophysics, 

37:98–141, 1972. 

J. R. Wait. On the relation between telluric currents and the earth’s magnetic field. 

Geophysics, 19:281289, 1954. 

S. H. Ward. The electromagnetic method. in SEG Mining geophysics volume II, Mining 

geophysics, Tulsa, pages 236 – 372., 1967. 

J. T. Weaver. Mathematical Methods for Geo-Electromagnetic Induction. Wiley, New 

York, 1994. 

P. Weidelt. The inverse problem of geomagnetic induction. Zeitschrift für Geophysik, 38: 

257–289., 1972. 

P. J. Werbos. Backpropagation through time: What it does and how to do it. Proc. 

IEEE, 78:1550 – 1560., 1990. 

D. E. Wight and F. X. Bostick. Cascade decimation: A technique for real time estimation 

of power spectra. in Vozoff, K. (ed) Magnetotelluric methods: SEG Geophysics Reprint 

Series 5, pages 215–218., 1980. 

J. Winer, R. J. A., R. J. R., and R. Moll. Predicting carbonate permeabilities from 

wireline logs using back propagation networks. 61st SEG meeting, Houston, USA.( 

Expanded abstract), pages 285–288., 1991.

147 

E. Yee, P. R. Kosteniuk, and K. V. Paulson. The reconstruction of the magnetotelluric 

impedance tensor: An adaptive parametric time-domain approach. Geophysics, 53: 

1080–1087., 1988. 

Y. Zhang and K. V. Paulson. Magnetotelluric inversion using regularized Hopfield neural 

networks. Geophys. Prosp., 45:725–743., 1997. 

Z. Zhang. Robust M estimators. Appeared at Internet URL http://wwwsop.inria.fr/robotvis/personnel/zzhzng/Publis/Tutorial-Estim., 

1996. 

Y. Zhao and K. Takano. An artificial neural network approach for broadband seismic 

picking. Bull. Seis. Soc. Am., 89:670–680, 1999. 

K. L. Zonge and L. J. Hughes. Controlled source audio frequency magnetotellurics. in EM 

methods in Applied Geophysics, ed M.N. Nabighian, Society of Exploration Geophysics. 

Tulsa, USA, 1991.

Errata 

The Following changes/ additions have been incorporated into the thesis based on the 

examiners comments. 

1. Case in which noise is difficult to be removed is given in §2.1, page 19. A description 

of noises that cause the scatter in the processed MT impedances is given in the 

second paragraph of §6.1, page 89. Error bars are defined in §3.3.4, Page 46. 

2. Two sentences on quantifying the noise in MT data after processing are inserted in 

§5.8, page 86 (for ANN) and §6.2.4.6, page 101 (for robust processing). 

3. Coherent and incoherent noises are defined in the first paragraph of §3.3.3, page 

45. 

4. Use of coherency to screen MT data in ”dead band” is given in the second paragraph 

of §3.3.3, page 45. 

5. Choices of data rejection gates other than coherency are discussed in the last paragraph 

of §3.3.3, page 45. 

6. Shortcomings of Kao and Rankin [1977]’s iterative MT processing scheme is given 

in the last paragraph of §3.3.5, page 46. 

7. Specific improvements obtained by band averaging are inserted in the second paragraph 

of §6.4.10, page 119. 

8. The thesis does not claim or deals with the averaging of ”up” and ”down” biased 

MT impedances. 

9. MT processing results along the Vellar-Palani profile in the SGT are given in §6.4.9, 

page 118.

Magnetotelluric data analysis using advances in ... - Geomagnetism

Create successful ePaper yourself

Delete template?

Save as template?