P. Schmoldt, PhD - MTNet - DIAS
P. Schmoldt, PhD - MTNet - DIAS P. Schmoldt, PhD - MTNet - DIAS
2. Sources for magnetotelluric recording Wave type Location of generation external (e) or internal (i) Process of generation Continuous pulsations Pc5 i Drift resonance Pc4 i Bounce resonance Pc3 e During times when the solar wind velocity is high and the solar wind magnetic field is radial Pc2 i Generated by electromagnetic ion O(+) cyclotron effects Pc1 i Gyro resonance or cyclotron instability Irregular pulsations Pi2 i Bursty Earthward flows during geomagnetic activity in the plasma sheet on the night-side of the Earth, radiating Alfvén waves that travel to the auroral ionosphere where they are reflected and forced to travel back and interact with the initial flow Pi1 i Cavity resonance between the topside of the ionosphere and the auroral acceleration region at ∼1 Re altitude that is excited by fluctuating field aligned currents Tab. 2.3.: Description of the location and process of generation for the different types of ultra low frequency (ULF) waves (also referred to as pulsation) as they are understood by today; after McPherron [2005], extended by the information regarding Pc2 using results presented by Inhester et al. [1985]; Sarma et al. [1974] horizontal wave number k (i.e. the inverse of the wavelength: k = λ −1 ) with the value 1/2 of ω + k · vσµ0 . Thus, influences of the wave frequency ω, velocity of the source v (usually assumed to be zero), and the conductivity of the subsurface σ are taken into account. The approach by Mareschal [1986] is based on the solution of the wave equation for electromagnetic fields (cf. Sec. 3.2), i.e. where F is either the electric or magnetic field and ∇ 2 F = γ 2 F (2.1) γ 2 = k 2 + ıωµσ + µεω 2 (2.2) (for a non-moving source) with µ: magnetic permeability, ε: permittivity. Assuming that the effect of permittivity is negligible (cf. Sec. 3.5), that µ = µ0 (cf. Sec. 3.6), and including the contribution of the moving source yields 22 ˆγ 2 = k 2 + ı(ω + kv)µσ. (2.3)
log 10 (|k|/(|ω+kv|σμ 0 ) 1/2 ) (dimensionless) -2 -3 -4 -5 -6 -7 Influence of non-uniform source -8 -3 -2 -1 0 1 2 3 4 5 log (Period) (s) 10 2.3. Deviation from plane wave assumption σ=10 -4 , v=0 σ=10 -2 , v=0 σ=10 -1 , v=0 Fig. 2.16.: Estimation of plane wave validity for magnetotelluric (MT) data using the relation given in Equation 2.4 proposed by Mareschal [1986]. Validity is therein dependent on period range T, subsurface conductivity σ, and velocity of the source v. Values for source velocities of 10 km/s are plotted as well, but are overlapped by the graph for v = 0 because of the small difference. Validity of the plane wave assumption can then be estimated as the ratio between the different terms: αdeviation = k ω + k . 1/2 · v µ0σ (2.4) Re-arranging Equation 2.4 using the relations |k| = f /c, ω = 2π f , and f = T −1 with c denoting the speed of light and f and T the frequency and period of the wave respectively, one obtains αdeviation = 2π + |v| µ0c c 2 −1/2 σT . (2.5) From Equation 2.5 it becomes apparent that the motion of the source is negligible for velocities that are small in comparison with the speed of light. Hence, the plane wave validity is dominated by the influence of period range and subsurface conductivity; see Figure 2.16 for an illustration of these relationships. A more detailed evaluation of the deviation effect is possible when data from co-located stations are available, allowing for a calculation of the wave’s spatial change. Mathematically speaking, one looks for situations where the surface from an inclining magnetic wave can be sufficiently described using only the first order terms of the magnetic field, i.e. ∂yHy = 0, where y refers to the horizontal direction orthogonal to wave propagation. Dmitriev and Berdichevsky [1979] and Berdichevsky et al. [1981] expressed the magnetotelluric relations for a 1D Earth approximation in terms of power series using the kernel definition by Schmucker [1970, 1980]. The authors show that for MT, the effect of nonplane waves can be represented through additional terms appended to the traditional MT 23
- Page 9 and 10: List of Figures 2.1. Amplitude of t
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- Page 13 and 14: List of Figures 8.2. Ambient noise
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- Page 20 and 21: List of Tables xviii 5.5. Parameter
- Page 22 and 23: List of Acronyms FE finite element
- Page 25 and 26: List of Symbols Below is a list of
- Page 27 and 28: Symbol SI unit Denotation φ · pha
- Page 29: Abstract The Tajo Basin and Betic C
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- Page 34 and 35: Acknowledgements Team, namely Colin
- Page 37 and 38: Introduction 1 The Iberian Peninsul
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- Page 41: Part I Theoretical background of ma
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log 10 (|k|/(|ω+kv|σμ 0 ) 1/2 ) (dimensionless)<br />
-2<br />
-3<br />
-4<br />
-5<br />
-6<br />
-7<br />
Influence of non-uniform source<br />
-8<br />
-3 -2 -1 0 1 2 3 4 5<br />
log (Period) (s)<br />
10<br />
2.3. Deviation from plane wave assumption<br />
σ=10 -4 , v=0<br />
σ=10 -2 , v=0<br />
σ=10 -1 , v=0<br />
Fig. 2.16.: Estimation of plane wave validity for magnetotelluric (MT) data using the relation given in Equation 2.4 proposed by<br />
Mareschal [1986]. Validity is therein dependent on period range T, subsurface conductivity σ, and velocity of the source v. Values for<br />
source velocities of 10 km/s are plotted as well, but are overlapped by the graph for v = 0 because of the small difference.<br />
Validity of the plane wave assumption can then be estimated as the ratio between the<br />
different terms:<br />
<br />
<br />
<br />
<br />
αdeviation =<br />
k<br />
<br />
<br />
<br />
<br />
<br />
ω<br />
<br />
+ k<br />
<br />
. 1/2<br />
· v <br />
µ0σ<br />
(2.4)<br />
Re-arranging Equation 2.4 using the relations |k| = f /c, ω = 2π f , and f = T −1 with c<br />
denoting the speed of light and f and T the frequency and period of the wave respectively,<br />
one obtains<br />
αdeviation =<br />
<br />
2π + |v|<br />
<br />
µ0c<br />
c<br />
2 −1/2 σT . (2.5)<br />
From Equation 2.5 it becomes apparent that the motion of the source is negligible for<br />
velocities that are small in comparison with the speed of light. Hence, the plane wave<br />
validity is dominated by the influence of period range and subsurface conductivity; see<br />
Figure 2.16 for an illustration of these relationships.<br />
A more detailed evaluation of the deviation effect is possible when data from co-located<br />
stations are available, allowing for a calculation of the wave’s spatial change. Mathematically<br />
speaking, one looks for situations where the surface from an inclining magnetic<br />
wave can be sufficiently described using only the first order terms of the magnetic field,<br />
i.e. ∂yHy = 0, where y refers to the horizontal direction orthogonal to wave propagation.<br />
Dmitriev and Berdichevsky [1979] and Berdichevsky et al. [1981] expressed the magnetotelluric<br />
relations for a 1D Earth approximation in terms of power series using the kernel<br />
definition by Schmucker [1970, 1980]. The authors show that for MT, the effect of nonplane<br />
waves can be represented through additional terms appended to the traditional MT<br />
23
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