P. Schmoldt, PhD - MTNet - DIAS
P. Schmoldt, PhD - MTNet - DIAS P. Schmoldt, PhD - MTNet - DIAS
Contents 2.3. Deviation from plane wave assumption . . . . . . . . . . . . . . . . . . . 21 2.3.1. Mathematical description . . . . . . . . . . . . . . . . . . . . . . 21 2.3.2. Location of recording . . . . . . . . . . . . . . . . . . . . . . . . 25 2.3.3. Distance to source region . . . . . . . . . . . . . . . . . . . . . . 27 2.3.4. Used period range and subsurface conductivity . . . . . . . . . . 27 3. Mathematical description of electromagnetic relations 31 3.1. Basic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.1.1. Maxwell’s Equations . . . . . . . . . . . . . . . . . . . . . . . . 31 3.1.2. Ohm’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.1.3. Vector calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.2. Deriving magnetotelluric parameters . . . . . . . . . . . . . . . . . . . . 32 3.2.1. Common notation for magnetotelluric relations . . . . . . . . . . 35 3.2.2. Relationships for simple subsurface cases . . . . . . . . . . . . . 36 3.2.3. Vertical magnetic transfer function . . . . . . . . . . . . . . . . . 37 3.3. Magnetotelluric induction area . . . . . . . . . . . . . . . . . . . . . . . 37 3.4. Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.4.1. Horizontal interfaces . . . . . . . . . . . . . . . . . . . . . . . . 41 3.4.2. Lateral interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.5. The influence of electric permittivity . . . . . . . . . . . . . . . . . . . . 43 3.6. The influence of magnetic permeability . . . . . . . . . . . . . . . . . . 48 4. Distortion of magnetotelluric data 49 4.1. Types of distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.1.1. Galvanic distortion . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.1.2. Inductive distortion . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.1.3. Anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.2. Dimensionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.2.1. Frequency-dependent dimensionality . . . . . . . . . . . . . . . 63 4.3. General mathematical representation . . . . . . . . . . . . . . . . . . . . 67 4.4. Removal of distortion effects . . . . . . . . . . . . . . . . . . . . . . . . 68 4.4.1. Swift angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.4.2. Bahr parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.4.3. Weaver-Agarwal-Lilley tensor invariants . . . . . . . . . . . . . 71 4.4.4. Groom and Bailey decomposition . . . . . . . . . . . . . . . . . 73 4.4.5. Caldwell-Bibby-Brown phase tensor . . . . . . . . . . . . . . . . 75 4.4.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 5. Earth’s properties observable with magnetotellurics 81 5.1. Electric charge transport in rocks and minerals . . . . . . . . . . . . . . . 83 5.1.1. Electrolytic conduction . . . . . . . . . . . . . . . . . . . . . . . 83 5.1.2. Electronic conduction . . . . . . . . . . . . . . . . . . . . . . . 86 ii
Contents 5.1.3. Semiconduction . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.2. Variation of electric conductivity with depth . . . . . . . . . . . . . . . . 87 5.2.1. The Earth’s crust . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.2.2. The Earth’s mantle . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.2.3. The Earth’s core . . . . . . . . . . . . . . . . . . . . . . . . . . 98 5.3. Parameters controlling the conductivity of the Earth’s mantle . . . . . . . 99 6. Using magnetotellurics to gain information about the Earth 105 6.1. Recording of magnetotelluric signals . . . . . . . . . . . . . . . . . . . . 105 6.1.1. Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 6.1.2. Station setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 6.2. Processing of magnetotelluric data . . . . . . . . . . . . . . . . . . . . . 108 6.2.1. Pre-processing of the time-series data . . . . . . . . . . . . . . . 109 6.2.2. Transformation into the frequency domain . . . . . . . . . . . . . 110 6.2.3. Robust remote reference processing . . . . . . . . . . . . . . . . 111 6.3. Deriving subsurface structure using magnetotelluric data . . . . . . . . . 114 6.3.1. Analytical direct transformation . . . . . . . . . . . . . . . . . . 114 6.3.2. Forward modelling . . . . . . . . . . . . . . . . . . . . . . . . . 116 6.3.3. Inversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 II. Geology of the study area 132 7. Geology of the Iberian Peninsula 133 7.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 7.2. Betic Mountain Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 7.2.1. Previous geophysical studies in the region . . . . . . . . . . . . . 136 7.3. Tajo Basin and central Spain . . . . . . . . . . . . . . . . . . . . . . . . 143 7.3.1. Tectonic evolution and characteristics . . . . . . . . . . . . . . . 143 7.3.2. Previous geophysical studies in the region . . . . . . . . . . . . . 152 7.3.3. Summary and conclusions . . . . . . . . . . . . . . . . . . . . . 165 III. A novel inversion approach for oblique geoelectric strike directions in crust and mantle 167 8. Recovering a synthetic 3D subsurface model using lower-dimensional inversion schemes 169 8.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 8.2. Generating synthetic 3D model data . . . . . . . . . . . . . . . . . . . . 171 8.2.1. Generating the synthetic 3D model . . . . . . . . . . . . . . . . . 171 8.2.2. Data preparation and analysis . . . . . . . . . . . . . . . . . . . 172 iii
- Page 1: Multidimensional isotropic and anis
- Page 6 and 7: Contents 8.3. Inversion of 3D model
- Page 9 and 10: List of Figures 2.1. Amplitude of t
- Page 11 and 12: List of Figures 4.17. Visual repres
- Page 13 and 14: List of Figures 8.2. Ambient noise
- Page 15 and 16: List of Figures 10.10.RMS misfit va
- Page 17: List of Figures A.15.Result of anis
- 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
- Page 32 and 33: Publications Poster presentations x
- Page 34 and 35: Acknowledgements Team, namely Colin
- Page 37 and 38: Introduction 1 The Iberian Peninsul
- Page 39 and 40: ections from enhanced one-dimension
- Page 41: Part I Theoretical background of ma
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Contents<br />
2.3. Deviation from plane wave assumption . . . . . . . . . . . . . . . . . . . 21<br />
2.3.1. Mathematical description . . . . . . . . . . . . . . . . . . . . . . 21<br />
2.3.2. Location of recording . . . . . . . . . . . . . . . . . . . . . . . . 25<br />
2.3.3. Distance to source region . . . . . . . . . . . . . . . . . . . . . . 27<br />
2.3.4. Used period range and subsurface conductivity . . . . . . . . . . 27<br />
3. Mathematical description of electromagnetic relations 31<br />
3.1. Basic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31<br />
3.1.1. Maxwell’s Equations . . . . . . . . . . . . . . . . . . . . . . . . 31<br />
3.1.2. Ohm’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32<br />
3.1.3. Vector calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . 32<br />
3.2. Deriving magnetotelluric parameters . . . . . . . . . . . . . . . . . . . . 32<br />
3.2.1. Common notation for magnetotelluric relations . . . . . . . . . . 35<br />
3.2.2. Relationships for simple subsurface cases . . . . . . . . . . . . . 36<br />
3.2.3. Vertical magnetic transfer function . . . . . . . . . . . . . . . . . 37<br />
3.3. Magnetotelluric induction area . . . . . . . . . . . . . . . . . . . . . . . 37<br />
3.4. Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40<br />
3.4.1. Horizontal interfaces . . . . . . . . . . . . . . . . . . . . . . . . 41<br />
3.4.2. Lateral interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . 43<br />
3.5. The influence of electric permittivity . . . . . . . . . . . . . . . . . . . . 43<br />
3.6. The influence of magnetic permeability . . . . . . . . . . . . . . . . . . 48<br />
4. Distortion of magnetotelluric data 49<br />
4.1. Types of distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50<br />
4.1.1. Galvanic distortion . . . . . . . . . . . . . . . . . . . . . . . . . 52<br />
4.1.2. Inductive distortion . . . . . . . . . . . . . . . . . . . . . . . . . 57<br />
4.1.3. Anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59<br />
4.2. Dimensionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62<br />
4.2.1. Frequency-dependent dimensionality . . . . . . . . . . . . . . . 63<br />
4.3. General mathematical representation . . . . . . . . . . . . . . . . . . . . 67<br />
4.4. Removal of distortion effects . . . . . . . . . . . . . . . . . . . . . . . . 68<br />
4.4.1. Swift angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68<br />
4.4.2. Bahr parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . 69<br />
4.4.3. Weaver-Agarwal-Lilley tensor invariants . . . . . . . . . . . . . 71<br />
4.4.4. Groom and Bailey decomposition . . . . . . . . . . . . . . . . . 73<br />
4.4.5. Caldwell-Bibby-Brown phase tensor . . . . . . . . . . . . . . . . 75<br />
4.4.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79<br />
5. Earth’s properties observable with magnetotellurics 81<br />
5.1. Electric charge transport in rocks and minerals . . . . . . . . . . . . . . . 83<br />
5.1.1. Electrolytic conduction . . . . . . . . . . . . . . . . . . . . . . . 83<br />
5.1.2. Electronic conduction . . . . . . . . . . . . . . . . . . . . . . . 86<br />
ii
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