Book contents
- Frontmatter
- Contents
- Preface
- Symbols
- 1 Introduction
- 2 Basic theoretical concepts
- 3 Planning a field campaign
- 4 From time series to transfer functions: data processing
- 5 Dimensionality and distortion
- 6 Numerical forward modelling
- 7 Inversion of MT data
- 8 The general link to other geosciences: conduction mechanisms
- 9 The special link to other geosciences
- 10 Other EM induction techniques
- Appendix 1 Theorems from vector calculus
- Appendix 2 The transfer function in the wavenumber-frequency domain and equivalence transfer functions
- Appendix 3 Probability distributions
- Appendix 4 Linear regression
- Appendix 5 Fourier analysis
- Appendix 6 Power and cross spectra
- Glossary
- References
- Index
2 - Basic theoretical concepts
Published online by Cambridge University Press: 03 December 2009
- Frontmatter
- Contents
- Preface
- Symbols
- 1 Introduction
- 2 Basic theoretical concepts
- 3 Planning a field campaign
- 4 From time series to transfer functions: data processing
- 5 Dimensionality and distortion
- 6 Numerical forward modelling
- 7 Inversion of MT data
- 8 The general link to other geosciences: conduction mechanisms
- 9 The special link to other geosciences
- 10 Other EM induction techniques
- Appendix 1 Theorems from vector calculus
- Appendix 2 The transfer function in the wavenumber-frequency domain and equivalence transfer functions
- Appendix 3 Probability distributions
- Appendix 4 Linear regression
- Appendix 5 Fourier analysis
- Appendix 6 Power and cross spectra
- Glossary
- References
- Index
Summary
Starting from Maxwell's equations, we derive the diffusion equation for the electric field. Diffusion governs not only electromagnetic induction but also the spreading of thermal fields. Therefore, there is an analogue in your kitchen: pre-heat the oven to 250 ℃, and put a roast (2 kg) into it. Remove after 15 minutes and cut in two halves. The outermost 2 cm are cooked but the inner bit is quite raw. This tells us that 2 cm is the penetration depth of a thermal field with period 15 min in beef. A shorter period would yield a smaller penetration depth and a longer period would penetrate deeper. In addition, the thermal field arrives with a delay inside the beef. This delay is governed by the thermal conductivity of the beef. Electromagnetic induction in the earth is governed by the skin effect and behaves in a similar way to the beef analogue: there is a period-dependent penetration depth, and we observe the delayed penetration (phase lag) and decay of an electromagnetic field into the conductive subsoil. Due to the phase lag of the penetrating fields we have a complex penetration depth, which we call a ‘transfer function’. Electromagnetic sounding is a volume sounding. Therefore, for the simplest case of an homogeneous Earth, MT transfer functions contain information about the electrical conductivity in a hemisphere, with the magnetotelluric site located at the centre of the bounding horizon.
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- Practical Magnetotellurics , pp. 15 - 36Publisher: Cambridge University PressPrint publication year: 2005
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