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The same mathematical formalism of the wave equation can be used to describe anelastic and electromagnetic wave propagation. In this work, we obtain the mathematical analogy for the reflection/refraction (transmission) problem of two layers, considering the presence of anisotropy and attenuation -- viscosity in the viscoelastic case and resistivity in the electromagnetic case. The analogy is illustrated for SH (shear-horizontally polarised) and TM (transverse-magnetic) waves. In particular, we illustrate examples related to the magnetotelluric method applied to geothermal systems and consider the effects of anisotropy. The solution is tested with the classical solution for stratified isotropic media.
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- E. Tonti, On the mathematical structure of a large class of physical theories, Accademia Nazionale dei Lincei, estratto dai Rendiconti della Classe di Scienze Fisiche, Matematiche e Naturali, Serie VIII, Vol. LII, fasc. 1, 1972.
- J.M. Carcione, F. Cavallini, On the acousticelectromagnetic analogy, Wave Motion 21: 149–162, 1995.
- J.M. Carcione, B. Ursin, J.I. Nordskag, Crossproperty relations between electrical conductivity and the seismic velocity of rocks, Geophysics 72: E193–E204, 2007.
- J.M. Carcione, E. Robinson, On the acousticelectromagnetic analogy for the reflection-refraction problem, Studia Geoph. et Geod. 46: 321–345, 2002.
- J.M. Carcione, V. Gru¨nhut, A. Osella, Mathematical analogies in physics. Thin-layer wave theory, Annals of Geophysics 57: 1–10, 2014.
- A. Osella, P. Martinelli, Magnetotelluric response of anisotropic 2-D structures, Geophys. J. Internat. 115: 819–828, 1993.
- P. Martinelli, A. Osella, A., MT forward modeling of 3-D anisotropic electrical conductivity structures using the Rayleigh-Fourier method, J. Geomag. Geoelectr. 49: 1499–1518, 1997.
- J.M. Carcione, Wave Fields in Real Media. Theory and numerical simulation of wave propagation in anisotropic, anelastic, porous and electromagnetic media, 3rd edition, Elsevier, 2014.
- M. Born, E. Wolf, Principles of Optics, Oxford, Pergamon Press, 1964.
- A. Mart’ı, The role of electrical anisotropy in magnetotelluric responses: From modelling and dimensionality analysis to inversion and interpretation, Surv. Geophys. 35: 179–218, 2014.
- F. Simpson, K. Bahr, Practical magnetotellurics, Cambridge University Press, 2005.
- J. Pek, F.A.M. Santos, Magnetotelluric impedances and parametric sensitivities for 1-D anisotropic layered media, Computers & Geosciences 28: 939–950, 2002.
- J.R. Wait, On the relation between telluric currents and the earth's magnetic field, Geophysics 19: 281– 289, 1954.
- J.R. Wait, Geo-electromagnetism, Academic Press, New York, 1982.