Abstract
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.
Highlights
The role of mathematical analogies has been well illustrated and explained by Tonti [1]
Carcione and Robinson [4] establish the analogy for the reflection-transmission problem at a single interface, showing that contrasts in compressibility yield the reflection coefficient for light polarized perpendicular to the plane of incidence (Fresnel’s sine law – the electric vector perpendicular to the plane of incidence), and density contrasts yields the reflection coefficient for light polarized in the plane of incidence (Fresnel’s tangent law)
Theories describing wave propagation and field diffusion in different fields of physics consist in partial differential equations, which have identical or similar mathematical expressions
Summary
The role of mathematical analogies has been well illustrated and explained by Tonti [1]. Carcione and Cavallini [2] found analogies between anelastic and electromagnetic vector wave fields, while Carcione et al [3] relate the medium properties. Carcione and Cavallini [2] show that the 2-D Maxwell equations describing propagation of the transverse-magnetic mode in anisotropic media is mathematically equivalent to the SH wave equation in an anisotropic-viscoelastic solid where attenuation is described with the Maxwell mechanical model. Carcione et al [5] considered the reflection/transmission problem through an anisotropic and lossy layer. They obtained the analogy among P and SH elastic waves, TE and TM electromagnetic waves and wave mechanics in quantum theory.
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