Mathematical analogies in physics. Thin-layer wave theory

CARCIONE, JOSÉ; GRUNHUT, VIVIAN; OSELLA, A.,

ANNALS OF GEOPHYSICS

EDITRICE COMPOSITORI BOLOGNA

Lugar: Bologna; Año: 2014 vol. 57 p. 1 - 10

1593-5213

Field theory applies to elastodynamics, electromagnetism, quantum mechanics,gravitation and other similar fields of physics, where the basic equations describing thephenomenon are based on constitutive relations and balance equations. For instance,in elastodynamics, these are the stress-strain relations and the equations of momentumconservation (Euler-Newton law). In these cases, the same mathematical theory canbe used, by establishing appropriate mathematical equivalences (or analogies) betweenmaterial properties and field variables. For instance, the wave equation and the relatedmathematical developments can be used to describe anelastic and electromagnetic wavepropagation, and are extensively used in quantum mechanics.In this work, we obtain the mathematical analogy for the reflection/refraction(transmission) problem of a thin layer embedded between dissimilar media, consideringthe presence of anisotropy and attenuation ? viscosity in the viscoelastic case, conductivity in the electromagnetic case and a potential barrier in quantumphysics (thetunnel effect). The analogy is mainly illustrated with geophysical examplesof propagation of S (shear), P (compressional), TM (transverse-magnetic)and TE (transverse-electric) waves. The tunnel effect is obtained as a special caseof viscoelastic waves at normal incidence.