Abstract
<p>Field theory applies to elastodynamics, electromagnetism, quantum mechanics, gravitation and other similar fields of physics, where the basic equations describing the phenomenon are based on constitutive relations and balance equations. For instance, in elastodynamics, these are the stress-strain relations and the equations of momentum conservation (Euler-Newton law). In these cases, the same mathematical theory can be used, by establishing appropriate mathematical equivalences (or analogies) between material properties and field variables. For instance, the wave equation and the related mathematical developments can be used to describe anelastic and electromagnetic wave propagation, 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, considering the presence of anisotropy and attenuation/viscosity in the viscoelastic case, conductivity in the electromagnetic case and a potential barrier in quantum physics (the tunnel effect). The analogy is mainly illustrated with geophysical examples of propagation of S (shear), P (compressional), TM (transverse-magnetic) and TE (transverse-electric) waves. The tunnel effect is obtained as a special case of viscoelastic waves at normal incidence.</p>
Highlights
The 19th century was a period when scientists had a global vision of science, making wide use of analogies between different field of physics, in particular the analogy between light and elastic waves to study the behaviour of light in matter
Theories describing wave phenomena - and diffusion - in different fields of physics consist in partial differential equations, which have identical or similar mathematical expressions
The equations hold for any layer thickness, not necessarily thin, their uses are relevant for thin layers, i.e., when the wavelength of the signal is much larger than the thickness
Summary
The 19th century was a period when scientists had a global vision of science, making wide use of analogies between different field of physics, in particular the analogy between light and elastic waves to study the behaviour of light in matter. Fresnel’s formulae and Maxwell’s equations were obtained from mathematical analogies with shear wave propagation and Hooke’s law, respectively [e.g., Carcione and Cavallini 1995, Carcione and Robinson 2002]. This practice dates back to the 17th century. An anisotropic elastic medium having orthorhombic symmetry, mathematically analogous to Fresnel’s crystal, exists This medium was found by Carcione and Helbig [2008], who obtained the differential equations describing the wave motion.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
