The generalized SH‐wave equation

Abstract

We present a generalization of the SH‐wave equation for anisotropic and dissipative media. The most general case in which SH‐waves are decoupled from P‐ and SV‐waves at all propagation angles is that of propagation in the plane of symmetry of a monoclinic medium. In the isotropic case, the SH constitutive equation involves only one elastic coefficient (the rigidity); here, three elastic coefficients are needed. Moreover, dissipation is introduced by using Boltzmann’s law based on several relaxation mechanisms. Anisotropic attenuation and velocity dispersion are guaranteed by choosing different relaxation functions for the principal axes. The wave equation, in the displacement and velocity‐stress formulations, is solved by using time‐domain spectral modeling techniques. The snapshots and seismograms of the computed displacement field show attenuation and anisotropy effects on traveltime (mainly because of anisotropy) and amplitude (because of combined anisotropy and dissipation), in agreement with the theoretical patterns of energy velocity and attenuation curves.