The generalized SH-wave equation

We present a generalization of the SH-wave equa-tion 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 mecha-nisms. Anisotropic attenuation and velocity dispersion are guaranteed by choosing different relaxation func-tions 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 displace-ment 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 veloc-ity and attenuation curves