Synthetic seismograms for SH waves in anelastic transversely isotropic media

Abstract

SUMMARY Following the first-principle procedure outlined by Buchen (1971a) and Borcherdt (1973), we describe the derivation of SH-wave propagation in a homogeneous transversely isotropic linear viscoelastic (HTILV) solid. A plane SH wave propagates with the frequency-dependent complex phase velocity: β2(ω) =β2h(ω) sin2b+β2v(ω) cos2b where βh and βv are complex shear-wave velocities perpendicular and parallel to the axis of symmetry of the medium and b is a complex angle that the complex wave vector makes with the axis. The energy flows in a direction governed by the propagation vector, attenuation vector and the rigidities. The attenuation angle between the propagation vector and the attenuation vector can be uniquely determined by the complex ray parameter at the saddle point of the complex traveltime function. Complex rays can be traced between source and receiver locations with intermediate coordinates being complex. By means of the method of steepest descent, the wavenumber integral representing the exact SH-wave field generated by a line source for the layered-medium problem can be approximated to give complex ray amplitudes for reflected and transmitted body waves. The factor accounting for cylindrical divergence is similar in form to that of the isotropic case. For a simple two half-spaces model, the complex ray result agrees well with the ω-k solution in regions away from the critical area. For pure SH-mode propagation through a planar HTILV multi-layered structure with 20 per cent velocity anisotropy in each layer (Qv= Qh), the reflected amplitudes in the two cases (transversely isotropic and isotropic) generally do not differ much, but traveltimes differ significantly. This suggests that one can, in the case we considered, neglect the effect of weak anisotropy on amplitudes, but not on propagation phase.