A ONE-WAY WAVE EQUATION FOR MODELLING VARIATIONS IN SEISMIC WAVEFORMS DUE TO ELASTIC ANISOTROPY

Abstract

A new one-way wave equation for 3-D anisotropic elastic media and its finite-difference implementation are described. Backscattering is neglected, but the method should provide a sufficiently accurate, efficient (slower than ray theory, faster than full wave equation finite differences) and robust simulation of the primary wave(s) passing through a region of variable and possibly strong anisotropy. In particular, frequency-dependent wave-type coupling and the effects of rapidly rotating polarization eigenvectors will be included. Example waveforms are presented for rock elasticities representative of mantle, crustal and basin-scale applications. These have been computed only for homogeneous regions, which facilitates comparison with a separation-of-variables reference solution. Nevertheless, seemingly characteristic waveform effects associated with conical points, or acoustic axes, are observed and these effects should only be modified in degree rather than style by smooth parameter gradients (e.g. in the upper mantle). These characteristics include: merging/splitting pulses, sometimes resulting in simple pulse broadening; wave-front ‘tearing’; gaps/lacunae/polarity reversals in the ‘anomalous’ component arising from the eigenpolarization rotation; and incipient Hilbert transform-like first-motion changes due to indentations of the slow shear-wave slowness sheet.