QUASI-COMPRESSIONAL GROUP VELOCITY APPROXIMATION IN A GENERAL 21-PARAMETER WEAKLY ANISOTROPIC MEDIUM

摘要

Using a linearized approximation of the phase velocity, related to quasi-compressional (qP) wave propagation in a general 21-parameter weakly anisotropic medium, an approximate eikonal equation is constructed. The corresponding expression for the related group velocity is then derived. The degenerate (ellipsoidal) case of (qP) wave propagation in an anisotropic medium is explored and an exact group velocity expression obtained, together with the exact expressions for the slowness vector components, for this reduced case. This ellipsoidal group velocity is taken as the reference or background velocity surface. Slowness vector components are determined in terms of the group velocity vector angles. The reference group velocity is employed as a trial solution in the approximate eikonal equation to obtain an expression for group velocity in a general 21-parameter weakly anisotropic medium. Group velocity expressions, both approximate and exact, are numerically compared for anisotropic models that may be classified as weakly anisotropic or possibly more accurately, weakly anellipsoidal, as the background group velocity surface used is an ellipsoid.