Radiation from point sources in general anisotropic media

Abstract

SUMMARY A procedure to evaluate the geometrical properties of the slowness surface for arbitrary anisotropic media is presented. This allows us to use results for computing the displacement field from point sources in general anisotropic media utilizing the Gaussian curvature of the slowness surface of the considered waves. Since the formulae used are based on high frequency asymptotics the procedure gives reliable results as long as no parabolic points of the slowness surface are encountered. Radiation patterns of point sources for models representing rocks in the crust and upper mantle are presented and discussed. The radiation from point sources in anisotropic models is compared with the radiation from point sources in average isotropic models to emphasize the differences. Anisotropy is either caused by aligned cracks (crustal rocks) or by aligned olivine crystals (upper mantle rocks). Considering models of aligned cracks differing only in the physical parameters of the crack material (water or gas) significantly different radiation patterns are obtained. Models with wet cracks exhibit focusing of quasi S-wave energy for some directions whereas this effect is not observed for the corresponding model with dry cracks. The quasi S-wave radiation pattern from explosions are multilobed and the wet crack models exhibit more lobes than the dry crack models. The radiation of single forces in olivine shows strong energy focusing (wave tuning) of quasi S waves, however, for realistic compositions of upper mantle rocks with some 10 per cent of preferentially orientated olivine this wave tuning is less pronounced.