Scattering of elastic waves in 2-D composite media I. Theory and test

Abstract

Localised regions in the earth's crust exhibiting complex variations of density and seismic wave velocities can be represented by random distribution of cavities, in a manner described by Matsunami (1983) for two-dimensional (2-D) media. In order to studt the multiple scattering of seismic waves propagating in such media, we develop an indirect boundary integral scheme with discretisation based on wave source distribution around the cavities. Numerical experiments using seven generic 2-D models and incident P, SV and SH plane waves, as well as explosive line sources, are carried out. These experiments are intended to both assess the accuracy of the method, and to examine the character of attenuation of the direct wave, coda waveforms, and travel time features that emerge from pure scattering (no intrinsic attenuation), computed in all cases for wavelengths comparable to the size of the heterogeneities. The wavefield computed for one cavity shows a remarkable diffracted wave that creeps around it, for all the incident waves, regardless of the shape of its cross-section. This wave contributes significantly to the multiple scattering caused by the direct and all reflected/converted waves in the presence of many cavities. For complex regions defined by random distribution of cavities, an explosive line source located below the region produces slight amplification of the horizontal component of the wavefield, apparently due to constructive interference, at observation points above the region, while the vertical component is strongly attenuated. The durations of the seismograms are about the same for observation points located towards both ends of the region. These results appear to be reversed when the source is above the region. In this case, the horizontal component is strongly attenuated, and the duration of the seismograms is significantly larger at observation points on the side of the incidence than at the opposite side, suggesting the dominant effect of backscattering. The amplitudes of the multiple scattered phases, the attenuation of the direct wave and the duration of the seismograms, appear to be larger when the line source is very near or within the heterogeneous region, than when it is outside. For the same geometry of the scattering region, the seismograms appear to be more complex and amplitudes of multiple scattered phases larger for a plane SH wave in a half-space.