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We simulate SH wave scattering by 2-D parallel cracks using the finite difference method (FDM), instead of the popularly used boundary integral equation method (BIEM). Here special emphasis is put on simplicity; we apply a standard FDM (fourth-order velocity-stress scheme with a staggered grid) to media including tractionfree cracks, which are expressed by arrays of grid points with zero traction. Two types of accuracy tests based on comparison with a reliable BIEM, suggest that the present method gives practically sufficient accuracy, except for the wavefields in the vicinity of cracks, which can be well handled if the second-order FDM is used instead. As an application of this method, we also simulate wave propagation in media with randomly distributed cracks of the same length. We experimentally determine the attenuation and velocity dispersion induced by scattering from the synthetic seismograms, using a waveform averaging technique. It is shown that the results are well explained by a theory based on the Foldy approximation for crack densities of up to about 0.1. The presence of a free surface does not affect the validity of the theory. A preliminary experiment also suggests that the validity will not change even for multi-scale cracks.

Simulations of SH wave scattering due to cracks by the 2-D finite difference method