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This paper reviews the application of the boundary integral method to measure scattering and attenuation of high-frequency seismic waves in a deterministic manner. While many numerical approaches such as a finite difference method deal with media with continuous velocity fluctuations, we choose boundary methods because the observed nature of scattering of high-frequency seismic waves such as coda waves is attributed mainly to small-scale heterogeneities characterized by irregular boundaries with strong impedance contrast. First, basic formulations for wavefield in media with many cavities as heterogeneities are presented. Accuracy and numerical stability are checked with simple models, followed by models to simulate wave field in random media. With stationary random media, we investigate frequency dependencies of both the scattering attenuation and the temporal attenuation of coda. Finally, we calculate seismograms in media with localized heterogeneities and point out many new characteristics not observed for stationary random media. For example, there is a spectral peak of scattered waves whose frequency corresponds to the entire spatial extent of heterogeneities, in addition to the original spectral peak for each heterogeneity. In the near future, this approach should be extended into realistic 3-D and layered media, together with any imaging technique including effects of non-isotropic and multiple scattering, in order to make more quantitative comparison with observed seismograms.

Scattering and Attenuation of High-frequency Seismic Waves Using Synthetic Seismograms by the Boundary Integral Method