Prospect of the Study on Seismic-wave Scattering

Abstract

Scattering phenomena of seismic waves give us lots of physical information about the heterogeneous structure of the Earth. Discrete scatterers such as cracks, voids and inclusions are known to be ubiquitous in the Earth's crust. Diverse methods of mathematical analyses have been developed on the scattering of elastic waves for isolated scatterers. These analyses seem to be quite satisfactory while there are both advantages and disadvantages in each method. Recent attention is directed to the analysis of densely distributed scatterers. We have to rely on numerical treatments in these cases and many of the studies are based on the boundary integral equation method. It is still difficult, in spite of advance in computer technology, to assume many scatterers enough for reliable statistical analysis of scattered elastic waves. In addition, detailed investigation of crack response to transmission waves is required under the compressive load condition for quantitative evaluation of the scattering in the crust since most researchers have developed crack models on the assumption of non-compressive load. Random fluctuations of elastic parameters are often used for modeling the heterogeneous Earth medium instead of a distribution of cracks and voids. Not only the coda wave envelopes but also the whole seismogram envelopes of local earthquakes are explained by using the Born approximation for wave scattering through random media. The broadening of S-wave envelopes can be explained by diffraction and/or multiple forward scattering due to velocity inhomogeneities on the basis of the stochastic treatment of wave equation. As a phenomenological approach, the radiative transfer theory has been developed to explain seismogram envelopes of local earthquakes in high frequencies. This theory well describes the energy transport through media having a constant background velocity and a random distribution of scatterers disregarding phase information. From the coda analysis, the scattering coefficient characterizing the scattering power per unit volume has been measured in the world. The inversion method by using the envelope derived from the radiative transfer theory as a Green function is useful especially for the study of highfrequency energy radiation from earthquake faults. It is necessary to develop this theory to adopt the depth dependence of scattering coefficient and intrinsic absorption in addition to the depth dependence of background velocity. We note that stochastic and deterministic approaches are complementary to each other for imaging the heterogeneity of the Earth and the earthquake rupture process in a broad band frequency range.