Scattering Theory for Short-Period Seismic Waves : Velocity Shift and Envelopes in Random Media

Abstract

This paper deals with the stochastic scattering theory for short-period seismic waves in random media. The stochastic approaches to simulate the seismic wave propagation in the heterogeneous lithosphere was employed by K. Aki in seismology in 1970s. His pioneering studies proved that stochastic approaches are very useful for understanding short-period seismic wavefield which is usually too complicated to simulate by deterministic approaches. Numerous researches have since employed stochastic methods to study short-period seismograms. H. Sato and his colleagues have greatly contributed to the development of the scattering theory. Analyses of seismograms based on the theory have revealed that the random inhomogeneity in the lithosphere is well characterized by a power-law spectrum, with the regional variation related to seismotectonic conditions. Recent observations and advanced data analyses, however, are requiring more development of the scattering theory to simulate seismic wave propagation not only in isotropic random media but also in anisotropic random media. This paper covers multiple-forward scattering theories for velocity shift and seismogram envelopes. The achievement of the scattering theory in isotropic random media and the recent progress in anisotropic random media are reported.