Time domain solution for multiple scattering and the coda envelopes

This article summarizes work on multiple scattering based on models of media with randomly distributed scatterers. The scatterers are isotropic and statistically uniform. Measuring distance in terms of mean-free pathL_s and time in terms of the mean-free timesL_s/V, whereV is the velocity of scattered waves, we have more convenient dimensionless distance and time. It can be shown that after the dimensionless time equals 0.65 energy contributed from multiple scattering becomes predominant. Thus the later coda reflects the effect of multiple scattering rather than single scattering. Treating the seismic record, including starting and tail parts, as a whole, the diffusion theory predicts that at a dense distribution of scatterers and a small distance between source and receiver, codas reflect mainly intrinsicQ_i. Of course, this conclusion is coincident with the presumption of the diffusion theory,Q_s>Q_i. However, from a new integral equation of multiple scattering, which deals with the scattered waves and primary waves separately, the conclusion is similar but clearer. This article quotes the new expression for coda energy in two-dimensional space. It shows that if the receiver is close to the source, the coda decay reflects only intrinsicQ_i, then as the distance increases, effects of scatteringQ_s, are involved in the decay feature. The theoretical plots of coda decay show that it seems in most cases in the earthQ_i should not be smaller than one tenth ofQ_s.Project Sponsored by the Joint Earthquake Science Foundation of China.