Multiple Scattering and Energy Transfer of Seismic Waves—Separation of Scattering Effect from Intrinsic Attenuation II. Application of the Theory to Hindu Kush Region

Abstract

In order to separate the scattering effect from intrinsic attenuation, we need a multiple scattering model for seismic wave propagation in random heterogeneous media. In paper I (Wu, 1985), radiative transfer theory is applied to seismic wave propagation and the energy density distribution (or the average intensity) in space for a point source is formulated in the frequency domain. It is possible to separate the scattering effect and the absorption based on the measured energy density distribution curves. In this paper, the data from digital recordings in the Hindu Kush region are used as an example of application of the theory. We also discuss two approximate solutions of coda envelope in the time domain: the single scattering approximation and the diffusion approximation and discuss the relation with the frequency domain solution. We point out that in only two cases can the apparent attenuation be expressed as an exponential decay form. One is the dark medium case, i.e., when B o ≫ 0.5, where B o = ŋ s /(ŋ s + ŋ a ) is the seismic albedo, ŋ s is the scattering coefficient, ŋ a is the absorption coefficient. In this case the absorption is dominant, the apparent attenuation b can be approximated by the coherent wave attenuation b = ŋ s +ŋ a The other case is the diffuse scattering regime, i.e., when B o ≫ 0.5 (bright medium) and R≫ L s ,t ≫ τs, where R and t are the propagation distance and lapse time, L s and τ s are the scattering lengths (mean free path) and scattering time (mean free time), respectively. However, in this case the envelope decays with a rate close to the intrinsic attenuation, while the intensity decreases with distance with a coefficient b≈d 0 (ŋ a +ŋ s ) ≈ d s ŋ s where d o d s are the diffusion multipliers (0 < d o , d s > 1).For the Hindu Kush region, by comparing the theory with data from two digital stations of 53 events distributed up to depths of 350 km, we find that the scattering is not the dominant factor for the measured apparent attenuation of S waves in the frequency range 2-20 Hz. From the observation on high frequency (f > 20 Hz) seismograms, we suggest the existence of a strong-scattering surface layer with fine scale heterogeneities in the crust, at least for this region.