HR: 1340h
AN: S53B-1260    [Abstracts]
TI: Scattering Attenuation Due to Weak Discrete Inhomogeneities: Comparison of the Born and Foldy Approximations
AU: * Kawahara, J
EM: junk@mx.ibaraki.ac.jp
AF: Faculty of Science, Ibaraki University, 2-1-1 Bunkyo, Mito, 310-8512, Japan
AB: There are two approaches for predicting scattering attenuation due to randomly inhomogeneous media. One approach models the media by weak (and usually continuous) perturbation of material properties; the resultant scattering loss is evaluated using the Born approximation. The other treats media with randomly distributed discrete inhomogeneities, such as inclusions and cracks; the first-order solution of the attenuation was obtained by Foldy (1945). Despite the different appearances of the both model media, the Born approximation could be also applied to the inclusions, if the autocorrelation functions for them would be given. In the case of the sparse distributions and the low material contrasts between the inclusions and the matrices, the both approaches would yield virtually the same results. The present study confirms this inference in cases of simple-shaped inclusions, for which the Foldy approximation solutions are analytically obtained. The traveltime correction is not considered here. We first treat the SH wave scattering due to 2-D circular inclusions with the same size. We assume that the S- wave velocity of the matrix is c₀, that of a half of the inclusions is c₀(1+ξ), and that of the rest is c₀(1-ξ), with 0<ξ\ll1. The density perturbation is made proportional to ξ. We also assume the sparse distribution to make the Foldy approximation reliable. The Born approximation solution is evaluated using the autocorrelation function taken from Stoyan et al. (1995). It is shown that the scattering Q values based on the both approximations are highly consistent within the Rayleigh-Gans scattering regime (kaξ\ll1; ka is the wavenumber multiplied by the inclusion radius), as expected. Relying on the Foldy approximation, one may conclude that the Born approximation is approximately valid up to ka~1/ξ and breaks down beyond it. In a special case with density perturbation only (causing no traveltime fluctuation), however, the Born approximations is valid for any ka. We next extend the model to 3-D (spherical inclusions with P-wave velocity perturbation added) and evaluate the scattering attenuation of P waves due to them. The results based on the both approximations are again highly consistent within the Rayleigh-Gans scattering regime, implying the generality of this feature.
DE: 3285 Wave propagation (0689, 2487, 4275, 4455, 6934)
DE: 5144 Wave attenuation
DE: 7200 SEISMOLOGY
DE: 7203 Body waves
DE: 7260 Theory
SC: Seismology [S]
MN: 2007 Fall Meeting