HR: 1340h
AN: S23B-0303    [Abstracts]
TI: Scattering Attenuation And Dispersion Of {\it SH} Waves In 2-D Elastic Media With Densely Distributed Cracks
AU: * Murai, Y
EM: murai@eos.hokudai.ac.jp
AF: Institute of Seismology and Volcanology, Graduate School of Science, Hokkaido University, N-10 W-8, Kita-ku, Sapporo, 060-0810 Japan
AB: We compute the synthetic seismograms of multiply scattered {\it SH} waves in 2-D elastic media with densely distributed parallel cracks. We assume two spatial distributions; elastic media with periodic distribution of cracks in a zone and randomly distributed cracks in a rectangle bounded region. The calculated attenuation coefficient $Q^{-1}$ of the primary wave is directly proportional to the crack density in the ranges of $\nu a^2 \leq 0.05$, where $\nu$ and $a$ are the number density and half length of cracks, respectively. This is consistent with that obtained by a stochastic analysis based on Foldy's approximation. When cracks are distributed densely ($\nu a^2=0.075$ and 0.1), our result on $Q^{-1}$ still agrees with it for the random crack distribution models but appears to differ from it for the periodic distribution of cracks especially in the low wavenumber ranges. This suggests that the effect of multiple interactions among densely distributed cracks depends on not only the density but also the spatial distribution of cracks at low wavenumbers. The calculated phase velocity of the primary wave is consistent with that from the stochastic analysis in the ranges of $\nu a^2 \leq 0.1$ and does not depend on the spatial distribution of cracks. This suggests that the multiple crack interactions have a small effect to the phase velocity. Therefore the crack density can be estimated from the values of the phase velocity for the cases of densely distributed cracks even if the effect of the multiple crack interactions is not considered. We can clearly observe the reflected waves in the synthetic seismograms. The reflection coefficient shows a periodical behavior in low wavenumber ranges and its wavenumber dependence is identical to that of an anisotropic layer. The elastic constants and thickness of the cracked zone are estimated by fitting the reflection coefficients to those of a single anisotropic layer for both cases of normal and oblique incidence. The estimated thickness and elastic constants are shown to be reasonable. The elastic constants depend on a crack density, so that it is possible to estimate the density of cracks distributed in a fracture zone when the elastic constants are obtained from the frequency dependence of the reflection coefficients.
DE: 7260 Theory and modeling
DE: 5144 Wave attenuation
DE: 7203 Body wave propagation
SC: Seismology [S]
MN: 2004 AGU Fall Meeting