HR: 09:30h
AN: S31E-07    [Abstracts]
TI: Multi-scale issues and two scale homogenization solutions for the direct and inverse problems in seismology for layered earth model and beyond.
AU: * Capdeville, Y
EM: capdevil@ipgp.jussieu.fr
AF: Institut de Physique du Globe de Paris,CNRS, Équipe de sismologie, Case 89 4 place Jussieu, T24-14, 4eme, Paris Cedex 05, 75252, France
AU: Guillot, L
EM: guillot@ipgp.jussieu.fr
AF: Institut de Physique du Globe de Paris,CNRS, Équipe de sismologie, Case 89 4 place Jussieu, T24-14, 4eme, Paris Cedex 05, 75252, France
AU: Marigo, J
EM: marigo@lmm.jussieu.fr
AF: Laboratoire de Modèlisation en Mécanique, UMR7607, 4 place Jussieu, Paris Cedex 05, 75252, France
AB: In many cases, in the seismic wave propagation modeling context, scales much smaller than the minimum wavelength are present in the earth model we wish to propagate in. For many numerical methods these small scales are a challenge leading to high numerical cost. The purpose of the work presented here is to understand and to build the effective medium and equations allowing to average the small scales of the original medium without losing the accuracy of the wavefield computation. We show that high order two scale homogenization provides a promising solution to this king of problem. The presentation will be mostly limited to the layered model case. In that case, it appears that the order 0 homogenization gives the result that was obtained by Backus in 1962 which implies that order 0 homogenized model is transversely isotropic even though the original model is isotropic. It appears the order 0 is not enough to obtain surface wave with correct group and phase velocities and that higher order homogenization terms up to 2 are often required, which implies to modify the wave equation and the boundary conditions. We show how to extend the theory from the periodic case to the non-periodic case. Examples in periodic and non-periodic medium are given. Applications to numerical method like the spectral element method as well as preliminary results of homogenization in media varying rapidly in all direction will be presented. The implication of this work on tomography parameterization will be discussed.
DE: 7255 Surface waves and free oscillations
DE: 7260 Theory
DE: 7270 Tomography (6982, 8180)
DE: 7290 Computational seismology
SC: Seismology [S]
MN: 2007 Fall Meeting