HR: 1340h
AN: S23B-0305    [Abstracts]
TI: Is Markov Approximation Valid for Transmission Fluctuation Problems?
AU: * Zheng, Y
EM: yzheng@es.ucsc.edu
AF: IGPP, University of California, Santa Cruz, 1156 High Street, Santa Cruz, CA 95064 United States
AB: We know that the Markov approximation is a widely-used and a key approximation in the theoretical developments for the wave propagation in random media. In seismology, transmission fluctuation functions are used to infer the statistical structure of the heterogeneities in the Earth mantle. The scale and the pattern of the heterogeneities in the mantle will bear important implications for the mantle material physical properties and even the earth internal dynamics. However, recent numerical simulations and field studies have found some discrepancies with the theoretical predictions for the phase (travel-time) fluctuations across a seismic array of the teleseismic waves. In order to confirm this disagreement and to find the causes that account for the discrepancy, we have carried out extensive numerical experiments and theoretical analysis. The validities of the basic approximations in the theory (Chernov, 1960; Wu and Flatte, 1990), such as the Rytov approximation, one-way approximation, parabolic approximation, and the Markov approximation, have been examined and calibrated. Numerical simulations using full-wave finite difference, wavelet-based full-wave simulations, one-way propagators (generalized screen propagators), Rytov simulations, and parabolic simulations have been conducted to help evaluate the importance of each approximation. We have found that the Rytov and the one-way approximations are generally valid when the medium perturbation is not too large, but a valid parabolic approximation requires a medium with really small perturbations; nevertheless the validities of these approximations are also functions of the wavelengths and the heterogeneity scales. Based on our preliminary study, it seems that the Markov approximation is the most important factor in producing the discrepancy between the theory and the valid numerical experiments. In this presentation, we will isolate and discuss the influences of different approximations in the theoretical derivation and the validity of the Markov approximation in the calculation of the phase fluctuation functions for the transmitted waves.
DE: 7260 Theory and modeling
DE: 7200 SEISMOLOGY
DE: 7203 Body wave propagation
SC: Seismology [S]
MN: 2004 AGU Fall Meeting