HR: 1340h
AN: S43B-1322    [Abstracts]
TI: Analytical Computation of Effective Grid Parameters for the Finite-Difference Seismic Waveform Modeling With the PREM, IASP91, SP6, and AK135
AU: * Toyokuni, G
EM: toyokuni@geo.kyushu-u.ac.jp
AF: Department of Earth and Planetary Sciences, Kyushu University, 6-10-1 Hakozaki, Higashi- ku, Fukuoka, 812-8581, Japan
AU: Takenaka, H
EM: takenaka@geo.kyushu-u.ac.jp
AF: Department of Earth and Planetary Sciences, Kyushu University, 6-10-1 Hakozaki, Higashi- ku, Fukuoka, 812-8581, Japan
AB: We propose a method to obtain effective grid parameters for the finite-difference (FD) method with standard Earth models using analytical ways. In spite of the broad use of the heterogeneous FD formulation for seismic waveform modeling, accurate treatment of material discontinuities inside the grid cells has been a serious problem for many years. One possible way to solve this problem is to introduce effective grid elastic moduli and densities (effective parameters) calculated by the volume harmonic averaging of elastic moduli and volume arithmetic averaging of density in grid cells. This scheme enables us to put a material discontinuity into an arbitrary position in the spatial grids. Most of the methods used for synthetic seismogram calculation today receives the blessing of the standard Earth models, such as the PREM, IASP91, SP6, and AK135, represented as functions of normalized radius. For the FD computation of seismic waveform with such models, we first need accurate treatment of material discontinuities in radius. This study provides a numerical scheme for analytical calculations of the effective parameters for an arbitrary spatial grids in radial direction as to these major four standard Earth models making the best use of their functional features. This scheme can analytically obtain the integral volume averages through partial fraction decompositions (PFDs) and integral formulae. We have developed a FORTRAN subroutine to perform the computations, which is opened to utilization in a large variety of FD schemes ranging from 1-D to 3-D, with conventional- and staggered-grids. In the presentation, we show some numerical examples displaying the accuracy of the FD synthetics simulated with the analytical effective parameters.
DE: 0500 COMPUTATIONAL GEOPHYSICS (3200, 3252, 7833)
DE: 0560 Numerical solutions (4255)
DE: 3200 MATHEMATICAL GEOPHYSICS (0500, 4400, 7833)
DE: 7200 SEISMOLOGY
DE: 7290 Computational seismology
SC: Seismology [S]
MN: 2007 Fall Meeting