HR: 1340h
AN: S13A-0183 [Abstracts]
TI: A New Accurate Finite-Difference Scheme Based on the Optimally Accurate Operators and
Boundary-Condition Consistent Material Parameterization
AU: Kristek, J
EM: kristek@fmph.uniba.sk
AF: Comenius University, Mlynska dolina F1, Bratislava, 84248
Slovakia (Slovak Republic)
AU: * Moczo, P
EM: moczo@fmph.uniba.sk
AF: Comenius University, Mlynska dolina F1, Bratislava, 84248
Slovakia (Slovak Republic)
AU: Galis, M
EM: mgalis@fmph.uniba.sk
AF: Comenius University, Mlynska dolina F1, Bratislava, 84248
Slovakia (Slovak Republic)
AB:
Geller and Takeuchi (1995) developed optimally accurate finite-difference (FD) operators. The operators minimize the error of
the numerical solution of the discretized equation of motion. The criterion for obtaining the optimally accurate operators
requires that the leading term of the truncation error of the discretized homogeneous (without body-force term) equation of
motion (that is if operand is an eigenfunction and frequency is equal to eigenfrequency) is zero. Consequently, the optimally
accurate operators satisfy (up to the leading term of the truncation error) homogeneous equation of motion. The grid
dispersion of an optimally accurate FD scheme is significantly smaller than that of a standard FD scheme.
A heterogeneous FD scheme cannot be anything else than a FD approximation to the heterogeneous formulation of the equation of
motion (the same form of the equation for a point away from a material discontinuity and a point at the material
discontinuity). If an optimally accurate FD scheme for heterogeneous media is to be obtained, the optimally accurate
operators have to be applied to the heterogeneous formulation of the equation of motion.
Moczo et al. (2002) found a heterogeneous formulation and developed a FD scheme based on standard staggered-grid 4th-order
operators. The scheme is capable to sense both smooth material heterogeneity and material discontinuity at any position in a
spatial grid.
We present a new FD scheme that combines optimally accurate operators of Geller and Takeuchi (1995) with a material
parameterization of Moczo et al. (2002). Models of a single material discontinuity, interior constant-velocity layer, and
interior layer with the velocity gradient were calculated with the new scheme, conventional-operator scheme and analytically.
Numerical results clearly isolate and demonstrate effects of the boundary and grid dispersion. The results demonstrate
significant accuracy improvement compared to previous FD schemes.
DE: 7200 SEISMOLOGY
DE: 7203 Body waves
DE: 7260 Theory
DE: 7290 Computational seismology
SC: Seismology [S]
MN: Fall Meeting 2005