HR: 1340h
AN: S13A-0185    [Abstracts]
TI: Numerical dispersion, stability, and phase-speed for 3D time-domain finite-difference seismic wave propagation algorithms
AU: * Haney, M M
EM: mmhaney@sandia.gov
AF: Sandia National Laboratories, Geophysics Department P.O. Box 5800 MS 0750, Albuquerque, NM 87185-0750 United States
AU: Aldridge, D F
EM: dfaldri@sandia.gov
AF: Sandia National Laboratories, Geophysics Department P.O. Box 5800 MS 0750, Albuquerque, NM 87185-0750 United States
AU: Symons, N P
EM: npsymon@sandia.gov
AF: Sandia National Laboratories, Geophysics Department P.O. Box 5800 MS 0750, Albuquerque, NM 87185-0750 United States
AB: Numerical solution of partial differential equations by explicit, time-domain, finite-difference (FD) methods entails approximating temporal and spatial derivatives by discrete function differences. Thus, the solution of the difference equation will not be identical to the solution of the underlying differential equation. Solution accuracy degrades if temporal and spatial gridding intervals are too large. Overly coarse spatial gridding leads to spurious artifacts in the calculated results referred to as numerical dispersion, whereas coarse temporal sampling may produce numerical instability (manifest as unbounded growth in the calculations as FD timestepping proceeds). Quantitative conditions for minimizing dispersion and avoiding instability are developed by deriving the dispersion relation appropriate for the discrete difference equation (or coupled system of difference equations) under examination. A dispersion relation appropriate for FD solution of the 3D velocity-stress system of isotropic elastodynamics, on staggered temporal and spatial grids, is developed. The relation applies to either compressional or shear wave propagation, and reduces to the proper form for acoustic propagation in the limit of vanishing shear modulus. A stability condition and a plane-wave phase-speed formula follow as consequences of the dispersion relation. The mathematical procedure utilized for the derivation is a modern variant of classical von Neumann analysis, and involves a 4D discrete space/time Fourier transform of the nine, coupled, FD updating formulae for particle velocity vector and stress tensor components. The method is generalized to seismic wave propagation within anelastic and poroelastic media, as well as sound wave propagation within a uniformly-moving atmosphere. A significant extension of the approach yields a stability condition for wave propagation across an interface between dissimilar media with strong material contrast (e.g., the earth's surface, the seabed, salt/sediment contacts, underground air-filled cavities or voids, and two-phase porous media). Sandia National Laboratories is a multiprogram science and engineering facility operated by Sandia Corporation, a Lockheed-Martin company, for the United States Department of Energy under contract DE-AC04-94AL85000.
DE: 0920 Gravity methods (1219)
DE: 3215 Instability analysis
DE: 3285 Wave propagation (0689, 2487, 4275, 4455, 6934)
DE: 7260 Theory
DE: 7290 Computational seismology
SC: Seismology [S]
MN: Fall Meeting 2005