Poroelastic Wave Propagation With a 3D Velocity-Stress-Pressure Finite-Difference Algorithm
Abstract
Seismic wave propagation within a three-dimensional, heterogeneous, isotropic poroelastic medium is numerically simulated with an explicit, time-domain, finite-difference algorithm. A system of thirteen, coupled, first-order, partial differential equations is solved for the particle velocity vector components, the stress tensor components, and the pressure associated with solid and fluid constituents of the two-phase continuum. These thirteen dependent variables are stored on staggered temporal and spatial grids, analogous to the scheme utilized for solution of the conventional velocity-stress system of isotropic elastodynamics. Centered finite-difference operators possess 2nd-order accuracy in time and 4th-order accuracy in space. Seismological utility is enhanced by an optional stress-free boundary condition applied on a horizontal plane representing the earth's surface. Absorbing boundary conditions are imposed on the flanks of the 3D spatial grid via a simple wavefield amplitude taper approach. A massively parallel computational implementation, utilizing the spatial domain decomposition strategy, allows investigation of large-scale earth models and/or broadband wave propagation within reasonable execution times. Initial algorithm testing indicates that a point force density and/or moment density source activated within a poroelastic medium generates diverging fast and slow P waves (and possibly an S-wave)in accord with Biot theory. Solid and fluid particle velocities are in-phase for the fast P-wave, whereas they are out-of-phase for the slow P-wave. Conversions between all wave types occur during reflection and transmission at interfaces. Thus, although the slow P-wave is regarded as difficult to detect experimentally, its presence is strongly manifest within the complex of waves generated at a lithologic or fluid boundary. Very fine spatial and temporal gridding are required for high-fidelity representation of the slow P-wave, without inducing excessive numerical dispersion. However, this wave attenuates extremely rapidly when appreciable fluid viscosity (even for water) is assigned. 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.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2004
- Bibcode:
- 2004AGUFM.S31B1059A
- Keywords:
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- 7260 Theory and modeling;
- 5114 Permeability and porosity;
- 5144 Wave attenuation;
- 7203 Body wave propagation