Computational Memory Reduction for Finite-Difference Elastic Wave Propagation Algorithms

Numerical simulation of seismic wave propagation in three spatial dimensions may require substantial computational memory and execution time. A 3D time-domain finite-difference (FD) algorithm that solves the velocity-stress equations of isotropic elastodynamics requires at least 48N bytes of memory, where N is the number of spatial gridpoints. The earth model (P and S wavespeeds, mass density) is stored with 12N bytes and the elastic wavefield (3 velocity vector components and 6 independent stress tensor components) is stored with 36N bytes. In this study, three strategies for reducing computational memory demand are examined. In the first approach, an earth model is represented by a finite number of homogeneous units or formations. The 3D spatial distribution of material properties is described by a single, integer-valued, pointer array. If 1-byte integer encoding is sufficient, the earth model is stored in N+12M bytes, where M is the number of model units. A second approach is applicable to earth models that are stratified in one predominant direction. The two spatial grid intervals normal to this direction may enlarged, yielding an elementary FD grid cell that is rectangular rather than cubic. This leads to a reduction in storage for both the earth model and the wavefield components. Finally, a non-uniform grid FD implementation of the velocity-stress equations achieves substantial memory savings (for both model and wavefield) in portions of the 3D grid that contain high seismic velocities. Such high velocity zones are spatially oversampled with conventional uniform grid FD algorithms. Although each approach yields a reduction in memory, associated limitations and/or pitfalls should be recognized. Method 1 restricts material parameter variability; method 2 can enhance numerical dispersion and anisotropy, especially for rectangular grid cells with large aspect ratio. Finally, method 3 involves increased in code complexity, for both wave propagation and earth model construction algorithms. Representative synthetic seismograms demonstrate the feasibility and the limitations of each approach. \it{Sandia National Laboratories is a multiprogram science and engineering facility operated by Sandia Corporation, a Lockheed-Martin company, for the US Department of Energy under contract DE-AC04-94AL85000.}