This research project focuses on the development of improved techniques for solving the acoustic and elastic wave equations. The work has applications to seismic exploration, nondestructive testing, sonar interpretation, and other fields. The immediate aim is to enhance numerical methods for the so-called forward problem, in which initial-boundary data and material properties are assumed known. However, the research has the ultimate objective of using accurate forward solvers in an iterative fashion to attack the inverse problem, in which one seeks estimates of material properties (wave velocities) given observed responses of the medium to seismic waves. The project represents a continuation of earlier research at Wyoming, in which codes were developed for solving the acoustic and elastic wave equations in three space dimensions. The project addresses several numerical approaches. Among these are the representation of interfaces between strata having different wave velocities, the construction of spatial grids that will yield accurate discretizations in highly heterogeneous media, the design of efficient time-stepping schemes and associated numerical linear algebra, and the adaptation of numerical procedures to parallel- and vector architecture machines. Another important element of the project is the continued development of object-oriented graphics software to aid in the visualization of large-scale model results.
