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Cellular automata are arrays of discrete variables that follow local interaction rules and are capable of modeling many physical systems. A successful recent application has been in fluid dynamics, in which the Navier-Stokes equations are solved by creating a model in which space, time, and the velocity of particles are all discrete. Acoustic waves can be obtained from these fluid models when perturbations of the idealized fluid are small. Because seismic P-waves can be approximated by the acoustic wave equation, cellular automata can be adapted for seismic wave computations. This study shows how to model P-waves in two dimensions by using a modified form of the cellular-automaton rules for fluids. Propagation, reflection, and the computation of synthetic seismograms are demonstrated. Because no arithmetic calculations are needed and each lattice site can be updated simultaneously, this method is well-suited for implementation on massively parallel computers. Among the many potential advantages are unconditional stability, no round-off errors, and the possibility for devising novel approaches for modeling waves in inhomogeneous media.