Application of cellular automata modeling to seismic elastodynamics

Abstract

This article details application of a physics-based cellular automata (CA) computational approach to model seismic events in an idealized linear-elastic medium. Application of rectangular-celled CA to the seismic problem is shown to yield discrete equations equivalent to the centered-difference finite difference (FD) approach. However, it is emphasized that the discrete equations are arrived at from the ‘bottom up’ using local rules vice ‘top-down’ discretization of global partial differential equations. A further distinction between the two methods concerns the location of stresses and its impact on boundary conditions: the CA approach assigns stresses to the cell faces while the FD approach assigns stress collocated with displacement components at a single node. These differences may provide important perspective on modeling arbitrary geometry with a finite difference-like approach based on cell assembly, similar to finite element analysis. Implementation of the CA paradigm using autonomous, local cells fits naturally with object-oriented programming practices and lends itself readily to distributed computing. Results are provided for an example ground-shock simulation in which a differentiated Gaussian pulse acts on the surface of a linear-elastic half-space. The CA perspective suggests a simple treatment for the free-surface boundary condition. Comparison of the computed pressure, shear, and surface waves to those computed using a staggered-grid finite difference approach demonstrates very good agreement. In addition, the simulation results suggest that the CA approach may exhibit less ‘ringing’ as waves pass, and more symmetry in left-ward and right-ward moving waves. Future directions exploiting attractive attributes of the CA approach are suggested, to include large-scale simulation, multi-resolution analysis, and coupled-field modeling.