Immersive boundary conditions: Theory, implementation, and examples

Many applications in computational geophysics involve the modeling of seismic wave propagation on a set of closely related subsurface models. In such scenarios, it is of interest to recompute the seismic wavefields locally (only in the regions of change), instead of in the full subsurface model. We have developed a method for local acoustic wavefield recomputation that makes it possible to fully immerse a local modeling domain within a larger domain of arbitrary extent and complexity, such that the wave propagation in the full domain is completely accounted for. The method enables wavefield modeling on much smaller local domains, while relying on the up-front generation of a large number of Green's functions and a wavefield extrapolation step at each time step of the simulation. A Kirchhoff-Helmholtz extrapolation integral is used to predict the interaction of the wavefield leaving the local domain with the exterior domain. The outward propagating wavefield and the wavefield reentering the local domain are applied as a boundary condition along the edges. Thanks to these dynamically calculated boundary conditions, all higher order long-range interactions between the two domains are fully accounted for. We have implemented the method in a conventional finite-difference time-domain scheme and determined that the locally calculated wavefields are equal to wavefields generated on the full domain to within numerical precision. The efficiency of the local modeling algorithm will greatly depend on the nature and size of the problem.