Gridding Requirements For Accurate Finite Difference Simulation

Finite difference simulation in heterogeneous models is subject to two kinds of error. The first type results in frequencydependent grid dispersion. High order schemes successfully control this well-known dispersive error. The second error type stems from misalignment of grids and model parameter discontinuity surfaces. This error is of first order (proportional to the grid spacing or time step) and is insensitive to scheme order. The study reported here examined the influence of this second error type in modeling variable density acoustic wave propagation using staggered grid schemes. The examples suggest that the grid-interface misalignment error can be quite large. Achieving accurate simulation output for such models appears to require a far larger number of gridpoints per wavelength than common rules, derived from homogeneous medium analysis, suggest.