Cost-effective staggered numerical integration of the wave equation

Abstract

Finite-difference (FD) schemes for the numerical integration of the wave equation are generally designed with one of two criteria: (a) maximize the numerical accuracy order (as In the case of conventional FD operators); (b) minimize the simulation error of some physical feature of wave propagation (e.g. the dispersion relation) within a spectral frequency band (as introduced recently by Holberg). The analysis of cost-effectiveness for a required error bound of the second schemes has neglected the role played by time discretization in the overall accuracy. In this paper we define a computational cost for the numerical solution of wave equations, which includes the effect of approximate temporal differencing. For some representative schemes based on leap-frog time differencing we provide an optimal operating point (time sampling rate and number of grid points per shortest wavelength) which minimizes the computational cost for a given error threshold. We also introduce a new method for designing optimal operators for staggered schemes. The new FD operators are designed and their optimal operating point is found by minimizing the computational cost for a prescribed error bound. The cost of the proposed schemes is shown to be less than that of known FD operators and compares favorably with pseudo-spectral (PS) operators. Numerical simulations are presented to illustrate the effectiveness of the new operators. © 1989 Society of Exploration Geophysicists. All rights reserved.