Abstract
This paper presents a cost‐effectiveness analysis of explicit Finite Difference (FD) methods for the numerical integration of the wave equation. Formal notions of computational cost (expressed in floating point operations) and numerical dispersion error are introduced. Restricting the analysis to leapfrog timemarching, for sake of simplicity, various spatial discrete differentiators are examined. For each scheme, by minimizing the cost at a given error threshold, a cost‐effective operating poin (time sampling rate and number of gridpoints per shortest wavelength) is obtained, which is remarkably different from the stability limit. Different schemes, each operated at its cost‐effective point, are then compared. High‐order dispersion‐bounded operators, in the sense of Holberg,1 are found to be competitive with the Pseudo‐spectral (PS) method. New optimal schemes improving over the Holberg’s spatial differentiators are introduced together with accurate expansions of the convolutional weights is terms of the design error threshold. It is also shown that the composition of two distinct Holberg’s operators of consecutive orders, with opposite phase properties, minimizes dispersion and yields cost‐effective schemes. Numerical experiments illustrate the suitability of the new methods for large‐scale wave‐equation seismic modelling. Copyright © 1995 John Wiley & Sons, Ltd
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