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# Introduction

Some important aspects of accurate finite-difference elastic modeling algorithms are the use of high-order differential operators, staggered grid computations, and a two-step implementation of the spatial operator by first obtaining the strains and then the stresses (Virieux, 1984, Dablain, 1986; Mora, 1986; Etgen, 1989). The high-order operators are required to avoid numerical anisotropy and dispersion, while the staggered scheme is important to allow the use of more accurate and stable operators, which have an even number of points, in a spatially synchronized way. One problem with these schemes is the lack of distinction between model and wavefield properties. The same differential operators are applied to the components of the wavefield and to the components of the stiffness tensor. This is appropriate for smooth models but not for blocky, discontinuous models, in which two-point operators are more suitable than larger operators for computing the derivatives of the elastic parameters of the model.

The method developed in Cunha (1991) observes this important distinction by completely decoupling the computation of stiffness derivatives from the computation of wavefield derivatives. I test here an improved version of this method which uses the equivalence relations defined in the algebra of Schoenberg and Muir (1989), and a modified version of the conventional staggered grid introduced in wave-equation modeling by Virieux (1984; 1986) to implement the discretization process. A complete description of this method, which is referred to as the dual-operator method, is given in Cunha (1992). This approach was efficiently implemented on a parallel platform and the resulting wavefields were compared with the analytical solution and with the results from other elastic modeling schemes. For the simple model tested the dual-operator method proved to be more accurate than the traditional finite-difference method, using operators of same order in time and space.

Next: DYNAMIC BEHAVIOR Up: Cunha: Elastic Modeling Previous: Cunha: Elastic Modeling
Stanford Exploration Project
11/18/1997