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 (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 guarantee the spatial synchronization of the two-step 1-D operators used in the strain-stress implementation. Using the exact solution of a discrete physical system (Cunha, 1991) as guide for the discretization, and following the equivalence relations defined in the algebra of Shoenberg and Muir (1989), I have derived an alternative one-step scheme, which avoids the intermediate computation of strains and does not require the use of the staggered grid for its implementation. The decoupling in the computations of the spatial derivatives of fields and elastic parameters obtained with this scheme allows the use of operators of different size (order). This is particularly important for modelingblocky models in which two-point operators aree more appropriate for computing the derivatives of the elastic constants than large operators.