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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
modeling*blocky* models in which two-point operators aree more
appropriate for computing the derivatives of the elastic constants than
large operators.

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Stanford Exploration Project

12/18/1997