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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 (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.

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** Up:** Cunha: Elastic Modeling
** Previous:** Cunha: Elastic Modeling
Stanford Exploration Project

11/18/1997