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Elastic modeling of a spatially-discrete system can be formulated as
an eigenvalue decomposition problem. Using this formulation, the exact
solution can be obtained for an arbitrarily complex model, without
the need for time discretization. The unavoidable drawback of this
formulation is its prohibitively high computing time, which is
proportional to *N*^{3}, where *N* is the number of cells in the mesh.
Building up a discrete physical model has some advantages over the
usual numerical discretization of a continuous system.
If the physical model is solved exactly, then stability is guaranteed
since natural systems are always stable for impulsive sources.
In addition, the resulting 2-D differencing star tends to
cause less numerical anisotropy than the star obtained by
straightforward discretization.
An alternative solution in the time domain allows for an effective
implementation of the modeling scheme in a massively
parallel architecture machine.

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Stanford Exploration Project

12/18/1997