Simplifying 3-D migration operators
using Givens rotations

Steve Cole

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ABSTRACT

The pentadiagonal form of the 2-D Laplacian makes 3-D migration schemes inaccurate (with splitting) or expensive. Using Givens rotations, and assuming that velocity is constant or varies only with depth, it is easy and inexpensive to reduce the pentadiagonal system to a tridiagonal form, since the algorithm lends itself well to a parallel implementation. Unfortunately, for the case of lateral velocity variation, the matrix rapidly becomes less sparse as rotations are performed, making the method too expensive. But, even in the presence of lateral velocity variation, this scheme may be a useful preconditioner for other solution methods.