3-D depth migration by a predictor-corrector method

Dave Nichols

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ABSTRACT

3-D depth migration can be cast as an explicit or implicit finite difference problem. The explicit problem is cheap to solve, but unstable. The stable implicit problem can be solved by direct or iterative methods. Direct methods are expensive and iterative methods are slow to converge at low frequencies. I experiment with the use of a predictor-corrector method, using iterative refinement of an approximate solution to the implicit problem. The approximate solution is obtained by solving the explicit problem. The iterative, conjugate gradient method is still slow to converge at low frequencies. A preconditioned conjugate gradient method would converge faster.