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Generalized Full Wavefield Modeling: Beyond Neumann
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, 80th EAGE Conference and Exhibition 2018, Jun 2018, Volume 2018, p.1 - 5
Abstract
Summary
Generalized Full Wavefield Modeling is a directional modeling method that incorporates reflection and transmission operators. It employs Neumann’s method, an iterative inversion scheme for obtaining the solutions (the wavefields), which is, nonetheless, well-known not to be necessarily convergent for all situations. Thus, we use two methods that represent a generalization of the Neumann’s solution; one is stationary overrelaxation, and the other is successive overrelaxation. Both methods attempt to scale the wavefield residual such that it does not grow with increasing number of iterations. One method, stationary overrelaxation, uses a constant scale factor while the other, successive overrelaxation, varies the scale factor with iterations. A numerical example shows clearly that successive overrelaxation yields a stable solution, unlike the other two methods (Neumann’s and stationary overrelaxation), since it forces the residual to be reducing in each iteration.
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