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International Journal of Geophysics
Volume 2012, Article ID 479492, 14 pages
Research Article

Three-Dimensional Complex Padé FD Migration: Splitting and Corrections

1Department of Petroleum Engineering, CEP/UNICAMP, 1303-970 Campinas, SP, Brazil
2DMA/IMECC, University of Campinas, 13083-859 Campinas, SP, Brazil
3Faculty of Geophysics, Federal University of Pará, 66075-110 Belém, PA, Brazil
4National Institute of Petroleum Geophysics (INCT-GP), Brazil

Received 6 January 2012; Accepted 28 February 2012

Academic Editor: Mauricio D. Sacchi

Copyright © 2012 D. Mondini et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Three-dimensional wave-equation migration techniques are still quite expensive because of the huge matrices that need to be inverted. Several techniques have been proposed to reduce this cost by splitting the full 3D problem into a sequence of 2D problems. To reduce errors, the Li correction is applied at regular multiples of depth extrapolation increment. We compare the performance of splitting techniques in wave propagation for 3D finite-difference (FD) migration in terms of image quality and computational cost. We study the behaviour of the complex Padé approximation in combination with two- and alternating four-way splitting, that is, splitting into the coordinate directions at one depth and the diagonal directions at the next depth level. We also extend the Li correction for use with the complex Padé expansion and diagonal directions. From numerical examples in inhomogeneous media, we conclude that alternate four-way splitting is the most cost-effective strategy to reduce numerical anisotropy in complex Padé 3D FD migration.