Three-dimensional Complex Padé Fd Migration: Splitting And Corrections

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. © 2012 D. Mondini et al.2012Li Zhiming, Compensating finite-difference errors in 3-D migration and modeling (1991) Geophysics, 56 (10), pp. 1650-1660Claerbout, J.F., Toward a unified theory of reflector mapping (1971) Geophysics, 36, pp. 467-481Leontovich, M.A., Fock, V.A., Solution of the problem of propagation of electromagnetic waves along the earth's surface by the method of parabolic equation (1946) Journal of Experimental and Theoretical Physics, 16, pp. 557-573Aguilera-Navarro, M.C.K., Aguilera-Navarro, V.C., Ferreira, R.C., Teramon, N., Os aproximantes de Padé (1999) Matemática Universitária, 26-27, pp. 49-66Bamberger, A., Engquist, B., Halpern, L., Joly, P., Higher order paraxial wave equation approximations in heterogeneous media (1988) Journal of Applied Mathematics, 48, pp. 129-154Claerbout, J.F., (1985) Imaging the Earth's Interior, , Blackwell Scientific PublicationsAmazonas, D., Costa, J.C., Schleicher, J., Pestana, R., Wide-angle FD and FFD migration using complex Padé approximations (2007) Geophysics, 72 (6), pp. S215-S220. , DOI 10.1190/1.2785813Milinazzo, F.A., Zala, C.A., Brooke, G.H., Rational square-root approximations for parabolic equation algorithms (1997) Journal of the Acoustical Society of America, 101 (2), pp. 760-766. , DOI 10.1121/1.418038Brown, D.L., Applications of operator separation in reflection seismology (1983) Geophysics, 48 (3), pp. 288-294. , 2-s2.0-0020971841Ristow, D., Rühl, T., 3-D implicit finite-difference migration by multiway splitting (1997) Geophysics, 62 (2), pp. 554-567. , 2-s2.0-0031104122Lloyd, S., Least squares quantization in PCM (1982) IEEE Transactions on Information Theory, 28 (2), pp. 127-135. , 2-s2.0-0020102027Biondi, B., Stable wide-angle Fourier finite-difference downward extrapolation of 3-D wavefields (2002) Geophysics, 67 (3), pp. 872-882Costa, J.C., Mondini, D., Schleicher, J., Novais, A., A comparison of splitting techniques for 3D complex Padé Fourier finite difference migration (2011) International Journal of Geophysics, 2011, p. 12. , 714781 10.1155/2011/71478