Artículos de revistas
Iterative Methods For 3d Implicit Finite-difference Migration Using The Complex Padé Approximation
Registro en:
Journal Of Geophysics And Engineering. , v. 10, n. 4, p. - , 2013.
17422132
10.1088/1742-2132/10/4/045011
2-s2.0-84881485784
Autor
Costa C.A.N.
Campos I.S.
Costa J.C.
Neto F.A.
Schleicher J.
Novais A.
Institución
Resumen
Conventional implementations of 3D finite-difference (FD) migration use splitting techniques to accelerate performance and save computational cost. However, such techniques are plagued with numerical anisotropy that jeopardises the correct positioning of dipping reflectors in the directions not used for the operator splitting. We implement 3D downward continuation FD migration without splitting using a complex Padé approximation. In this way, the numerical anisotropy is eliminated at the expense of a computationally more intensive solution of a large-band linear system. We compare the performance of the iterative stabilized biconjugate gradient (BICGSTAB) and that of the multifrontal massively parallel direct solver (MUMPS). It turns out that the use of the complex Padé approximation not only stabilizes the solution, but also acts as an effective preconditioner for the BICGSTAB algorithm, reducing the number of iterations as compared to the implementation using the real Padé expansion. As a consequence, the iterative BICGSTAB method is more efficient than the direct MUMPS method when solving a single term in the Padé expansion. The results of both algorithms, here evaluated by computing the migration impulse response in the SEG/EAGE salt model, are of comparable quality. © 2013 Sinopec Geophysical Research Institute. 10 4
Amazonas, 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 10.1190/1.2785813 Amestoy, P.R., Duff, I.S., Koster, J., L'Excellent, J.Y., A fully asynchronous multifrontal solver using distributed dynamic scheduling (2001) SIAM J. Matrix Anal. Appl., 23 (1), pp. 15-41. , 10.1137/S0895479899358194 0895-4798 Amestoy, P.R., Guermouche, A., L'Excellent, J.-Y., Pralet, S., Hybrid scheduling for the parallel solution of linear systems (2006) Parallel Computing, 32 (2), pp. 136-156. , DOI 10.1016/j.parco.2005.07.004, PII S0167819105001328, Parallel Matrix Algorithms and Applications (PMAA '04) Aminzadeh, F., Burkhard, N., Kunz, T., Nicoletis, L., Rocca, F., 3D modeling project: 3rd report (1995) Learn. Edge, 14 (2), pp. 125-128. , 10.1190/1.1437102 1070-485X Bamberger, A., Engquist, B., Halpern, L., Joly, P., Higher order paraxial wave equation approximations in heterogeneous media (1988) SIAM J. Appl. Math., 48 (1), pp. 129-154. , 10.1137/0148006 0036-1399 Brown, C.L., Application of operator separation in reflection seismology (1983) Geophysics, 48 (3), pp. 288-294. , 10.1190/1.1441468 0016-8033 Claerbout, J.F., (1985) Imaging the Earth's Interior Cole, S., (1989) Stanford Exploration Project Report Costa, J.C., Mondini, D., Schleicher, J., Novais, A., A comparison of splitting techniques for 3D complex Padé Fourier finite difference migration (2011) Int. J. Geophys., 2011. , 714781 Fei, T., Etgen, J., Domain decomposition for 3D finite-difference depth extrapolation (2002) 72nd Annu. Int. Meeting SEG Technical Program Expanded Abstracts, pp. 1160-1163 Iserles, A., (1996) A First Course in the Numerical Analysis of Differential Equations Kao, J.C., Li, G., Yang, C.W., Preconditioned iterative 3-D finite-difference depth migration or modeling on the CRAY T3D massively parallel processors (1993) 1993 SEG Annu. Meeting: SEG Technical Program Expanded Abstracts, pp. 185-188 Li Zhiming, Compensating finite-difference errors in 3-D migration and modeling (1991) Geophysics, 56 (10), pp. 1650-1660 Milinazzo, 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 10.1121/1.418038 Mondini, D., Costa, J.C., Schleicher, J., Novais, A., Three-dimensional complex Padé FD migration: Splitting and corrections (2012) Int. J. Geophys., 2012. , 479492 Nichols, D., (1997) Stanford Exploration Project Report Rickett, J., Claerbout, J., Fomel, S., Implicit 3D depth migration by wavefield extrapolation with helical boundary conditions (1998) 68th Annu. Int. Meeting: SEG Technical Program Expanded Abstracts, pp. 1124-1127 Ristow, D., Rühl, T.D., 3D implicit finite-difference migration by multiway splitting (1997) Geophysics, 62 (2), pp. 554-567. , 10.1190/1.1444165 0016-8033 Van Der Vorst, H.A., Bi-CGSTAB: A fast and smoothly converging variant of BI-CG for nonsymmetric linear systems (1992) SIAM J. Sci. Stat. Comput., 13 (2), pp. 631-644. , 10.1137/0913035 0196-5204 Wang, Y., ADI plus interpolation: Accurate finite-difference solution to 3D paraxial wave equation (2001) Geophysical Prospecting, 49 (5), pp. 547-556. , DOI 10.1046/j.1365-2478.2001.00278.x Zhang, G., Zhang, Y., Zhou, H., Helical finite-difference schemes for 3D depth migration (2000) 70th Annu. Int. Meeting: SEG Technical Program Expanded Abstracts, pp. 862-865 Zhang, L., Hua, B., Calandra, H., 3D Fourier finite difference anisotropic depth migration (2005) SEG Technical Program Expanded Abstracts, 24, pp. 1914-1917. , 10.1190/1.2148079 Zhang, L., Rector, J.W., Hoversten, G.M., Split-step complex Padé migration (2003) J. Seismic Explor., 12, pp. 229-236 Zhang, L., Rector, J.W., Hoversten, G.M., Fomel, S., Split-step complex Padé-Fourier depth migration (2004) SEG Technical Program Expanded Abstracts, 23, pp. 989-992 Zhang, L., Rector III, J.W., Hoversten, G.M., Fomel, S., Split-step complex Padé-Fourier depth migration (2007) Geophysical Journal International, 171 (3), pp. 1308-1313. , DOI 10.1111/j.1365-246X.2007.03610.x