Massively parallel structured direct solver for equations describing time-harmonic qP-polarized waves in TTI media

Geophysics

Volumn 77, Issue 3, 2012, Pages

  Wang, Shen ^a   Xia, Jianlin ^a   De Hoop, Maarten V ^a   Li, Xiaoye S ^b  

^a PURDUE UNIVERSITY   (United States)

^b LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

Author keywords

3D; Anisotropy; Finite difference; Wave equation

Indexed keywords

ANISOTROPIC MEDIA; DISSECTION; DOMAIN DECOMPOSITION METHODS; FINITE DIFFERENCE METHOD; MATHEMATICAL OPERATORS; WAVE EQUATIONS; ANISOTROPY;

APPROXIMATE SOLUTION; FINITE DIFFERENCE SCHEME; FULL-WAVEFORM INVERSION; HIERARCHICALLY SEMISEPARABLE MATRIXES; HIGHER ORDER ACCURACY; PARTIAL DIFFERENTIAL OPERATORS; STRUCTURED DIRECT SOLVERS; TRANSVERSELY ISOTROPIC;

ANISOTROPY; FINITE DIFFERENCE METHOD;

ACCURACY ASSESSMENT; DATA INVERSION; FINITE DIFFERENCE METHOD; HARMONIC ANALYSIS; NUMERICAL MODEL; P-WAVE; TIME SERIES ANALYSIS; WAVE EQUATION;

EID: 84861696160     PISSN: 00168033     EISSN: None     Source Type: Journal    
DOI: 10.1190/geo2011-0163.1     Document Type: Article

References (26)

1. Agullo, E., A. Guermouche and J. L'Excellent, 2008, A parallel out-of-core multifrontal method: Storage of factors on disk and analysis of models for an out-of-core active memory: Parallel Computing, 34, 296-317, doi: 10.1016/j.parco.2008.03.007. 10.1016/j.parco.2008.03.007 PACOEJ 0167-8191
2. Alkhalifah, T., 1998, Acoustic approximations for processing in transversely isotropic media: Geophysics, 63, 623-631, doi: 10.1190/1.1444361. 10.1190/1.1444361 GPYSA7 0016-8033
3. Alkhalifah, T., 2000, An acoustic wave equation for anisotropic media: Geophysics, 65, 1239-1250, doi: 10.1190/1.1444815. 10.1190/1.1444815 GPYSA7 0016-8033
4. Alkhalifah, T. and I. Tsvankin, 1995, Velocity analysis for transversely isotropic media: Geophysics, 60, 1550-1566, doi: 10.1190/1.1443888. 10.1190/1.1443888 GPYSA7 0016-8033
5. Berenger, J., 1994, A perfect matched layer for absorption of electromagnetic waves: Journal of Computational Physics, 114, 185-200, doi: 10.1006/jcph.1994.1159. 10.1006/jcph.1994.1159 JCTPAH 0021-9991
6. Crawley, S., S. Brandsberg-Dahl and J. McClean, 2010, 3D TTI RTM using the pseudoanalytic method: 80th Annual International Meeting, SEG, Expanded Abstracts, 3216-3220.
7. Dencker, N., 1982, On the propagation of polarization sets for systems of real principal type: Journal of Functional Analysis, 46, 351-372, doi: 10.1016/0022-1236(82)90051-9. 10.1016/0022-1236(82)90051-9 JFUAAW 0022-1236
8. Duveneck, E. and P. Bakker, 2011, Stable P-wave modeling for reverse-time migration in tilted TI medium: Geophysics, 76, no. 2, S65-S75, doi: 10.1190/1.3533964. 10.1190/1.3533964 GPYSA7 0016-8033
9. Duveneck, E., P. Milcik and P. Bakker, 2008, Acoustic VTI wave equations and their application for anisotropic reverse-time migration: 78th Annual International Meeting, SEG, Expanded Abstracts, 2186-2190.
10. Fletcher, R., X. Du and P. Fowler, 2008, A new pseudo-acoustic wave equation for TI media: 78th Annual International Meeting, SEG, Expanded Abstracts, 2082-2086.
11. Fletcher, R., X. Du and P. Fowler, 2009, Stablizing acoustic reverse-time migration in TTI medium: 80th Annual International Meeting, SEG, Expanded Abstracts, 2985-2989.
12. George, A. and J. Liu, 1981, Computer solutions of large sparse positive definite systems: Prentice Hall.
13. George, J., 1973, Nested dissection of a regular finite element mesh: SIAM Journal on Numerical Analysis, 10, 345-363, doi: 10.1137/0710032. 10.1137/0710032 SJNAEQ 0036-1429
14. Grechka, V., L. Zhang and J. Rector, 2004, Shear waves in acoustic anisotropic media: Geophysics, 69, 576-582, doi: 10.1190/1.1707077. 10.1190/1.1707077 GPYSA7 0016-8033
15. Liu, J., 1992, The multifrontal method for sparse matrix solution: Theory and practice: SIAM Review, 34, 82-109, doi: 10.1137/1034004. 10.1137/1034004 SIREAD 0036-1445
16. Operto, S., J. Virieux, P. Amestoy, J. L'Excellent, L. Giraud and H. Hadj Ali, 2007, 3D finite-difference frequency-domain modeling of visco-acoustic wave propagation using a massively parallel direct solver: A feasibility study: Geophysics, 72, no. 5, SM195-SM211, doi: 10.1190/1.2759835. 10.1190/1.2759835 GPYSA7 0016-8033
17. Operto, S., J. Virieux, A. Ribodetti and J. Anderson, 2009, Finite-difference frequency domain modeling of viscoacoustic wave propagation in 2D tilted transversely isotropic (TTI) media: Geophysics, 74, no. 5, T75-T95, doi: 10.1190/1.3157243. 10.1190/1.3157243 GPYSA7 0016-8033
18. Stolk, C. and M. de Hoop, 2002, Microlocal analysis of seismic inverse scattering in anisotropic elastic media, in S. R. S. Varadhan, ed., Communications on Pure and Applied Mathematics, 55, 261-301, doi: 10.1002/(ISSN)1097-0312. 10.1002/(ISSN)1097-0312 CPMAMV 0010-3640
19. Thomsen, L., 1986, Weak elastic anisotropy: Geophysics, 51, 1954-1966, doi: 10.1190/1.1442051. 10.1190/1.1442051 GPYSA7 0016-8033
20. Wang, S., M. de Hoop and J. Xia, 2010, Seismic inverse scattering via Helmholtz operator factorization and optimization: Journal of Computational Physics, 229, 8445-8462, doi: 10.1016/j.jcp.2010.07.027. 10.1016/j.jcp.2010.07.027 JCTPAH 0021-9991
21. Wang, S., M. de Hoop and J. Xia, 2011, On 3D modeling of seismic wave propagation via a structured parallel multifrontaldirect Helmholtz solver: Geophysical Prospecting, 59, 857-873. GPPRAR 0016-8025
22. Xia, J., 2010a, Efficient structured multifrontal factorization for large sparse matrices: preprint, http://math.purdue.edu/xiaj/work/mfhss.pdf.
23. Xia, J., 2010b, On the complexity of some hierarchical structured matrices: submitted to SIAM Journal on Matrix Analysis and Applications, http://www.math.purdue.edu/~xiaj/work/hsscost.pdf.
24. Xia, J., S. Chandrasekaran, M. Gu and X. Li, 2019, Superfast multifrontal method for large structured linear systems of equations: SIAM Journal on Matrix Analysis and Applications, 31, 1382-1411, doi: 10.1137/09074543X. 10.1137/09074543X SJMAEL 0895-4798
25. Xia, J., S. Chandrasekaran, M. Gu and X. Li, 2010, Fast algorithms for hierarchically semiseparable matrices: Numerical Linear Algebra with Applications, 17, 953-976, doi: 10.1002/nla.v17.6. 10.1002/nla.v17.6 1070-5325
26. Zhou, H., G. Zhang and R. Bloor, 2006, An anisotropic acoustic wave equation for modeling and migration in 2D TTI media: 76th Annual International Meeting, SEG, Expanded Abstracts, 194-198.