基于静主元消元法的频率域波动方程正演(英文)
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摘要
频率域波动方程正演是求解一个大型线性稀疏方程组问题,其受到计算效率和内存存储问题的限制。常规的高斯消元法不能满足大型数据的并行计算,本文提出基于静主元消元法(GESP)进行稀疏矩阵LU分解和多炮有限差分正演,该方法不仅提高了稳定性,更有利于单频点内LU分解的分布式并行计算。通过Marmousi模型模拟试验,单频波场和转化到时间域地震剖面的试验表明模拟精度和计算效率得到提高,节约并充分利用内存,为波形反演奠定基础。
Frequency domain wave equation forward modeling is a problem of solving large scale linear sparse systems which is often subject to the limits of computational efficiency and memory storage. Conventional Gaussian elimination cannot resolve the parallel computation of huge data. Therefore, we use the Gaussian elimination with static pivoting (GESP) method for sparse matrix decomposition and multi-source finite-difference modeling. The GESP method does not only improve the computational efficiency but also benefit the distributed parallel computation of matrix decomposition within a single frequency point. We test the proposed method using the classic Marmousi model. Both the single-frequency wave field and time domain seismic section show that the proposed method improves the simulation accuracy and computational efficiency and saves and makes full use of memory. This method can lay the basis for waveform inversion.
Frequency domain wave equation forward modeling is a problem of solving large scale linear sparse systems which is often subject to the limits of computational efficiency and memory storage. Conventional Gaussian elimination cannot resolve the parallel computation of huge data. Therefore, we use the Gaussian elimination with static pivoting (GESP) method for sparse matrix decomposition and multi-source finite-difference modeling. The GESP method does not only improve the computational efficiency but also benefit the distributed parallel computation of matrix decomposition within a single frequency point. We test the proposed method using the classic Marmousi model. Both the single-frequency wave field and time domain seismic section show that the proposed method improves the simulation accuracy and computational efficiency and saves and makes full use of memory. This method can lay the basis for waveform inversion.
引文
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Bleibinhaus, F., Hole, J. A., Ryberg, T., and Fuis, G., 2007,Structure of the California coast ranges and San Andreasfault at SAFOD from seismic waveform inversion andreflection imaging: Journal of Geophysical Research,112, B06315.
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Gao, F., Levander, A., Pratt, R. G., Zelt, C. A., andFradelizio, G. L., 2007, Waveform tomography at agroundwater contamination site: Surface reflection data:Geophysics, 72, G45 – G55.
Hustedt, B., Operto, S., and Virieux, J., 2004, Mixed-grid and staggered-grid finite difference methods forfrequency-domain acoustic wave modeling: GeophysicalJournal International, 157, 1269 – 1296.
Jo, C. H., Shin, C., and Suh, J. H., 1996, An optimal9-point, finite-difference, frequency-space, 2-D scalarwave extrapolator: Geophysics, 61, 529 – 537.
Levander, A. R., 1988, Fourth-order finite difference P-SVseismograms: Geophysics, 53, 1425 – 1436.
Li, X. S., and Demmel, J. W., 1998, Making sparseGaussian elimination scalable by static pivoting: InProceedings of SC98, High Performance Networking and Computing Conference, Orlando, USA.
Li, X. S., and Demmel, J. W., 2003, SuperLU DIST: Ascalable distributed-memory sparse direct solver forunsymmetric linear systems: ACM Trans. MathematicalSoftware, 29(2), 110 – 140.
Malinowski, M., and Operto, S., 2008, Quantitativeimaging of the Permo-Mesozoic complex and itsbasement by frequency domain waveform tomographyof wide-aperture seismic data from the Polish Basin:Geophysical Prospecting, 56, 805 – 825.
Mora, P., 1987a, Nonlinear two-dimensional elasticinversion of multioffset seismic data: Geophysics, 52,121l – 1228.
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Marfurt, K., 1984, Accuracy of finite-difference andfinite-elements modeling of the scalar and elastic waveequation: Geophysics, 49, 533 – 549.
Mulder, W. A., and Plessix, R. E., 2004, How to choosea subset of frequencies in frequency-domain finite-difference migration: Geophysical Journal International,158, 801 – 812.
Operto, S., Ravaut, C., Improta, L., Virieux, J., Herrero, andP. dell’Aversana, 2004, Quantitative imaging of complexstructures from multi-fold wide-aperture data: A casestudy: Geophysical Prospecting, 52, 625 – 651.
Operto, S., Virieux, J., Amestoy, P., Giraud, L., and L’Excellent, J. Y., 2006, 3D frequency-domain finite-difference modeling of acoustic wave propagation usinga massively parallel direct solver: a feasibility study:76th Ann. Internat. Mtg., Soc. Expl. Geophys., ExpandedAbstracts, 2265 – 2269.
Pratt, R. G., 1999, Seismic waveform inversion in thefrequency domain, part 1: Theory and verification in aphysical scale model: Geophysics, 64, 888 – 901.
Pratt, R. G., 2004, Velocity models from frequency-domainwaveform tomography: Past, present and future: TheEAGE 66th Conference & Exhibition, Paris, 7 – 10 June,Z – 99.
Pratt, R. G., Shin, C., and Hicks, G. H., 1998, Gauss-Newton and full Newton methods in frequency-spaceseismic waveform inversion: Geophysical JournalInternational, 133, 341 – 362.
Pratt, R. G., Song, Z., and Warner, M., 1996, Two-dimensional velocity models from wide-angle seismicdata by wavefield inversion: Geophysical JournalInternational, 124, 323 – 340.
Ravaut, C., Operto, S., Improta, L., Virieux, J., Herrero,A., and dell’Aversana, P., 2004, Multi-scale imagingof complex structures from multi-fold wide-aperture seismic data by frequency-domain full-wavefieldinversions: Application to a thrust belt: GeophysicalJournal International, 159, 1032 – 1056.
Riyanti, C. D., Erlangga, Y. A., Plessix, R. E., Mulder, W. A.,Vuik, C., and Oosterlee, C., 2006, A new iterative solverfor the time-harmonic wave equation: Geophysics, 71,E57 – E63.
Saenger, E. H., Gold, N., and Shapiro, A., 2000, Modelingthe propagation of elastic waves using a modified finite-difference grid: Wave Motion, 31, 77 – 92.
Sirgue L., and Pratt, R. G., 2004, Efficient waveforminversion and imaging: A strategy for selecting temporalfrequencies: Geophysics, 69, 231 – 248.
Song, J., 2009, Full waveform inversion in frequencydomain: Master’s Thesis, China University of Petroleum,Beijing.
tekl, I., and Pratt, R. G., 1998, Accurate viscoelasticmodeling by frequency domain finite differences usingrotated operators: Geophysics, 63, 1779 – 1794.
Tarantola, A., 1984a, Linearized inversion of seismicreflection data: Geophys. Prosp., 32, 998 – 1015.
Tarantola, A., 1984b, Inversion of seismic reflection data in the acoustic approximation: Geophysics, 49, 1259 –1266.
Yin, W., 2004, Forward modeling and parallel algorithmbased on high order finite 2D difference method infrequency domain: Journal of Jilin University, 38, 144 –151.
Yu, Z., 2001, Parallel program technique of high performancecomputation MPI parallel program design: TsinghuaUniversity Press, Beijing.
Bleibinhaus, F., Hole, J. A., Ryberg, T., and Fuis, G., 2007,Structure of the California coast ranges and San Andreasfault at SAFOD from seismic waveform inversion andreflection imaging: Journal of Geophysical Research,112, B06315.
Dablain, M. A., 1986, The application of higher order forthe differencing to the scalar wave equation: Geophysics,51, 54 – 66.
Demmel, J. W., 1997, Applied numerical linear algebra:Society for Industrial and Applied Mathematics, USA.
Gao, F., Levander, A., Pratt, R. G., Zelt, C. A., andFradelizio, G. L., 2007, Waveform tomography at agroundwater contamination site: Surface reflection data:Geophysics, 72, G45 – G55.
Hustedt, B., Operto, S., and Virieux, J., 2004, Mixed-grid and staggered-grid finite difference methods forfrequency-domain acoustic wave modeling: GeophysicalJournal International, 157, 1269 – 1296.
Jo, C. H., Shin, C., and Suh, J. H., 1996, An optimal9-point, finite-difference, frequency-space, 2-D scalarwave extrapolator: Geophysics, 61, 529 – 537.
Levander, A. R., 1988, Fourth-order finite difference P-SVseismograms: Geophysics, 53, 1425 – 1436.
Li, X. S., and Demmel, J. W., 1998, Making sparseGaussian elimination scalable by static pivoting: InProceedings of SC98, High Performance Networking and Computing Conference, Orlando, USA.
Li, X. S., and Demmel, J. W., 2003, SuperLU DIST: Ascalable distributed-memory sparse direct solver forunsymmetric linear systems: ACM Trans. MathematicalSoftware, 29(2), 110 – 140.
Malinowski, M., and Operto, S., 2008, Quantitativeimaging of the Permo-Mesozoic complex and itsbasement by frequency domain waveform tomographyof wide-aperture seismic data from the Polish Basin:Geophysical Prospecting, 56, 805 – 825.
Mora, P., 1987a, Nonlinear two-dimensional elasticinversion of multioffset seismic data: Geophysics, 52,121l – 1228.
Mora, P., 1987b, Elastic wavefield inversion for low and highwavenumbers of the P- and S-wave velocities, a possiblesolution: in Worthington, M., Ed., Deconvolution andInversion: Blackwell Scientific, London.
Marfurt, K., 1984, Accuracy of finite-difference andfinite-elements modeling of the scalar and elastic waveequation: Geophysics, 49, 533 – 549.
Mulder, W. A., and Plessix, R. E., 2004, How to choosea subset of frequencies in frequency-domain finite-difference migration: Geophysical Journal International,158, 801 – 812.
Operto, S., Ravaut, C., Improta, L., Virieux, J., Herrero, andP. dell’Aversana, 2004, Quantitative imaging of complexstructures from multi-fold wide-aperture data: A casestudy: Geophysical Prospecting, 52, 625 – 651.
Operto, S., Virieux, J., Amestoy, P., Giraud, L., and L’Excellent, J. Y., 2006, 3D frequency-domain finite-difference modeling of acoustic wave propagation usinga massively parallel direct solver: a feasibility study:76th Ann. Internat. Mtg., Soc. Expl. Geophys., ExpandedAbstracts, 2265 – 2269.
Pratt, R. G., 1999, Seismic waveform inversion in thefrequency domain, part 1: Theory and verification in aphysical scale model: Geophysics, 64, 888 – 901.
Pratt, R. G., 2004, Velocity models from frequency-domainwaveform tomography: Past, present and future: TheEAGE 66th Conference & Exhibition, Paris, 7 – 10 June,Z – 99.
Pratt, R. G., Shin, C., and Hicks, G. H., 1998, Gauss-Newton and full Newton methods in frequency-spaceseismic waveform inversion: Geophysical JournalInternational, 133, 341 – 362.
Pratt, R. G., Song, Z., and Warner, M., 1996, Two-dimensional velocity models from wide-angle seismicdata by wavefield inversion: Geophysical JournalInternational, 124, 323 – 340.
Ravaut, C., Operto, S., Improta, L., Virieux, J., Herrero,A., and dell’Aversana, P., 2004, Multi-scale imagingof complex structures from multi-fold wide-aperture seismic data by frequency-domain full-wavefieldinversions: Application to a thrust belt: GeophysicalJournal International, 159, 1032 – 1056.
Riyanti, C. D., Erlangga, Y. A., Plessix, R. E., Mulder, W. A.,Vuik, C., and Oosterlee, C., 2006, A new iterative solverfor the time-harmonic wave equation: Geophysics, 71,E57 – E63.
Saenger, E. H., Gold, N., and Shapiro, A., 2000, Modelingthe propagation of elastic waves using a modified finite-difference grid: Wave Motion, 31, 77 – 92.
Sirgue L., and Pratt, R. G., 2004, Efficient waveforminversion and imaging: A strategy for selecting temporalfrequencies: Geophysics, 69, 231 – 248.
Song, J., 2009, Full waveform inversion in frequencydomain: Master’s Thesis, China University of Petroleum,Beijing.
tekl, I., and Pratt, R. G., 1998, Accurate viscoelasticmodeling by frequency domain finite differences usingrotated operators: Geophysics, 63, 1779 – 1794.
Tarantola, A., 1984a, Linearized inversion of seismicreflection data: Geophys. Prosp., 32, 998 – 1015.
Tarantola, A., 1984b, Inversion of seismic reflection data in the acoustic approximation: Geophysics, 49, 1259 –1266.
Yin, W., 2004, Forward modeling and parallel algorithmbased on high order finite 2D difference method infrequency domain: Journal of Jilin University, 38, 144 –151.
Yu, Z., 2001, Parallel program technique of high performancecomputation MPI parallel program design: TsinghuaUniversity Press, Beijing.
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