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本文基于逆散射理论利用正则化有限差分对比源反演算法对地震波传播速度进行反演, 该方法是基于波动方程的频率域波形反演算法, 利用非线性共轭梯度法, 通过最小化目标优化函数不断迭代更新速度模型. 由于地球物理反演问题的病态性和不稳定性, 通过基于反演参数总变差的正则化处理, 使反演问题变为良性问题且算法具有较强的抗噪声干扰能力. 反演过程中使用了频率-空间域9点差分正演算子以及PML吸收边界条件. 与其他反演算法相比, 由于背景模型在反演迭代过程中保持不变, 可以避免在每次迭代过程中重新构造正演算子及矩阵分解等相关计算过程, 使得该算法非常适合于大规模三维反演计算. 此外, 本文采用基于MPI的并行计算, 进一步提高了反演计算的效率. 二维CSEG模型反演结果表明该方法可以反演得到高分辨率的地震波速度重建结果, 为地震勘探数据处理及解释提供准确的速度信息.In this paper, the regularized finite difference contrast source inversion algorithm based on inverse scattering theory is utilized to invert the seismic velocity distribution in the underground medium, and this algorithm is a waveform inversion method in frequency domain based on wave equation. Velocity distribution is updated iteratively by minimizing the cost function using the nonlinear conjugate gradient method. The geophysical inversion problem has the characters of ill-posedness and instability, we handle this problem by adding an additional regularization item based on total variation of inversion parameter, making the inversion problem become a well-posed problem, and the algorithm has the ability of anti-noise interference. In the inversion process we use the frequency-space domain 9-point difference propagation operator under PML absorption boundary condition. Compared with other inversion algorithm, the construction of forward modeling operator and other matrix factorization calculation process can be avoided in each iterative step because the background medium remains unchanged throughout the inversion process, this makes the algorithm more suitable for large-scale three-dimensional inversion. In addition, the MPI parallel computation is applied, by which the efficiency of inversion process is improved greatly. The two-dimensional CSEG model inversion results show that this algorithm can obtain high resolution seismic velocity reconstruction, and provide an accurate velocity information for seismic data processing and interpretation.
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Keywords:
- inversion /
- seismic velocity /
- inverse scattering /
- regularization
[1] Li C P, Liu X W, Wang X C, Yang L 2005 Progress in Exploration Geophysics 28 81 (in Chinese) [李灿苹, 刘学伟, 王祥春, 杨丽 2005 勘探地球物理进展 28 81]
[2] Li C P, Liu X W, Li M F, Wang X C 2006 Geophysical Prospecting For Petroleum 45 134 (in Chinese) [李灿苹, 刘学伟, 李敏锋, 王祥春 2006 石油物探 45 134]
[3] Yin J J, Liu X W, Huang X J, Li W H, Hu D H, Jia L M 2005 Geophysical Prospecting For Petroleum 44 58 (in Chinese) [尹军杰, 刘学伟, 黄雪继, 李文慧, 胡东海, 贾烈明 2005 石油物探 44 58]
[4] Oristaglio M 1985 J. Opt. Soc. Am. A 2 1987
[5] Devaney A J 1981 Opt. Lett. 6 374
[6] Virieux J, Operto S 2009 Geophysics 74 WCC127
[7] Wang J Y 2007 Chinese Journal of Engineering Geophysics 4 81 (in Chinese) [王家映 2007 工程地球物理学报 4 81]
[8] Sen M K, Stoffa P L 1991 Geophysics 56 1624
[9] Zhang Y, Paulson K V 1997 Geophys Prospect 45 725
[10] Yong Ma, Dave Hale 2012 Geophysics 77 R207
[11] Moghaddam M, Chew W C 1992 IEEE T Geosci Remote 30 147
[12] Pratt R G 1999 Geophysics 64 888
[13] Van den Berg P M, Abubakar A 2001 Prog In Electromagn Res. 34 189
[14] Abubakar A, Van den Berg P M 2004 J. Comput. Phys. 195 236
[15] Abubakar A, Van den Berg P M, Fokkema J T 2003 Geophys Prospect 51 285
[16] Van den Berg P M, Kleinman R E 1997 Inverse Probl. 13 1607
[17] Ding L, Liu P G, He J G, Amer Z, Joe L 2014 Acta Phys. Sin. 63 044102 (in Chinese) [丁亮, 刘培国, 何建国, Amer Z, Joe L 2014 物理学报 63 044102]
[18] Abubakar A, W Hu, Van den Berg P M, Habashy T M 2008 Inverse Probl. 24 1
[19] Abubakar A, Wenyi Hu, Habashy T M, Van den Berg P M 2009 Geophysics 74 WCC47
[20] Beylkin G 1985 J. Math. Phys. 26 99
[21] Bleistein N, Gray S H 1985 Geophys Prospect 33 999
[22] Yang W C 1995 Geophysical Prospecting For Petroleum 34 114 (in Chinese) [杨文采 1995 石油物探 34 114]
[23] Ding K, Song S G 2004 Oil Geophysical Prospecting 39 287 (in Chinese) [丁科, 宋守根 2004 石油地球物理勘探 39 287]
[24] Xu J X, Wang P, Lin B 2006 China Petroleum Exploration 4 61 (in Chinese) [徐基祥, 王平, 林蓓 2006 中国石油勘探 4 61]
[25] Scales J A, Docherty P, Gersztenkorn A 1990 Inverse Probl. 6 115
[26] Hansen P C 1998 Rank-defficient and discrete ill-posed problems: Numerical aspects of linear inversion (Vol. 1) (Philadelphia: Society for Industrial & Applied Mathematics Press) P99
[27] Vogel C R, Oman M E 1996 SIAM J Sci Comput 17 227
[28] Rudin L I, Osher S, Fatemi E 1992 Physica D: Nonlinear Phenomena 60 259
[29] Askan A, Bielak J 2008 B SEISMOL SOC AM 98 2975
[30] Wenyi Hu, Abubakar A, Habashy T M 2009 Geophysics 74 R1
[31] Churl-Hyun J, Changsoo S, Jung H S 1996 Geophysics 61 529
[32] Chew W C, Weedon W H 1994 Microw Opt. Technol. Lett. 7 599
[33] Miao J H 2008 Ph. D. Dissertation (Kassel: Kassel University)
[34] Haak K F 1999 Ph. D. Dissertation (Delft: Delft University)
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[1] Li C P, Liu X W, Wang X C, Yang L 2005 Progress in Exploration Geophysics 28 81 (in Chinese) [李灿苹, 刘学伟, 王祥春, 杨丽 2005 勘探地球物理进展 28 81]
[2] Li C P, Liu X W, Li M F, Wang X C 2006 Geophysical Prospecting For Petroleum 45 134 (in Chinese) [李灿苹, 刘学伟, 李敏锋, 王祥春 2006 石油物探 45 134]
[3] Yin J J, Liu X W, Huang X J, Li W H, Hu D H, Jia L M 2005 Geophysical Prospecting For Petroleum 44 58 (in Chinese) [尹军杰, 刘学伟, 黄雪继, 李文慧, 胡东海, 贾烈明 2005 石油物探 44 58]
[4] Oristaglio M 1985 J. Opt. Soc. Am. A 2 1987
[5] Devaney A J 1981 Opt. Lett. 6 374
[6] Virieux J, Operto S 2009 Geophysics 74 WCC127
[7] Wang J Y 2007 Chinese Journal of Engineering Geophysics 4 81 (in Chinese) [王家映 2007 工程地球物理学报 4 81]
[8] Sen M K, Stoffa P L 1991 Geophysics 56 1624
[9] Zhang Y, Paulson K V 1997 Geophys Prospect 45 725
[10] Yong Ma, Dave Hale 2012 Geophysics 77 R207
[11] Moghaddam M, Chew W C 1992 IEEE T Geosci Remote 30 147
[12] Pratt R G 1999 Geophysics 64 888
[13] Van den Berg P M, Abubakar A 2001 Prog In Electromagn Res. 34 189
[14] Abubakar A, Van den Berg P M 2004 J. Comput. Phys. 195 236
[15] Abubakar A, Van den Berg P M, Fokkema J T 2003 Geophys Prospect 51 285
[16] Van den Berg P M, Kleinman R E 1997 Inverse Probl. 13 1607
[17] Ding L, Liu P G, He J G, Amer Z, Joe L 2014 Acta Phys. Sin. 63 044102 (in Chinese) [丁亮, 刘培国, 何建国, Amer Z, Joe L 2014 物理学报 63 044102]
[18] Abubakar A, W Hu, Van den Berg P M, Habashy T M 2008 Inverse Probl. 24 1
[19] Abubakar A, Wenyi Hu, Habashy T M, Van den Berg P M 2009 Geophysics 74 WCC47
[20] Beylkin G 1985 J. Math. Phys. 26 99
[21] Bleistein N, Gray S H 1985 Geophys Prospect 33 999
[22] Yang W C 1995 Geophysical Prospecting For Petroleum 34 114 (in Chinese) [杨文采 1995 石油物探 34 114]
[23] Ding K, Song S G 2004 Oil Geophysical Prospecting 39 287 (in Chinese) [丁科, 宋守根 2004 石油地球物理勘探 39 287]
[24] Xu J X, Wang P, Lin B 2006 China Petroleum Exploration 4 61 (in Chinese) [徐基祥, 王平, 林蓓 2006 中国石油勘探 4 61]
[25] Scales J A, Docherty P, Gersztenkorn A 1990 Inverse Probl. 6 115
[26] Hansen P C 1998 Rank-defficient and discrete ill-posed problems: Numerical aspects of linear inversion (Vol. 1) (Philadelphia: Society for Industrial & Applied Mathematics Press) P99
[27] Vogel C R, Oman M E 1996 SIAM J Sci Comput 17 227
[28] Rudin L I, Osher S, Fatemi E 1992 Physica D: Nonlinear Phenomena 60 259
[29] Askan A, Bielak J 2008 B SEISMOL SOC AM 98 2975
[30] Wenyi Hu, Abubakar A, Habashy T M 2009 Geophysics 74 R1
[31] Churl-Hyun J, Changsoo S, Jung H S 1996 Geophysics 61 529
[32] Chew W C, Weedon W H 1994 Microw Opt. Technol. Lett. 7 599
[33] Miao J H 2008 Ph. D. Dissertation (Kassel: Kassel University)
[34] Haak K F 1999 Ph. D. Dissertation (Delft: Delft University)
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