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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 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 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 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 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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