LSQR法在位场反演中的分析与评价
|
摘要
LSQR法具有计算效率高、对计算机内存要求低的优点,适合于大规模问题的求解。为探讨其应用于位场反演的稳定性和可靠性,笔者以加入不同噪声的两个合成模型数据为实验对象,比较分析了Tikhonov正则化与LSQR法求解结果,显示直接利用LSQR法求解位场反问题能够得到满意的正则化解,其解模型相对Tikhonov正则化,最大相对误差仅为0.36%,说明直接利用LSQR法求解位场反问题是可行的。将其应用于四川盆地雅安地区重力三维反演,极大地降低计算成本,获取了区内沉积盆及主要断裂分布情况,为页岩气靶区优选提供了有力支撑。
The LSQR method has the advantages of high computing efficiency and low memory requirement,and is thus suitable for solving large-scale ill-posed problems. In order to discuss its application in the stability and reliability of potential field inversion,the authors,on the basis of two synthetic models data with different noises as the object of the experiment,studied Tikhonov regularization and LSQR method,and the results show that the LSQR method can satisfy the requirement for solving potential field inversion with the regularization solution. In comparison with Tikhonov regularization,the maximum relative error of the LSQR method is only 0.36%,indicating that the use of LSQR method to solve potential field inverse problems is feasible. It was applied to 3 D inversion of gravity in Ya'an area of Sichuan basin,which greatly reduced computation cost and obtained the distribution of sedimentary basins and main faults in the area,thus providing strong support for shale gas target area optimization.
The LSQR method has the advantages of high computing efficiency and low memory requirement,and is thus suitable for solving large-scale ill-posed problems. In order to discuss its application in the stability and reliability of potential field inversion,the authors,on the basis of two synthetic models data with different noises as the object of the experiment,studied Tikhonov regularization and LSQR method,and the results show that the LSQR method can satisfy the requirement for solving potential field inversion with the regularization solution. In comparison with Tikhonov regularization,the maximum relative error of the LSQR method is only 0.36%,indicating that the use of LSQR method to solve potential field inverse problems is feasible. It was applied to 3 D inversion of gravity in Ya'an area of Sichuan basin,which greatly reduced computation cost and obtained the distribution of sedimentary basins and main faults in the area,thus providing strong support for shale gas target area optimization.
引文
[1]管志宁.地磁场与磁力勘探[M].北京:地质出版社,2005.Guan Z N. Geomagnetic field and magnetic exploration[M]. Beijing:Professor of Geophysics,2005.
[2]刘天佑.位场勘探数据处理新方法[M].北京:科学出版社,2007.Liu T Y.New data processing methods for potential field exploration[M].Beijing:Science Press,2007.
[3]刘伊克,常旭.地震层析成像反演中解的定量评价及其应用[J].地球物理学报,2000,43(2):251-256.Li Y K,Chang X. Quatitative asessment of invension solution of seismic tomographys and its applicatiom[J].Chinese Journal of Geophysics,2000,43(2):251-256.
[4]潘克家,王文娟,谭永基,等.基于混合差分进化算法的地球物理线性反演[J].地球物理学报,2009,52(12):3083-3090.Pan K J,Wang W J,Tan Y J,et al. Geophysical linear inversion based on hybrid differential evolution algorithm[J]. Chinese Journal of Geophysics,2009,52(12):3083-3090.
[5]常旭,卢孟夏,刘伊克.地震层析成像反演中3种广义解的误差分析与评价[J].地球物理学报,1999,42(5):695-701.Chang X,Lu M X,Liu Y K.Error analysis and appraisals for three general solution in seismic tomography[J].Chinese Journal of Geophysics,1999,42(5):695-701.
[6] Leiss E L,Pan J M,曹辉.含噪声数据的各种地球物理层析成象反演技术的比较[C]//美国勘探地球物理学家学会年会,1992:147-156.Leiss E L,Pan J M,Cao H. Comparison of geophysical inversion technology with noise data[C]//SEG,1992:147-156
[7] Abedi M,Gholami A,Norouzi G H,et al.Fast inversion of magnetic data using Lanczos bidiagonalization method[J].Journal of Applied Geophysics,2013,90(90):126-137.
[8] Rezaie M,Moradzadeh A,Kalateh A N.Fast 3D inversion of gravity data using solution space priorconditioned lanczos bidiagonalization[J].Journal of Applied Geophysics,2017,136:42-50.
[9] Portniaguine O,Zhdanov M S.3-D magnetic inversion with data compression and image focusing[J]. Geophysics,2002,67(5):1532-1541.
[10] Pilkington M.3-D magnetic imaging using conjugate gradients[J].Geophysics,1997,62(4):1132-1142.
[11] Li Y G,Oldenburg D W.Fast inversion of large-scale magnetic data using wavelet transforms and a logarithmic barrier method[J].Geophysical Journal International,2003,152(2):251-265.
[12]杨文采,杜剑渊.层析成像新算法及其在工程检测上的应用[J].地球物理学报,1994,37(2):239-244.Yang W C,Du J Y.A new algorithm of seismic tomography with application to engineering detections[J].Chinese Journal of Geophysics,1994,37(2):239-244.
[13]杨辉,戴世坤,牟永光.三维重力地震剥层联合反演[J].石油地球物理勘探,2004,39(4):468-471.Yang H,Dai S K,Mu Y G. Joint Layer-stripped inversion of 3-D gravity and seismic data[J]. Oil Geophysical Prospecting,2004,39(4):468-471.
[14] Ye Z,Tenzer R,Sneeuw N.Comparison of methods for a 3-D density inversion from airborne gravity gradiometry[J]. Studia Geophysica Et Geodaetica,2017:1-16.
[15] Paige C C,Saunders M A.LSQR:An algorithm for sparse linear equations and sparse least squares[J].Acm Transactions on Mathematical Software,1982,8(1):43-71.
[16] Li Y G,Oldenburg D W.3-D inversion of magnetic data[J].Geophysics,1996,61(2):394-408.
[17] Li Y G,Oldenburg D W.3-D inversion of gravity data[J].Geophysics,1998,63(1):109-119.
[18] Golub G H,Heath M,Wahba G.Generalized cross-validation as a method for choosing a good ridge parameter[J]. Technometrics,1979,21:215-223.
[19] Hansen P C.Analysis of discrete Ill-posed problems by means of the L-curve[J].Siam Review,1992,34(4):561-580.
[20] Hansen P C,Jensen T K,Rodriguez G.An adaptive pruning algorithm for the discrete L-curve criterion[J]. Journal of Computational&Applied Mathematics,2007,198(2):483-492.
[21]姚长利,郝天珧,管志宁,等.重磁遗传算法三维反演中高速计算及有效存储方法技术[J].地球物理学报,2003,46(2):252-258.Yao C L,Hao T Y,Guan Z N,Zhang Y W. High-speed computation and efficient storage in 3-D gravity and magnetic inversion based on genetic alogorithms[J]. Chinese Journal of Geophysics,2003,46(2):252-258.
[22]姚长利,郑元满,张聿文.重磁异常三维物性反演随机子域方法技[J].地球物理学报,2007,50(5):1576-1583.Yao C L,Zheng Y M,Zhang Y W.3-D gravity and magnetic inversion for physical properties using stochastic subspaces[J].Chinese Journal of Geophysics,2007,50(5):1576-1583.
[23]侯遵泽,杨文采,刘家琦.中国大陆地壳密度差异多尺度反演[J].地球物理学报,1998,41(5):642-651.Hou Z Z,Yang W C,Liu J Q. Multiscle inversion of the density contrast within the crust of China[J]. Acta Geophysica Sinica,1998,41(5):642-651.
[24]吴文鹂,高艳芳,顾观文.起伏地形重磁三维快速正演计算[J].物探化探计算技术,2009,31(3):179-182.Wu W L,Gao Y F,Gu G W.Gravity and magnetic 3D fast forward computing with rolling topography[J]. Computing Techniques for Geophyscal and Geochemcal Exploration,2009,31(3):179-182.
[25]王桥,郭镜,王永华,等.四川盆地雅安地区页岩气靶区优选——来自非震地球物理的证据[G].中国地质学会2017年学术年会论文摘要汇编(下册),2017:219-221.Wang Q,Guo J,Wang Y H,et al.Shale gas target selection in Ya'an area,Sichuan:Evidence from non-seismic geophysics[G].2017 Conference of Geological Society Of China,2017,2019-221.
[26]梁生贤.互相关系数自约束的重力三维反演与高效求解.吉林大学学报:地球科学版,2018,48(5):1473-1482.Liang S X.A self-constrained 3D inversion of gravity data based on cross-correlation coefficient method and efficient solver[J].Journal of Jilin University:Earth Science Edition,2018,48(5):1473-1482.
[27]焦彦杰,黄旭日,李光明,等.藏南扎西康矿集区深部结构与成矿:来自地球物理的证据[J].地球科学.Jiao Y J,Huang X R,Li G M,et al.Deep Structure and mineralization of the Zhaxikang Ore-concentration area,Southern Tibet:evidence from geophysics[J/OL].Earth Science.http://kns.cnki.net/kcms/detail/42.1874.P.20181107.1100.010.html
[28]梁生贤,焦彦杰,樊文鑫,等.基于LSQR法与相关系数自约束的磁异常三维反演[J].地球物理学进展.Liang S X,Jiao Y J,Fan W X,et al.3D inversion of magnetic data based on LSQR method and correlation coefficient self constrained[J/OL].Progress in Geophysics.http://kns.cnki.net/kcms/detail/11.2982.P.20181101.0843.004.html
[29]郭镜,李文昌,李光明,等.多尺度综合地球物理方法在扎西康铅锌锑金多金属矿找矿预测中的应用[J].地球科学.Guo J,Li W C,Li G M,et al.Application of multi-scale integrated geophysical method in prospecting prediction of Zhaxikang Pb-ZnSb-Au polymetallic deposit[J/OL].Earth Science.http://kns.cnki.net/kcms/detail/42.1874.P.20181122.0921.002.html
[2]刘天佑.位场勘探数据处理新方法[M].北京:科学出版社,2007.Liu T Y.New data processing methods for potential field exploration[M].Beijing:Science Press,2007.
[3]刘伊克,常旭.地震层析成像反演中解的定量评价及其应用[J].地球物理学报,2000,43(2):251-256.Li Y K,Chang X. Quatitative asessment of invension solution of seismic tomographys and its applicatiom[J].Chinese Journal of Geophysics,2000,43(2):251-256.
[4]潘克家,王文娟,谭永基,等.基于混合差分进化算法的地球物理线性反演[J].地球物理学报,2009,52(12):3083-3090.Pan K J,Wang W J,Tan Y J,et al. Geophysical linear inversion based on hybrid differential evolution algorithm[J]. Chinese Journal of Geophysics,2009,52(12):3083-3090.
[5]常旭,卢孟夏,刘伊克.地震层析成像反演中3种广义解的误差分析与评价[J].地球物理学报,1999,42(5):695-701.Chang X,Lu M X,Liu Y K.Error analysis and appraisals for three general solution in seismic tomography[J].Chinese Journal of Geophysics,1999,42(5):695-701.
[6] Leiss E L,Pan J M,曹辉.含噪声数据的各种地球物理层析成象反演技术的比较[C]//美国勘探地球物理学家学会年会,1992:147-156.Leiss E L,Pan J M,Cao H. Comparison of geophysical inversion technology with noise data[C]//SEG,1992:147-156
[7] Abedi M,Gholami A,Norouzi G H,et al.Fast inversion of magnetic data using Lanczos bidiagonalization method[J].Journal of Applied Geophysics,2013,90(90):126-137.
[8] Rezaie M,Moradzadeh A,Kalateh A N.Fast 3D inversion of gravity data using solution space priorconditioned lanczos bidiagonalization[J].Journal of Applied Geophysics,2017,136:42-50.
[9] Portniaguine O,Zhdanov M S.3-D magnetic inversion with data compression and image focusing[J]. Geophysics,2002,67(5):1532-1541.
[10] Pilkington M.3-D magnetic imaging using conjugate gradients[J].Geophysics,1997,62(4):1132-1142.
[11] Li Y G,Oldenburg D W.Fast inversion of large-scale magnetic data using wavelet transforms and a logarithmic barrier method[J].Geophysical Journal International,2003,152(2):251-265.
[12]杨文采,杜剑渊.层析成像新算法及其在工程检测上的应用[J].地球物理学报,1994,37(2):239-244.Yang W C,Du J Y.A new algorithm of seismic tomography with application to engineering detections[J].Chinese Journal of Geophysics,1994,37(2):239-244.
[13]杨辉,戴世坤,牟永光.三维重力地震剥层联合反演[J].石油地球物理勘探,2004,39(4):468-471.Yang H,Dai S K,Mu Y G. Joint Layer-stripped inversion of 3-D gravity and seismic data[J]. Oil Geophysical Prospecting,2004,39(4):468-471.
[14] Ye Z,Tenzer R,Sneeuw N.Comparison of methods for a 3-D density inversion from airborne gravity gradiometry[J]. Studia Geophysica Et Geodaetica,2017:1-16.
[15] Paige C C,Saunders M A.LSQR:An algorithm for sparse linear equations and sparse least squares[J].Acm Transactions on Mathematical Software,1982,8(1):43-71.
[16] Li Y G,Oldenburg D W.3-D inversion of magnetic data[J].Geophysics,1996,61(2):394-408.
[17] Li Y G,Oldenburg D W.3-D inversion of gravity data[J].Geophysics,1998,63(1):109-119.
[18] Golub G H,Heath M,Wahba G.Generalized cross-validation as a method for choosing a good ridge parameter[J]. Technometrics,1979,21:215-223.
[19] Hansen P C.Analysis of discrete Ill-posed problems by means of the L-curve[J].Siam Review,1992,34(4):561-580.
[20] Hansen P C,Jensen T K,Rodriguez G.An adaptive pruning algorithm for the discrete L-curve criterion[J]. Journal of Computational&Applied Mathematics,2007,198(2):483-492.
[21]姚长利,郝天珧,管志宁,等.重磁遗传算法三维反演中高速计算及有效存储方法技术[J].地球物理学报,2003,46(2):252-258.Yao C L,Hao T Y,Guan Z N,Zhang Y W. High-speed computation and efficient storage in 3-D gravity and magnetic inversion based on genetic alogorithms[J]. Chinese Journal of Geophysics,2003,46(2):252-258.
[22]姚长利,郑元满,张聿文.重磁异常三维物性反演随机子域方法技[J].地球物理学报,2007,50(5):1576-1583.Yao C L,Zheng Y M,Zhang Y W.3-D gravity and magnetic inversion for physical properties using stochastic subspaces[J].Chinese Journal of Geophysics,2007,50(5):1576-1583.
[23]侯遵泽,杨文采,刘家琦.中国大陆地壳密度差异多尺度反演[J].地球物理学报,1998,41(5):642-651.Hou Z Z,Yang W C,Liu J Q. Multiscle inversion of the density contrast within the crust of China[J]. Acta Geophysica Sinica,1998,41(5):642-651.
[24]吴文鹂,高艳芳,顾观文.起伏地形重磁三维快速正演计算[J].物探化探计算技术,2009,31(3):179-182.Wu W L,Gao Y F,Gu G W.Gravity and magnetic 3D fast forward computing with rolling topography[J]. Computing Techniques for Geophyscal and Geochemcal Exploration,2009,31(3):179-182.
[25]王桥,郭镜,王永华,等.四川盆地雅安地区页岩气靶区优选——来自非震地球物理的证据[G].中国地质学会2017年学术年会论文摘要汇编(下册),2017:219-221.Wang Q,Guo J,Wang Y H,et al.Shale gas target selection in Ya'an area,Sichuan:Evidence from non-seismic geophysics[G].2017 Conference of Geological Society Of China,2017,2019-221.
[26]梁生贤.互相关系数自约束的重力三维反演与高效求解.吉林大学学报:地球科学版,2018,48(5):1473-1482.Liang S X.A self-constrained 3D inversion of gravity data based on cross-correlation coefficient method and efficient solver[J].Journal of Jilin University:Earth Science Edition,2018,48(5):1473-1482.
[27]焦彦杰,黄旭日,李光明,等.藏南扎西康矿集区深部结构与成矿:来自地球物理的证据[J].地球科学.Jiao Y J,Huang X R,Li G M,et al.Deep Structure and mineralization of the Zhaxikang Ore-concentration area,Southern Tibet:evidence from geophysics[J/OL].Earth Science.http://kns.cnki.net/kcms/detail/42.1874.P.20181107.1100.010.html
[28]梁生贤,焦彦杰,樊文鑫,等.基于LSQR法与相关系数自约束的磁异常三维反演[J].地球物理学进展.Liang S X,Jiao Y J,Fan W X,et al.3D inversion of magnetic data based on LSQR method and correlation coefficient self constrained[J/OL].Progress in Geophysics.http://kns.cnki.net/kcms/detail/11.2982.P.20181101.0843.004.html
[29]郭镜,李文昌,李光明,等.多尺度综合地球物理方法在扎西康铅锌锑金多金属矿找矿预测中的应用[J].地球科学.Guo J,Li W C,Li G M,et al.Application of multi-scale integrated geophysical method in prospecting prediction of Zhaxikang Pb-ZnSb-Au polymetallic deposit[J/OL].Earth Science.http://kns.cnki.net/kcms/detail/42.1874.P.20181122.0921.002.html