基于柯西分布约束和快速近端目标函数优化的三维重力反演方法
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摘要
优化算法的选取在很大程度上影响着三维重力反演的计算效率,从而制约着三维重力反演的实用性.在复杂地质构造背景下,不同岩性单元之间可能会发生物性突变,产生尖锐边界.为此,本文提出了一种新的基于柯西分布约束和快速近端目标函数(Fast Proximal Objective Function,FPOF)优化的三维重力反演方法.FPOF优化方法的一个突出特点是在每一步迭代过程中逐一计算剖分网格内的未知密度参数,因此,有较低的计算复杂度和较高的计算效率.此外,目标函数中柯西范数(Cauchy norm)的引入会对反演结果施加稀疏性,有助于产生块状效果.理论模型测试表明,本文方法不仅能产生更加聚焦的反演效果,而且反演所需的时间也比传统的共轭梯度优化方法少.最后将本文方法应用于我国西部某地区实际重力数据,反演结果与已知的地质信息有较好的一致性.
The choice of an optimization algorithm affects computational efficiency of 3D gravity data inversion to a great extent and thereby constrains its application in the industry.In the context of complex subsurface geological settings,sharp boundaries may exist between different rock units that have large physical property contrasts.To this end,we propose a novel 3D gravity inversion method based on Cauchy distribution constraint and fast proximal objective function(FPOF)optimization.A salient characteristic of FPOF optimization is to calculate the unknown density in each subdivided unit of the inversion domain one by one at each iteration,thus reducingcomputational complexity and improving computational efficiency.In addition,the inclusion of Cauchy norm into objective function imposes sparseness on model parameters to be inverted and consequently facilitates a blocky density distribution.The test of synthetic data demonstrates that the proposed inversion method not only recovers more focused anomalous density bodies but also costs less run time than conventional CG optimization method.At last,the application of the proposed inversion method to real gravity data in the Western China shows that the recovered 3D density model agrees well with the known geological knowledge.
The choice of an optimization algorithm affects computational efficiency of 3D gravity data inversion to a great extent and thereby constrains its application in the industry.In the context of complex subsurface geological settings,sharp boundaries may exist between different rock units that have large physical property contrasts.To this end,we propose a novel 3D gravity inversion method based on Cauchy distribution constraint and fast proximal objective function(FPOF)optimization.A salient characteristic of FPOF optimization is to calculate the unknown density in each subdivided unit of the inversion domain one by one at each iteration,thus reducingcomputational complexity and improving computational efficiency.In addition,the inclusion of Cauchy norm into objective function imposes sparseness on model parameters to be inverted and consequently facilitates a blocky density distribution.The test of synthetic data demonstrates that the proposed inversion method not only recovers more focused anomalous density bodies but also costs less run time than conventional CG optimization method.At last,the application of the proposed inversion method to real gravity data in the Western China shows that the recovered 3D density model agrees well with the known geological knowledge.
引文
Abedi M,Gholami A,Norouzi G H,et al.2013.Fast inversion of magnetic data using Lanczos bidiagonalization method.Journal of Applied Geophysics,90:126-137.
Blakely R J.1995.Potential Theory in Gravity and Magnetic Applications.Cambridge:Cambridge University Press.
Caratori Tontini F,Cocchi L,Carmisciano C.2009.Rapid 3-Dforward model of potential fields with application to the Palinuro Seamount magnetic anomaly(southern Tyrrhenian Sea,Italy).Journal of Geophysical Research:Solid Earth,114:B02103,doi:10.1029/2008JB005907.
Chen Z X,Meng X H,Guo L H,et al.2012.GICUDA:A parallel program for 3Dcorrelation imaging of large scale gravity and gravity gradiometry data on graphics processing units with CUDA.Computers&Geosciences,46:119-128.
Dai R H,Zhang F C,Liu H Q.2016.Seismic inversion based on proximal objective function optimization algorithm.Geophysics,81(5):R237-R246.
Gao X H,Huang D N.2017.Research on 3Dfocusing inversion of gravity gradient tensor data based on a conjugate gradient algorithm.Chinese Journal of Geophysics(in Chinese),60(4):1571-1583,doi:10.6038/cjg20170429.
Geng M X,Huang D N,Yu P,et al.2016.Three-dimensional constrained inversion of full tensor gradiometer data based on cokriging method.Chinese Journal of Geophysics(in Chinese),59(5):1849-1860,doi:10.6038/cjg20160528.
Guo L H,Meng X H,Shi L,et al.2009.3-D correlation imaging for gravity and gravity gradiometry data.Chinese Journal of Geophysics(in Chinese),52(4):1098-1106,doi:10.3969/j.issn.0001-5733.2009.04.027.
Li Y G,Oldenburg D W.1998.3-D inversion of gravity data.Geophysics,63(1):109-119.
Li Y G,Oldenburg D W.2003.Fast inversion of large-scale magnetic data using wavelet transforms and a logarithmic barrier method.Geophysical Journal International,152(2):251-265.
Liu G F,Meng X H,Chen Z X.2012.3Dmagnetic inversion based on probability tomography and its GPU implement.Computers&Geosciences,48:86-92.
Liu J X,Sun H L,Chen B,et al.2016.Review of the gravity and magnetic methods in the exploration of metal deposits.Progress in Geophysics(in Chinese),31(2):713-722,doi:10.6038/pg20160229.
Liu K,Hao T Y.2014.Application of potential field method in the unconventional oil and gas exploration.Progress in Geophysics(in Chinese),29(2):786-797,doi:10.6038/pg20140243.
Liu Z,Yu H Z,Chen T.2011.3Dinversion method of density based on double constraint.Journal of China University of Petroleum(Edition of Natural Science)(in Chinese),35(6):43-50.
Marchetti P,Coraggio F,Gabbriellini G,et al.2014.Large-scale3D gravity data space inversion in hydrocarbon exploration.∥2014SEG Annual Meeting.Denver,Colorado,USA:SEG,1269-1274.
Martin R,Monteiller V,Komatitsch D,et al.2013.Gravity inversion using wavelet-based compression on parallel hybrid CPU/GPU systems:application to southwest Ghana.Geophysical Journal International,195(3):1594-1619.
Meng X H,Liu G F,Chen Z X,et al.2012.3-D gravity and magnetic inversion for physical properties based on residual anomaly correlation.Chinese Journal of Geophysics(in Chinese),55(1):304-309,doi:10.6038/j.issn.0001-5733.2012.01.030.
Meng Z H,Li F T,Xu X C,et al.2017.Fast inversion of gravity data using the symmetric successive over-relaxation(SSOR)preconditioned conjugate gradient algorithm.Exploration Geophysics,48(3):294-304.
Moorkamp M,Jegen M,Roberts A,et al.2010.Massively parallel forward modeling of scalar and tensor gravimetry data.Computers&Geosciences,36(5):680-686.
Nabighian M N,Ander M E,Grauch V J S,et al.2005.Historical development of the gravity method in exploration.Geophysics,70(6):63ND-89ND.
Peng G M,Liu Z,Xu K J.2017.An efficient 3Dgravity inversion based on proximal objective function optimization.∥79th EAGE Conference and Exhibition 2017.EAGE.
Pilkington M.1997.3-D magnetic imaging using conjugate gradients.Geophysics,62(4):1132-1142.
Pilkington M.2009.3D magnetic data-space inversion with sparseness constraints.Geophysics,74(1):L7-L15.
Portniaguine O,Zhdanov M S.1999.Focusing geophysical inversion images.Geophysics,64(3):874-887.
Portniaguine O,Zhdanov M S.2002.3-D magnetic inversion with data compression and image focusing.Geophysics,67(5):1532-1541.
Qin P B,Huang D N.2016.Integrated gravity and gravity gradient data focusing inversion.Chinese Journal of Geophysics(in Chinese),59(6):2203-2224,doi:10.6038/cjg20160624.
Rezaie M,Moradzadeh A,Kalateh A N.2017.Fast 3Dinversion of gravity data using solution space priorconditioned lanczos bidiagonalization.Journal of Applied Geophysics,136:42-50.
Rockafellar R T.1976.Monotone operators and the proximal point algorithm.SIAM Journal on Control&Optimization,14(5):877-898.
Yao C L,Hao T Y,Guan Z N,et al.2003.High-speed computation and efficient storage in 3-D gravity and magnetic inversion based on genetic algorithms.Chinese Journal of Geophysics(in Chinese),46(2):252-258.
Zeng H L.1999.Progress in gravity and magnetic petroleum exploration.Oil Geophysical Prospecting(in Chinese),34(S1):115-124.
高秀鹤,黄大年.2017.基于共轭梯度算法的重力梯度数据三维聚焦反演研究.地球物理学报,60(4):1571-1583,doi:10.6038/cjg20170429.
耿美霞,黄大年,于平等.2016.基于协同克里金方法的重力梯度全张量三维约束反演.地球物理学报,59(5):1849-1860,doi:10.6038/cjg20160528.
郭良辉,孟小红,石磊等.2009.重力和重力梯度数据三维相关成像.地球物理学报,52(4):1098-1106,doi:10.3969/j.issn.0001-5733.2009.04.027.
柳建新,孙欢乐,陈波等.2016.重磁方法在国内外金属矿中的研究进展.地球物理学进展,31(2):713-722,doi:10.6038/pg20160229.
刘康,郝天珧.2014.位场方法在非常规油气勘探中的应用.地球物理学进展,29(2):786-797,doi:10.6038/pg20140243.
刘展,于会臻,陈挺.2011.双重约束下的密度三维反演.中国石油大学学报(自然科学版),35(6):43-50.
孟小红,刘国峰,陈召曦等.2012.基于剩余异常相关成像的重磁物性反演方法.地球物理学报,55(1):304-309,doi:10.6038/j.issn.0001-5733.2012.01.030.
秦朋波,黄大年.2016.重力和重力梯度数据联合聚焦反演方法.地球物理学报,59(6):2203-2224,doi:10.6038/cjg20160624.
姚长利,郝天珧,管志宁等.2003.重磁遗传算法三维反演中高速计算及有效存储方法技术.地球物理学报,46(2):252-258.
曾华霖.1999.石油重磁勘探的进展.石油地球物理勘探,34(增刊):115-124.
Blakely R J.1995.Potential Theory in Gravity and Magnetic Applications.Cambridge:Cambridge University Press.
Caratori Tontini F,Cocchi L,Carmisciano C.2009.Rapid 3-Dforward model of potential fields with application to the Palinuro Seamount magnetic anomaly(southern Tyrrhenian Sea,Italy).Journal of Geophysical Research:Solid Earth,114:B02103,doi:10.1029/2008JB005907.
Chen Z X,Meng X H,Guo L H,et al.2012.GICUDA:A parallel program for 3Dcorrelation imaging of large scale gravity and gravity gradiometry data on graphics processing units with CUDA.Computers&Geosciences,46:119-128.
Dai R H,Zhang F C,Liu H Q.2016.Seismic inversion based on proximal objective function optimization algorithm.Geophysics,81(5):R237-R246.
Gao X H,Huang D N.2017.Research on 3Dfocusing inversion of gravity gradient tensor data based on a conjugate gradient algorithm.Chinese Journal of Geophysics(in Chinese),60(4):1571-1583,doi:10.6038/cjg20170429.
Geng M X,Huang D N,Yu P,et al.2016.Three-dimensional constrained inversion of full tensor gradiometer data based on cokriging method.Chinese Journal of Geophysics(in Chinese),59(5):1849-1860,doi:10.6038/cjg20160528.
Guo L H,Meng X H,Shi L,et al.2009.3-D correlation imaging for gravity and gravity gradiometry data.Chinese Journal of Geophysics(in Chinese),52(4):1098-1106,doi:10.3969/j.issn.0001-5733.2009.04.027.
Li Y G,Oldenburg D W.1998.3-D inversion of gravity data.Geophysics,63(1):109-119.
Li Y G,Oldenburg D W.2003.Fast inversion of large-scale magnetic data using wavelet transforms and a logarithmic barrier method.Geophysical Journal International,152(2):251-265.
Liu G F,Meng X H,Chen Z X.2012.3Dmagnetic inversion based on probability tomography and its GPU implement.Computers&Geosciences,48:86-92.
Liu J X,Sun H L,Chen B,et al.2016.Review of the gravity and magnetic methods in the exploration of metal deposits.Progress in Geophysics(in Chinese),31(2):713-722,doi:10.6038/pg20160229.
Liu K,Hao T Y.2014.Application of potential field method in the unconventional oil and gas exploration.Progress in Geophysics(in Chinese),29(2):786-797,doi:10.6038/pg20140243.
Liu Z,Yu H Z,Chen T.2011.3Dinversion method of density based on double constraint.Journal of China University of Petroleum(Edition of Natural Science)(in Chinese),35(6):43-50.
Marchetti P,Coraggio F,Gabbriellini G,et al.2014.Large-scale3D gravity data space inversion in hydrocarbon exploration.∥2014SEG Annual Meeting.Denver,Colorado,USA:SEG,1269-1274.
Martin R,Monteiller V,Komatitsch D,et al.2013.Gravity inversion using wavelet-based compression on parallel hybrid CPU/GPU systems:application to southwest Ghana.Geophysical Journal International,195(3):1594-1619.
Meng X H,Liu G F,Chen Z X,et al.2012.3-D gravity and magnetic inversion for physical properties based on residual anomaly correlation.Chinese Journal of Geophysics(in Chinese),55(1):304-309,doi:10.6038/j.issn.0001-5733.2012.01.030.
Meng Z H,Li F T,Xu X C,et al.2017.Fast inversion of gravity data using the symmetric successive over-relaxation(SSOR)preconditioned conjugate gradient algorithm.Exploration Geophysics,48(3):294-304.
Moorkamp M,Jegen M,Roberts A,et al.2010.Massively parallel forward modeling of scalar and tensor gravimetry data.Computers&Geosciences,36(5):680-686.
Nabighian M N,Ander M E,Grauch V J S,et al.2005.Historical development of the gravity method in exploration.Geophysics,70(6):63ND-89ND.
Peng G M,Liu Z,Xu K J.2017.An efficient 3Dgravity inversion based on proximal objective function optimization.∥79th EAGE Conference and Exhibition 2017.EAGE.
Pilkington M.1997.3-D magnetic imaging using conjugate gradients.Geophysics,62(4):1132-1142.
Pilkington M.2009.3D magnetic data-space inversion with sparseness constraints.Geophysics,74(1):L7-L15.
Portniaguine O,Zhdanov M S.1999.Focusing geophysical inversion images.Geophysics,64(3):874-887.
Portniaguine O,Zhdanov M S.2002.3-D magnetic inversion with data compression and image focusing.Geophysics,67(5):1532-1541.
Qin P B,Huang D N.2016.Integrated gravity and gravity gradient data focusing inversion.Chinese Journal of Geophysics(in Chinese),59(6):2203-2224,doi:10.6038/cjg20160624.
Rezaie M,Moradzadeh A,Kalateh A N.2017.Fast 3Dinversion of gravity data using solution space priorconditioned lanczos bidiagonalization.Journal of Applied Geophysics,136:42-50.
Rockafellar R T.1976.Monotone operators and the proximal point algorithm.SIAM Journal on Control&Optimization,14(5):877-898.
Yao C L,Hao T Y,Guan Z N,et al.2003.High-speed computation and efficient storage in 3-D gravity and magnetic inversion based on genetic algorithms.Chinese Journal of Geophysics(in Chinese),46(2):252-258.
Zeng H L.1999.Progress in gravity and magnetic petroleum exploration.Oil Geophysical Prospecting(in Chinese),34(S1):115-124.
高秀鹤,黄大年.2017.基于共轭梯度算法的重力梯度数据三维聚焦反演研究.地球物理学报,60(4):1571-1583,doi:10.6038/cjg20170429.
耿美霞,黄大年,于平等.2016.基于协同克里金方法的重力梯度全张量三维约束反演.地球物理学报,59(5):1849-1860,doi:10.6038/cjg20160528.
郭良辉,孟小红,石磊等.2009.重力和重力梯度数据三维相关成像.地球物理学报,52(4):1098-1106,doi:10.3969/j.issn.0001-5733.2009.04.027.
柳建新,孙欢乐,陈波等.2016.重磁方法在国内外金属矿中的研究进展.地球物理学进展,31(2):713-722,doi:10.6038/pg20160229.
刘康,郝天珧.2014.位场方法在非常规油气勘探中的应用.地球物理学进展,29(2):786-797,doi:10.6038/pg20140243.
刘展,于会臻,陈挺.2011.双重约束下的密度三维反演.中国石油大学学报(自然科学版),35(6):43-50.
孟小红,刘国峰,陈召曦等.2012.基于剩余异常相关成像的重磁物性反演方法.地球物理学报,55(1):304-309,doi:10.6038/j.issn.0001-5733.2012.01.030.
秦朋波,黄大年.2016.重力和重力梯度数据联合聚焦反演方法.地球物理学报,59(6):2203-2224,doi:10.6038/cjg20160624.
姚长利,郝天珧,管志宁等.2003.重磁遗传算法三维反演中高速计算及有效存储方法技术.地球物理学报,46(2):252-258.
曾华霖.1999.石油重磁勘探的进展.石油地球物理勘探,34(增刊):115-124.
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