基于MPI并行算法的电阻率法多种装置数据的三维联合反演
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摘要
由于地表电阻率法受到浅地表局部异常体的干扰,反演精度受到影响,井中装置数据资料参与反演虽然可以减小浅地表局部异常体的干扰,但是由于钻井位置的局限性,数据量得不到保障,也会导致反演精度降低.为此,本文开发了一套结合地表、地-井、井-地和井-井装置数据的三维联合反演算法.首先,利用有限差分法实现正演模拟,采用非线性共轭梯度法(NLCG)恢复电阻率结构;其次,调用Message Passing Interface(MPI)函数库加速正演模拟和灵敏度矩阵运算,当开辟12个进程时,反演程序获得最大加速比4.51;最后,通过合成数据和实测数据算例证明该反演算法的有效性,也证实了多种装置组合数据体反演结果明显优于单一地表装置数据体反演结果.
Because of interference from local anomaly bodies in the shallow subsurface,the inversion accuracy of ground-based resistivity method is limited.Although such interference can be reduced by virtue of borehole data in the inversion,due to the limitation of drilling position,the amount of data is not guaranteed,thus precision of inversion can be reduced.In this paper,a set of threedimensional joint inversion algorithms that can simultaneously invert surface,surface-borehole,borehole-surface and borehole-borehole array data is developed.Firstly,forward modeling is conducted by the finite different method,and restoration of the resistivity structure is made by the Nonlinear Conjugate Gradient method(NLCG).Secondly,the Message Passing Interface(MPI)function library is used to accelerate forward modeling and sensitivity matrix calculation.The maximum speedup ratio of 4.51 is achieved by the inversion program when the 12 processes areopened up.Finally,the validity of the inversion algorithm is proved by numerical examples of synthetic data and measured data,and it is also proved that the inversion results of the combined data set of multiple arrays are obviously superior to those of a single surface array data set.
Because of interference from local anomaly bodies in the shallow subsurface,the inversion accuracy of ground-based resistivity method is limited.Although such interference can be reduced by virtue of borehole data in the inversion,due to the limitation of drilling position,the amount of data is not guaranteed,thus precision of inversion can be reduced.In this paper,a set of threedimensional joint inversion algorithms that can simultaneously invert surface,surface-borehole,borehole-surface and borehole-borehole array data is developed.Firstly,forward modeling is conducted by the finite different method,and restoration of the resistivity structure is made by the Nonlinear Conjugate Gradient method(NLCG).Secondly,the Message Passing Interface(MPI)function library is used to accelerate forward modeling and sensitivity matrix calculation.The maximum speedup ratio of 4.51 is achieved by the inversion program when the 12 processes areopened up.Finally,the validity of the inversion algorithm is proved by numerical examples of synthetic data and measured data,and it is also proved that the inversion results of the combined data set of multiple arrays are obviously superior to those of a single surface array data set.
引文
Bai D H,Yu S.1995.Theory and methods of resistivity tomography.Progress in Geophysics(in Chinese),10(1):56-75.
Barde-Cabusson S,Bolós X,Pedrazzi D,et al.2013.Electrical resistivity tomography revealing the internal structure of monogenetic volcanoes.Geophysical Research Letters,40(11):2544-2549,doi:10.1002/grl.50538.
Boonchaisuk S,Vachiratienchai C,Siripunvaraporn W.2008.Twodimensional direct current(DC)resistivity inversion:Data space Occam′s approach.Physics of the Earth and Planetary Interiors,168(3-4):204-211,doi:10.1016/j.pepi.2008.06.022.
Diaferia I,Barchi M,Loddo M,et al.2006.Detailed imaging of tectonic structures by multiscale earth resistivity tomographies:the Colfiorito normal faults(central Italy).Geophysical Research Letters,33(9):L09305,doi:10.1029/2006GL025828.
Ellis R G,Oldenburg D W.1994.The pole-pole 3-D DC-resistivity inverse problem:a conjugategradient approach.Geophysical Journal International,119(1):187-194,doi:10.1111/j.1365-246X.1994.tb00921.x.
Fan G D.2017.Application of resistivity method in Peiling geological conditions of shale gas drilling platform.∥China Petroleum Institute Geophysical Technology Workshop(in Chinese).Tianjin,880-883.
Feng Y D,Chi X B,Wang W,et al.2008.Fastcomputing for LURR of earthquake prediction.Pure and Applied Geophysics,165(3-4):749-759,doi:10.1007/s00024-008-0313-0.
Hauck C.2002.Frozen ground monitoring using DC resistivity tomography.Geophysical Research Letters,29(21):12-1-12-4.
Jones K A,Ingham M,Pringle D J,et al.2010.Temporal variations in sea ice resistivity:Resolving anisotropic microstructure through cross-borehole DC resistivity tomography.Journal of Geophysical Research:Oceans,115:C11023,doi:10.1029/2009JC006049.
Kelbert A,Meqbel N,Egbert G D,et al.2014.ModEM:Amodular system for inversion of electromagnetic geophysical data.Computers&Geosciences,66:40-53,doi:10.1016/j.cageo.2014.01.010.
Krautblatter M,Hauck C.2007.Electrical resistivity tomography monitoring of permafrost in solid rock walls.Journal of Geophysical Research:Earth Surface,112:F02S20,doi:10.1029/2006JF000546.
Li S C,Nie L C,Liu B,et al.2015.Advanced detection and physical model test based on multi-electrode sources array resistivity method in tunnel.Chinese Journal of Geophysics(in Chinese),58(4):1434-1446,doi:10.6038/cjg20150429.
Li Y,Hu X Y,Kim K,et al.2010.Research of 1-D magnetotelluric parallel computation based on MPI.Progress in Geophysics(in Chinese),25(5):1612-1616,doi:10.3969/j.issn.1004-2903.2010.05.012.
Li Y G,Oldenburg D W.1992.Approximate inverse mappings in DC resistivity problems.Geophysical Journal International,109(2):343-362.
Li Y G,Oldenburg D W.2000.3-D inversion of induced polarization data.Geophysics,65(6):1931-1945.
Li Y X.2014.Seismic exploration in 2Dfrequency-domain forward based on parallel algorithms[Master′s thesis](in Chinese).Beijing:China University of Geosciences(Beijing).
Ma H,Tan H D,Guo Y.2015.Three-dimensional induced polarization parallel inversion using nonlinear conjugate gradients method.Mathematical Problems in Engineering,2015:Article ID 464793,doi:10.1155/2015/464793.
Oldenburg D W,Li Y G.1994.Inversion of induced polarization data.Geophysics,59(9):1327-1341.
Park S K,Van G P.1991.Inversion of pole-pole data for 3-Dresistivity structure beneath arrays of electrodes.Geophysics,56(7):951-960.
Pelton W H,Rijo L,Swift C M Jr.1978.Inversion of twodimensional resistivity and induced-polarization data.Geophysics,43(4):788-803.
Petrick W R Jr,Sill W R,Ward S H.1981.Three-dimensional resistivity inversion using alpha centers.Geophysics,46(8):1148-1162.
Revil A,Johnson T C,Finizola A.2010.Three-dimensional resistivity tomography of Vulcan′s forge,Vulcano Island,southern Italy.Geophysical Research Letters,37:L15308,doi:10.1029/2010GL043983.
Schwarzbach C,B9rner R U,Spitzer K.2005.Two-dimensional inversion of direct current resistivity data using aparallel,multi-objective genetic algorithm.Geophysical Journal International,162(3):685-695.
Shi G L,Zhang G X.2008.Macroscopic Field Theory(in Chinese).Wuhan:China University of Geosciences Publishing House.
Singh U K,Tiwari R K,Singh S B.2010.Inversion of 2-D DCresistivity data using rapid optimization and minimal complexity neural network.Nonlinear Processes in Geophysics,17(1):65-76.
Spitzer K.1995.A 3-D finite-difference algorithm for DC resistivity modeling using conjugate gradient methods.Geophysical Journal International,123(3):903-914.
Tan H D,Tong T,Lin C H.2006.The parallel 3Dmagnetotelluric forward modeling algorithm.Applied Geophysics,3(4):197-202,doi:10.1007/s11770-006-4001-5.
Tang J T,Zhang J F,Feng B,et a1.2007.Determination of borders for resistive oil and gas reservoirs by deviation rate using thehole-to-surface resistivity method.Chinese Journal of Geophysics(in Chinese),50(3):926-931.
van der Vorst H A.1992.Bi-CGSTAB:A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems.SIAM Journal on Scientific and Statistical Computing,13(2):631-644,doi:10.1137/0913035.
Wang J Y.2002.Inverse Theory in Geophysics.2nd ed.(in Chinese).Beijing:Higher Education Press.
Weiss C J.2013.Project APhiD:A Lorenz-gauged A-φdecomposition for parallelized computation of ultra-broadband electromagnetic induction in a fully heterogeneous Earth.Computers&Geosciences,58:40-52,doi:10.1016/j.cageo.2013.05.002.
Wu X P,Wang T T.2001.Study on some problems for 3Dresistivity inversion using conjugate gradient.Seismology and Geology(in Chinese),23(2):321-327.
Wu X P,Xu G M.2000.Study on 3-D resistivity inversion using conjugate gradient method.Chinese Journal of Geophysics(in Chinese),43(3):420-427.
Xiong J,Zou C C,Meng X H.2012.Using the BICGSTABalgorithm with the incomplete LU factorization precondictioning to implement2DFDFD induction logging fast forward modeling.Geoscience(in Chinese),26(6):1283-1288.
Yuval D,Oldenburg W.1996.DC resistivity and IP methods in acid mine drainage problems:results from the Copper Cliff mine tailings impoundments.Journal of Applied Geophysics,34(3):187-198,doi:10.1016/0926-9851(95)00020-8.
Zhang J,Mackie R L,Madden T R.1995.3-D resistivity forward modeling and inversion using conjugate gradients.Geophysics,60(5):1313-1325.
白登海,于晟.1995.电阻率层析成象理论和方法.地球物理学进展,10(1):56-75.
范国栋.2017.电阻率法在涪陵页岩气钻井平台地质条件勘查中的应用.∥中国石油学会2017年物探技术研讨会.天津,880-883.
李术才,聂利超,刘斌等.2015.多同性源阵列电阻率法隧道超前探测方法与物理模拟试验研究.地球物理学报,58(4):1434-1446,doi:10.6038/cig20150429.
李焱,胡祥云,金钢燮等.2010.基于MPI的一维大地电磁并行计算研究.地球物理学进展,25(5):1612-1616,doi:10.3969/j.issn.1004-2903.2010.05.012.
李祎昕.2014.地震勘探频率域二维正演并行算法研究[硕士论文].北京:中国地质大学(北京).
施国良,张国雄.2008.宏观场论.武汉:中国地质大学出版社.
汤井田,张继锋,冯兵等.2007.井地电阻率法歧离率确定高阻油气藏边界.地球物理学报,50(3):926-931.
王家映.2002.地球物理反演理论.2版.北京:高等教育出版社.
吴小平,汪彤彤.2001.利用共轭梯度方法的电阻率三维反演若干问题研究.地震地质,23(2):321-327.
吴小平,徐果明.2000.利用共轭梯度法的电阻率三维反演研究.地球物理学报,43(3):420-427.
熊杰,邹长春,孟小红.2012.不完全LU分解预条件BICGSTAB算法实现感应测井二维FDFD快速正演模拟.现代地质,26(6):1283-1288.
Barde-Cabusson S,Bolós X,Pedrazzi D,et al.2013.Electrical resistivity tomography revealing the internal structure of monogenetic volcanoes.Geophysical Research Letters,40(11):2544-2549,doi:10.1002/grl.50538.
Boonchaisuk S,Vachiratienchai C,Siripunvaraporn W.2008.Twodimensional direct current(DC)resistivity inversion:Data space Occam′s approach.Physics of the Earth and Planetary Interiors,168(3-4):204-211,doi:10.1016/j.pepi.2008.06.022.
Diaferia I,Barchi M,Loddo M,et al.2006.Detailed imaging of tectonic structures by multiscale earth resistivity tomographies:the Colfiorito normal faults(central Italy).Geophysical Research Letters,33(9):L09305,doi:10.1029/2006GL025828.
Ellis R G,Oldenburg D W.1994.The pole-pole 3-D DC-resistivity inverse problem:a conjugategradient approach.Geophysical Journal International,119(1):187-194,doi:10.1111/j.1365-246X.1994.tb00921.x.
Fan G D.2017.Application of resistivity method in Peiling geological conditions of shale gas drilling platform.∥China Petroleum Institute Geophysical Technology Workshop(in Chinese).Tianjin,880-883.
Feng Y D,Chi X B,Wang W,et al.2008.Fastcomputing for LURR of earthquake prediction.Pure and Applied Geophysics,165(3-4):749-759,doi:10.1007/s00024-008-0313-0.
Hauck C.2002.Frozen ground monitoring using DC resistivity tomography.Geophysical Research Letters,29(21):12-1-12-4.
Jones K A,Ingham M,Pringle D J,et al.2010.Temporal variations in sea ice resistivity:Resolving anisotropic microstructure through cross-borehole DC resistivity tomography.Journal of Geophysical Research:Oceans,115:C11023,doi:10.1029/2009JC006049.
Kelbert A,Meqbel N,Egbert G D,et al.2014.ModEM:Amodular system for inversion of electromagnetic geophysical data.Computers&Geosciences,66:40-53,doi:10.1016/j.cageo.2014.01.010.
Krautblatter M,Hauck C.2007.Electrical resistivity tomography monitoring of permafrost in solid rock walls.Journal of Geophysical Research:Earth Surface,112:F02S20,doi:10.1029/2006JF000546.
Li S C,Nie L C,Liu B,et al.2015.Advanced detection and physical model test based on multi-electrode sources array resistivity method in tunnel.Chinese Journal of Geophysics(in Chinese),58(4):1434-1446,doi:10.6038/cjg20150429.
Li Y,Hu X Y,Kim K,et al.2010.Research of 1-D magnetotelluric parallel computation based on MPI.Progress in Geophysics(in Chinese),25(5):1612-1616,doi:10.3969/j.issn.1004-2903.2010.05.012.
Li Y G,Oldenburg D W.1992.Approximate inverse mappings in DC resistivity problems.Geophysical Journal International,109(2):343-362.
Li Y G,Oldenburg D W.2000.3-D inversion of induced polarization data.Geophysics,65(6):1931-1945.
Li Y X.2014.Seismic exploration in 2Dfrequency-domain forward based on parallel algorithms[Master′s thesis](in Chinese).Beijing:China University of Geosciences(Beijing).
Ma H,Tan H D,Guo Y.2015.Three-dimensional induced polarization parallel inversion using nonlinear conjugate gradients method.Mathematical Problems in Engineering,2015:Article ID 464793,doi:10.1155/2015/464793.
Oldenburg D W,Li Y G.1994.Inversion of induced polarization data.Geophysics,59(9):1327-1341.
Park S K,Van G P.1991.Inversion of pole-pole data for 3-Dresistivity structure beneath arrays of electrodes.Geophysics,56(7):951-960.
Pelton W H,Rijo L,Swift C M Jr.1978.Inversion of twodimensional resistivity and induced-polarization data.Geophysics,43(4):788-803.
Petrick W R Jr,Sill W R,Ward S H.1981.Three-dimensional resistivity inversion using alpha centers.Geophysics,46(8):1148-1162.
Revil A,Johnson T C,Finizola A.2010.Three-dimensional resistivity tomography of Vulcan′s forge,Vulcano Island,southern Italy.Geophysical Research Letters,37:L15308,doi:10.1029/2010GL043983.
Schwarzbach C,B9rner R U,Spitzer K.2005.Two-dimensional inversion of direct current resistivity data using aparallel,multi-objective genetic algorithm.Geophysical Journal International,162(3):685-695.
Shi G L,Zhang G X.2008.Macroscopic Field Theory(in Chinese).Wuhan:China University of Geosciences Publishing House.
Singh U K,Tiwari R K,Singh S B.2010.Inversion of 2-D DCresistivity data using rapid optimization and minimal complexity neural network.Nonlinear Processes in Geophysics,17(1):65-76.
Spitzer K.1995.A 3-D finite-difference algorithm for DC resistivity modeling using conjugate gradient methods.Geophysical Journal International,123(3):903-914.
Tan H D,Tong T,Lin C H.2006.The parallel 3Dmagnetotelluric forward modeling algorithm.Applied Geophysics,3(4):197-202,doi:10.1007/s11770-006-4001-5.
Tang J T,Zhang J F,Feng B,et a1.2007.Determination of borders for resistive oil and gas reservoirs by deviation rate using thehole-to-surface resistivity method.Chinese Journal of Geophysics(in Chinese),50(3):926-931.
van der Vorst H A.1992.Bi-CGSTAB:A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems.SIAM Journal on Scientific and Statistical Computing,13(2):631-644,doi:10.1137/0913035.
Wang J Y.2002.Inverse Theory in Geophysics.2nd ed.(in Chinese).Beijing:Higher Education Press.
Weiss C J.2013.Project APhiD:A Lorenz-gauged A-φdecomposition for parallelized computation of ultra-broadband electromagnetic induction in a fully heterogeneous Earth.Computers&Geosciences,58:40-52,doi:10.1016/j.cageo.2013.05.002.
Wu X P,Wang T T.2001.Study on some problems for 3Dresistivity inversion using conjugate gradient.Seismology and Geology(in Chinese),23(2):321-327.
Wu X P,Xu G M.2000.Study on 3-D resistivity inversion using conjugate gradient method.Chinese Journal of Geophysics(in Chinese),43(3):420-427.
Xiong J,Zou C C,Meng X H.2012.Using the BICGSTABalgorithm with the incomplete LU factorization precondictioning to implement2DFDFD induction logging fast forward modeling.Geoscience(in Chinese),26(6):1283-1288.
Yuval D,Oldenburg W.1996.DC resistivity and IP methods in acid mine drainage problems:results from the Copper Cliff mine tailings impoundments.Journal of Applied Geophysics,34(3):187-198,doi:10.1016/0926-9851(95)00020-8.
Zhang J,Mackie R L,Madden T R.1995.3-D resistivity forward modeling and inversion using conjugate gradients.Geophysics,60(5):1313-1325.
白登海,于晟.1995.电阻率层析成象理论和方法.地球物理学进展,10(1):56-75.
范国栋.2017.电阻率法在涪陵页岩气钻井平台地质条件勘查中的应用.∥中国石油学会2017年物探技术研讨会.天津,880-883.
李术才,聂利超,刘斌等.2015.多同性源阵列电阻率法隧道超前探测方法与物理模拟试验研究.地球物理学报,58(4):1434-1446,doi:10.6038/cig20150429.
李焱,胡祥云,金钢燮等.2010.基于MPI的一维大地电磁并行计算研究.地球物理学进展,25(5):1612-1616,doi:10.3969/j.issn.1004-2903.2010.05.012.
李祎昕.2014.地震勘探频率域二维正演并行算法研究[硕士论文].北京:中国地质大学(北京).
施国良,张国雄.2008.宏观场论.武汉:中国地质大学出版社.
汤井田,张继锋,冯兵等.2007.井地电阻率法歧离率确定高阻油气藏边界.地球物理学报,50(3):926-931.
王家映.2002.地球物理反演理论.2版.北京:高等教育出版社.
吴小平,汪彤彤.2001.利用共轭梯度方法的电阻率三维反演若干问题研究.地震地质,23(2):321-327.
吴小平,徐果明.2000.利用共轭梯度法的电阻率三维反演研究.地球物理学报,43(3):420-427.
熊杰,邹长春,孟小红.2012.不完全LU分解预条件BICGSTAB算法实现感应测井二维FDFD快速正演模拟.现代地质,26(6):1283-1288.