CSAMT法一维层状介质灵敏度分析
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摘要
为改善CSAMT一维反演的实用性,本文以电磁场数值模拟为基础,推导出偶极源激发下频率域电磁反演中的偏导数公式.并以三层水平层状地电模型为例,针对同线装置和赤道装置两种形式,利用扰动法对本文的半解析算法结果进行验证.对比结果表明无论同线还是赤道装置,本文半解析结果和扰动法计算结果拟合程度非常好,验证了偏导数公式推导及程序代码的正确性.进而,分析了CSAMT观测数据对中间薄层参数的灵敏度.灵敏度特征分析表明:CSAMT观测资料对中间低阻薄层比较敏感,对高阻薄层的分辨率较低,但对层厚度,即便是高阻薄层,仍存在较高的灵敏度.频率对层参数的灵敏度有重要影响.实际应用中,应同时考虑资料和参数加权,以提高中间层参数的求解能力.本文的算法不仅有助于CSAMT资料反演解释,同时为地下薄目标层的有效识别提供理论依据.
In order to improve the practicability of 1DCSAMT inversion,we derive the partial derivative of EM field with respect to earth parameters for a dipole transmitter.Taking a three-layer earth as example,we check the partial derivative results with those obtained from the perturbation method for both in-line and cross-line configurations.The comparison shows the good fitness,which indicates our formulas and codes are correct.Further we analyze the sensitivities of the CSAMT survey data to the parameters of a thin intermediate layer in the earth.The characteristics of the sensitivity curves show the relations between the resolution capability and the parameters of the middle layer.The sensitivities to low resistivity is higher than to high resistivity.However,the sensitivities to the thickness of the middle layer is high whether the middle layer is of low resistivity or not.Another parameter,frequencies,affect the sensitivity more in the observation.Therefore,in order to improve the stability of the solution of the middle layer,the weight techniques among data and parameters should be considered in the inversion.The study in this paper serves not only to the CSAMT data inversion,but also to the effective solution of a thin-layer target in the earth.
In order to improve the practicability of 1DCSAMT inversion,we derive the partial derivative of EM field with respect to earth parameters for a dipole transmitter.Taking a three-layer earth as example,we check the partial derivative results with those obtained from the perturbation method for both in-line and cross-line configurations.The comparison shows the good fitness,which indicates our formulas and codes are correct.Further we analyze the sensitivities of the CSAMT survey data to the parameters of a thin intermediate layer in the earth.The characteristics of the sensitivity curves show the relations between the resolution capability and the parameters of the middle layer.The sensitivities to low resistivity is higher than to high resistivity.However,the sensitivities to the thickness of the middle layer is high whether the middle layer is of low resistivity or not.Another parameter,frequencies,affect the sensitivity more in the observation.Therefore,in order to improve the stability of the solution of the middle layer,the weight techniques among data and parameters should be considered in the inversion.The study in this paper serves not only to the CSAMT data inversion,but also to the effective solution of a thin-layer target in the earth.
引文
Anderson W L.1989.A hybrid fast Hankel transform algorithm forelectromagnetic modeling[J].Geophysics,54(2):263-266.
Di Q Y,Unsworth M,Wang M Y.2004.2.5-D CSAMT modelingwith the finite element method over 2-D complex earth media[J].Chinese J.Geophys.(in Chinese),47(4):723-730.
Lei D.2010.Studies and applications of 2-D CSAMT modeling andinversion with a dipole source and topography[J].Chinese J.Geophys.(in Chinese),53(4):982-993.
Li X B,Oskooi B,Laust B P.2000.Inversion of controlled-sourcetensor magnetotelluric data for a layered earth with azimuthalanisotropy[J].Geophysics,65(2):452-464.
Lin C H,Tan H D,Tong T.2011.The possibility of obtainingnearby 3Dresistivity structure from magnetotelluric 2Dprofiledata using 3Dinversion[J].Chinese J.Geophys.(in Chinese),54(1):245-256.
Lugao P P D,Wannamaker P E.1996.Calculating the twodimensional magnetotelluric Jacobian in finite elements usingreciprocity[J].Geophys.J.Int.,127:806-810.
MeGillivra P R,Oldenburg D W,Ellis R G,et al.1994.Calculationof sensitivities for the frequeney domain electromagneticproblem[J].Geophys.J.Int.,116(1):1-4.
Ou D X,Wang J L.2005.The fast magnetotelluric inversion of 2-Dblock structrue[J].Geophysical Prospecting for Petroleum(GPP)(in Chinese),44(5):525-528.
Pan Y,Wang G E,Chen L S,et al.1987.Analytic method for MTdata of 2Delectric structure[J].Oil Geophysical Prospecting(in Chinese),22(3):315-328.
Piao H R.1990.Theory of Electromagnetic sounding(in Chinese)[M].Beijing:Geology Press.
Portniaguine O,Zhdanov M S.1999.Focusing geophysical inversionimages[J].Geophysics,64(3):874-887.
Shen J S,Sun W B.2008.Reciprocity of electromagnetic responseand its application in sen-sitivity calculation[J].Progress inExploration Geophysics(PEG)(in Chinese),31(1):25-33.
Shi X M,Wang J Y.1998.One dimensional magnetotelluricsounding inversion using simulated annealing[J].Journal ofEarth Science(in Chinese),23(5):542-545.
Tan H D,Yu Q F,Booker J,et al.2003.Three-dimensional rapidrelaxation inversion for the magnetotelluric method[J].ChineseJ.Geophys.(in Chinese),46(6):850-854.
Tang J T,He J S.2005.Controlled source audio frequencymagnetotelluric method and its application(in Chinese)[M].Changsha:Central South University Press.
Wang R,Wang M Y 2007.Inversion of 1-D full CSAMT data[J].Oil Geophysical Prospecting(OGP)(in Chinese),42(1):107-114.
Wang R,Wang M Y,Lu Y L.2008.RRI inversion ofelectromagnetic sounding in frequency domain[J].Progress inGeophys(in Chinese),23(5):1560-1567.
Wang R,Yin C C,Wang M Y,et al.2012.Simulated annealing forcontrolled-source audio-frequency magnetotelluric data inversion[J].Geophysics,77(2):127-133.
Xiong B,Luo Y Z,Qiang J K.2004.Methods for calculatingsensitivities for 2.5Dtransient electromagnetic inversion[J].Progress in Geophysics(in Chinese),19(3):616-620.
Yang C F,Lin C Y.1994.The magnetotelluric parameterizedinversion of 2-D layered model[J].Northwestern SeismologicalJournal(in Chinese),16(4):10-19.
Yang H,Wang Y T,Wang J L,et al.2001.Pseudo 2Dsimulatedannealing constraint inversion for MT data[J].MarinePetroleum Geology(in Chinese),6(1):47-52.
Yin C C.1994.One-dimensional modeling of CSAMT method andevaluation of calculation precision[J].Journal of ChangchunUniversity of Earth Sciences(in Chinese),24(4):438-453.
Zhang L C.2011.Controlled Source Audio-frequencyMagnetotelluric Inversion for Minimum Structure(in Chinese)[D].Changsha:Central South University.
底青云,Unsworth M,王妙月.2004.复杂介质有限元法2.5维可控源音频大地电磁法数值模拟[J].地球物理学报,47(4):723-730.
雷达.2010.起伏地形下CSAMT二维正反演研究与应用[J].地球物理学报,53(4):982-993.
林昌洪,谭捍东,佟拓.2011.利用大地电磁三维反演方法获得二维剖面附近三维电阻率结构的可行性[J].地球物理学报,54(1):245-256.
欧东新,王家林.2005.二维块状结构大地电磁快速反演[J].石油物探,44(5):525-528.
潘渝,王光愕,陈乐寿,等.1987.二维地电构造大地电磁测深资料的解析方法[J],石油地球物理勘探,22(3):315-328.
朴化荣.1990.电磁测深法原理[M].北京:地质出版社.
沈金松,孙文博.2008.电磁响应的互换原理及其在响应灵敏度计算中的应用[J].勘探地球物理进展,31(1):26-33.
师学明,王家映.1998.一维层状介质大地电磁模拟退火反演法[J].地球科学—中国地质大学学报,23(5):542-545.
谭捍东,余钦范,Booker J,等.2003.大地电磁法三维快速松弛反演[J].地球物理学报,46(6):850-854.
汤井田,何继善.2005.可控源音频大地电磁法及应用[M].长沙:中南大学出版社.
王若,王妙月.2007.一维全资料CSAMT反演[J].石油地球物理勘探,42(1):107-114.
王若,王妙月,卢元林.2008.频率域2维电磁测深资料的RRI反演[J].地球物理学进展,23(5):1560-1567.
王若,王妙月,底青云,等.2014.CSAMT三维单分量有限元正演[J].地球物理学进展,29(2):839-845.
熊彬,罗延钟,强建科.2004.瞬变电磁法2.5维反演中灵敏度矩阵计算方法(I)[J].地球物理学进展,19(3):616-620.
杨长福,林长佑.1994.大地电磁二维层状模型参数化反演[J].西北地震学报,16(4):10-19.
杨辉,王永涛,王家林,等.2001.大地电磁测深拟二维模拟退火约束反演[J].海相油气地质,6(1):47-52.
殷长春.1994.可控源音频磁大地电流法一维正演及精度评价[J].长春地质学学报,24(4):438-453.
张林成.2011.可控源音频大地电磁测深最小构造反演[D].长沙:中南大学.
Di Q Y,Unsworth M,Wang M Y.2004.2.5-D CSAMT modelingwith the finite element method over 2-D complex earth media[J].Chinese J.Geophys.(in Chinese),47(4):723-730.
Lei D.2010.Studies and applications of 2-D CSAMT modeling andinversion with a dipole source and topography[J].Chinese J.Geophys.(in Chinese),53(4):982-993.
Li X B,Oskooi B,Laust B P.2000.Inversion of controlled-sourcetensor magnetotelluric data for a layered earth with azimuthalanisotropy[J].Geophysics,65(2):452-464.
Lin C H,Tan H D,Tong T.2011.The possibility of obtainingnearby 3Dresistivity structure from magnetotelluric 2Dprofiledata using 3Dinversion[J].Chinese J.Geophys.(in Chinese),54(1):245-256.
Lugao P P D,Wannamaker P E.1996.Calculating the twodimensional magnetotelluric Jacobian in finite elements usingreciprocity[J].Geophys.J.Int.,127:806-810.
MeGillivra P R,Oldenburg D W,Ellis R G,et al.1994.Calculationof sensitivities for the frequeney domain electromagneticproblem[J].Geophys.J.Int.,116(1):1-4.
Ou D X,Wang J L.2005.The fast magnetotelluric inversion of 2-Dblock structrue[J].Geophysical Prospecting for Petroleum(GPP)(in Chinese),44(5):525-528.
Pan Y,Wang G E,Chen L S,et al.1987.Analytic method for MTdata of 2Delectric structure[J].Oil Geophysical Prospecting(in Chinese),22(3):315-328.
Piao H R.1990.Theory of Electromagnetic sounding(in Chinese)[M].Beijing:Geology Press.
Portniaguine O,Zhdanov M S.1999.Focusing geophysical inversionimages[J].Geophysics,64(3):874-887.
Shen J S,Sun W B.2008.Reciprocity of electromagnetic responseand its application in sen-sitivity calculation[J].Progress inExploration Geophysics(PEG)(in Chinese),31(1):25-33.
Shi X M,Wang J Y.1998.One dimensional magnetotelluricsounding inversion using simulated annealing[J].Journal ofEarth Science(in Chinese),23(5):542-545.
Tan H D,Yu Q F,Booker J,et al.2003.Three-dimensional rapidrelaxation inversion for the magnetotelluric method[J].ChineseJ.Geophys.(in Chinese),46(6):850-854.
Tang J T,He J S.2005.Controlled source audio frequencymagnetotelluric method and its application(in Chinese)[M].Changsha:Central South University Press.
Wang R,Wang M Y 2007.Inversion of 1-D full CSAMT data[J].Oil Geophysical Prospecting(OGP)(in Chinese),42(1):107-114.
Wang R,Wang M Y,Lu Y L.2008.RRI inversion ofelectromagnetic sounding in frequency domain[J].Progress inGeophys(in Chinese),23(5):1560-1567.
Wang R,Yin C C,Wang M Y,et al.2012.Simulated annealing forcontrolled-source audio-frequency magnetotelluric data inversion[J].Geophysics,77(2):127-133.
Xiong B,Luo Y Z,Qiang J K.2004.Methods for calculatingsensitivities for 2.5Dtransient electromagnetic inversion[J].Progress in Geophysics(in Chinese),19(3):616-620.
Yang C F,Lin C Y.1994.The magnetotelluric parameterizedinversion of 2-D layered model[J].Northwestern SeismologicalJournal(in Chinese),16(4):10-19.
Yang H,Wang Y T,Wang J L,et al.2001.Pseudo 2Dsimulatedannealing constraint inversion for MT data[J].MarinePetroleum Geology(in Chinese),6(1):47-52.
Yin C C.1994.One-dimensional modeling of CSAMT method andevaluation of calculation precision[J].Journal of ChangchunUniversity of Earth Sciences(in Chinese),24(4):438-453.
Zhang L C.2011.Controlled Source Audio-frequencyMagnetotelluric Inversion for Minimum Structure(in Chinese)[D].Changsha:Central South University.
底青云,Unsworth M,王妙月.2004.复杂介质有限元法2.5维可控源音频大地电磁法数值模拟[J].地球物理学报,47(4):723-730.
雷达.2010.起伏地形下CSAMT二维正反演研究与应用[J].地球物理学报,53(4):982-993.
林昌洪,谭捍东,佟拓.2011.利用大地电磁三维反演方法获得二维剖面附近三维电阻率结构的可行性[J].地球物理学报,54(1):245-256.
欧东新,王家林.2005.二维块状结构大地电磁快速反演[J].石油物探,44(5):525-528.
潘渝,王光愕,陈乐寿,等.1987.二维地电构造大地电磁测深资料的解析方法[J],石油地球物理勘探,22(3):315-328.
朴化荣.1990.电磁测深法原理[M].北京:地质出版社.
沈金松,孙文博.2008.电磁响应的互换原理及其在响应灵敏度计算中的应用[J].勘探地球物理进展,31(1):26-33.
师学明,王家映.1998.一维层状介质大地电磁模拟退火反演法[J].地球科学—中国地质大学学报,23(5):542-545.
谭捍东,余钦范,Booker J,等.2003.大地电磁法三维快速松弛反演[J].地球物理学报,46(6):850-854.
汤井田,何继善.2005.可控源音频大地电磁法及应用[M].长沙:中南大学出版社.
王若,王妙月.2007.一维全资料CSAMT反演[J].石油地球物理勘探,42(1):107-114.
王若,王妙月,卢元林.2008.频率域2维电磁测深资料的RRI反演[J].地球物理学进展,23(5):1560-1567.
王若,王妙月,底青云,等.2014.CSAMT三维单分量有限元正演[J].地球物理学进展,29(2):839-845.
熊彬,罗延钟,强建科.2004.瞬变电磁法2.5维反演中灵敏度矩阵计算方法(I)[J].地球物理学进展,19(3):616-620.
杨长福,林长佑.1994.大地电磁二维层状模型参数化反演[J].西北地震学报,16(4):10-19.
杨辉,王永涛,王家林,等.2001.大地电磁测深拟二维模拟退火约束反演[J].海相油气地质,6(1):47-52.
殷长春.1994.可控源音频磁大地电流法一维正演及精度评价[J].长春地质学学报,24(4):438-453.
张林成.2011.可控源音频大地电磁测深最小构造反演[D].长沙:中南大学.