带井观测高密度电阻率法2.5维非结构化网格反演
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摘要
在地表高密度电阻率勘探的基础上引入井中电极实现带井高密度电阻率测量,可以有效扩展探测范围、提高分辨率.本文基于非结构化网格研究了带井高密度电阻率数据的2.5维正则化反演.反演采用最小结构稳定因子构建正则化反演目标函数,并对非结构化网格模型梯度算子的计算进行了推导;采用高斯-牛顿法求解反演目标函数,并通过稳定双共轭梯度法求解高斯-牛顿方程,实现了反演目标函数的快速、稳定求解.在设计算法的基础上,对三种在野外常用的带井观测方式进行反演试算,并与地表观测方式相比较,讨论了不同的布极方式对反演结果的影响,验证了带井观测高密度方法的优越性,为实际工作提供了参考.算法成功应用于浙江某滨海区公路基岩面调查工作,得到了理想的反演效果.
On the basis of surface multi-electrode DC exploration, introducting electrodes into a borehole can effectively expand the detection depth and detection area, the resolution can also be improved by this way. The research have studied the 2.5 D regularized inversion about borehole and surface multi-electrode DC data, the whole process used the unstructured meshing. The function adopted the minimum structural stability factor, and the calculation of unstructured grid model gradient operator also is deduced in this paper. To solve the regularized inversion cost function, using the Gauss-Newton method, and adopted the bi-conjugate gradient stabilized algorithm to solve the Gauss-Newton equation stably.Using the designed inversion scheme, three different electrode arrangements about the surface and borehole multi-electrode DC method are discussed in this paper, which could be used to guide the actual work in the field.. Comparing the results with the surface observation method, it verified the superiority of the method of borehole and surface multi-electrode DC method. Finally, we take an application for exploring bedrock in the littoral area of Zhejiang Province, and getting a successful exploration.
On the basis of surface multi-electrode DC exploration, introducting electrodes into a borehole can effectively expand the detection depth and detection area, the resolution can also be improved by this way. The research have studied the 2.5 D regularized inversion about borehole and surface multi-electrode DC data, the whole process used the unstructured meshing. The function adopted the minimum structural stability factor, and the calculation of unstructured grid model gradient operator also is deduced in this paper. To solve the regularized inversion cost function, using the Gauss-Newton method, and adopted the bi-conjugate gradient stabilized algorithm to solve the Gauss-Newton equation stably.Using the designed inversion scheme, three different electrode arrangements about the surface and borehole multi-electrode DC method are discussed in this paper, which could be used to guide the actual work in the field.. Comparing the results with the surface observation method, it verified the superiority of the method of borehole and surface multi-electrode DC method. Finally, we take an application for exploring bedrock in the littoral area of Zhejiang Province, and getting a successful exploration.
引文
Barbosa V C F,Silva J A O B.1994.Generalized compact gravity inversion [J].Geophysics,59(1):57- 68.
FAN Jian,MA Wei,XIA Xun-yin,et al.2018.Application of high density resistivity method on site-slection for the oyster reefs museum in QiLihai,Tianjin [J].Progress in Geophysics (in Chinese),33(2):0790- 0796,doi:10.6038/pg2018BB0168.
Farquharson C G.,Oldenburg D W.2000.Automatic estimation of the trade-off parameter in nonlinear inverse problems using the GCV and L-curve criteria [J].SEG Technical Program Expanded Abstracts,19(1):265-268.
Greaves D M,Borthwick A G L.1999.Hierarchical tree-based finite element mesh generation [J].Int.J.Numer.Methods Eng.,45(4):447- 471.
Haber E,Heldmann S,Ascher U.2007.Adaptive finite volume method for distributed non-smooth parameter identification [J].Inverse Probl.,23(4):1659-1676.
HAN Bo,DOU Yi-xin,DING Liang.2012.Electrical resistivity tomography by using a hybrid regularization [J].Chinese Journal of Geophysics (in Chinese),55(3):970-980,doi:10.6038/j.issn.0001-5733.2012.03.027.
Hermann V,K?ser M,Castro CE.2011.Non-conforming hybrid meshes for efficient 2-D wave propagation using the Discontinuous Galerkin Method [J].Geophysical Journal International,184(2):746-758.
KE Gan-pan,HUANG Qing-hua.2009.3D Forward and Inversion Problems of Borehole-to-Surface Electrical Method [J].Acta Scientiarum Naturalium Universitatis Pekinensis (in chinese),45(2):264-272.
Lelièvre P G,Farquharson C G.2013.Gradient and smoothness regularization operators for geophysical inversion on unstructured meshes [J].Geophys.J.Int.,195(1):330-341.
LI Man,LIN Wen-dong.2014.The study of regularization inversion for 2.5 dimension dc resistivity based on minimum support stabilizing factor [J].Journal of East China Institute of Technology (Natural Science Edition) (in Chinese),37(3):292-298.
LI Yong,LIN Ping-rong,Liu Wei-qiang,et al.2017.2.5-D numerical simulation of the marine controlled-source electromagnetic method based on isoparametric FEM for the conductivity orthotropic medium [J].Chinese J.Geophys.(in Chinese),60(2):748-765,doi:10.6038/cjg20170226.
LI Y G,Oldenburg D W.1992.Approximate inverse mappings in DC resistivity problems [J].Geophys.J.Internet,109(2):343-362.
LI Y G,Oldenburg D W.2000.3-D inversion of induced polarization data [J].Geophysics,65(6):1931-1945.
LIU Xiao-jun,WANG Jia-ling,CHEN Bing,et al.2007.The Focusing inversion of 2-D magnetotelluric [J].Oil Geophysical Prospecting (in Chinese),42(3):338-342.
Lokea M H,Dahlin T.2002.A comparison of the Gauss-Newton and quasi-Newton methods in resistivity imaging inversion [J].Journal of Applied Geophysics,49(3):149-162.
RUAN Bai-yao.2001.Generation method of the partial derivatives of the apparent resistivity with respect to the model resistivity parameter [J].Geology and Prospecting (in chinese),37(6):39- 41.
RUAN Bai-yao,XIONG Bin.2002.A finite element modeling of three-dimensional resistivity sounding with continuous conductivity [J].Chinese Journal of Geophysics (in chinese),45(1):131-138,doi:10.3321/j.issn:0001-5733.2002.01.016.
Saad Y.2003.Iterative Methods for Sparse Linear Systems [M].Minnessota Twin Cities:Society for Industrial and Applied Mathematics,267-268.
Stenerud V R,Lie K,Kippe V.2009.Generalized travel-time inversion on unstructured grids [J].Petrol.Sci.Eng,65(3- 4):175-187.
TANG Jin-tian,WANG Fei-yan,REN Zheng-yong.2010.2.5-D DC resistivity modeling by adaptive finite-element method with unstructured triangulation [J].Chinese J.Geophys.(in chinese),53(3):708-716,doi:10.3969/j.issn.0001-5733.2010.03.026.
WANG Qi-jun,HU Yan-lin,DU Xing-feng,et al.2009.Application of the high-density resistivity method in project exploration [J].Progress in Geophysics (in chinese),24(01):335-339.
WANG Ya-lu,DI Qing-yun,WANG Ruo.2017.Three-dimensional modeling of controlled-source audio-frequency magnetotellurics using the finite element method on an unstructured grid [J].Chinese J.Geophys.(in Chinese),60(3):1158-1167,doi:10.6038/cjg20170326.
Williams NC.2008.Geologically-constrained UBC-GIF gravity and magnetic inversions with examples from the Agnew-Wiluna greenstone belt,Western Australia [D].Canada:University of British Columbia.
WU Xiao-ping.2005.3-D Resistivity inversion under the condition of uneven terrain [J].Chinese J.Geophys.(in Chinese),48(4):932-936,doi:10.3321/j.issn:0001-5733.2005.04.028.
XU Shi-zhe.1994.The Finite element method in Geophysics [M].Beijing:Science Press,178-193.
YIN Chang-chun,ZHANG Bo,LIU Yun-he,et al.2017.A goal-oriented adaptive algorithm for 3D magnetotelluric forward modeling [J].Chinese J.Geophys.(in Chinese),60(1):327-336,doi:10.6038/cjg20170127.
ZHANG Zhi-yong,LI Man,DENG Juzhi,et al.2015a.Secondary Field-Based Two-Dimensional Magnetotelluric Numerical Simulation by Finite Element Method [J].Journal of TongJi University (Natural Science) (in Chinese),43(8):1259-1265.
ZHANG Zhi-yong,LIU Qing-cheng.2013.2D MT numerical simulation using FEM based on bi-tree grid [J].Oil Geophysical Prospecting (in Chinese),48(3):482- 487.
ZHANG Zhi-yong,ZHOU Feng,LI Ze-lin.2015b.2.5D focusing inversion for borehole-surface electrical data based on minimum gradient support function [J].The Chinese Journal of Nonferrous Metals (in Chinese),25(11):3182-3189.
Zhdanov M S.2002.Geophysical inverse theory and regularization problems [M].Elsevier Science,65-84.
Zhdanov M S,Fang S.1996.3-D quasi-linear electromagnetic inversion [J].Radio Science,4(3):741-745.
ZHOU Bing,Greenhalgh S.1997.A synthetic study on crosshole resistivity imaging with different electrode arrays [J].Explor.Geophys.,28(1-2):1-5.
范剑,马为,夏训银,等.2018.高密度电阻率法在天津市七里海牡蛎礁博物馆选址中的应用[J].地球物理学进展,33(2):0790- 0796,doi:10.6038/pg2018BB0168.
韩波,窦以鑫,丁亮.2012.电阻率成像的混合正则化反演算法[J].地球物理学报,55(3):970-980,doi:10.6038/j.issn.0001-5733.2012.03.027.
柯敢攀,黄清华.2009.井地电法的三维正反演研究[J].北京大学学报:自然科学版,45(2):264-272.
李曼,林文东.2014.基于最小支持的2.5维直流电阻率正则化反演研究[J].东华理工大学学报:自然科学版,37(3):292-298.
刘小军,王家林,陈冰,等.2007.二维大地电磁数据的聚焦反演算法探讨[J].石油地球物理勘探,42(3):338-342.
李勇,林品荣,刘卫强,等.2017.2.5维电导率正交各向异性海洋可控源电磁等参有限元数值模拟[J].地球物理学报,60(2):748-765,doi:10.6038/cjg20170226.
阮百尧.2001.视电阻率对模型电阻率的偏导数矩阵计算方法[J].地质与勘探,37(6):39- 41.
阮百尧,熊彬.2002.电导率连续变化的三维电阻率测深有限元模拟[J].地球物理学报,45(1):131-138,doi:10.3321/j.issn:0001-5733.2002.01.016.
汤井田,王飞燕,任政勇.2010.基于非结构化网格的2.5-D直流电阻率自适应有限元数值模拟[J].地球物理学报,53(3):708-716,doi:10.3969/j.issn.0001-5733.2010.03.026.
王启军,胡延林,都兴锋,等.2009.高密度电阻率法在工程勘查中的应用[J].地球物理学进展,24(01):335-339.
王亚璐,底青云,王若.2017.三维CSAMT法非结构化网格有限元数值模拟[J].地球物理学报,60(3):1158-1167,doi:10.6038/cjg20170326.
吴小平.2005.非平坦地形条件下电阻率三维反演[J].地球物理学报,48(4):932-936,doi:10.3321/j.issn:0001-5733.2005.04.028.
徐世浙.1994.地球物理中的有限单元法[M].北京:科学出版社,178-193.
殷长春,张博,刘云鹤,等.2017.面向目标自适应三维大地电磁正演模拟[J].地球物理学报,60(1):327-336,doi:10.6038/cjg20170127.
张志勇,李曼,邓居智,等.2015a.基于二次场算法的大地电磁二维有限单元法正演[J].同济大学学报:自然科学版.43(8):1259-1265.
张志勇,刘庆成.2013.基于收缩二叉树结构网格剖分的大地电磁二维有限单元法正演研究[J].石油地球物理勘探,48(03):482- 487.
张志勇,周峰,李泽林.2015b.基于最小梯度支撑的2.5D井地电位法正则化聚焦反演[J].中国有色金属学报,25(11):3182-3189.
FAN Jian,MA Wei,XIA Xun-yin,et al.2018.Application of high density resistivity method on site-slection for the oyster reefs museum in QiLihai,Tianjin [J].Progress in Geophysics (in Chinese),33(2):0790- 0796,doi:10.6038/pg2018BB0168.
Farquharson C G.,Oldenburg D W.2000.Automatic estimation of the trade-off parameter in nonlinear inverse problems using the GCV and L-curve criteria [J].SEG Technical Program Expanded Abstracts,19(1):265-268.
Greaves D M,Borthwick A G L.1999.Hierarchical tree-based finite element mesh generation [J].Int.J.Numer.Methods Eng.,45(4):447- 471.
Haber E,Heldmann S,Ascher U.2007.Adaptive finite volume method for distributed non-smooth parameter identification [J].Inverse Probl.,23(4):1659-1676.
HAN Bo,DOU Yi-xin,DING Liang.2012.Electrical resistivity tomography by using a hybrid regularization [J].Chinese Journal of Geophysics (in Chinese),55(3):970-980,doi:10.6038/j.issn.0001-5733.2012.03.027.
Hermann V,K?ser M,Castro CE.2011.Non-conforming hybrid meshes for efficient 2-D wave propagation using the Discontinuous Galerkin Method [J].Geophysical Journal International,184(2):746-758.
KE Gan-pan,HUANG Qing-hua.2009.3D Forward and Inversion Problems of Borehole-to-Surface Electrical Method [J].Acta Scientiarum Naturalium Universitatis Pekinensis (in chinese),45(2):264-272.
Lelièvre P G,Farquharson C G.2013.Gradient and smoothness regularization operators for geophysical inversion on unstructured meshes [J].Geophys.J.Int.,195(1):330-341.
LI Man,LIN Wen-dong.2014.The study of regularization inversion for 2.5 dimension dc resistivity based on minimum support stabilizing factor [J].Journal of East China Institute of Technology (Natural Science Edition) (in Chinese),37(3):292-298.
LI Yong,LIN Ping-rong,Liu Wei-qiang,et al.2017.2.5-D numerical simulation of the marine controlled-source electromagnetic method based on isoparametric FEM for the conductivity orthotropic medium [J].Chinese J.Geophys.(in Chinese),60(2):748-765,doi:10.6038/cjg20170226.
LI Y G,Oldenburg D W.1992.Approximate inverse mappings in DC resistivity problems [J].Geophys.J.Internet,109(2):343-362.
LI Y G,Oldenburg D W.2000.3-D inversion of induced polarization data [J].Geophysics,65(6):1931-1945.
LIU Xiao-jun,WANG Jia-ling,CHEN Bing,et al.2007.The Focusing inversion of 2-D magnetotelluric [J].Oil Geophysical Prospecting (in Chinese),42(3):338-342.
Lokea M H,Dahlin T.2002.A comparison of the Gauss-Newton and quasi-Newton methods in resistivity imaging inversion [J].Journal of Applied Geophysics,49(3):149-162.
RUAN Bai-yao.2001.Generation method of the partial derivatives of the apparent resistivity with respect to the model resistivity parameter [J].Geology and Prospecting (in chinese),37(6):39- 41.
RUAN Bai-yao,XIONG Bin.2002.A finite element modeling of three-dimensional resistivity sounding with continuous conductivity [J].Chinese Journal of Geophysics (in chinese),45(1):131-138,doi:10.3321/j.issn:0001-5733.2002.01.016.
Saad Y.2003.Iterative Methods for Sparse Linear Systems [M].Minnessota Twin Cities:Society for Industrial and Applied Mathematics,267-268.
Stenerud V R,Lie K,Kippe V.2009.Generalized travel-time inversion on unstructured grids [J].Petrol.Sci.Eng,65(3- 4):175-187.
TANG Jin-tian,WANG Fei-yan,REN Zheng-yong.2010.2.5-D DC resistivity modeling by adaptive finite-element method with unstructured triangulation [J].Chinese J.Geophys.(in chinese),53(3):708-716,doi:10.3969/j.issn.0001-5733.2010.03.026.
WANG Qi-jun,HU Yan-lin,DU Xing-feng,et al.2009.Application of the high-density resistivity method in project exploration [J].Progress in Geophysics (in chinese),24(01):335-339.
WANG Ya-lu,DI Qing-yun,WANG Ruo.2017.Three-dimensional modeling of controlled-source audio-frequency magnetotellurics using the finite element method on an unstructured grid [J].Chinese J.Geophys.(in Chinese),60(3):1158-1167,doi:10.6038/cjg20170326.
Williams NC.2008.Geologically-constrained UBC-GIF gravity and magnetic inversions with examples from the Agnew-Wiluna greenstone belt,Western Australia [D].Canada:University of British Columbia.
WU Xiao-ping.2005.3-D Resistivity inversion under the condition of uneven terrain [J].Chinese J.Geophys.(in Chinese),48(4):932-936,doi:10.3321/j.issn:0001-5733.2005.04.028.
XU Shi-zhe.1994.The Finite element method in Geophysics [M].Beijing:Science Press,178-193.
YIN Chang-chun,ZHANG Bo,LIU Yun-he,et al.2017.A goal-oriented adaptive algorithm for 3D magnetotelluric forward modeling [J].Chinese J.Geophys.(in Chinese),60(1):327-336,doi:10.6038/cjg20170127.
ZHANG Zhi-yong,LI Man,DENG Juzhi,et al.2015a.Secondary Field-Based Two-Dimensional Magnetotelluric Numerical Simulation by Finite Element Method [J].Journal of TongJi University (Natural Science) (in Chinese),43(8):1259-1265.
ZHANG Zhi-yong,LIU Qing-cheng.2013.2D MT numerical simulation using FEM based on bi-tree grid [J].Oil Geophysical Prospecting (in Chinese),48(3):482- 487.
ZHANG Zhi-yong,ZHOU Feng,LI Ze-lin.2015b.2.5D focusing inversion for borehole-surface electrical data based on minimum gradient support function [J].The Chinese Journal of Nonferrous Metals (in Chinese),25(11):3182-3189.
Zhdanov M S.2002.Geophysical inverse theory and regularization problems [M].Elsevier Science,65-84.
Zhdanov M S,Fang S.1996.3-D quasi-linear electromagnetic inversion [J].Radio Science,4(3):741-745.
ZHOU Bing,Greenhalgh S.1997.A synthetic study on crosshole resistivity imaging with different electrode arrays [J].Explor.Geophys.,28(1-2):1-5.
范剑,马为,夏训银,等.2018.高密度电阻率法在天津市七里海牡蛎礁博物馆选址中的应用[J].地球物理学进展,33(2):0790- 0796,doi:10.6038/pg2018BB0168.
韩波,窦以鑫,丁亮.2012.电阻率成像的混合正则化反演算法[J].地球物理学报,55(3):970-980,doi:10.6038/j.issn.0001-5733.2012.03.027.
柯敢攀,黄清华.2009.井地电法的三维正反演研究[J].北京大学学报:自然科学版,45(2):264-272.
李曼,林文东.2014.基于最小支持的2.5维直流电阻率正则化反演研究[J].东华理工大学学报:自然科学版,37(3):292-298.
刘小军,王家林,陈冰,等.2007.二维大地电磁数据的聚焦反演算法探讨[J].石油地球物理勘探,42(3):338-342.
李勇,林品荣,刘卫强,等.2017.2.5维电导率正交各向异性海洋可控源电磁等参有限元数值模拟[J].地球物理学报,60(2):748-765,doi:10.6038/cjg20170226.
阮百尧.2001.视电阻率对模型电阻率的偏导数矩阵计算方法[J].地质与勘探,37(6):39- 41.
阮百尧,熊彬.2002.电导率连续变化的三维电阻率测深有限元模拟[J].地球物理学报,45(1):131-138,doi:10.3321/j.issn:0001-5733.2002.01.016.
汤井田,王飞燕,任政勇.2010.基于非结构化网格的2.5-D直流电阻率自适应有限元数值模拟[J].地球物理学报,53(3):708-716,doi:10.3969/j.issn.0001-5733.2010.03.026.
王启军,胡延林,都兴锋,等.2009.高密度电阻率法在工程勘查中的应用[J].地球物理学进展,24(01):335-339.
王亚璐,底青云,王若.2017.三维CSAMT法非结构化网格有限元数值模拟[J].地球物理学报,60(3):1158-1167,doi:10.6038/cjg20170326.
吴小平.2005.非平坦地形条件下电阻率三维反演[J].地球物理学报,48(4):932-936,doi:10.3321/j.issn:0001-5733.2005.04.028.
徐世浙.1994.地球物理中的有限单元法[M].北京:科学出版社,178-193.
殷长春,张博,刘云鹤,等.2017.面向目标自适应三维大地电磁正演模拟[J].地球物理学报,60(1):327-336,doi:10.6038/cjg20170127.
张志勇,李曼,邓居智,等.2015a.基于二次场算法的大地电磁二维有限单元法正演[J].同济大学学报:自然科学版.43(8):1259-1265.
张志勇,刘庆成.2013.基于收缩二叉树结构网格剖分的大地电磁二维有限单元法正演研究[J].石油地球物理勘探,48(03):482- 487.
张志勇,周峰,李泽林.2015b.基于最小梯度支撑的2.5D井地电位法正则化聚焦反演[J].中国有色金属学报,25(11):3182-3189.
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