井地2.5维DC反演研究
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摘要
开展了不同观测方式的井地2.5D直流电阻率反演研究。①从2.5维直流电阻率满足的边值问题出发,采用变分原理结合节点线性基函数推导了2.5维井地DC满足的积分弱解形式;②构建了二阶最大平滑稳定泛函的2.5维井地直流电阻率正则化目标函数,采用共轭梯度算法对正则化目标函数进行最优化求解,并采用逐步衰减正则化因子的求解策略来提高反演的稳定性;③设计了均匀半空间模型得到的数值解与解析解对比,电位的相对误差在2%以内,阐述正演算法的正确性和高精度。另外,分析了不同观测装置的2.5维井地直流电阻率异常体特征,并对不同观测方式对2.5维井地DC理论数据进行反演研究。研究结果表明,井中数据的引入提高了2.5 DC对纵向探测的分辨率能力,同时提高了2.5 DC反演有效性以及准确性。
In this paper, the inversion of 2.5 D DC resistivity in well ground with different observation modes is carried out. First of all, based on the boundary value problem of 2.5 D DC resistivity, the integral weak solution form of 2.5 D well ground DC is deduced by the variational principle and the node linear basis function. Secondly, the objective function of 2.5-D well ground DC resistivity is constructed for the second order maximum smooth stability functional, and the conjugate gradient algorithm is used to optimize the regularization objective function and the gradual Attenuation regularization factor solution strategy to improve the stability of inversion; Finally, The numerical solution obtained by the uniform half-space model is compared with the analytical solution. The relative error of the potential is within 2%, and the correctness and high precision of the forward algorithm are expounded. In addition, the characteristics of DC resistivity anomalies in 2.5-well wells with different observation devices are analyzed, and the theoretical data of 2.5-well well DCs are inversely studied by different observation methods. The results show that the introduction of well data improves the resolution of 2.5 DC for longitudinal detection, while improving the validity and accuracy of 2.5 DC inversion.
In this paper, the inversion of 2.5 D DC resistivity in well ground with different observation modes is carried out. First of all, based on the boundary value problem of 2.5 D DC resistivity, the integral weak solution form of 2.5 D well ground DC is deduced by the variational principle and the node linear basis function. Secondly, the objective function of 2.5-D well ground DC resistivity is constructed for the second order maximum smooth stability functional, and the conjugate gradient algorithm is used to optimize the regularization objective function and the gradual Attenuation regularization factor solution strategy to improve the stability of inversion; Finally, The numerical solution obtained by the uniform half-space model is compared with the analytical solution. The relative error of the potential is within 2%, and the correctness and high precision of the forward algorithm are expounded. In addition, the characteristics of DC resistivity anomalies in 2.5-well wells with different observation devices are analyzed, and the theoretical data of 2.5-well well DCs are inversely studied by different observation methods. The results show that the introduction of well data improves the resolution of 2.5 DC for longitudinal detection, while improving the validity and accuracy of 2.5 DC inversion.
引文
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[11] 徐世浙.地球物理中的有限单元法[M].北京:科学出版社,1994.XU S Z.The Finite element method in Geophysics[M].Beijing:Science Press,1994.(In Chinese)
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[2] BING ZHOU ,STEWART A,GREENHALGH.Rapid 2-D/3-D crosshole resistivity imaging using the analytic sensitivity function[J].Geophysics,2002,67(3):755-765.
[3] WILKINSON P B,CHAMBERS J E.Extreme sensitivity of cross-hole electrical resistivity tomography measurements to geometric errors[J].Geophy J Int,2008,173(3):49-62.
[4] 王志刚,何展翔,魏文博.Born近似快速三维反演井地电法数据[J].地球物理学进展,2007,22(02):508-513.WANG Z G,HE Z X,WEI W B.Fast 3D inversion of borehole ground electrical method data based on Born approximation[J].Progress in Geophysics,2007,22(02):508-513.(In Chinese)
[5] 王志刚,何展翔,魏文博,等.井地电法的准解析近似三维反演研究[J].石油地球物理勘探,2007,42(2):220-225.WANG Z G,HE Z X,WEI W B,et al.Quasi-analytic approximate three-dimensional inversion of well ground electrical method [J].Petroleum geophysical Prospecting,2007,42 (2):220-225.(In Chinese)
[6] 王志刚,何展翔,魏文博.积分方程法三维模拟井地电法并行算法研究[J].物探化探计算技术,2007,29(5):425-436.WANG Z G,HE Z X,WEI W B.Parallel algrorithm research of integer equation method to 3-d bopehole-surface electrom agnetic modeling[J].Computing Techniques for Geophysical and Geochemical Exploration,2007,29(5):425-436.(In Chinese)
[7] 吕玉增,阮百尧,黄俊革.直流电井间三维直接成像[J].物探化探计算技术,2003,25(1):60-64.LV Y Z,RUAN B Y,HUANG J G.The 3-D immediate corsshole tomography with direct current[J].Computing Techniques for Geophysical and Geochemical Exploration ,2003,25(1):60-64.(In Chinese)
[8] 岳建华,刘志新.井-地三维电阻率成像技术[J].地球物理学进展,2005,20(2):407-411.YUE J H ,LIU Z X.Three dimension resistivity tomography of mine ground[J].Progress in Geophysics,2005,20(2):407-411.(In Chinese)
[9] 徐凯军,李桐林,张辉,等.基于共轭梯度法的垂直有限线源三维电阻率反演[J].煤田地质与勘探,2006,34(3):69-71.XU K J,LI T L,ZHANG H ,et al.3D resistivity inversion of vertical finite line source using conjugate gradients[J].Coal Geology & Exploration,2006,34(3):69-71.(In Chinese)
[10] 蓝泽鸾,张志勇,邓居智等.基于TV井地2_5D直流电阻率正则化反演[M].北京:科学出版社,2015.LAN Z L,ZHANG Z Y,DENG J Z,et al.based on the TV well ground 2_5d direct current resistivity inversion [M].Beijing:Science Press,2015.(In Chinese)
[11] 徐世浙.地球物理中的有限单元法[M].北京:科学出版社,1994.XU S Z.The Finite element method in Geophysics[M].Beijing:Science Press,1994.(In Chinese)
[12] TIKHONOV A N,ARSENIN V Y.Solution of ill-Posed Problems [M].Washington.DC:V H Winston and Sons ,p 258,1977.
[13] 安然,李桐林,徐凯军.井地三维电阻率反演研究[J].地球物理学进展,2007,22(1):247-249.AN R,LI T L;XU K J.Well-surface 3-D resistivity inversion[J].Progress in Geophysics,2007,22(1):247-249.(In Chinese)
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