Analysis of response characteristics of IP differential device based on 3D numerical simulation
LING Jiaxuan1, CHEN Zhifang2, DENG Wei1, DAI Shikun3, ZHOU Yinming4, CHEN Qingrui5
1. School of Computer Science and Engineering, Guilin University of Aerospace Technology, Guilin, Guangxi 541004, China; 2. Survey and Design Institute of Zhejiang Qiantang River Administration Bureau, Hangzhou, Zhejiang 310016, China; 3. School of Geosciences and Info-physics, Central South University, Changsha, Hunan 410083, China; 4. School of Computer Science and Engineering, Hunan University of Science and Technology, Xiangtan, Hunan 411201, China; 5. College of Meteorology and Oceanography, National University of Defense Technology, Changsha, Hunan 410073, China
Abstract：To analyze the response properties of the induced polarization (IP) differential device, this paper proposes a high-precision and high-efficiency 3D numerical simulation method.The proposed method transforms the 3D IP numerical simulation problem into a 1D numerical simulation problem in the wavenumber domain using a 2D Fourier transform method and solves it using a 1D finite element method.Operators are introduced for iterative computations, which eventually lead to high-precision numerical solutions.This approach avoids directly solving large sparse linear equations, greatly reducing the computational complexity and storage requirements and improving computational efficiency.The paper uses the proposed 3D numerical simulation method as a tool to analyze the response properties of the IP differential device.The test results of a high-polarization anomalous bulk model with high/low resistance indicate that the differential device for single well-well azimuthal measurement has a better resolution effect on blind ore near the well than the other devices, and the low resistance body has a stronger sensitivity to current than the high resistance body.Tests of low-resistance and high-polarization anomalous bulk models using different background media have shown that the apparent resistivity and polarizability of the differential device under well-ground measurement conditions can more accurately reflect the vertical spatial distribution properties of the background media and the anomalous bulk than those of pole-pole device.Therefore, the IP differential device has an advantage over the other devices, and the research conclusions can provide a reference for the selection of field exploration and measurement equipment.
宋滔, 白禹.时间域激发极化法各向异性介质响应分析[J].贵阳学院学报(自然科学版), 2021, 16(4):107-110, 114.SONG Tao, BAI Yu.Analysis of the response of anisotropic media in the time-domain induced polarization method[J].Journal of Guiyang College (Natural Sciences), 2021, 16(4):107-110, 114.
[5]
MICHALSKI K A, MOSIG J R.Multilayered media Green's functions in integral equation formulations[J].IEEE Transactions on Antennas and Propagation, 1997, 45(3):508-519.
[6]
MÉNDEZ-DELGADO S, GÓMEZ-TREVIÑO E, PÉREZ-FLORES M A.Forward modelling of direct current and low-frequency electromagnetic fields using integral equations[J].Geophysical Journal International, 1999, 137(2):336-352.
[7]
郭飞, 马西奎, 邱关源.一种适于直流电阻率正演模拟求解地表电位的积分方程法[J].西安交通大学学报, 1999, 33(10):17-22.GUO Fei, MA Xikui, QIU Guanyuan.Integral equation applied to modeling of surface potential in DC resistivity[J].Journal of Xi'an Jiaotong University, 1999, 33(10):17-22.
[8]
REN Z, CHEN H, TANG J, et al.A volume-surface integral approach for direct current resistivity problems with topography[J].Geophysics, 2018, 83(5):E293-E302.
[9]
徐世浙.地球物理中的有限单元法[M].北京:科学出版社, 1994.
[10]
熊彬, 阮百尧, 罗延钟.复杂地形条件下直流电阻率异常三维数值模拟研究[J].地质与勘探, 2003, 39(4):60-64.XIONG Bin, RUAN Baiyao, LUO Yanzhong.3-D numerical simulation study of DC resistivity anomaly under complicated terrain[J].Geology and Prospecting, 2003, 39(4):60-64.
[11]
LI Y, SPITZER K.Finite element resistivity modelling for three-dimensional structures with arbitrary anisotropy[J].Physics of the Earth and Planetary Interiors, 2005, 150(1-3):15-27.
[12]
强建科, 罗延钟.三维地形直流电阻率有限元法模拟[J].地球物理学报, 2007, 50(5):1606-1613.QIANG Jianke, LUO Yanzhong.The resistivity FEM numerical modeling on 3-D undulating topography[J].Chinese Journal of Geophysics, 2007, 50(5):1606-1613.
[13]
殷长春, 杨志龙, 刘云鹤, 等.基于环形扫面测量的三维直流电阻率法任意各向异性模型响应特征[J].吉林大学学报(地球科学版), 2018, 48(3):872-880.YIN Changchun, YANG Zhilong, LIU Yunhe, et al.Characteristics of 3D DC resistivity response for arbitrary anisotropic models using circular scanning measurement[J].Journal of Jilin University (Earth Science Edition), 2018, 48(3):872-880.
[14]
赵宁, 黄明卫, 申亚行, 等.高阶自适应有限元三维直流电阻率正演方法及其在沁水盆地煤气层压裂监测中的应用[J].石油地球物理勘探, 2021, 56(1):209-216.ZHAO Ning, HUANG Mingwei, SHEN Yahang, et al.Forward modeling of 3D DC resistivity based on high-order adaptive finite element and its application in Qinshui Basin[J].Oil Geophysical Prospecting, 2021, 56(1):209-216.
[15]
许巍, 魏然, 黄航, 等.油气储层低频界面极化效应数值模型[J].石油地球物理勘探, 2022, 57(6):1481-1488.XU Wei, WEI Ran, HUANG Hang, et al.Numerical simulation of polarization effect in low-frequency interface of oil-gas reservoirs[J].Oil Geophysical Prospecting, 2022, 57(6):1481-1488.
[16]
LOKE M H, BARKER R D.Practical techniques for 3D resistivity surveys and data inversion[J].Geophysical Prospecting, 1996, 44(3):499-523.
[17]
ZHOU B, GREENHALGH S A.Finite element three dimensional direct current resistivity modelling:accuracy and efficiency considerations[J].Geophysical Journal International, 2010, 145(3):679-688.
[18]
马欢, 谭捍东, 林昌洪.井地、地井、井间和地面激电资料三维共轭梯度反演研究[C].第十一届中国国际地球电磁学术讨论会论文集, 2013, 219-221.MA Huan, TAN Handong, LIN Changhong.Three-dimensional conjugate inversion of surface-borehole, borehole-surface, borehole-borehole and surface IP data[C].Proceedings of the 11th China International Geoelectromagnetic Symposium, 2013, 219-221.
[19]
HOHMANN G W.Three-dimensional induced polarization and electromagnetic modeling[J].Geophysics, 1975, 40(2):309-324.
[20]
朴化荣, 薛爱民, 金东, 等.积分方程法求解三度极化体的激发极化效应[J].物化探计算技术, 1985(4):310-325.PIAO Huarong, XUE Aimin, JIN Dong, et al.Computation of the IP response of three-dimensional polarizable bodies using integral equation[J].Computing Techniques for Geophysical and Geochemical Exploration, 1985(4):310-325.
[21]
张辉, 李桐林, 董瑞霞.体积分方程法模拟复电阻率三维体电磁响应[J].煤田地质与勘探, 2006, 34(1):70-74.ZHANG Hui, LI Tonglin, DONG Ruixia.Modeling electromagnetic responses of complex resistivity 3-D body using volume integral equation method[J].Coal Geology & Exploration, 2006, 34(1):70-74.
[22]
TSOURLOS P I, OGILVY R D.An algorithm for the 3-D inversion of tomographic resistivity and induced polarization data:preliminary results[J].Journal of the Balkan Geophysical Society, 1999, 2(2):30-45.
[23]
黄俊革.三维电阻率/极化率有限元正演模拟与反演成像[D].湖南长沙:中南大学, 2003.HUANG Junge.3-D Resistivity/IP Modeling and Inversion Based on FEM[D].Central South University, Changsha, Hunan, 2003.
[24]
吕玉增.地-井、井-地IP三维快速正反演研究[D].湖南长沙:中南大学, 2008.LYU Yuzeng.The Research on 3-D Fast Forward and Inversion of Surface-borehole and Borehole-surface IP Methods[D].Central South University, Changsha, Hunan, 2008.
[25]
王智.井中激电正反演及其应用研究[D].湖北武汉:中国地质大学(武汉), 2015.WANG Zhi.Research on Forward and Inversion of Induced Polarization in Borehole and Application[D].China University of Geosciences(Wuhan), Wuhan, Hubei, 2015.
[26]
周峰, 潘和平, 文国军, 等.基于有限差分的井中激发极化三维正演[J].电波科学学报, 2010, 25(4):785-792.ZHOU Feng, PAN Heping, WEN Guojun, et al.Three-dimensional forward modeling of induced of polarization borehole using finite difference method[J].Chinese Journal of Radio Science, 2010, 25(4):785-792.
[27]
李长伟.井中激发极化法正反演及快速迭代求解技术研究[D].湖南长沙:中南大学, 2012.LI Changwei.Study on Forward and Inversion of Induced-polarization Well Logging and Fast Iterative Solvers[D].Central South University, Changsha, Hunan, 2012.
[28]
高文龙, 严良俊, 周磊.井中激电三维数值模拟及井眼影响因素分析[J].地球物理学进展, 2021, 36(3):1257-1266.GAO Wenlong, YAN Liangjun, ZHOU Lei.3D numerical simulation of in-hole IP and analysis of borehole influencing factors[J].Progress in Geophysics, 2021, 36(3):1257-1266.
[29]
李静和, 何展翔, 杨俊, 等.针对渗漏型目标的新型接触式激电法及应用[J].石油地球物理勘探, 2021, 56(3):659-669.LI Jinghe, HE Zhanxiang, YANG Jun, et al.Contact-type induced polarization and its application for detecting leakage[J].Oil Geophysical Prospecting, 2021, 56(3):659-669.
BOISVERT R F.Algorithms for special tridiagonal systems[J].SIAM Journal on Scientific and Statistical Computing, 1991, 12(2):423-442.
[32]
柴玉璞.偏移抽样理论及其应用[M].北京:石油工业出版社, 1997.
[33]
陈龙伟, 戴世坤, 吴美平.应用任意采样点数FFT算法时离散频率计算[J].地球物理学进展, 2016, 31(1):164-169.CHEN Longwei, DAI Shikun, WU Meiping.Computation of discrete frequency when using FFT algorithm with random sampling points[J].Progress in Geophysics, 2016, 31(1):164-169.
戴世坤, 赵东东, 李昆, 等.基于矢量位和标量位的空间波数混合域电磁三维正演模拟[J].地球物理学报, 2022, 65(1):404-416.DAI Shikun, ZHAO Dongdong, LI Kun, et al.Forward modeling of 3D electromagnetic problems using vector and scalar potentials in a mixed space-wavenumber domain[J].Chinese Journal of Geophysics, 2022, 65(1):404-416.
[36]
戴世坤, 陈轻蕊, 凌嘉宣, 等.空间-波数域三维大地电磁场积分方程法数值模拟[J].地球物理学报, 2022, 65(6):2294-2310.DAI Shikun, CHEN Qingrui, LING Jiaxuan, et al.Three-dimensional numerical simulation of magnetotelluric field in the space-wavenumber domain[J].Chinese Journal of Geophysics, 2022, 65(6):2294-2310.
[37]
潘纪顺, 葛为中, 折京平.地面/井地/井间超高密度电阻率成像技术[J].华北水利水电学院学报, 2010, 31(2):74-78.PAN Jishun, GE Weizhong, SHE Jingping.High-density electrical resistivity imaging technique of ground/borehole-to-surface/inter-well[J].Journal of North China Institute of Water Conservancy and Hydroelectric Power, 2010, 31(2):74-78.
[38]
吕玉增, 阮百尧, 彭苏萍.地-井方位激电观测异常特征研究[J].地球物理学进展, 2012, 27(1):201-216.LYU Yuzeng, RUAN Baiyao, PENG Suping.A study on anomaly of surface-borehole direction induced polarization survey[J].Progress in Geophysics, 2012, 27(1):201-216.
