井地电阻率法三维正反演研究
|
摘要
井地电阻率电法是指通过开发井的套管向井下供入大功率的电流,在地表测量由套管流入地层中的“漏电流”在非均匀电性变化的地下介质中形成的地表电位分布的方法,起源于俄罗斯,主要用于圈定已知油气藏边界和预测已知油气藏周边的含油气有利区块。这是目前油气勘探开发中一类重要而又急需的方法技术。
论文简要介绍了井地电阻率法的基本原理及其发展与研究现状,以稳定场电流关系式为基础,推导出求解点源三维地电场的方程组。用有限差分法解决点电源三维地电场的正演问题,重点推导了关于网格节点系数的计算公式,并根据前人的研究成果开发了点电源井地电阻率法三维正演数值模拟软件。在开发过程中,为了避免计算量过大以及对计算机内存要求比较高的困难,引入了不完全Cholesky共轭梯度方法,从而大大提高了运算效率,为三维电阻率反演奠定了基础。
对比均匀半空间和垂直接触带模型的数值解与解析解相对误差,结果表明正演算法具有较高的准确性。在此基础上通过对简单模型的三维数值模拟计算,分析低阻异常体在不同体积大小、不同埋藏深度等状态时所引起的异常响应,证明正演计算具有可靠性和稳定性,可以用于接下来的反演研究。
在现有基础上进一步探索三维反演算法,使用最小构造反演的共轭梯度算法来解决求解雅可比矩阵G和GTG的逆矩阵的问题,避免存储G和GTG的逆矩阵,同时也节省了内存,加快了反演速度。由于反演参数较多,求模型光滑约束的最小构造反演能够有效消除多余的构造信息,得到稳定、可靠的反演结果。传统的最小构造反演通常需要数十次迭代才能收敛,文中借鉴前人方法对传统的最小构造反演进行改进,即用实验法确定相对最佳的拉格朗日乘子,并在反演迭代过程中保持不变直至收敛。对多个模型的试算结果表明,三维反演的结果能够较好的反映异常的赋存状态,表明该算法的反演结果是可靠的。
The borehole-ground DC electrical resistivity method is one of electrical prospecting methods by placing an electric current electrode in a drill hole and measuring the distribution of electric potential on the surface of the earth. It stems from Russia, and is mainly used to delimit a known hydrocarbon reservoir and detect possible hydrocarbon-bearing blocks adjacent to the known reservoir. It is regarded as an important and urgent technique for hydrocarbon exploration.
This paper introduces the basic principle and the research present situation of borehole-ground DC electrical resistivity method briefly. Taking the stable field current relationship as the foundation, we infer the equations of 3D electric field caused by point source. The numerical calculation software of 3D forward of point source borehole-ground DC charged-body potential method uses finite difference principle. And we study the formula of the grid node. In order to avoid the problem of the computation load oversized as well as the high computer memory, we chose the method of incomplete Cholesky conjugate gradient. This way could raise the operation efficiency greatly, and establish foundation for 3D inversion.
After comparing the relative error of the numerical solution with the analytic solution, we could has the conclusion that algorithm is accurate. Then we do some 3D forward numerical calculations, and analyze the responses of low-resiistivity anomalous bodies with different size and depth. It verifies that the result is credible and steady.
Further exploration of the 3D inversion algorithm has been done, when we solve the Jacobian matrix G and the reverse matrix GTG by the way of the smallest tectonic conjugate gradient algorithm, it could avoid the storage of the matrix G and the reverse matrix GTG, it also could save the memory and speed up the inversion. The smoothly restraint of the model could be solved by the way of the smallest tectonic inversion, and help us to eliminates the unnecessary structure information. We also have improved the traditional minimum structure inversion algorithm, because the traditional algorithm requires tens of inversion iterations. A new iterative technique has been developed by Xiaoping Wu. A relative proper value of Lagrange multiplier is given after we do some test, and it will be kept unchangeable until convergence.
Some models have been computed by the 3D inversion software, and the result could reflect the condition of the anomalous bodies. It indicated that the inversion result is reliable.
论文简要介绍了井地电阻率法的基本原理及其发展与研究现状,以稳定场电流关系式为基础,推导出求解点源三维地电场的方程组。用有限差分法解决点电源三维地电场的正演问题,重点推导了关于网格节点系数的计算公式,并根据前人的研究成果开发了点电源井地电阻率法三维正演数值模拟软件。在开发过程中,为了避免计算量过大以及对计算机内存要求比较高的困难,引入了不完全Cholesky共轭梯度方法,从而大大提高了运算效率,为三维电阻率反演奠定了基础。
对比均匀半空间和垂直接触带模型的数值解与解析解相对误差,结果表明正演算法具有较高的准确性。在此基础上通过对简单模型的三维数值模拟计算,分析低阻异常体在不同体积大小、不同埋藏深度等状态时所引起的异常响应,证明正演计算具有可靠性和稳定性,可以用于接下来的反演研究。
在现有基础上进一步探索三维反演算法,使用最小构造反演的共轭梯度算法来解决求解雅可比矩阵G和GTG的逆矩阵的问题,避免存储G和GTG的逆矩阵,同时也节省了内存,加快了反演速度。由于反演参数较多,求模型光滑约束的最小构造反演能够有效消除多余的构造信息,得到稳定、可靠的反演结果。传统的最小构造反演通常需要数十次迭代才能收敛,文中借鉴前人方法对传统的最小构造反演进行改进,即用实验法确定相对最佳的拉格朗日乘子,并在反演迭代过程中保持不变直至收敛。对多个模型的试算结果表明,三维反演的结果能够较好的反映异常的赋存状态,表明该算法的反演结果是可靠的。
The borehole-ground DC electrical resistivity method is one of electrical prospecting methods by placing an electric current electrode in a drill hole and measuring the distribution of electric potential on the surface of the earth. It stems from Russia, and is mainly used to delimit a known hydrocarbon reservoir and detect possible hydrocarbon-bearing blocks adjacent to the known reservoir. It is regarded as an important and urgent technique for hydrocarbon exploration.
This paper introduces the basic principle and the research present situation of borehole-ground DC electrical resistivity method briefly. Taking the stable field current relationship as the foundation, we infer the equations of 3D electric field caused by point source. The numerical calculation software of 3D forward of point source borehole-ground DC charged-body potential method uses finite difference principle. And we study the formula of the grid node. In order to avoid the problem of the computation load oversized as well as the high computer memory, we chose the method of incomplete Cholesky conjugate gradient. This way could raise the operation efficiency greatly, and establish foundation for 3D inversion.
After comparing the relative error of the numerical solution with the analytic solution, we could has the conclusion that algorithm is accurate. Then we do some 3D forward numerical calculations, and analyze the responses of low-resiistivity anomalous bodies with different size and depth. It verifies that the result is credible and steady.
Further exploration of the 3D inversion algorithm has been done, when we solve the Jacobian matrix G and the reverse matrix GTG by the way of the smallest tectonic conjugate gradient algorithm, it could avoid the storage of the matrix G and the reverse matrix GTG, it also could save the memory and speed up the inversion. The smoothly restraint of the model could be solved by the way of the smallest tectonic inversion, and help us to eliminates the unnecessary structure information. We also have improved the traditional minimum structure inversion algorithm, because the traditional algorithm requires tens of inversion iterations. A new iterative technique has been developed by Xiaoping Wu. A relative proper value of Lagrange multiplier is given after we do some test, and it will be kept unchangeable until convergence.
Some models have been computed by the 3D inversion software, and the result could reflect the condition of the anomalous bodies. It indicated that the inversion result is reliable.
引文
[1] 李金铭. 地电场与电法勘探. 北京:中国地质大学(北京),2004
[2] 王家映. 地球物理反演理论. 武汉:中国地质大学出版社,1998
[3] 邹长春,尉中良.地球物理测井教程. 北京:中国地质大学(北京),2006
[4] 越建华,刘树才. 矿井直流电法勘探. 北京:中国矿业大学出版社,1999
[5] 徐士良. FORTRAN 常用算法程序集. 北京:清华大学出版社,1992
[6] 彭国伦. Fortran 95 程序设计. 北京:中国电力出版社,2002
[7] 罗延钟,张桂青.电子计算机在电法勘探中的应用。武汉:武汉地质学院出版社,1987
[8] 许新刚,刘志新,王大庆.矿井电阻率成像技术的现状与展望.地球物理学进展,2004,19(1):52~55.
[9] 吴小平,徐果明. 不完全 Cholesky 共轭梯度法及其在地电场计算中的应用.石油地球物理勘探,1998,33(1):89~94
[10] 吴小平,徐果明. 电阻率三维反演中偏导数矩阵的求取与分析,1999,34(4):363～373
[11] 吴小平,徐果明.利用共轭梯度法的电阻率三维反演研究,2000,73(3):420~426
[12] 吴小平,汪彤彤. 电阻率三维反演方法研究进展. 地球物理学进展,2002,17(1):156～162
[13] 吴小平,汪彤彤. 电阻率三维复杂结构的快速反演. 煤田地质与勘探, 2001,29(2):48～52
[14] 吴小平,汪彤彤. 电阻率三维反演稳定性和可靠性研究. 煤田地质与勘探,2002,30 (1):57～60
[15] 吴小平,汪彤彤. 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, 2001,23(2):321～327
[16] 吴小平. 利用共轭梯度方法的激发激化三维快速反演. 煤田地质与勘探,2004,32 (5):62～64
[17] 吴小平,徐果明,李时灿. 利用不完全 Cholesky 共轭梯度法求解点源三维电场,地球物理学报,1998,41 (6):848～855
[18] 王志刚,何展翔,魏文博.井地直流电法三维数值模拟中若干问题研究,物探化探计算技术,2006,28 (4):322～327
[19] 岳建华, 刘志新. 井地三维电阻率成像技术.地球物理学进展,2005,20(2):407～411
[20] 刘昱,王志刚,何展翔.井地电法供电电场分布模拟研究.工程地球物理学报,2006,3 (5):331～336
[21] 安然,李桐林,徐凯军.井地三维电阻率反演研究.地球物理学进展,2007,22(1):247～249
[22] 王贤君,李建阁,冯立.应用井地电位测量技术判断油层高渗透带方向.中国石油大学学报(自然科学版),2006,30 (5):67～70
[23] 聂在平.电法测井数值模拟研究进展,电子科技大学学报,1995,24(7):58～61
[24] 杨华,李金铭,桂峰. 电阻率层析成像方法技术近年发展概况,地球物理学进展,1998,13(4):90～96
[25] 曹立斌,孟永良,周建兰.电阻率层析成像技术的回顾与展望,勘探地球物理进展,2004,27(3):170～174
[26] 吴小平. 利用共轭梯度方法的电阻率三维正、反演研究:[博士学位论文]. 安徽:中国科学技术大学,1998
[27] K.Spitzer. A 3D finite-difference algorithm for DC resistivity modeling using conjugate gradient methods. Geopyhs.J.Int,1995(123),903～914
[28] Kershaw,D.S.,The incomplete Cholesky-conjugate gradient method for the iterative solution of systems of linear equations,J.Comp.Phys.,1978,26:43~65
[29] Zhang J,Mackie R L,Madden T R,Three-dimensional resistivity forwad medeling and inversion using conjugate gradient. Geopgysics,1995,60(5):1313-1325
[30] Ellis R G and Oldenberg D W. The pole-pole 3-D DC-resistivity inverse problem: a conjugate gradient approach. Geophys J Internat ,1994,119:187-194
[31] Spitzer,K. The three-dimensional DC sensitivity for the surface and surface sources]. Geophys.J.Int.,1998,134:736~746
[32] Loke M H .Barker R D. Pratical technique for 3D resistivity surveys and data inversion. Geophysical Prospecting. 1999,44:499~523
[33] New man G A,Alumbaugh D L. Three-dimensional magnetotelluric inversion using non-linear conjugate gradients.Geophys J Int, 2000,140:410~424
[34] LE Masne POIRMEUR A T. et al. Three-dimensional results for an electrical hole-to-surface method: application to the interpretation of field survey.Geophysics,1987, 52(4): 85-103
[35] J.Daniels,J.J ., Hole-to-surfacere sistivitym easurements:Geophysics, 1983,48:87-98
[36] Zhdanov M S, Tartaras E, Fast 3D imaging from a single borehole using tensor induction logging data, Petrophysics, 2004, 45(2)
[37] Jeffery J.Daniels Hole-to-surface resistivity measurements Geophysics,1986,Vo1.48:P.87-97
[2] 王家映. 地球物理反演理论. 武汉:中国地质大学出版社,1998
[3] 邹长春,尉中良.地球物理测井教程. 北京:中国地质大学(北京),2006
[4] 越建华,刘树才. 矿井直流电法勘探. 北京:中国矿业大学出版社,1999
[5] 徐士良. FORTRAN 常用算法程序集. 北京:清华大学出版社,1992
[6] 彭国伦. Fortran 95 程序设计. 北京:中国电力出版社,2002
[7] 罗延钟,张桂青.电子计算机在电法勘探中的应用。武汉:武汉地质学院出版社,1987
[8] 许新刚,刘志新,王大庆.矿井电阻率成像技术的现状与展望.地球物理学进展,2004,19(1):52~55.
[9] 吴小平,徐果明. 不完全 Cholesky 共轭梯度法及其在地电场计算中的应用.石油地球物理勘探,1998,33(1):89~94
[10] 吴小平,徐果明. 电阻率三维反演中偏导数矩阵的求取与分析,1999,34(4):363～373
[11] 吴小平,徐果明.利用共轭梯度法的电阻率三维反演研究,2000,73(3):420~426
[12] 吴小平,汪彤彤. 电阻率三维反演方法研究进展. 地球物理学进展,2002,17(1):156～162
[13] 吴小平,汪彤彤. 电阻率三维复杂结构的快速反演. 煤田地质与勘探, 2001,29(2):48～52
[14] 吴小平,汪彤彤. 电阻率三维反演稳定性和可靠性研究. 煤田地质与勘探,2002,30 (1):57～60
[15] 吴小平,汪彤彤. 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, 2001,23(2):321～327
[16] 吴小平. 利用共轭梯度方法的激发激化三维快速反演. 煤田地质与勘探,2004,32 (5):62～64
[17] 吴小平,徐果明,李时灿. 利用不完全 Cholesky 共轭梯度法求解点源三维电场,地球物理学报,1998,41 (6):848～855
[18] 王志刚,何展翔,魏文博.井地直流电法三维数值模拟中若干问题研究,物探化探计算技术,2006,28 (4):322～327
[19] 岳建华, 刘志新. 井地三维电阻率成像技术.地球物理学进展,2005,20(2):407～411
[20] 刘昱,王志刚,何展翔.井地电法供电电场分布模拟研究.工程地球物理学报,2006,3 (5):331～336
[21] 安然,李桐林,徐凯军.井地三维电阻率反演研究.地球物理学进展,2007,22(1):247～249
[22] 王贤君,李建阁,冯立.应用井地电位测量技术判断油层高渗透带方向.中国石油大学学报(自然科学版),2006,30 (5):67～70
[23] 聂在平.电法测井数值模拟研究进展,电子科技大学学报,1995,24(7):58～61
[24] 杨华,李金铭,桂峰. 电阻率层析成像方法技术近年发展概况,地球物理学进展,1998,13(4):90～96
[25] 曹立斌,孟永良,周建兰.电阻率层析成像技术的回顾与展望,勘探地球物理进展,2004,27(3):170～174
[26] 吴小平. 利用共轭梯度方法的电阻率三维正、反演研究:[博士学位论文]. 安徽:中国科学技术大学,1998
[27] K.Spitzer. A 3D finite-difference algorithm for DC resistivity modeling using conjugate gradient methods. Geopyhs.J.Int,1995(123),903～914
[28] Kershaw,D.S.,The incomplete Cholesky-conjugate gradient method for the iterative solution of systems of linear equations,J.Comp.Phys.,1978,26:43~65
[29] Zhang J,Mackie R L,Madden T R,Three-dimensional resistivity forwad medeling and inversion using conjugate gradient. Geopgysics,1995,60(5):1313-1325
[30] Ellis R G and Oldenberg D W. The pole-pole 3-D DC-resistivity inverse problem: a conjugate gradient approach. Geophys J Internat ,1994,119:187-194
[31] Spitzer,K. The three-dimensional DC sensitivity for the surface and surface sources]. Geophys.J.Int.,1998,134:736~746
[32] Loke M H .Barker R D. Pratical technique for 3D resistivity surveys and data inversion. Geophysical Prospecting. 1999,44:499~523
[33] New man G A,Alumbaugh D L. Three-dimensional magnetotelluric inversion using non-linear conjugate gradients.Geophys J Int, 2000,140:410~424
[34] LE Masne POIRMEUR A T. et al. Three-dimensional results for an electrical hole-to-surface method: application to the interpretation of field survey.Geophysics,1987, 52(4): 85-103
[35] J.Daniels,J.J ., Hole-to-surfacere sistivitym easurements:Geophysics, 1983,48:87-98
[36] Zhdanov M S, Tartaras E, Fast 3D imaging from a single borehole using tensor induction logging data, Petrophysics, 2004, 45(2)
[37] Jeffery J.Daniels Hole-to-surface resistivity measurements Geophysics,1986,Vo1.48:P.87-97