井地电阻率法及双频激电三维数值模拟与反演研究
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摘要
本文主要研究点状电流源(单点或多点)及任意线电流源供电时,在井中供电—地面接收方式下的三维电阻率正、反演问题。通过引入Cole-Cole复电阻率模型,解决了相应的频率域井地双频激电的正、反演问题。
在三维电阻率正演方面,通过对地下点电流源的线积分,计算出任意线电源供电时,在均匀介质情况下的空间任意点的理论电位。三维电阻率的有限差分法正演计算使用ICCG算法对正演方程组求解,可以大大加快正演计算的速度。任意线电源供电时,三维离散化网格在边界节点采用异常电位为零的强制边界条件,在不均匀网格剖分(边界网格长度远大于中间网格长度)的情况下,正演计算仍能取得非常高的精度,简化了正演计算。视电阻率幅值响应与电阻率异常体的空间关系的数值模拟试验,为野外观测系统的设计提供了非常有意义的指导。
在三维电阻率反演方面,针对不同的实际地电模型的反演需求,采用了多种不同的计算Jacobi矩阵元素的方法。从Jacobi矩阵元素的物理意义上认识到了在垂直方向上,较深部电阻率异常体被反演计算过程重构成浅部的异常块体的原因,即反演的异常体重心上飘现象。研究证明:三维电阻率反演的水平分辨率较高,垂向分辨率在很大程度上取决于最佳Lagrange乘子λ。
以Cole-Cole模型来模拟地下电性单元的复电阻率,双频激电的数值模拟结果与物理模拟结果非常相似,证明了Cole-Cole模型的正确性,也证明了0.nHz～nHz频率的双频电流对极化体反映的灵敏性。适用于井地观测方式的二极法观测系统的数值模拟试验显示了井地双频激电对电性异常体、极化异常体的反映十分灵敏,其视谱剖面的梯度带能非常好的勾绘出异常体的水平投影。不同观测方式的零频电阻率的反演结果说明了对于双频激电,用低频视振幅(或视实分量)剖面曲线或图像来反演零频电阻率的可行性;极化率的反演结果说明用高频视相位(或视幅频率、视虚分量)剖面曲线或图像来反演极化率的合理性;在固定反演区地下网格单元的时间常数和频率相关系数的情况下,反演出的极化率并不代表异常体真实的极化率,应该是极化体激发极化效应的综合反映,其空间参数的意义大于其幅值的意义。
最后,通过数值模拟,对井地观测方式的伪随机多频波供电勘探方法进行了可行性分析。
In this study, we have mainly studied the 3-D resistivity forward and inversion problems under the condition which an electric current is injected from the borehole, and is received on the ground with different kinds of power supplied,such as point electric current (including single-point or multi-point) , And we have also settled the problem of dual frequency induced polarization in the model of borehole-to-ground, in which the numerical simulation and inversion problem corresponding with frequency domain are solved by introducing the Cole-Cole complex resistivity model.
For the 3-D geoelectric field forward modeling scheme, we can compute the theoretic potential in equality medium at any points by line-integration toward the point electrical current source when an electric current is furnished by the line electrical current source. Utilizing ICCG arithmetic for the forward equation and using a finite-difference method to setup the 3-D resistivity forward modeling, we can solve the equation and obtain the calculated results at a high speed. If the injected current is offered by the random line-electrical current source and the 3-D grid cells are divided by using asymmetry grid space (the length between two boundary grids is larger than the length between middle grids), and if a condition of zero potential is imposed on the boundary grids, the forward modeling can still acquired a very high precision with a simple calculation process. Our results, about the relation between an apparent resistivity value and the position of resistivity anomalous body, provide a useful guidance for designing observation system in field.
For the 3-D resistivity inversion scheme, we have used a few different methods for computing Jacobi matrix according to the different inversion commands for practical geoelectric model . Analyzing the physics character of Jacobi matrix element, we can know the reason why the deeper resistivity body is reconstructed as a superficial resistivity body in the vertical direction during the inversion process, and in other words, why the barycenter of anomalous body shifts shallower. Our results proved that the resolution in the horizontal direction is very high, however , the resolution in the vertical direction depends on the goodish Lagrange operator (λ).
Based on the Cole-Cole model, we have simulated the complex resistivity of underground cell, and found the results between the numerical and the physical simulations are very similar for dual frequency induced polarization. Our results not only testified the relative correctness of Cole-Cole model but also indicated the sensitivity of the dual frequency injecting current using 0.nHz～nHz frequency to polarized body. The results of numerical simulation for the ambipolar observation system, which is adapt to the mode of borehole-to-ground, showed that the borehole-to-ground dual frequency induced polarization is also very sensitive to the electric and polarizable body, and its gradient strip of apparent spectrum in a plane section can depict distinctly the horizontal projection of anomalous body. The results of zero-frequency-resistivity inversion testified the low frequency apparent amplitude (or apparent real component) in plane section or images can be used to calculate the DC resistivity. The polarizability inversion results similarly proved that the high frequency apparent phase in plane section (or apparent amplitude-frequency, or apparent imaginary component) or images can be used to deduce the polarizability. Finally, we can conclude that the polarizability inversion results can not denote the real polarizability of anomalous body if the time constant and frequency dependence coefficient of the subterranean grids in the inversion area are given, but should be the total responds of the induced polarization, which presents that the dimensional parameter is more important than its value in physical meanings.
Eventually,we analyze the feasibility of the borehole-to-ground prospect means of using the Pseudo-random Multi-frequency electric current by numerical simulations.
在三维电阻率正演方面,通过对地下点电流源的线积分,计算出任意线电源供电时,在均匀介质情况下的空间任意点的理论电位。三维电阻率的有限差分法正演计算使用ICCG算法对正演方程组求解,可以大大加快正演计算的速度。任意线电源供电时,三维离散化网格在边界节点采用异常电位为零的强制边界条件,在不均匀网格剖分(边界网格长度远大于中间网格长度)的情况下,正演计算仍能取得非常高的精度,简化了正演计算。视电阻率幅值响应与电阻率异常体的空间关系的数值模拟试验,为野外观测系统的设计提供了非常有意义的指导。
在三维电阻率反演方面,针对不同的实际地电模型的反演需求,采用了多种不同的计算Jacobi矩阵元素的方法。从Jacobi矩阵元素的物理意义上认识到了在垂直方向上,较深部电阻率异常体被反演计算过程重构成浅部的异常块体的原因,即反演的异常体重心上飘现象。研究证明:三维电阻率反演的水平分辨率较高,垂向分辨率在很大程度上取决于最佳Lagrange乘子λ。
以Cole-Cole模型来模拟地下电性单元的复电阻率,双频激电的数值模拟结果与物理模拟结果非常相似,证明了Cole-Cole模型的正确性,也证明了0.nHz～nHz频率的双频电流对极化体反映的灵敏性。适用于井地观测方式的二极法观测系统的数值模拟试验显示了井地双频激电对电性异常体、极化异常体的反映十分灵敏,其视谱剖面的梯度带能非常好的勾绘出异常体的水平投影。不同观测方式的零频电阻率的反演结果说明了对于双频激电,用低频视振幅(或视实分量)剖面曲线或图像来反演零频电阻率的可行性;极化率的反演结果说明用高频视相位(或视幅频率、视虚分量)剖面曲线或图像来反演极化率的合理性;在固定反演区地下网格单元的时间常数和频率相关系数的情况下,反演出的极化率并不代表异常体真实的极化率,应该是极化体激发极化效应的综合反映,其空间参数的意义大于其幅值的意义。
最后,通过数值模拟,对井地观测方式的伪随机多频波供电勘探方法进行了可行性分析。
In this study, we have mainly studied the 3-D resistivity forward and inversion problems under the condition which an electric current is injected from the borehole, and is received on the ground with different kinds of power supplied,such as point electric current (including single-point or multi-point) , And we have also settled the problem of dual frequency induced polarization in the model of borehole-to-ground, in which the numerical simulation and inversion problem corresponding with frequency domain are solved by introducing the Cole-Cole complex resistivity model.
For the 3-D geoelectric field forward modeling scheme, we can compute the theoretic potential in equality medium at any points by line-integration toward the point electrical current source when an electric current is furnished by the line electrical current source. Utilizing ICCG arithmetic for the forward equation and using a finite-difference method to setup the 3-D resistivity forward modeling, we can solve the equation and obtain the calculated results at a high speed. If the injected current is offered by the random line-electrical current source and the 3-D grid cells are divided by using asymmetry grid space (the length between two boundary grids is larger than the length between middle grids), and if a condition of zero potential is imposed on the boundary grids, the forward modeling can still acquired a very high precision with a simple calculation process. Our results, about the relation between an apparent resistivity value and the position of resistivity anomalous body, provide a useful guidance for designing observation system in field.
For the 3-D resistivity inversion scheme, we have used a few different methods for computing Jacobi matrix according to the different inversion commands for practical geoelectric model . Analyzing the physics character of Jacobi matrix element, we can know the reason why the deeper resistivity body is reconstructed as a superficial resistivity body in the vertical direction during the inversion process, and in other words, why the barycenter of anomalous body shifts shallower. Our results proved that the resolution in the horizontal direction is very high, however , the resolution in the vertical direction depends on the goodish Lagrange operator (λ).
Based on the Cole-Cole model, we have simulated the complex resistivity of underground cell, and found the results between the numerical and the physical simulations are very similar for dual frequency induced polarization. Our results not only testified the relative correctness of Cole-Cole model but also indicated the sensitivity of the dual frequency injecting current using 0.nHz～nHz frequency to polarized body. The results of numerical simulation for the ambipolar observation system, which is adapt to the mode of borehole-to-ground, showed that the borehole-to-ground dual frequency induced polarization is also very sensitive to the electric and polarizable body, and its gradient strip of apparent spectrum in a plane section can depict distinctly the horizontal projection of anomalous body. The results of zero-frequency-resistivity inversion testified the low frequency apparent amplitude (or apparent real component) in plane section or images can be used to calculate the DC resistivity. The polarizability inversion results similarly proved that the high frequency apparent phase in plane section (or apparent amplitude-frequency, or apparent imaginary component) or images can be used to deduce the polarizability. Finally, we can conclude that the polarizability inversion results can not denote the real polarizability of anomalous body if the time constant and frequency dependence coefficient of the subterranean grids in the inversion area are given, but should be the total responds of the induced polarization, which presents that the dimensional parameter is more important than its value in physical meanings.
Eventually,we analyze the feasibility of the borehole-to-ground prospect means of using the Pseudo-random Multi-frequency electric current by numerical simulations.
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