The 3-D Numerical Simulation And Inversion For Borehole-to-ground Resistivity Survey & Dual Frequency Induced Polarization

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.