Research On 3D Forward Modeling And Inversion Of Borehole-Ground Electrical Resistivity Method

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.