Research On Regularization Inversion Of Multi-electrode Resistivity Method And Application

Multi-electrode resistivity method is an important shallow geophysical method,which is widely used in many fields, especially increasingly deep used in hydrology geological survey, engineering geological survey, environmental geological survey. In order to improve the accuracy and efficiency, at the same time to make it achieve better application effect, multi-electrode resistivity inversion technique is essential.Therefore, it is necessary to do more research and discussion for resistivity inversion technique.The paper has realized the 2.5D multi-electrode resistivity forward modeling research use the finite element method and based on Tikhonov regularization inversion ideological to construct inversed objective function to realize the different optimization algorithms and different stabilizing factor inversion in 2.5D multi-electrode resistivity inversion study. Firstly, the paper starts from the differential equations and boundary conditions for 2.5D multi-electrode resistivity deduced variational questions about potential. Adopting triangular elements mesh generation technology derived expression linear interpolation of unit stiffness matrix, while using an efficient variable speed storage technology to store the stiffness matrix and direct binding of linear equations solving technology, ultimately realized the 2.5D multi-electrode resistivity forward modeling calculation. By setting the horizontally layered model and vertical contact strip model confirmed the effectiveness of the algorithm. Secondly, as to multi-electrode resistivity inversion, the paper constructed a multi-electrode resistivity inversion regularized objective function, used the electrode exchange principle to achieve a rapid calculation of partial derivative matrix and research the convergence of different optimization methods and analyze the inversion results in detail. Studying the different stabilizing factors and carrying out alot of model calculation, and analyzing a detailed influence of stabilizing factors on the inversion results. Adopting the improved L-curve algorithm inversion technology automatically selects regularization factor to improve the stability of the solution.By studying the optimization algorithms the paper found, Conjugate Gradient inversion effect was stable and has a moderate convergence speed, Gauss-Newton inversion got a better inversion result and a fast convergence speed, Quasi-Newton method has a fairly convergence rate with the Gauss-Newton method, and the Steepest Descent method was the least effective method. The main function of stabilizing factor is to limit the model solution space and to reduce multiple solutions,ultimately obtain a stable solution. Stabilizing factors research shows that, in the inversion of Gauss-Newton method, the abnormal model boundary of minimum norm stabilizing factor and the maximum smoothness stabilizing factor is smooth gradient.The minimum gradient support stabilizing factor has well ability to recognize abrupt change anomaly boundary. It is conducive to realize the abrupt change boundary inversion.