Research On Resistivity Inversion Based On The Supervised Descent Method

Dc resistivity method is an important geophysical prospecting method,which has been widely used in mineral exploration,hydrologic survey,geological survey and environmental geophysics.The inversion imaging technology is a basic method of Dc resistivity data processing and is the main methods to achieve the spatial location and morphological characterization of underground anomalies.At present,conventional linear inversion methods are difficult to balance calculation accuracy and efficiency,and the use of prior information is insufficient.With the rapid development of machine learning technology in recent years,the above problems are expected to be solved.This paper mainly studies the application of the supervised descent method in machine learning in resistivity imaging.The advantage of this algorithm is that the calculation of partial derivatives is not involved in the calculation process,and the calculation accuracy and efficiency are high.In the forward modeling,the differential equation of the stable current field is given,and the formula of the direct current sounding forward modeling is derived,then the variational problem of the two-dimensional stable current field is derived.The calculation process of solving the variational problem by triangular element subdivision and linear interpolation is developed in detail.In the aspect of inversion,it first introduces the basic theory of objective function and regularization,and summarizes the differences and advantages of several conventional inversion methods.Secondly,the principle of supervised descent method is elaborated,the inversion formula of the supervised descent method is derived,and its principle is further introduced.In terms of model and measured data examples,a three-layered model is established in onedimensional case for the supervised descent inversion to verify the feasibility and generalization ability.In two-dimensional case,the feasibility and generalization ability of the method are further verified by numerical simulation and measured data inversion.The experimental results show that the supervised descent method has high inversion accuracy,fast convergence speed,strong anti-noise ability and good generalization ability,which can be popularized and applied.