Three-dimensional Adaptive Finite Element Forward Modeling And Finite Memory Quasi-newton Inversion Of Controlled Source Audio-frequency Magnetotelluric Data

Inversion techniques have been effective methods for quantitative interpretation of electromagnetic exploration with the increasing development of geophysical forward and inversion techniques.There are only one-dimensional and two-dimensional models on early forward modeling.However,it is necessary to build three-dimensional models with rolling topography,even complex anisotropic medium today.The numerical simulation method has also developed from the integral equation method and the finite difference method to the present adaptive finite element method.Nowadays,the onedimensional and two-dimensional inversion have been commercialized.The threedimensional inversion method is becoming more and more popular since the inversion techniques have been further developed.For three-dimensional inversion,it is difficult to cope with the large amount of actual observation data and the geoelectric anomaly body with complex physical properties and shape.Therefore,the research hotspot is improving the efficiency and precision of inversion.The focus of this paper is the Controlled Source Audio-frequency Magnetotelluric(CSAMT),which is a surface electric prospecting method by using frequency domain couple source.The CSAMT method presents three-dimensional features.In order to simulate its complex three-dimensional source and geoelectric structure,this paper derives the differential equation of the three-dimensional electromagnetic field potential,and solves the problem of electromagnetic field continuity and the singularity of the electric dipole source.This paper was using to divide the region were the unstructured grid,and besides,the node finite element method is applied to discretize and solve the equation.The conventional segmentations make the part of interest denser in the calculation region,but it lacks the measurement of the grid quantization index and numerical solution.This paper uses the adaptive algorithm based on gradient recovery technique to optimize the mesh and improve the accuracy of the numerical solution.The three-dimensional CSAMT forward algorithm is of great significance for understanding the distribution law of three-dimensional electromagnetic fields and guiding field work,and also determines the efficiency and accuracy of the inversion algorithm.The three-dimensional inversion uses the finite memory quasi-Newton method(LBFGS).Since the amount of data obtained by tensor CSAMT three-dimensional observation is relatively large,improving the inversion efficiency is one of the research priorities,and the finite memory quasi-Newton method is a good choice.The finite memory quasi-Newton inversion is a regularized inversion that constrains the model space.Compared with the traditional quasi-Newton method,the finite memory quasiNewton inversion greatly reduces the memory space used,improves the inversion efficiency,and obtains good inversion results.