Three-dimensional Adaptive Finite Element Forward Modeling And Finite Memory Quasi-Newton Inversion Of Magnetotelluric Method

Magnetotelluric exploration is a geophysical exploration method with natural electromagnetic field as its source.Because of its advantages of convenient construction and wide exploration depth,it has been widely used in mineral resources survey,oil and gas field exploration,deep geological structure and other geophysical fields.Therefore,in theory and practice,domestic and foreign scholars have conducted in-depth research on magnetotelluric exploration.With the rapid development of computer technology,three-dimensional magnetotelluric forward and inversion has become a hotspot in recent 20 years.How to improve the computational efficiency and the accuracy of forward and inversion results is the goal of domestic and foreign scholars.In this paper,the forward and inversion of three-dimensional magnetotelluric data are studied in the light of computational efficiency and accuracy.Three-dimensional magnetotelluric forward evolution based on unstructured grid is studied.Based on Maxwell's equations,the boundary value problem and finite element method of magnetotelluric are studied in depth in this paper.The traditional finite element method is used to solve the magnetic vector potential-electric scaling problem for three-dimensional magnetotelluric forward modeling.Tetgen open source code is used for unstructured mesh generation,and FORTRAN language is used to compile the forward code of three-dimensional finite element method for magnetotelluric,and the correctness is verified by using layered and three-dimensional model evolution.Forward modeling of complex anomalous bodies proves that unstructured grids have obvious advantages in simulating complex geological bodies.Based on the three-dimensional forward modeling of magnetotelluric based on unstructured grids,this paper studies the adaptive three-dimensional finite element forward modeling of magnetotelluric.The adaptive finite element technique avoids the drawbacks of artificial mesh generation and has the advantage of automatic mesh generation to obtain the optimal mesh.In this paper,the concept of object-oriented is used to make the encrypted area focus on the areas related to the research sites,and to optimize the defects of adaptive finite element technology in the field of magnetotelluric.Finally,an object-oriented adaptive finite element three-dimensional MT forward algorithm is realized by using the posterior error estimation of the restoration gradient.The simulation and optimization of complex geological bodies is a necessary way to improve the inversion accuracy and calculation efficiency.Therefore,electromagnetic inversion based on unstructured grids is a research hotspot at home and abroad.The finite memory quasi-Newton(LBFGS)inversion method adopted in this paper has the advantages of fast calculation efficiency and small memory requirement.The quasi-forward method avoids the calculation of sensitivity matrix and optimizes the algorithm.Finally,the inversion algorithm of three-dimensional MT based on unstructured mesh is realized,and the classical model and complex multi-model are inverted.