MT Forward Algorithm And Implementation Based On Qudtree Mesh

In recent decades,with the leap of computer technology,the magnetotelluric(MT)has been developing rapidly.The two most widely used numerical simulation methods,the finite element method and the finite difference method,have a good application effect in magnetotelluric forward modeling and have made remarkable progress.The development of grid subdivision technology also provides more ideas for MT.The forward modeling theory of magnetotelluric has matured and forward modeling methods have been flourishing.The finite element method(FEM)has higher precision and is suitable for the irregular geophysical model.The finite difference method(FDM)is more efficient,but it has a poor effect on the model with complex electrical distribution.In view of this,this paper introduces the quadtree data structure into MT forward modeling.Combining it with finite-difference forward modeling,two-dimensional forward modeling of magnetotelluric was realized.It works very efficiently.In this paper,starting from Maxwell's equations,the basic characteristics of the magnetotelluric field are studied,and the partial differential equations of the two-dimensional MT of the magnetotelluric sounding are deduced,and the boundary conditions are given.The algorithm for two-dimensional forward modeling with FDM is introduced.The solutions for large sparse complex-coefficient linear equations are discussed.Several commonly used direct method solvers are introduced.Secondly,the application of quadtree data structure and quadtree data structure in grid subdivision is introduced,and a geophysical modeling software based on quadtree meshes is developed.In this paper,the difference equation coefficients of various grid nodes under quadtree grid are derived,and FDM forward algorithm based on quadtree mesh is realized(QFDM).Then,QFDM is used to perform forward calculation for different actual models.The positive results of the algorithm are compared with FDM and FEM to verify the correctness of the algorithm.This algorithm was used to study the forward results of various two-dimensional models,and the apparent resistivity response and impedance phase response of the TE and TM polarization modes obtained from the forward analysis were analyzed,and some important laws were summarized.Some useful conclusions provide theoretical guidance for practical work.Precision and efficiency of the algorithm is analyzed and calculated.And It comes to a conclusion: the algorithm in the appropriate conditions of quadtree mesh subdivision,its computation efficiency,the use of computer resources and computing accuracy is superior to FDM.Finally,this algorithm is extended to three-dimensional positive performance,which is the possibility of using octree grid to perform finite difference.It provides the thought for future research.