Two-dimensional Magnetotelluric Modeling By Finite Difference Method Using Quadtree Mesh

Among the existing 2D and 3D forward algorithms of magnetotelluric(MT)method,the algorithms based on the structured mesh are fast,but the ability to simulate a complex model is poor.Unstructured mesh algorithms can simulate complex models,but requires high mesh quality and slow computing speed.How to find an efficient and fast forward algorithm with strong adaptability to complex models has become a hot and difficult problem in the current research.It is also the key to the application and popularization of MT 3D inversion.Quadtree mesh has the flexibility of unstructured mesh,it can overcome the instability of unstruct ured mesh,and has the characteristic of fast solution of structured mesh.In this paper,quadtree mesh was introduced into MT 2D forward modeling,and the research of MT finite-difference 2D forward modeling based on quadtree mesh was carried out.Firstly,the basic idea of quadtree mesh was introduced briefly,and the data structure and implementation method of quadtree mesh was constructed.This paper also realized the automatic refinement and refinement of any element in the mesh by the logarithmic gradient of resistivity.The Z-shaped coding strategy was used to sort the quad mesh.The automatic discretization and adaptive refinement of arbitrary geoelectric models based on quadtree mesh were used to realize.The feasibility and stability of the algorithm were verified by several typical geoelectric models,which provide theoretical guidance for forward calculation.Then,based on the electric field equation of TE mode and the magnetic field equation of TM mode,the quadtree mesh discretization formula based on mesh center discretization was derived.The row compression(CSR)format was used to store the discrete linear equations,and the PARDISO mathematical solver was used to realize the 2D forward calculation of MT.Subsequently,the implemented algorithm is used to calculate the one-dimensional layered model and COMMEMI2D-1/4 models,and the accuracy and feasibility of the algorithm are verified by comparing with the analytical solution.The results show that under the condition of reasonable threshold quadtree mesh generation,the calculation accuracy and efficiency can be improved,which provides a new idea for MT 2D / 3D forward calculation.Finally,the influencing factors and response rules of MT in the water area are analyzed and discussed,which provides guidance for the practical work of MT and data interpretation.