Three Dimensional MT Forward Study Based On Fast Quasi-linear Integral Equation

Magnetotelluric sounding(MT)is a frequency-domain electromagnetic survey method,which studies the geology of different depths by electromagnetic waves of different frequencies generated by natural alternating electromagnetic fields;because the method does not require manual addition of sources,it has a field survey.The process can reduce costs,is simple to operate,will not be shielded by high-resistance bodies,and has high resolution for low-resistance bodies,so it is widely used in field surveys,geological surveys,and deep geological structure studies.In this paper,we study the magnetotelluric forward numerical simulation by combining the magnetotelluric method with the quasi-linear integral equation method,which enables us to understand more deeply the laws of the electromagnetic field generated by different underground electrical media.Firstly,the paper introduces the idea of combining the quasi-linear integral equation method and the magnetotelluric method into the paper,deriving from the MAXWELL equations,and considering the computational speed and memory occupation in the paper,the quasi-linear approximation method and the integral equation method are studied to solve the problem.The time spent and compared;for its accuracy,the quasi-linear integral equation method is also very high in the numerical simulation approximation method of the electromagnetic field,and it is characterized by fastness.Compared with the finite difference method and the finite element method,only the abnormal region is needed.The splitting can be done,which greatly saves the memory occupation and improves the computational efficiency.Therefore,the introduction ofthe quasi-linear approximation method to the three-dimensional forward magnetotelluric study is of great significance.Secondly,based on previous researches,this paper studies the theoretical part of the quasi-linear integral equations in depth.By compressing the spatial symmetry of the Green’s function and applying the swap theorem,the purpose of reducing the calculation of the Green’s function is achieved.The speed of the generation of the coefficient matrix is significantly improved,and the effect of rapid generation is further achieved,thus significantly increasing the calculation speed.By designing the layered and uniform half-space model and comparing it with the known analytical solution,the calculated accuracy of the solution is very high,thus further verifying the correctness of this method.On this basis,designing more models for research shows that this method is applicable to a wide range of aspects;the fineness of the model is also studied,and corresponding explanations are given for the time spent in the calculations.Compared with the integral equation method,the linear integral equation method is much faster than the finite element method,which achieves the purpose of accurate calculation,wide application,and high efficiency.In the end,the paper further looks forward to the next work,hoping to help the future inversion research,and further elaborates the deficiencies in this article.