Two-dimensional And Three-dimensional Forward Modeling Of Magnetotelluric Based On Spatial Wavenumber Mixed Domain Method

The magnetotelluric sounding method is a geophysical method that uses the natural electromagnetic field as the field source.It is widely used in metal ores,oil and gas resources and engineering exploration.Efficient three-dimensional magnetotelluric forward modeling is the premise of large-scale magnetotelluric exploration and constitutes a key part of electromagnetic method research.However,the efficiency of conventional numerical simulation methods decreases with the increase of mesh division,which limits the practical application of the magnetotelluric method.The spatial wavenumber mixed domain forward modeling method utilizes the high efficiency of the frequency domain and the high precision of the spatial domain to convert the forward modeling problem into the wavenumber and spatial mixed domain for solving,so it can achieve efficient forward modeling under the condition of guaranteed accuracy.This paper mainly studies the application of the space wavenumber mixed domain method in the magnetotelluric method.Based on the diffusion equation of electromagnetic field,the two-dimensional and threedimensional forward modeling problems are studied.Aiming at the two-dimensional forward modeling problem,the electromagnetic method in the space wavenumber domain converts the two-dimensional partial differential equation into a one-dimensional ordinary differential equation with different wave numbers independent of each other through the one-dimensional Fourier transform,and then uses the finite difference method to solve it.The validity of the spatial wavenumber mixed domain method is verified by the standard model COMMEMI-2D1 model.For 3D forward modeling,since 3D forward modeling requires divergence correction,we add a regularization factor to the double curl equation of the electric field based on a divergence-free strategy to achieve divergence-free correction.Then,the three-dimensional partial differential equation is transformed into a one-dimensional ordinary differential equation with different wave numbers independent of each other through the two-dimensional Fourier transform,and the finite difference is used to solve it.Finally,the value in the space domain is obtained through the inverse Fourier transform.The correctness of the algorithm is verified by the COMMEMI-3D1 models,and a groundelectric model with a low resistance abnormal body and a ground-electric model with a high and low resistance body are designed to test the algorithm.The numerical test results show that the algorithm proposed in this paper is efficient,and the method due to the advantages of less memory and highly parallelized fits for solving large-scale forward modeling problems,which lays the foundation for subsequent efficient inversion.