Forward modeling of three-dimensional magnetotelluric based on Lorenz gauge in space-wavenumber domain

The magnetotelluric method (MT) is widely used for the geophysical exploration of mineral resource exploration, oil-gas exploration, and study of deep structure because of its advantages of low cost, simple construction, and large detecting depth. How to improve the accuracy and efficiency of the 3D MT forward modeling in large scale is focus of study. Based on the space-wavenumber domain method, we study the 3D MT forward modeling in the space wavenumber domain based on the Lorenz gauge. We adopt secondary field method, by introducing the Lorenz gauge, the Maxwell equations can be converted into Helmholtz equations of the vector potential. With the help of the horizontal 2D Fourier transform, the 3D partial differential equation can be transformed into independent ordinary differential equations of several different wavenumbers. The equations are solved by the finite element method of quadratic interpolation, the linear equations are constant bandwidth, low-calculation and highly parallel, we further improve the efficiency of the algorithm by using a chasing method. The compact operator is applied to iterative computing method to approach the real solution. It makes full use of the advantages of the space-wavenumber domain method, like high numerical accuracy, low memory requirement, and high efficiency. We design a prism model to verify the accuracy and discuss the convergence of algorithm, we can conclude that the proposed method is suitable for different frequencies and large conductivity contrast anomalies. The results of Dublin(DTM1) model for 3D MT modeling show that compared with the existing spatial domain algorithms, based on fulfilling requirement for precision, the space-wavenumber domain methods spend less time and require less memory. The space-wavenumber domain algorithm of the Lorenz gauge is more efficient than that of the Coulomb gauge, increased by at least 3 times, which reflects the advantages of the new space-wavenumber domain method.