The forward modeling of 3D gravity and magnetic potential fields in space-wavenumber domains based on an integral method

Abstract

With the help of the horizontal 2D Fourier transform, 3D convolutions can be transformed into vertical 1D integrations of different wavenumbers. It has already been proven that the Fourier domain method can greatly improve the efficiency of numerical simulations of 3D gravity and magnetic anomalies. Based on the aforementioned strategy, we have developed an efficient 1D integration algorithm in the space-wavenumber domain, which is combined with a fast continuation algorithm along the z-axis for high-efficiency calculations of nonconstant density or magnetization anomalies in rugged terrains. The calculation accuracy and efficiency of four 1D vertical integration methods (i.e., rectangular integrals, quadratic interpolations, Gaussian integrals, and cubic spline interpolations) are compared by using complex models (variable density distribution model and topographic model). The results indicate that, among the four integration methods, the quadratic interpolation method combined with a fast continuation algorithm achieves the best accuracy and efficiency. Compared with other Fourier domain algorithms, the proposed best 1D integration method in space-wavenumber domains achieves good numerical performance in calculating fields on planar and undulating terrains. Moreover, the proposed method is used to calculate the terrain effect on an airborne gravity and magnetic data set for realistic topography modeling. The results indicate that the new algorithm is suitable for the high-efficiency calculation of large-scale complicated 3D models.