2D fast Fourier transform analytical solutions in all space for all gravity and magnetic components

Abstract

Forward modeling of potential field data is an important part of optimization algorithms used to invert large datasets such as those involving rugged terrain or borehole data. 2D fast Fourier transform (FFT) modeling with a prism or a dipole is one of the most efficient methods compared to the forward modeling in the space domain. However the exact solution of a prismatic source is limited to the case of a half‐space with the computation of data on a horizontal datum above the topography. Starting from the 3D Fourier forward modeling analytical formulation for a prism, an integration according to the wavenumber w is accomplished which allowed to find a 2D Fourier exact analytical formulation outside, at the interfaces of, and inside a prism for all potential field components. This new formulation requires the calculation of only four integrals. The gravity and magnetic fields are computed with this 2D FFT formulation in the entire domain, and compared with the analytical space domain and the 3D FFT formulations. From the 3D calculated field, each component can be interpolated with the tri‐linear interpolation method along a borehole or on a drape surface simulating an airborne survey. Based on experiments demonstrated in this work, the 2D formulation in the Fourier domain gave accurate results with greater speed of execution in comparison to modeling in the space domain. The forward modelling method is tested on real gravity data from the north of Alberta (Canada).This article is protected by copyright. All rights reserved