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

• Published in: Geophysical Prospecting Vol. 72; no. 2; pp. 809 - 832
• Main Author: Boulanger, Olivier
• Format: Journal Article
• Language: English
• Published: Houten Wiley Subscription Services, Inc 01.02.2024
• Subjects: Algorithms; Boreholes; Components; Computation; Dipoles; Exact solutions; fast Fourier transform; Fast Fourier transformations; Fourier transforms; gravity; Gravity data; Interfaces; Interpolation; Magnetic field; Magnetic fields; magnetics; Modelling; Potential fields; three‐dimensional modelling; Two dimensional analysis; Wavelengths
• ISSN: 0016-8025; 1365-2478
• DOI: 10.1111/1365-2478.13427

ABSTRACT Forward modelling 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. Two‐dimensional fast Fourier transform modelling with a prism or a dipole is one of the most efficient methods compared to the forward modelling 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 three‐dimensional Fourier forward modelling analytical formulation for a prism, an integration according to the wavenumber w is accomplished which allowed to find a two‐dimensional 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 two‐dimensional fast Fourier transform formulation in the entire domain and compared with the analytical space domain and the three‐dimensional fast Fourier transform formulations. From the three‐dimensional 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 two‐dimensional formulation in the Fourier domain gave accurate results with greater speed of execution in comparison to modelling in the space domain. The forward modelling method is tested on real gravity data from the north of Alberta (Canada).