A case study of forward calculations of the gravity anomaly by spectral method for a three-dimensional parameterised fault model

Abstract

Spectral methods provide many advantages for calculating gravity anomalies. In this paper, we derive a kernel function for a three-dimensional (3D) fault model in the wave number domain, and present the full Fortran source code developed for the forward computation of the gravity anomalies and related derivatives obtained from the model. The numerical error and computing speed obtained using the proposed spectral method are compared with those obtained using a 3D rectangular prism model solved in the space domain. The error obtained using the spectral method is shown to be dependent on the sequence length employed in the fast Fourier transform. The spectral method is applied to some examples of 3D fault models, and is demonstrated to be a straightforward and alternative computational approach to enhance computational speed and simplify the procedures for solving many gravitational potential forward problems involving complicated geological models. The proposed method can generate a great number of feasible geophysical interpretations based on a 3D model with only a few variables, and can thereby improve the efficiency of inversion.