Fourier-domain modeling of gravity effects caused by polyhedral bodies

Abstract

We present 2D and 3D Fourier-domain modeling of gravity effects, including the gravity potential and its first- and second- order derivatives, generated by an arbitrary polyhedron with constant and exponential density distributions. Fourier-domain expressions are obtained using Gauss’s divergence theorem repeatedly to transform the volume integral first into surface integrals and then to line integrals in the wave number domain. Both the derivation and the final expressions are simpler and more compact than space-domain ones. The highly accurate and efficient Gauss-FFT algorithm is then applied to transform the Fourier-domain expressions back to space-domain gravity fields. Synthetic and real model tests show that the Fourier-domain algorithm presented can provide forward results almost identical to space-domain analytical or numerical solutions at places where the exact solution changes smoothly. However, high-frequency truncation errors do become noticeable in the near vicinity of the source body, where the exact solution changes abruptly, or even discontinuously. The Fourier-domain algorithm captures almost all frequency components of the exact solution that are lower than the Nyquist frequency, which is determined by the chosen grid intervals. The algorithm offers a more efficient solution for 2D and 3D modeling of gravity fields on large and densely sampled regular grids than classical space-domain solutions, at the cost of a small loss of accuracy.