Publication Date:
2023-07-25
Description:
We present a new Non-Uniform Fast Fourier Transform (NUFFT) algorithm for efficient modeling of topographic gravitational effects using polyhedral representation. The essential idea of the algorithm is to split the Newton's integral kernel into multiple parts using Gaussian-sum representation and to take full advantage of its duality property in spatial-spectral domain. Smooth, slowly-decaying parts of the Newton’s kernel, which correspond to a series of band-limited spectra with increased cut-off frequency, can be efficiently evaluated using NUFFT algorithms with controlled accuracy based on optimal discretization and truncation of spectra. On the other hand, the rapidly-decaying part of the Newton’s kernel in the vicinity of its singularity, is non-bandlimited. However, application of the Gaussian-sum decomposition greatly speeds up the decay rate of this part, so that spatial-domain algorithms can be used for its calculation without significant loss of efficiency. By combining the two, our new algorithm achieves great efficiency-accuracy balance and has several advantages over existing spectral-domain algorithms: 1) It is suitable for solving both local, regional and global scale gravitational forward modeling problems, with spherical or ellipsoidal geometry taken into account properly; 2) It can be applied with high-accuracy even in the near vicinity of the source, e.g., the Earth’s surface, and is free from any divergence problems within the Brillouin sphere encountered by spherical/ellipsoidal harmonic series solutions; 3) It is equally applicable to small, irregularly-shaped asteroids and large, more spherical planets, guaranteed by the underlying convergence of the 3D Fourier series representation of gravitational fields.
Language:
English
Type:
info:eu-repo/semantics/conferenceObject
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