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Journal of Geodesy

, Volume 93, Issue 10, pp 1963–1984 | Cite as

Improved Fourier modeling of gravity fields caused by polyhedral bodies: with applications to asteroid Bennu and comet 67P/Churyumov–Gerasimenko

  • Leyuan WuEmail author
  • Longwei Chen
  • Bin Wu
  • Bing Cheng
  • Qiang Lin
Original Article
  • 160 Downloads

Abstract

This paper presents an improved algorithm for the 2D and 3D Fourier forward modeling of gravity fields caused by polyhedral bodies with constant and exponential density distributions. Three modifications have been made to the Fourier forward algorithm introduced in a previous paper. First, vertex-based Fourier-domain expressions are used instead of the original face-based Fourier-domain expressions, which simplify the computation of the anomaly spectrum considerably, especially in 3D modeling problems. Second, instead of using a pure Gauss-FFT sampling of the anomaly spectrum, we apply an improved sampling strategy by combining a nonuniform spherical sampling with a low-order Gauss-FFT sampling. In this way, the number of samplings required in the Fourier domain reduces to about \(\frac{1}{3}\) and \(\frac{1}{7}\) of those required in a pure Gauss-FFT algorithm for 2D and 3D modeling problems, respectively. A significant acceleration over the original algorithm is achieved. Third, we incorporate all three types of nonuniform fast Fourier transform algorithms to transform directly a uniform or nonuniform anomaly spectrum to gravity fields either on a regular grid, or at a set of arbitrary positions. Extra interpolation operations are no longer needed. Synthetic numerical tests show that for gravity vector components, the new algorithm runs about 3 times faster in 2D modeling and 7 times faster in 3D modeling than the original ones, while maintaining the same level of accuracy. For the gravity potential, the new algorithm is significantly superior to the pure Gauss-FFT solution both in numerical accuracy and in efficiency. We apply this novel approach to compute the gravitational fields of asteroid 101955 Bennu and comet \(67\hbox {P/Churyumov}\)–Gerasimenko. The 2D algorithm works very efficiently for the computation of gravity fields on horizontal planes. The 3D algorithm is valid both outside, on, and inside the source’s bounding surface, with relative errors less than 0.1% for the gravity potential and less than 2% for the gravity vector. By comparing to modeling results of analytical and spherical harmonic-based solutions, we generally conclude that the Fourier-based algorithm introduced here is an attractive alternative to these conventional solutions, especially for nonspherical, irregularly shaped bodies with complex geometries.

Keywords

Polyhedron Gravity Gauss-FFT NUFFT Bennu 67P/Churyumov–Gerasimenko 

Notes

Acknowledgements

The authors are very grateful to the editor and three anonymous reviewers for their critique, helpful comments, and valuable suggestions, which improve the manuscript significantly. This study was funded by the National Natural Science Foundation of China under Grant No. 41504089.

Author Contributions

LW conceived the idea and wrote the paper; LC helped design the numerical experiments; the remaining authors contributed to refining the ideas, carrying out additional analyses.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Center for Optics & Optoelectronics Research (COOR), College of ScienceZhejiang University of TechnologyHangzhouChina
  2. 2.College of Earth SciencesGuilin University of TechnologyGuilinChina

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