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Surveys in Geophysics

, Volume 39, Issue 3, pp 337–363 | Cite as

Analytic Expressions for the Gravity Gradient Tensor of 3D Prisms with Depth-Dependent Density

  • Li Jiang
  • Jie Liu
  • Jianzhong Zhang
  • Zhibing Feng
Article
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Accepted:

Abstract

Variable-density sources have been paid more attention in gravity modeling. We conduct the computation of gravity gradient tensor of given mass sources with variable density in this paper. 3D rectangular prisms, as simple building blocks, can be used to approximate well 3D irregular-shaped sources. A polynomial function of depth can represent flexibly the complicated density variations in each prism. Hence, we derive the analytic expressions in closed form for computing all components of the gravity gradient tensor due to a 3D right rectangular prism with an arbitrary-order polynomial density function of depth. The singularity of the expressions is analyzed. The singular points distribute at the corners of the prism or on some of the lines through the edges of the prism in the lower semi-space containing the prism. The expressions are validated, and their numerical stability is also evaluated through numerical tests. The numerical examples with variable-density prism and basin models show that the expressions within their range of numerical stability are superior in computational accuracy and efficiency to the common solution that sums up the effects of a collection of uniform subprisms, and provide an effective method for computing gravity gradient tensor of 3D irregular-shaped sources with complicated density variation. In addition, the tensor computed with variable density is different in magnitude from that with constant density. It demonstrates the importance of the gravity gradient tensor modeling with variable density.

Keywords

Gravity gradient tensor 3D right rectangular prism Polynomial density function 
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Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 41074077 and 41230318) and the Key Research and Development Program of Shandong Province (Grant No. 2017GSF16103). We thank Editor in Chief Michael J. Rycroft and an anonymous reviewer for their constructive comments that greatly improved this manuscript.

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Authors and Affiliations

  • Li Jiang
    • 1
  • Jie Liu
    • 1
  • Jianzhong Zhang
    • 1
    • 2
  • Zhibing Feng
    • 1
  1. 1.Key Laboratory of Submarine Geosciences and Prospecting Techniques of the Ministry of Education, College of Marine GeosciencesOcean University of ChinaQingdaoChina
  2. 2.Evaluation and Detection Technology Laboratory of Marine Mineral Resources, Qingdao National Laboratory for Marine Science and TechnologyQingdaoChina

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