Surveys in Geophysics

, Volume 39, Issue 3, pp 401–434 | Cite as

Efficient Modeling of Gravity Fields Caused by Sources with Arbitrary Geometry and Arbitrary Density Distribution

  • Leyuan Wu


We present a brief review of gravity forward algorithms in Cartesian coordinate system, including both space-domain and Fourier-domain approaches, after which we introduce a truly general and efficient algorithm, namely the convolution-type Gauss fast Fourier transform (Conv-Gauss-FFT) algorithm, for 2D and 3D modeling of gravity potential and its derivatives due to sources with arbitrary geometry and arbitrary density distribution which are defined either by discrete or by continuous functions. The Conv-Gauss-FFT algorithm is based on the combined use of a hybrid rectangle-Gaussian grid and the fast Fourier transform (FFT) algorithm. Since the gravity forward problem in Cartesian coordinate system can be expressed as continuous convolution-type integrals, we first approximate the continuous convolution by a weighted sum of a series of shifted discrete convolutions, and then each shifted discrete convolution, which is essentially a Toeplitz system, is calculated efficiently and accurately by combining circulant embedding with the FFT algorithm. Synthetic and real model tests show that the Conv-Gauss-FFT algorithm can obtain high-precision forward results very efficiently for almost any practical model, and it works especially well for complex 3D models when gravity fields on large 3D regular grids are needed.


Convolution-type integrals Gravity forward modeling Conv-Gauss-FFT algorithm Arbitrary geometry Arbitrary density distribution 



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


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Authors and Affiliations

  1. 1.Center for Optics and Optoelectronics Research (COOR), Collaborative Innovation Center for Information Technology in Biological and Medical Physics, College of ScienceZhejiang University of TechnologyHangzhouChina

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