# Forward calculation of gravity and its gradient using polyhedral representation of density interfaces: an application of spherical or ellipsoidal topographic gravity effect

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## Abstract

A density interface modeling method using polyhedral representation is proposed to construct 3-D models of spherical or ellipsoidal interfaces such as the terrain surface of the Earth and applied to forward calculating gravity effect of topography and bathymetry for regional or global applications. The method utilizes triangular facets to fit undulation of the target interface. The model maintains almost equal accuracy and resolution at different locations of the globe. Meanwhile, the exterior gravitational field of the model, including its gravity and gravity gradients, is obtained simultaneously using analytic solutions. Additionally, considering the effect of distant relief, an adaptive computation process is introduced to reduce the computational burden. Then features and errors of the method are analyzed. Subsequently, the method is applied to an area for the ellipsoidal Bouguer shell correction as an example and the result is compared to existing methods, which shows our method provides high accuracy and great computational efficiency. Suggestions for further developments and conclusions are drawn at last.

### Keywords

Density interface Polyhedron Gravity Gravity gradient Icosahedron## Notes

### Acknowledgements

We thank Dr. Walter Mooney, Dr. Mikhail Kaban and three anonymous reviewers for their precious suggestions for preparing and revising the manuscript. This study is supported by the China Scholarship Council (No. 1609130003) and the Natural Science Foundation of China (No. 41574070). The source code of the method is available upon request.

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