Journal of Geodesy

, Volume 92, Issue 8, pp 847–862 | Cite as

Forward modelling of global gravity fields with 3D density structures and an application to the high-resolution (~ 2 km) gravity fields of the Moon

  • M. ŠprlákEmail author
  • S.-C. Han
  • W. E. Featherstone
Original Article


Rigorous modelling of the spherical gravitational potential spectra from the volumetric density and geometry of an attracting body is discussed. Firstly, we derive mathematical formulas for the spatial analysis of spherical harmonic coefficients. Secondly, we present a numerically efficient algorithm for rigorous forward modelling. We consider the finite-amplitude topographic modelling methods as special cases, with additional postulates on the volumetric density and geometry. Thirdly, we implement our algorithm in the form of computer programs and test their correctness with respect to the finite-amplitude topography routines. For this purpose, synthetic and realistic numerical experiments, applied to the gravitational field and geometry of the Moon, are performed. We also investigate the optimal choice of input parameters for the finite-amplitude modelling methods. Fourth, we exploit the rigorous forward modelling for the determination of the spherical gravitational potential spectra inferred by lunar crustal models with uniform, laterally variable, radially variable, and spatially (3D) variable bulk density. Also, we analyse these four different crustal models in terms of their spectral characteristics and band-limited radial gravitation. We demonstrate applicability of the rigorous forward modelling using currently available computational resources up to degree and order 2519 of the spherical harmonic expansion, which corresponds to a resolution of ~ 2.2 km on the surface of the Moon. Computer codes, a user manual and scripts developed for the purposes of this study are publicly available to potential users.


Bulk density Newton’s integral Spherical harmonic expansion LOLA GRAIL 



This research was supported partially by the Australian Government through the Australian Research Council’s Discovery Projects funding scheme (project DP160104095). We thank Mark Wieczorek for sharing his own results of topography gravitational potential fields and the surface grain density, and Greg Neumann for his advice on the LOLA topography grid data. Thoughtful and constructive comments of the three anonymous reviewers are gratefully acknowledged. Thanks are also extended to the editor-in-chief Prof. Jürgen Kusche and to the responsible editor Prof. Ilias N. Tziavos for handling our manuscript.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of Engineering, Faculty of Engineering and Built EnvironmentUniversity of NewcastleCallaghanAustralia
  2. 2.Department of Spatial Sciences, The Institute for Geoscience ResearchCurtin University of TechnologyPerthAustralia

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