On inversion of the second- and third-order gravitational tensors by Stokes’ integral formula for a regional gravity recovery

Mohammad A. Sharifi, Mohsen Romeshkani, Robert Tenzer

Research output: Journal article publicationJournal articleAcademic researchpeer-review

11 Citations (Scopus)


A regional recovery of the Earth’s gravity field from satellite observables has become particularly important in various geoscience studies in order to better localize stochastic properties of observed data, while allowing the inversion of a large amount of data, collected with a high spatial resolution only over the area of interest. One way of doing this is to use observables, which have a more localized support. As acquired in recent studies related to a regional inversion of the Gravity field and steady-state Ocean Circulation Explorer (GOCE) data, the satellite gravity-gradient observables have a more localized support than the gravity observations. Following this principle, we compare here the performance of the second- and third-order derivatives of the gravitational potential in context of a regional gravity modeling, namely estimating the gravity anomalies. A functional relation between these two types of observables and the gravity anomalies is formulated by means of the extended Stokes’ integral formula (or more explicitly its second- and third-order derivatives) while the inverse solution is carried out by applying a least-squares technique and the ill-posed inverse problem is stabilized by applying Tikhonov’s regularization. Our results reveal that the third-order radial derivatives of the gravitational potential are the most suitable among investigated input data types for a regional gravity recovery, because these observables preserve more information on a higher-frequency part of the gravitational spectrum compared to the vertical gravitational gradients. We also demonstrate that the higher-order horizontal derivatives of the gravitational potential do not necessary improve the results. We explain this by the fact that most of the gravity signal is comprised in its radial component, while the horizontal components are considerably less sensitive to spatial variations of the gravity field.
Original languageEnglish
Pages (from-to)453-468
Number of pages16
JournalStudia Geophysica et Geodaetica
Issue number3
Publication statusPublished - 1 Jul 2017
Externally publishedYes


  • GOCE
  • gravitational curvature
  • gravity field modeling
  • inverse problem
  • satellite gradiometry

ASJC Scopus subject areas

  • Geophysics
  • Geochemistry and Petrology


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