Application of möbius coordinate transformation in evaluating Newton's integral

Robert Tenzer, Vladislav Gladkikh

Research output: Journal article publicationJournal articleAcademic researchpeer-review


We propose a numerical scheme which efficiently combines various existing methods of solving the Newton's volume integral. It utilises the analytical solution of Newton's integral for tesseroid in computing the near-zone contribution to gravitational field quantities (potential and its first radial derivative). The far-zone gravitational contribution is computed using the expressions derived based on applying Molodensky's truncation coefficients to a spectral representation of Newton's integral. The weak singularity of Newton's integral is treated analytically using formulas for the gravitational contribution of the cylindrical mass volume centered with respect to the observation point. All three solutions are defined and evaluated in the system of polar spherical coordinates. A conversion of the geographical to polar spherical coordinates of input data sets (digital terrain and density models) is based on the Möbius transformation with an enhanced integration grid resolution at vicinity of the observation point.
Original languageEnglish
Pages (from-to)95-115
Number of pages21
JournalContributions to Geophysics and Geodesy
Issue number2
Publication statusPublished - 9 Nov 2011
Externally publishedYes


  • Analytical integration
  • Forward modelling
  • Gravity field
  • Möbius transformation
  • Newton integral

ASJC Scopus subject areas

  • Geophysics


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