Journal Article

Application of M¨obius coordinate transformation in evaluating Newton’s integral

Vladislav GLADKIKH, Robert TENZER

2011

Overview

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 M¨obius transformation with an enhanced integration grid resolution at vicinity of the observation point.

• Publisher: Earth Science Institute, Slovak Academy of Sciences, Slovakia
• Subject: analytical integration, forward modelling, gravity field, m¨obius transformation, newton integral