Numerical Investigations in the Analytical and Semi-Analytical Computation of Gravimetric Terrain Effects

Abstract

A recently proposed method for the computation of the gravitational effect due to the topographic masses defined by a Digital Elevation Model (DEM) involves the representation of the surface relief by means of parts of bilinear surfaces. The so-called bilinear method delivers eventually the mathematical model for the gravitational attraction of a right rectangular prism, whose top is modeled by a bilinear surface. Scope of the paper is to assess the new method by conducting numerical tests using both real and synthetic data. The performance of the bilinear method is evaluated in terms of its computational efficiency as well as its precision by comparing it with other analytical methods available for the practical evaluation of gravitational terrain effects. The techniques considered for the assessment of the bilinear approximation are the vastly applied right rectangular prism method and the polyhedral modeling, a less popular but extremely flexible approach based on the closed expression for the gravity field of an arbitrarily shaped mass distribution defined by planar faces. The different geometric modeling of the topographic relief produces discrepancies to the gravitational attraction of up to several mGal. Thus the choice for the geometric representation of the terrain plays a fundamental role to the numerical computation of potential field quantities especially in the critical region surrounding the computation point.