Sub-regional Taylor-series modeling of the gravity potential based on von Eötvös’ torsion balance measurements

Abstract

This paper introduces a technique for modeling the gravity potential using a low-degree Taylor series expansion, specifically of three or four degrees and demonstrates its practical application. The coefficients for this gravity model are the derivatives of the gravity potential at a specified point. The coefficients are determined through Von Eötvös’ torsion balance measurements conducted on the ice sheet of Lake Balaton in Hungary, by minimizing the squares of the difference between the nearby measured (by torsion balance) and calculated second derivatives of gravity potential. The model is applicable over an area spanning several kilometers, encompassing multiple torsion balance measurements, and thus provides broader coverage compared to a strictly local model, thereby justifying its classification as a sub-regional model. The resulting gravity potential field is presented on two types of map, similarly to Eötvös’ work. The derived model characterizes the gravitational potential for the region where measurements were taken, yet it behaves unexpectedly and generates artifacts beyond this measurement area. Earlier geoid models for this region included torsion balance data; in contrast, our results provide a more detailed gravity potential model over a more confined area.