On the Two Different Formulas for the 3D Rectangular Prism Effect in Gravimetry
- 29 Downloads
The direct problem of simple geometrical bodies plays an important role in the gravimetrical processing and modelling tools. We focused on the 3D rectangular prism, which is widely used in such processes. Even though the solution for this body is well known, there are still some issues about it, which are not answered or not answered completely in the available literature, e.g. the presence of the singularities in the source-free points or a continuity of the solutions. We present the singularity-free solution valid for the each position of the calculation point. Next, the analysis of the two basic types of the formulae for the 3D rectangular prism’s gravitational effect is held on. We discuss the ways of their derivation, the validity and the problems connected with them. Later, special attention is paid at the problems with the citation of these two formulae types within the gravimetrical literature.
KeywordsGravimetry direct problem 3D rectangular prism
This work was supported by the project of the Scientific and Grant Agency of Slovak Republic (VEGA-1/0462/16).
- Everest, G. (1830). An account of the measurement of an arc of the meridian between the parallels of 18°3′ and 24°7′. London.Google Scholar
- Gradshteyn, I. S., & Ryzhik, I. M. (1962). Table of integrals, series and products. Moscow: State Publishing House of Physical and Mathematical Literature (in Russian).Google Scholar
- Haáz, I. B. (1953). Relation between the potential of the attraction of the mass contained in a finite rectangular prism and its first and second derivatives. Geofizikai Kőzlemenyek 2(7) (in Hungarian).Google Scholar
- MacMillan, W. D. (1930). The theory of the potential. New York: McGraw-Hill.Google Scholar
- Mader, K. (1951). Das Newtonsche Raumpotential prismatischer Körper und seine Ableitungen bis zur dritten Ordnung. Sonderheft 11 der Österreichischen Zeitschrift für Vermessungswesen. Wien: Österreichischer Verein für Vermessungswesen.Google Scholar
- Rektorys, K. (1968). The compendium of the applied mathematics (in Czech). Prague: Publishing House of Technical Literature.Google Scholar
- Sorokin, L. V. (1951). Gravimetry and gravimetrical prospecting. Moscow: State Technology Publishing (in Russian).Google Scholar