Open AccessA new method of computing geopotential fields
Author(s) -
Moon Wooil
Publication year - 1981
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1981.tb06950.x
Subject(s) - geopotential , gravitational field , interpolation (computer graphics) , piecewise , hydrostatic equilibrium , computation , gravitation , machine epsilon , gravitational potential , mathematics , field (mathematics) , mathematical analysis , statistical physics , classical mechanics , physics , algorithm , geophysics , motion (physics) , quantum mechanics , pure mathematics
Summary. A new method is proposed for the geopotential field computation and gravitational attraction modelling. The usual method is to use a uniform density discrete numerical integration to represent either the gravitational potential or the gravitational attraction from a given density configuration. In this paper, an interpolation scheme is explained, using a piecewise continuous basis function to represent the arbitrarily varying density configuration in one, two and three dimensions. This new approach greatly simplifies the potential integrations and, in certain cases where symmetry exists, analytical evaluation of the integrals is also possible. Numerical tests and examples are given for a hypothetical salt dome, a vertical dyke with varying density structure and the hydrostatic ellipticity of earth model 1066B. The numerical error in this method is limited to the analytical approximation and interpolation errors in each case. This new approach can also be used as efficiently for other potential field studies.