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ANALYTICAL EXPRESSIONS FOR GRAVITY DUE TO HOMOGENEOUS REVOLUTIONAL COMPARTMENTS IN THE GAUSSIAN DIVERGENCE APPROACH *
Author(s) -
OKABE M.
Publication year - 1982
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.1982.tb01297.x
Subject(s) - homogeneous , gravitation , divergence (linguistics) , gaussian , physics , newtonian fluid , coordinate system , geometry , cylinder , classical mechanics , spheroid , mathematical analysis , geology , mathematics , statistical physics , chemistry , linguistics , philosophy , quantum mechanics , biochemistry , in vitro
A bstract Complete analytical expressions are developed for the first and second derivatives of the Newtonian gravitational potential in arbitrary directions due to the homogeneous revolutional compartment with a polygonal vertical section by applying the Gaussian divergence theorem in the cylindrical coordinate system. Elementary solutions presented can easily be translated into magnetic anomalies caused by a uniformly magnetized body. The divergence approach in the polar coordinate system is also described, and gravity attractions in the radial direction are presented in closed form associated with a homogeneous cap compartment. The explicit solutions are tested against well‐known formulae for a cylinder, cone, infinite plate, and sphere.