Summary
In the present paper the gravity field of the earth in the neighbourhood of the local disturbing masses is studied. The object of the method presented consists of the approximation of the disturbing potentialT h , which fulfils Laplace's equation outside disturbing masses, on the earth's surface the fundamental boundary value condition of gravity and in infinity it is to be regular by the approximation of the disturbing potential (or by the discrete disturbing potential)T h , which fulfils the respective finite difference approximation of Laplace's equation and the boundary value conditions in infinity and on the earth's surface. It is also shown that the approximation of the disturbing potentialT h has the same properties as the disturbing potentialT. The method under consideration will be derived quite generally without any hypothesis about the distribution of the mass between the earth's surface and the geoid. It commences from the gravity data related to the earth's surface only-from the given geodetic measurements.
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References
M. Pick, J. Pícha andV. Vyskočil,Theory of the Earth's Gravity Field (Elsevier Amsterdam, NČSAV Praha). In print.
W. A. Heiskanen andH. Mortiz,Physical Geodesy (W. H. Freeman and Company, San Francisco and London 1967)
L. N. Sretenskij,Theory of the Newton Potential (OGIZ-Gos. Izdat. tech.-teoret. literatury, Moscow 1946).
D. Greenspan,Introductory Numerical Analysis of Elliptic Boundary Value Problems (Harper, New York 1965).
E. Batschelei;Über die Numerische Auflösung von Randwertproblem bei Elliptischen Partiellen Differentialgleichungen, Z. Angew. Math. Physik3, 165–193.
J. Nedoma,Application of Finite Difference Method for Studying Boundary Value Problems of Gravity Potential. International Union of Geodesy and Geophysics XVth General Assembly, Moscow, July–August 1971;International Association of Geodesy, List of Abstracts, Part 3, Mathematical Theories and Methods, Nos. 8–12.
J. Nedoma,Solution of boundary value problems of the gravity potential using finite difference methods, Studia geoph. et geodet. (in press).
J. Nedoma,Application of finite difference method for studying gravity field in the neighbourhood of the disturbing masses (in Czech.).Proceedings of the Symposium on Theory and Computers in Geophysics, Brno 1972 (in press).
J. Nedoma,The variational formulation of the boundary value problem of gravity potential. (Sent to Studia geoph. et geodet.)
J. Nedoma,Investigation of the gravity field from the point of view of the finite element method (in Czech.)Proceedings of the Symposium on Theory and Computers in Geophysics, Brno 1972 (in press).
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Nedoma, J. On the discrete outer gravity field. PAGEOPH 110, 1899–1910 (1973). https://doi.org/10.1007/BF00876552
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DOI: https://doi.org/10.1007/BF00876552