This paper introduces a class of nearly harmonic functions useful in analyzing gravity above a limited region of the earth’s surface. These “B functions” constitute a complete orthogonal set of functions over that portion of the surface of a sphere which lies between two latitudes and two longitudes. By an iteration process, the coefficients of a series of B functions can be determined in such a manner as to provide an optimum fit to the difference between the prediction of a global gravity model and gravity actually measured on the earth’s surface, thus bypassing the problem of reducing the data to a reference surface. Representation of local gravity as the sum of a global model in terms of spherical harmonics and a local model in terms of B functions appears to be an effective technique for handling the problem of altitude extension of surface data.
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September 1970
Research Papers
On a Local Representation of the Fine Structure in the Earth’s Gravitational Field
S. B. Batdorf
S. B. Batdorf
The Aerospace Corporation, San Bernardino, Calif.
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S. B. Batdorf
The Aerospace Corporation, San Bernardino, Calif.
J. Appl. Mech. Sep 1970, 37(3): 738-743 (6 pages)
Published Online: September 1, 1970
Article history
Received:
May 22, 1969
Online:
July 12, 2010
Citation
Batdorf, S. B. (September 1, 1970). "On a Local Representation of the Fine Structure in the Earth’s Gravitational Field." ASME. J. Appl. Mech. September 1970; 37(3): 738–743. https://doi.org/10.1115/1.3408604
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