On the accuracy of the coefficients in a series of spherical harmonics
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Date
1964-04
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Publisher
Ohio State University. Division of Geodetic Science
Abstract
The accuracy of the coefficients of a development in a series of spherical harmonics is investigated. Usually the coefficients are determined by numerical integration. Therefore, the surface of the sphere is divided into small surface elements and the mean value of the function for each surface element is estimated. Two sources of error are distinguished: 1. Representation error. This is the error of the estimation of the mean value of the function for each surface element. 2. Integration error. This is the error caused by the replacement of the integral by a numerical integration. Both errors are separately investigated. Two examples are considered at the end of this paper: 1. The topography in spherical harmonics. Here the main source of errors is the integration error. 2. The gravity anomalies in spherical harmonics. Here the main source of errors is the representation error.
Description
Prepared for Air Force Cambridge Research Laboratories, Office of Aerospace Research, United States Air Force, Bedford, Massachusetts: Contract No. AF 19(628)-2771, Project No. 7600, Task No. 76002