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RECONSTRUCTION OF FUNCTIONS FROM DISCRETE MEAN VALUES,
OHIO STATE UNIV COLUMBUS DEPT OF GEODETIC SCIENCE AND SURVEYING
For automatic processing, gravity anomalies and similar quantities are conveniently stored as mean values of standard-sized blocks formed by the grid of geographical coordinates say 5 minutes x 5 minutes or 1 degree x 1 degree. For the most part, these mean values can be directly used in the numerical integrations of physical geodesy. Near the computation point, however, where the integrand frequently becomes singular or nearly so, a more detailed representation of the gravity anomaly function may be necessary. For application to such and other purposes, the present paper considers the approximate reconstruction of the original form of a function of one or two variables from equidistant mean values by various methods, including Bernoulli polynomials and spectral analysis. Author