A FORTRAN IV program for the determination of the anomalous potential using stepwise least squares collocation
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Date
1974-07
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Ohio State University. Division of Geodetic Science
Abstract
The theory of sequential least squares collocation, as applied to the determination of an approximation Ť to the anomalous potential of the Earth T, and to the prediction and filtering of quantities related in a linear manner to T, is developed. The practical implementation of the theory in the form of a FORTRAN IV program is presented, and detailed instructions for the use of this program are given. The program requires the specification of (1) a covariance function of the gravity anomalies and (2) a set of observed quantities (with known standard deviations). The covariance function is required to be isotropic. It is specified by a set of empirical anomaly degree-variances all of degree less than or equal to an integer I and by selecting the anomaly degree-variances of degree greater than I according to one of three possible degree-variance models. The observations may be potential coefficients, mean or point gravity anomalies, height anomalies or deflections of the vertical. A filtering of the observations will take place simultaneously with the determination of Ť. The program may be used for the prediction of height anomalies, gravity anomalies and deflections of the vertical. Estimates of the standard error of the predicted quantities may be obtained as well. The observations may be given in a local geodetic reference system. In this case parameters for a datum shift to a geocentric reference system must be specified. The predictions will be given in both the local and the geocentric reference system. Ť may be computed stepwise, i.e. the observations may be divided in up to three groups. (The limit of three is only attained when potential coefficients are observed, in which case these quantities will form the first set of observations.) Each set of observations will determine a harmonic function and Ť will be equal to the sum of these functions. The function Ť determined by the program will be a (global or local) solution to the problem of Bjerhammar, i.e., it will be harmonic outside a sphere enclosed in the Earth, and it will agree with the filtered observations. [Some mathematical expressions are not fully represented in the metadata. Full text of abstract available in document.]