A comparison of Bjerhammar's methods and collocation in physical geodesy
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Date
1978-07
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Publisher
Ohio State University. Division of Geodetic Science
Abstract
In 1963 A. Bjerhammar solved the geodetic boundary value problem by applying Poisson's integral equation for a finite set of observed free-air gravity anomalies. Due to the relation between the number of observations (m) and the number of chosen unknowns (N) different solutions are obtained: non-singular (m = N), least squares (m >N) and minimum norm solutions (m < N). In the special case N → ∞ it is shown that the Bjerhammar solution with Poisson's kernel and a solution by collocation with the corresponding kernel are identical. Bjerhammar's method is generalized by using other kernel functions, and each minimum norm solution is shown to correspond to one specific set of degree variances in collocation. [Full text of abstract available in document.]