Abstract
When area means are given on a regular grid, their covariance functions, needed in least squares collocation to estimate quantities statistically related to the data, can be calculated as accurately as desired and very efficiently in the form of a Fourier series truncated at a suitably high frequency.
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O.L. COLOMBO: Optimal estimation from data regularly sampled on a sphere with applications to geodesy, Dept. of Geodetic Science, Ohio State Univ., Rep. No. 291, Columbus, 1979.
O.L. COLOMBO: Numerical methods for harmonic analysis on the sphere. Dept. of Geodetic Science, Ohio State Univ., Rep. No. 310, Columbus, 1981.
W.A. HEISKANEN and H. MORITZ:Physical Geodesy, W.H. Freeman and Co., 1967.
C. JEKELI: An investigation of two models for the degree variances of global covariance functions. Dept. of Geodetic Science, Ohio State Univ., Rep. No. 275, Columbus, 1978.
T. KRARUP: A contribution to the foundation of physical geodesy. Report of the Danish Geodetic Institute, Copenhagen 1969.
P. MEISSL: Study of covariance functions related to the Earth gravity potential. Dept. of Geodetic Science, Ohio State Univ., Rep. No. 151, Columbus, 1971.
M.K. PAUL: Recurrence relationships for integrals of the associate Legendre functions.Bull. Géodésique, 52, 1978.
L. SJÖBERG: Potential coefficient determinations from 10° terrestrial gravity data by means of collocation. Dept. of Geodetic Science, Ohio State Univ., Rep. No. 274, Columbus, 1978.
C.C. TSCHERNING and R.H. RAPP: Closed covariance expressions for gravity anomalies, geoid undulations, and deflections of the vertical implied by anomaly degree variance models. Dept. of Geodetic Science, Ohio State Univ., Rep. No. 208, Columbus, 1974.
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Colombo, O.L. Numerical calculation of covariances between area means. Bull. Geodesique 57, 131–137 (1983). https://doi.org/10.1007/BF02520919
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DOI: https://doi.org/10.1007/BF02520919