Arabelos D. and C.C. Tscherning, 2008, Error-covariances of the estimates of spherical harmonic coefficients computed by LSC, using second-order radial derivative functionals associated with realistic GOCE orbits. J.Geod., DOI: 10.1007/s00190-008-0250-9.CrossrefWeb of ScienceGoogle Scholar
Forsberg R. and C.C. Tscherning, 2008, An overview manual for the GRAVSOFT Geodetic Gravity Field Modelling Programs. 2.edition. Contract report for JUPEM. Available as: http://cct.gfy.ku.dk/publ_cct/cct1936.pdf Freeden W., 1982, On the Permanence Property in Spherical Spline Interpolation. Reports of the Department of Geodetic Science and Surveying, No. 341, The Ohio State University, Columbus, Ohio.Google Scholar
Heiskanen W.A. and H. Moritz, 1967, Physical Geodesy. W.H. Freeman & Co, San Francisco, 1967. Moritz H., 1980, Advanced Physical Geodesy. H.Wichmann Verlag, Karlsruhe.Google Scholar
Pavlis N.K., Holmes S.A., Kenyon S.C. and Factor J.K., 2012, The development and evaluation of the Earth Gravitational Model 2008 (EGM2008) Journal of Geophysical Research: Solid Earth (1978-2012) Volume 117, Issue B4, April.Google Scholar
Poder K. and C.C. Tscherning, 1973, Cholesky’s Method on a Computer. The Danish Geodetic Institute Internal Report No. 8. (Available as http://cct.gfy.ku.dk/publ_cct/cct42.pdf) Sanso F. and M.G. Sideris (Eds), 2013, Geoid Determination. Lecture Notes in Earth System Science 110, DOI: 10.1007/978-3-540-74700-0_7. Springer-Verlag, Berlin-Heidelberg. Moreaux G., C.C. Tscherning and F. Sansó, 1999: Approximation of Harmonic Covariance Functions on the sphere by non Harmonic Locally Supported functions. Journal of Geodesy, Vol. 73, pp. 555 - 567.CrossrefGoogle Scholar
Torge W. and J. Müller, 2012, Geodesy. 4th ed., de Gruyter.Google Scholar
Tscherning C.C.,1974, A FORTRAN IV Program for the Determination of the Anomalous Potential Using Stepwise Least Squares Collocation. Reports of the Department of Geodetic Science No. 212, The Ohio State University, Columbus, Ohio.Google Scholar
Tscherning C.C, 1978, A Users Guide to Geopotential Approximation by Stepwise Collocation on the RC 4000-Computer. Geodaetisk Institut Meddelelse No. 53.Google Scholar
Tscherning C.C. and K. Poder, 1982 Some Geodetic applications of Clenshaw Summation. Bolletino di Geodesia e Scienze Affini, Vol. XLI, no. 4,pp. 349-375.Google Scholar
Tscherning C.C. and M. Veicherts, 2008, Accelerating generalized Cholesky decomposition using multiple processors. Presentation, EGU 2008. Available as htt://cct.gfy.ku.dk/publ_cct/accelerating08.pptGoogle Scholar
Journal of Geodetic Science
Editor-in-Chief: Eshagh, Mehdi
Multi-processing least squares collocation: Applications to gravity field analysis
Least Squares Collocation (LSC) is used for the modeling of the gravity field, including prediction and error estimation of various quantities. The method requires that as many unknowns as number of data and parameters are solved for. Cholesky reduction must be used in a nonstandard form due to missing positive-definiteness of the equation system. Furthermore the error estimation produces a rectangular or triangular matrix which must be Cholesky reduced in the non-standard manner. LSC have the possibility to add new sets of data without processing previously reduced parts of the equation system. Due to these factors standard Cholesky reduction programs using multi-processing cannot easily be applied. We has therefore implemented Fortran Open Multi-Processing (OpenMP) to the non-standard Cholesky reduction. In the computation of matrix elements (covariances) as well as the evaluation spherical harmonic series used in the remove/restore setting we also take advantage of multi-processing. We describe the implementation using quadratic blocks, which aids in reducing the data transport overhead. Timing results for different block sizes and number of equations are presented. OpenMP scales favorably so that e.g. the prediction and error estimation of grids from GOCE TRF vertical gradient data and ground gravity data can be done in the less than two hours for a 25° by 25° area with data selected close to 0.125° nodes.
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