caa a22 4500 475737393 CHVBK 20180406123450.0 cr unu---uuuuu 170329e20000501xx s 000 0 eng 10.1007/s001900050292 doi (NATIONALLICENCE)springer-10.1007/s001900050292 Formation of surface spherical harmonic normal matrices and application to high-degree geopotential modeling [Elektronische Daten] [M. C. Kim, B. D. Tapley] Abstract.:  The structure of normal matrices occurring in the problem of weighted least-squares spherical harmonic analysis of measurements scattered on a sphere with random noises is investigated. Efficient algorithms for the formation of the normal matrices are derived using fundamental relations inherent to the products of two surface spherical harmonic functions. The whole elements of a normal matrix complete to spherical harmonic degree L are recursively obtained from its first row or first column extended to degree 2L with only O(L 4) computational operations. Applications of the algorithms to the formation of surface normal matrices from geoid undulations and surface gravity anomalies are discussed in connection with the high-degree geopotential modeling. Springer-Verlag Berlin Heidelberg, 2000 Key words: Spherical harmonics - Normal matrix - Geopotential modeling nationallicence Kim M. C. Center for Space Research, The University of Texas at Austin, 3925 West Braker Lane, Suite 200, Austin, TX 78759-5321, USA e-mail: mkim@csr.utexas.edu; Tel.: +1 512 471 8121; Fax: +1 512 471 3570, US aut Tapley B. D. Center for Space Research, The University of Texas at Austin, 3925 West Braker Lane, Suite 200, Austin, TX 78759-5321, USA e-mail: mkim@csr.utexas.edu; Tel.: +1 512 471 8121; Fax: +1 512 471 3570, US aut https://doi.org/10.1007/s001900050292 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s001900050292 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kim M. C. Center for Space Research, The University of Texas at Austin, 3925 West Braker Lane, Suite 200, Austin, TX 78759-5321, USA e-mail: mkim@csr.utexas.edu; Tel.: +1 512 471 8121; Fax: +1 512 471 3570, US aut NATIONALLICENCE 700 1- Tapley B. D. Center for Space Research, The University of Texas at Austin, 3925 West Braker Lane, Suite 200, Austin, TX 78759-5321, USA e-mail: mkim@csr.utexas.edu; Tel.: +1 512 471 8121; Fax: +1 512 471 3570, US aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer