The solution of linear inverse problems in satellite geodesy by means of spherical spline approximation

Journal of Geodesy

Volumn 71, Issue 1, 1996, Pages 2-15

  Schneider, F ^a  

^a Rheinland Pfälzische Technische Universität Kaiserslautern Landau   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

GEODESY; INVERSE METHOD; SPHERICAL SPLINE INTERPOLATION;

EID: 0030429713     PISSN: 09497714     EISSN: None     Source Type: Journal    
DOI: 10.1007/s001900050070     Document Type: Article

References (31)

1. Aronszajn N (1950) Theory of reproducing kernels. Trans. Am. Math. Soc. 68, 337-404
2. Beylkin G, Coifman R, Rokhlin V (1991) Fast wavelet transforms and numerical algorithms I. Comp. Pure and Appl. Math. 44, 141-183
3. Cui J, Freeden W (1995) Equidistribution on the sphere. AGTM-Report 142, University of Kaiserslautern, Geomathematics Group
4. Éskin GI (1981) Boundary value problems for elliptic pseudodifferential equations. Transl. of Math. Monogr. 52, American Math. Soc., Providence, Rhode Island
5. Freeden W (1979) Über eine Klasse von Integralformeln der Mathematischen Geodäsie. Veröff. Geod. Inst. RWTH Aachen, Heft 27
6. Freeden W (1981) On approximation by harmonic splines. Manuscr. Geod. 6, 193-244
7. Freeden W (1987) A spline interpolation method for solving boundary value problems of potential theory from discretely given data. Numer. Meth. of Partial Diff. Eq. 3, 375-398
8. Freeden W (1990) Spherical spline approximation and its application in physical geodesy. In: Geophysical data inversion methods and applications (A. Vogel, C.O. Ofeagbu, R. Gorenflo, B. Ursin eds), Vieweg Publication, 79-104
9. Freeden W, Witte B (1982) A combined (spline-) interpolation and smoothing method for the determination of the external gravitational potential from heterogeneous data. Bull. Geod. 56, 53-62
10. Grafarend EW (1972) Inverse potential problems of improperly posed type in physical geodesy and geophysics. Presented at the international symposium on earth gravity models and related problems, St. Louis 1972
11. Hackbusch W, Nowak ZP (1989) On the fast matrix multiplication in the boundary element method by panel clustering. Numer. Math. 54, 463-491
12. Jackson DD (1979) The use of a priori data to resolve nonuniqueness in linear inversion. Geophys. J. R. astr. Soc. 57, 137-157
13. Kaula WM (1966) Theory of satellite geodesy. Blasidell Publishing Company, London
14. Keller W, Hirsch M (1994) A boundary value approach to downward continuation. Manuscr. Geod. 19, 101-118
15. Kellogg OD (1967) Foundations of potential theory. Springer-Verlag Berlin Heidelberg New York
16. Louis AK (1989) Inverse und schlecht gestellte Probleme. B.G. Teubner Stuttgart
17. Meschkowski H (1962) Hilbertsche Räume mit Kernfunktionen. Springer-Verlag Berlin Göttingen Heidelberg
18. Moritz H (1989) Advanced physical geodesy. 2nd edition, Wichmann-Verlag, Karlsruhe
19. Müller C (1966) Spherical harmonics. Lecture Notes in Mathematics, 17, Springer-Verlag, Berlin, Heidelberg, New York
20. Nashed MZ and Wahba G (1974) Generalized inverses in reproducing kernel spaces: an approach to regularization of linear operator equations. SIAM J. Math. Anal., Vol 5, No. 6, 974-987
21. Rapp RH, Wang M, Pavlis N (1991) The Ohio State 1991 geopotential and sea surface topography harmonic coefficient model. Report no. 410, Department of Geodetic Science, Ohio State University, Columbus
22. Rummel R (1979) Determination of short-wavelength components of the gravity field from statellite-to-satellite tracking or satellite gradiometry - an attempt to an identification of problem areas. Manuscr. Geod. 4, 107-148
23. Rummel R (1986) Satellite gradiometry. In: Sünkel, H. ed., Lecture Notes in Earth Sciences 7, Mathematical and Numerical Techniques in Physcial Geodesy, Springer, Berlin, 318-363
24. Schaffrin B, Heidenreich E. Grafarend E (1977) A representation of the standard gravity field. Manuscr. Geod. 2, 135-174
25. Schreiner M (1994) Tensor spherical harmonics and their application in satellite gradiometry. Doctoral-Thesis. University of Kaiserslautern, Geomathematics Group
26. Svensson L (1984) Finite elements on the sphere. Journal of Approx. Theory 40, Academic Press, 246-260
27. Thalhammer M (1995) Regionale Gravitationsfeldbestimmung mit zukünftigen Satellitenmissionen (SST und Gradiometry). Deutsche Geodätische Kommission bei der Bayerischen Akademie der Wissenschaften, Reihe C, Dissertationen, Heft Nr. 437
28. Wahba G (1973) Convergence rates of certain approximate solutions to Fredholm integral equations of the first kind. J. of Approx. Theory 7, 167-185
29. Wahba G (1990) Spline models for observational data. CBMSNSF Regional Conference Series in Applied Mathematics 59
30. Xu PL (1992) Determination of surface gravity anomalies using gradiometric observables. Geophys. J. Int. 110, 321-332
31. Xu PL, Rummel R (1994) A simulation study of smoothness methods in recovery of regional gravity fields. Geophys. J. Int. 117, 472-486