Multiscale gravitational field recovery from GPS-satellite-to-satellite tracking

Studia Geophysica et Geodaetica

Volumn 43, Issue 3, 1999, Pages 229-264

  Freeden, Willi ^a   Glockner, Oliver ^a   Thalhammer, Markus ^b  

^a Rheinland Pfälzische Technische Universität Kaiserslautern Landau   (Germany)

^b TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Formulation as integral equation; GPS satellite to satellite tracking; Regularization by wavelets; Uniqueness

Indexed keywords

GPS; GRAVIMETRY; SATELLITE; TRACKING;

EID: 0032739224     PISSN: 00393169     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1023365209883     Document Type: Article

References (40)

1. Arabelos D. and Tscherning C.C., 1995: Regional Recovery of the Gravity Field from SGG and Gravity Vector Data Using Collocation. J. Geophys. Res., 100, No.B11, 22009-22015.
2. Backus G., 1967: Converting Vector and Tensor Equations to Scalar Equations in Spherical Coordinates. Geophys. J.R. Astron. Soc., 13, 61-101.
3. Barriot J.P., 1994: Line of Sight Operators in Planetary Geodesy. Manuscripta Geodaetica, 19, No.5, 269-283.
4. Barriot J.P. and Balmino G., 1992: Estimation of Local Planetary Gravity Fields using Line of Sight Gravity Data and an Integral Operator. Icarus, 99, 202-224.
5. Bayer M., 1996: Spherical Wavelets and Their Application to Linear Inverse Satellite Problems. Diploma Thesis, University of Kaiserslautern, Geomathematics Group
6. Bayer M., Beth S. and Freeden W., 1998: Geophysical Field Modelling by Multiresolution Analysis. Acta Geod. Geoph. Hung., 33, 289-319.
7. Bertero M., de Mol C. and Viano G.A., 1980: The Stability of Inverse Problems. In: Baltes (ed.): Inverse Scattering in Optics, Springer, New York, 161-214.
8. Driscoll J.R. and Healy R.M., 1994: Computing Fourier Transforms and Convolutions on the 2-Sphere. Adv. Appl. Math., 15, 202-250.
9. Freeden W., 1998: The Uncertainty Principle and Its Role in Physical Geodesy. In: W. Freeden (ed.) Progress in Geodetic Science (at GW98), Shaker, 225-236.
10. Freeden W. and Gervens T., 1991: Vector Spherical Spline Interpolation (Basic Theory and Computational Aspects). Math. Meth. Appl. Sci., 15, 151-183.
11. Freeden W., Gervens T. and Schreiner M., 1998: Constructive Approximation on the Sphere (with Applications to Geomathematics). Oxford Science Publication, Clarendon Press, Oxford
12. Freeden W., Glockner O. and Schreiner M., 1998a: Spherical Panel Clustering and Its Numerical Aspects. Journal of Geodesy, 72, 586-599.
13. Freeden W. and Kersten H., 1981: A Constructive Approximation Theorem for the Oblique Derivative Problem in Potential Theory. Math. Meth. Appl. Sci., 3, 104-114.
14. Freeden W. and Schneider F., 1998: An Integrated Wavelet Concept of Physical Geodesy. Journal of Geodesy, 72, 259-281.
15. Freeden W. and Schneider F., 1998a: Wavelet Approximation on Closed Surfaces and Their Application to Boundary-value Problems of Potential Theory. Math. Meth. in the Appl. Sci., 21, 129-165.
16. Freeden W., Schneider F. and Schreiner M., 1997: Gradiometry - An Inverse Problem in Modern Satellite Geodesy. In: H.W. Engl et al. (eds.), GAMM-SIAM Proceedings on Inverse Problems in Geophysical Applications, 179-239.
17. Freeden W. and Windheuser U., 1997: Combined Spherical Harmonic and Wavelet Expansion - A Future Concept in Earth's Gravitational Determination. Applied and Computational Analysis (ACHA), 4, 1-37.
18. Glockner O., 1997: Spherical Panel Clustering and Its Numerical Aspects in Spline and Wavelet Computation. Diploma Thesis, University of Kaiserslautern, Geomathematics Group
19. Ilk K.H., 1993: Regularization for High Resolution Gravity Field Recovery by Future Satellite Techniques. Inverse Problems: Principles and Applications in Geophysics, Technology and Medicine, In: G. Anger et al. (eds.), Math. Research, Vol. 74, Akademie Verlag, 189-214.
20. Ilk K.H., Reigber C. and Rummel R., 1978: The Use of Satellite-to-Satellite Tracking for Gravity Parameter Recovery. Proc. of the European Workshop on Space Oceanography, Navigation and Geodynamics (SONG), ESA SP-137.
21. Ilk K.H., Sigl R. and Thalhammer M., 1990: Regional Gravity Field Recovery from SST (GPS -ARISTOTELES), from Gradiometer Measurements and Their Combination. CIGAR II, WP's 4.30, 4.40, 4.50.
22. Kleusberg A. and Teunissen P.J.G. (eds), 1996: GPS for Geodesy. Lecture Notes in Earth Sciences, Vol. 60, Springer Heidelberg New York.
23. Louis A.K., 1989: Inverse und schlecht gestellte Probleme. B.G. Teubner, Stuttgart.
24. Meissl P.A., 1971: A Study of Covariance Functions Related to the Earth's Disturbing Potential. The Ohio State University, Departement of Geodetic Science and Surveying, Columbus, OSU Report No. 152.
25. Miranda C., 1970: Partial Differential Equations of Elliptic Type. Springer, New York, Heidelberg
26. Moritz H., 1969: On the Determination of the Potential from Gravity Disturbances along a fixed Direction. Tellus, 21, 4, 586-571.
27. Perosanz F., Marty J.C. and Balmino G., 1997: Dynamic orbit determination and gravity field model improvement from GPS, DORIS and LASER measurements on TOPEX/POSEIDON satellite. Journal of Geodesy, 71, 160-170.
28. Reigber C., 1989: Gravity Field Recovery from Satellite Tracking Data. In: F. Sanso and R. Rummel (eds), Theory of Satellite Geodesy and Gravity Field Determination, Lecture Notes in Earth Sciences, 25, Springer.
29. Reigber C., Bock R., Förste C., Grunwaldt L., Jakowski N., Lühr H., Schwintzer P. and Tilgner C., 1996: CHAMP - Phase B, Executive Summary. Scientific Technical Report STR96/13 GFZ, Potsdam.
30. Rummel R., 1975: Downward Continuation of Gravity Information from Satellite-to-Satellite Tracking or Satellite Gradiometry. Report No. 221, Dept. of Geodetic Science, Ohio State University, Columbus.
31. Rummel R., 1979: Determination of the Short-Wavelength Components of the Gravity Field from Satellite-to-Satellite Tracking or Satellite Gradiometry. Manuscr. Geod., 4, 107-148.
32. Rummel R., 1997: Spherical Spectral Properties of the Earth's Gravitational Potential and Its First and Second Derivatives. In: F. Sanso and R. Rummel (eds), Lecture Notes in Earth Sciences, Vol. 65, 359-404.
33. Rummel R., van Gelderen M., Koop R., Schrama E., Sanso F., Brovelli M., Miggliaccio F. and Sacerdote F., 1993: Spherical Harmonic Analysis of Satellite Gradiometry. Netherlands Geodetic Commission, New Series, No. 39
34. Schneider F., 1997: Inverse Problems in Satellite Geodey and Their Approximate Solution by Splines and Wavelets. Doctoral Thesis, University of Kaiserslautern, Geomathematics Group, Shaker.
35. Schwintzer P., Reigber C., Bode A., Kang Z., Zhu S.Y., Massmann F.H., Raimondo J.C., Biancale R., Balmino G., Lemoine J.M., Moynot B., Marty J.C., Barlier F. and Boudon Y., 1997: Long-Wavelength Global Gravity Field Models: GRIM4-S4, GRIM4-C4. Journal of Geodesy, 71, 189-208.
36. Sjogren W.L., Bills B.G., Birkeland W., Esposito P.B., Konopliv A.R., Mottinger N.A., Ritke S.J. and Philips R.J., 1983: Venus Gravity Anomalies and Their Correlation with Topography. J. Geophys. Res., 88, No.B2, 1119-1128.
37. Thalhammer M., 1995: Regionale Gravitationsfeldbestimmung mit zukünftigen Satellitenmissionen (SST und Gradiometrie). Deutsche Geodätische Kommission bei der Bayerischen Akademie der Wissenschaften, Reihe C, Dissertationen. Heft, Nr. 437.
38. Tikhonov A.N. and Arsenin V.Y., 1977: Solutions of Ill-posed Problems. Wiley, New York.
39. Tscherning C.C., Forsberg R. and Vermeer M., 1990: Methods for Regional Gravity Field Modelling from SST and SGG Data. Reports of the Finnish Geodetic Institute 90:2.
40. Wiejack W., Schrama E.J.O. and Rummel R., 1991: Spectral Representation of the Satellite-to-Satellite Tracking Observables. Adv. Space. Res., 11(6), 197-224.