Potential Theory and Static Gravity Field of the Earth

Treatise on Geophysics

Volumn 3, Issue , 2007, Pages 11-42

  Jekeli, C ^a  

^a OHIO STATE UNIVERSITY   (United States)

Author keywords

Boundary value problem; Disturbing potential; Geoid; Gravitation; Gravity; Gravity anomaly; Green's function; Normal gravity field; Potential theory; Spherical harmonics

Indexed keywords

EID: 84876337214     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1016/B978-044452748-6.00054-7     Document Type: Chapter

References (55)

1. Bursa M., Radej K., Sima Z., True S., Vatrt V. Determination of the geopotential scale factor from TOPEX/Poseidon satellite altimetry. Studia Geophysica et Geodaetica 1997, 41:203-216.
2. Mathematical theory of the Goddard Trajectory Determination System 1976, Goddard Space Flight Center, Greenbelt, MD, GSFC Document X-582-76-77. J.O. Cappelari, C.E. Velez, A.J. Fuchs (Eds.).
3. Chao B.F. On inversion for mass distribution form global (time-variable) gravity field. Journal of Geodynamics 2005, 29:223-230.
4. Courant R., Hilbert D. Methods of Mathematical Physics 1962, vol. II. Wiley, New York.
5. Cushing J.T. Applied Analytical Mathematics for Physical Scientists 1975, Wiley, New York.
6. Dziewonsky A.D., Anderson D.L. Preliminary reference Earth model. Physics of the Earth and Planetary Interiors 1981, 25:297.
7. Fei Z.L., Sideris M.G. A new method for computing the ellipsoidal correction for Stokes's formula. Journal of Geodesy 2000, 74(2):223-231.
8. Goodkind J.M. The superconducting gravimeter. Review of Scientific Instruments 1999, 70:4131-4152.
9. Groten E. Fundamental parameters and current (2004) best estimates of the parameters of common relevance to astronomy, geodesy, and geodynamics. Journal of Geodesy 2004, 77:10-11. (The Geodesist's Handbook pp. 724-731).
10. Gumert W.R. An historical review of airborne gravimetry. The Leading Edge 1998, 17(1):113-116.
11. Günter N.M. Potential Theory and Its Applications to Basic Problems of Mathematical Physics 1967, Frederick Ungar, New York.
12. Hammer S. Airborne gravity is here!. Oil and Gas Journal 1982, 80:2. (January 11, 1982).
13. Heiskanen W.A., Moritz H. Physical Geodesy 1967, Freeman, San Francisco, CA.
14. Helmert F.R. Die Mathematischen und Physikalischen Theorien der Höheren Geodäsie 1884, vol. 2. B.G. Teubner, Leipzig, Germany, (reprinted in 1962 by Minerva GMBH, Frankfurt/Main, Germany).
15. Hobson E.W. The Theory of Spherical and Ellipsoidal Harmonics 1965, Chelsea, New York.
16. Hofmann-Wellenhof B., Moritz H. Physical Geodesy 2005, Springer-Verlag, Berlin, Germany.
17. Hotine M. Mathematical Geodesy 1969, US Department of Commerce, Washington, DC.
18. Jekeli C. The exact transformation between ellipsoidal and spherical harmonic expansions. Manuscripta Geodaetica 1988, 14:106-113.
19. Jekeli C. Spherical harmonic analysis, aliasing, and filtering. Journal of Geodesy 1996, 70:214-223.
20. Jekeli C. The determination of gravitational potential differences from satellite-to-satellite tracking. Celestial Mechanics and Dynamical Astronomy 1999, 75(2):85-100.
21. Jekeli C. Inertial Navigation Systems with Geodetic Applications 2000, Walter deGruyter, Berlin, Germany.
22. Jekeli C. (2000b) Heights, the geopotential, and vertical Datums. Report no.459, Department of Civil and Environmental Engineering and Geodetic Science, Ohio State University. Columbus, OH: Ohio State University.
23. Jekeli C. High-resolution gravity mapping: The next generation of sensors. Geophysical Monograph 150, IUGG, vol. 19: The State of the Planet: Frontiers and Challenges in Geophysics 2004, 135-146. American Geophysical Union, Washington, DC. R.S.J. Sparks (Ed.).
24. Kaula W.M. Theory of Satellite Geodesy 1966, Blaisdell, London.
25. Kellogg O.D. Foundations of Potential Theory 1953, Dover, New York.
26. Kenyon S., Forsberg R. Arctic gravity project. SEG Technical Program Expanded Abstracts 2000, 19:410-413.
27. Kwon J.H., Jekeli C. A new approach for airborne vector gravimetry using GPS/INS. Journal of Geodesy 2001, 74:690-700.
28. Lambeck K. Geophysical Geodesy 1988, Clarendon Press, Oxford.
29. Lemoine F.G., Kenyon S.C., Factor J.K., et al. The development of the joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) geopotential model EGM96 1998, Goddard Space Flight Center, Greenbelt, MD, NASA Technical Paper NASA/TP-1998-206861.
30. Martin J.L. General Relativity: A Guide to Its Consequences for Gravity and Cosmology 1988, Wiley, New York.
31. Molodensky M.S., Eremeev V.G., Yurkina M.I. Methods for Study of the External Gravitational Field and Figure of the Earth 1962, Israel Program for Scientific Translations (Translation from Russian), Jerusalem, Israel.
32. Moritz H. Advanced Physical Geodesy 1980, Wichmann, Karlsruhe, Germany, (reprinted in 2001 by Civil and Environmental Engineering and Geodetic Science, Ohio State University, Columbus, OH).
33. Morse P.M., Feshbach H. Methods of Theoretical Physics, Parts I and II 1953, McGraw-Hill, New York.
34. Müller C. Spherical Harmonics. Lecture Notes in Mathematics 1966, Springer-Verlag, Berlin, Germany.
35. Nettleton L.L. Gravity and Magnetics in Oil Prospecting 1976, McGraw-Hill, New York.
36. Niebauer T., Sasagawa G., Faller J., Hilt R., Klopping F. A new generation of absolute gravimeters. Metrologia 1995, 32(3):159-180.
37. Pavlis D.E., Moore D., Luo S., McCarthy J.J., Luthcke S.B. GEODYN Operations Manual 1999, 5 vols. Raytheon ITSS, Greenbelt, MD.
38. Petrovskaya M.S. Upward and downward continuations in the geopotential determination. Bulletin Géodésique 1979, 53:259-271.
39. Rapp R.H. Analytical and numerical differences between two methods for the combination of gravimeter and satellite data. Bollettino di Geofisica Teorica ed Applicata 1969, XI(41-42):108-118.
40. Rapp R.H., Pavlis N.K. The development and analysis of geopotential coefficient models to spherical harmonic degree 360. Journal of Geophysical Research 1990, 95(B13):21885-21911.
41. Reigber Ch., Balmino G., Schwintzer P., et al. A high quality global gravity field model from CHAMP GPS tracking data and accelerometry (EIGEN-1S). Geophysical Research Letters 2002, 29(14):37-41. 10.1029/2002GL015064.
42. Rummel R., Balmino G., Johannessen J., Visser P., Woodworth P. Dedicated gravity field missions - Principles and aims. Journal of Geodynamics 2002, 33:3-20.
43. Sandwell D.T., Smith W.H.F. Marine gravity anomaly form GEOSAT and ERS-1 satellite altimetry. Journal of Geophysical Research 1996, 102(B5):10039-10054.
44. Lecture Notes in Earth Sciences 65: Geodetic Boundary Value Problems in View of the One Centimeter Geoid 1997, Springer-Verlag, Berlin, Germany. F. Sansò, R. Rummel (Eds.).
45. Seeber G. Satellite Geodesy, Foundations, Methods, and Applications 1993, Walter deGruyter, Berlin, Germany.
46. Sjöberg L.E. Refined least squares modifications of Stokes' formula. Manuscripta Geodaetica 1991, 16:367-375.
47. Tapley B.D. Statistical orbit determination theory. Recent Advances in Dynamical Astronomy 1973, 396-425. D. Reidel, Dordtecht, The Netherlands. B.D. Tapley, V. Szebehely (Eds.).
48. Tapley B.D., Bettadpur S., Ries J.C., Thompson P.F., Watkins M. GRACE measurements of mass variability in the Earth system. Science 2004, 305(5683):503-505.
49. Tapley B.D., Bettadpur S., Watkins M., Reigber Ch. The gravity recovery and climate experiment, mission overview and early results. Geophysical Research Letters 2004, 31(9):1501. 10.1029/2004GL019920.
50. Tapley B.D., Ries J., Bettadpur S., et al. GGM02 - An improved Earth gravity field model from GRACE. Journal of Geodesy 2005, 79:137-139. 10.1007/s00190-005-0480-z.
51. Torge W. Gravimetry 1989, Walter deGruyter, Berlin, Germany.
52. Torge W. Geodesy 2001, Walter de Gruyter, Berlin, Germany. 3rd edn.
53. Wolff M. Direct measurement of the Earth's gravitational potential using a satellite pair. Journal of Geophysical Research 1969, 74:5295-5300.
54. Yu J., Jekeli C., Zhu M. The analytical solutions of the Dirichlet and Neumann boundary value problems with ellipsoidal boundary. Journal of Geodesy 2002, 76(11-12):653-667.
55. Zumberge M.A., Rinker R.L., Faller J.E. A portable apparatus for absolute measurements of the Earth's gravity. Metrologia 1982, 18(3):145-152.