Formation of surface spherical harmonic normal matrices and application to high-degree geopotential modeling

Journal of Geodesy

Volumn 74, Issue 3-4, 2000, Pages 359-375

  Kim, M C ^a   Tapley, B D ^a  

^a The University of Texas at Austin   (United States)

Author keywords

Geopotential modeling; Normal matrix; Spherical harmonics

Indexed keywords

GEOPOTENTIAL; SPHERICAL HARMONICS;

EID: 0034027950     PISSN: 09497714     EISSN: None     Source Type: Journal    
DOI: 10.1007/s001900050292     Document Type: Article

References (47)

1. Arfken G (1985) Mathematical methods for physicists, 3rd edn. Academic Press, New York
2. Balmino G (1993) The spectra of the topography of the Earth, Venus, and Mars. Geophys Res Lett 20: 1063-1066
3. Bettadpur SV (1995) Hotine's geopotential formulation: revisited. Bull Geod 69: 135-142
4. Bosch W (1987) High degree spherical harmonic analysis by least squares. In: Proc XIX General Assembly, IUGG, Vancouver
5. Colombo OL (1981) Numerical methods for harmonic analysis on the sphere. Rep 310, Department of Geodetic Science, The Ohio State University, Columbus
6. Colombo OL (1984) The global mapping of gravity with two satellites. Publications on Geodesy, New Series 7(3), Netherlands Geodetic Commission, Delft
7. Dahlen FA (1976) The passive influence of the oceans upon the rotation of the earth. Geophys J R Astr Soc 46: 363-406
8. Dickman SR (1988) The self-consistent dynamic pole tide in non-global oceans. Geophys J 94: 519-543
9. Dickman SR (1989) A complete spherical harmonic approach to luni-solar tides. Geophys J Int 99: 457-468
10. Edmonds AR (1960) Angular momentum in quantum mechanics, 2nd edn. Princeton University Press, Princeton
11. Gaunt JA (1929) On the triplets of helium. Philos Trans R Soc Lond A228: 151-196
12. Gleason DM (1988) Comparing ellipsoidal corrections to the transformation between the geopotential's spherical and ellipsoidal spectrums. Manuscr Geod 13: 114-129
13. Golub GH, van Loan CF (1989) Matrix computations, 2nd edn. The Johns Hopkins University Press, Baltimore
14. Grafarend EW, Engels J (1992a) A global representation of ellipsoidal heights - geoidal undulations or topographic heights - in terms of orthonormal functions, part 1: "amplitude-modified" spherical harmonic functions. Manuscr Geod 17: 52-58
15. Grafarend EW, Engels J (1992b) A global representation of ellipsoidal heights - geoidal undulations or topographic heights - in terms of orthonormal functions, part 2: "phase-modified" spherical harmonic functions. Manuscr Geod 17: 59-64
16. Grafarend EW, Syffus R (1997) Mixed cylindric map projections of the ellipsoid of revolution. J Geod 71: 685-694
17. Grafarend EW, Engels J, Varga P (1997) The spacetime gravitational field of a deformable body. J Geod 72: 11-30
18. Greiner W, Müller B (1994) Quantum mechanics (symmetries), 2nd edn. Springer, Berlin Heidelberg New York
19. Gruber T, Anzenhofer M, Rentsch M, Schwintzer P (1997) Improvements in high resolution gravity field modeling in GFZ. In: Segawa J, Fujimoto H, Okubo S, Schwarz KP (eds) Gravity, geoid and marine geodesy. IAG Symp, vol 117. Springer, Berlin Heidelberg New York, pp 445-452
20. Hagiwara Y (1975) Applications of Gaunt's integral to some problems in physical geodesy. J Phys Earth 23: 311-321
21. Heiskanen WA, Moritz H (1967) Physical geodesy. WH Freeman, San Francisco
22. Hotine M (1969) Mathematical geodesy. US Department of Commerce, Environmental Science Administration, Washington, DC
23. Hwang C (1993) Fast algorithm for the formation of normal equations in a least-squares spherical harmonic analysis by FFT. Manuscr Geod 18: 46-52
24. Hwang C (1995) A method for computing the coefficients in the product-sum formula of associated Legendre functions. J Geod 70: 110-116
25. Infeld L, Hull TE (1951) The factorization method. Rev Modern Phys 23: 21-68
26. Jekeli C (1981) The downward continuation to the Earth's surface of truncated spherical and ellipsoidal harmonic series of the gravity and height anomalies. Rep 323, Department of Geodetic Science and Surveying, The Ohio State University, Columbus
27. Jekeli C (1988) The exact transformation between ellipsoidal and spherical harmonic expansions. Manuscr Geod 13: 106-113
28. Lai ST, Chiu YN (1990) Exact computation of the 3-j and 6-j symbols. Comput Phys Commun 61: 350-360
29. Lemoine FG, Kenyon SC, Factor JK, Trimmer RG, Pavlis NK, Chinn DS, Cox CM, Klosko SM, Luthcke SB, Torrence MH, Wang YM, Williamson RG, Pavlis EC, Rapp RH, Olson TR (1998) The development of the joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) geopotential model EGM96, NASA/TP 1988-206861. Goddard Space Flight Center, Greenbelt, MD
30. Levinson N (1947) The Wiener RMS (root mean square) error criterion in filter design and prediction. J Math Phys 25: 261-278
31. Masters G, Richards-Dinger K (1998) On the efficient calculation of ordinary and generalized spherical harmonics. Geophys J Int 135: 307-309
32. Metris G, Xu J, Wytrzyszczak I (1999) Derivatives of the gravity potential with respect to rectangular coordinates. Celest Mech Dynam Astr 71: 137-151
33. Pavlis NK (1988) Modeling and estimation of a low degree geopotential model from terrestrial gravity data. Rep 386, Department of Geodetic Science and Surveying, The Ohio State University, Columbus
34. Pavlis NK, Chan JC, Eerch FJ (1996) Alternative estimation techniques for global high-degree gravity modeling. In: Rapp RH, Cazenave AA, Nerem RS (eds) Global gravity field and its temporal variations, IAG Symp, vol 166. Springer, Berlin Heidelberg New York, pp 111-120
35. Pines S (1973) Uniform representation of the gravitational potential and its derivatives. Am Inst Aeronaut Astronaut J 11: 1508-1511
36. Rapp RH (1989) Combination of satellite, altimetric and terrestrial gravity data. In: Sanso F, Rummel R (eds) Theory of satellite geodesy and gravity field determination, Lecture notes in Earth sciences 25. Springer, Berlin Heidelberg New York, pp 261-284
37. Rapp RH (1994) Global geoid determination. In: Vanicek P, Christou NT (eds) Geoid and geophysical interpretations. CRC Press, Boca Raton, pp 57-76
38. Rapp RH (1999) Artifacts introduced in the point evaluation of functions expanded into a degree 360 spherical harmonic series. NASA/CR 1999-209229, Goddard Space Flight Center, Greenbelt, MD
39. Rapp RH, Wang YM, Pavlis NK (1991) The Ohio State 1991 geopotential and sea surface topography harmonic coefficient models. Rep 410, Department of Geodetic Science and Surveying, The Ohio State University, Columbus
40. Reigber C (1989) Gravity field recovery from satellite tracking data. In: Sanso F, Rummel R (eds) Theory of satellite geodesy and gravity field determination, Lecture notes in Earth sciences 25. Springer, Berlin Heidelberg New York, pp 197-234
41. Rose ME (1957) Elementary theory of angular momentum. John Wiley, New York
42. Rummel R, Sanso F, Gelderen MV, Brovelli M, Koop R, Miggliaccio F, Schrama E, Sacerdote F (1993) Spherical harmonic analysis of satellite gradiometry. Publications on Geodesy, New Series 39, Netherlands Geodetic Commission, Delft
43. Schwintzer P, Reigber Ch, Bode A, Kang Z, Zhu SY, Massmann FH, Raimondo JC, Biancale R, Balmino G, Lemoine JM, Moynot B, Marty JC, Barlier F, Boudon Y (1997) Long-wavelength global gravity field models: GRIM4-S4, GRIM4-C4. J Geod 71: 189-208
44. Sneeuw N, Bun R (1996) Global spherical harmonic computation by two-dimensional Fourier methods. J Geod 70: 224-232
45. Tapley BD (1989) Fundamentals of orbit determination. In: Sanso F, Rummel R (eds) Theory of satellite geodesy and gravity field determination, Lecture notes in Earth sciences 25. Springer, Berlin Heidelberg New York, pp 235-260
46. Tapley BD, Shum CK, Ries JC, Poole SR, Abusali PAM, Bettadpur SV, Eanes RJ, Kim MC, Rim HJ, Schutz BE (1997) The TEG 3 geopotential model. In: Sagawa J, Fujimoto H, Okubo S, Schwarz KP (eds) Gravity, geoid and marine geodesy, IAG Symp, vol 117. Springer, Berlin Heidelberg New York, pp 453-460
47. Yu JH, Cao HS (1996) Ellipsoidal harmonic series and the original Stokes problem with the boundary of the reference ellipsoid. J Geod 70: 431-439