Comparison of two approaches for considering laterally varying density in topographic effect on satellite gravity gradiometric data

• Autorzy: Eshagh M.
• Języki publikacji: EN

Abstrakty

EN

The satellite gravity gradiometric data are influenced by laterally varying density in topographic masses, while in most of studies a constant density for the masses was considered. This assumption causes an error in estimating the topographic effect. This paper theoretically and numerically investigates the methods of Sjöberg as well as Novák and Grafarend to consider the laterally varying density for topographic masses in formulation of topographic potential in spherical harmonics.

Słowa kluczowe

EN

satellite gravity gradiometry; topographic effect on SGG; lateral density variation on SGG

• Wydawca: Instytut Geofizyki PAN ; Springer
• Czasopismo: Acta Geophysica
• Rocznik: 2010
• Tom: Vol. 58, no. 4
• Strony: 661--686
• Opis fizyczny: Bibliogr. 52 poz.

Twórcy

autor

Eshagh M.

• Division of Geodesy, Royal Institute of Technology, Stockholm, Sweden,

Bibliografia

• Ågren, J. (2004), Regional geoid determination methods for the era of satellite gravimetry, Numerical investigations using synthetic Earth gravity models, Ph.D. Thesis in Geodesy, Royal Institute of Technology, Stockholm, Sweden.
• Bassin, C., G. Laske, and T.G. Masters (2000), The current limits of resolution for surface wave tomography in North America, EOS Trans AGU 81, F897.
• Eshagh, M. (2008), Non-singular expressions for the vector and the gradient tensor of a geocentric spherical frame, Comp. Geosci. 34, 12, 1762-1768.
• Eshagh, M. (2009a), On satellite gravity gradiometry, Ph.D. Thesis in Geodesy, Royal Institute of Technology, Stockholm, Sweden.
• Eshagh, M. (2009b), The effect of lateral density variations of crustal and topographic masses on GOCE gradiometric data: A study in Iran and Fennoscandia, Acta Geod. Geophys. Hung. 44, 4.
• Eshagh, M. (2009c), Impact of vectorization on global synthesis and analysis in gradiometry, Acta Geod. Geophys. Hung. 44, 3, 323-342.
• Eshagh, M. (2009d), Contribution of 1st-3rd order terms of a binomial expansion of topographic heights in topographic and atmospheric effects on satellite gravity gradiometric data, Artificial Satellites 44, 1, 21-31.
• Eshagh, M. (2009e), Alternative expressions for gravity gradients in local northoriented frame and tensor spherical harmonics, Acta Geophys. 58, 2.
• Eshagh, M., and L.E. Sjöberg (2008), Impact of topographic and atmospheric masses over Iran on validation and inversion of GOCE gradiometric data, J. Earth Space Phys. 34, 15-30.
• Eshagh, M., and L.E. Sjöberg (2009), Topographic and atmospheric effects on GOCE gradiometric data in a local north-oriented frame: A case study in Fennoscandia and Iran, Studia Geophys. Geod. 53, 1, 61-80.
• Heck, B. (2003), On Helmert’s methods of condensation, J. Geod. 77, 3-4, 155-170.
• Heiskanen, W., and H. Moritz (1967), Physical Geodesy, W.H. Freeman and Co., San Fransisco–London.
• Huang, J., P. Vaníček, S.D. Pagiatakis, and W. Brink (2001), Effect of topographical density on geoid in the Canadian Rocky Mountains, J. Geod. 74, 11-12, 805-815.
• Hunegnaw, A. (2001), The effect of lateral density variation on local geoid determination, Proc. IAG 2001 Scientific Assembly, Budapest, Hungary.
• Ilk, K.H. (1983), Ein Beitrag zür Dynamik ausgedehnter Körper-Gravitationswechselwirkung, Deutsche Geodätische Kommission, Reihe C, Heft 288, München.
• Kiamehr, R. (2006), The impact of lateral density variation model in the determination of precise gravimetric geoid in mountainous areas: a case study of Iran, Geophys. J. Int. 167, 521-527.
• Kühtreiber, N. (1998), Precise geoid determination using a density variation model, Phys. Chem. Earth 23, 1, 59-63.
• Lambeck, K. (1976), Lateral density anomalies in the upper mantle, J. Geophys. Res. 81, 35, 6333-6340.
• Li, X. (2001), Vertical resolution: Gravity versus vertical gravity gradient, The Leading Edge 20, 901-904.
• Li, Y. (2001a), Processing gravity gradiometer data using an equivalent source technique, Publications in Center For Gravity, Electrical and Magnetic Studies, Department of Geophysics, Colorado School of Mines.
• Li, Y. (2001b), 3-D inversion of gravity gradiometer data, Publications in Center for Gravity, Electrical and Magnetic Studies, Department of Geophysics, Colorado School of Mines.
• Loera, J.A., and T.B. McAllister (2006), On computation of Clebsch-Gordan coefficients and the dilation effect, Exp. Math. 15, 7-19.
• Makhloof, A. (2007), The use of topographic-isostatic mass information in geodetic applications, Ph.D. Thesis, Department of Theoretical and Physical Geodesy, Bonn, Germany.
• Makhloof, A., and K.H. Ilk (2005), Far-zone topography effects on gravity and geoid heights according to Helmert’s methods of condensation and based on Airy-Heiskanen model, Proc. 3rd Inter. Conf. Advanced Trends in Engineering, El-Minia, April 3-5, 2005.
• Makhloof, A., and K.H. Ilk (2006), Band-limited topography effects in airborne grawimetry using space localizing base functions, EGU Conf., 3 April, 2006.
• Martinec, Z. (1993), Effect of lateral density variations of topographical masses in view of improving geoid model accuracy over Canada, Contract Report for Geodetic Survey of Canada, Ottawa, Canada.
• Martinec, Z., and P. Vaníček (1994), Direct topographical effect of Helmert’s condensation for a spherical geoid, Manus. Geod. 19, 257-268.
• Martinec, Z., C. Matyska, E.W. Grafarend, and P. Vaníček (1993), On Helmert’s 2nd condensation method, Manus. Geod. 18, 417-421.
• Martinec, Z., P. Vaníček, A. Mainville, and M. Veronneau (1995), The effect of Lake water on geoidal height, Manus. Geod. 20, 193-203.
• Mickus, K.L., and J.H. Hinojosa (2001), The complete gravity gradient tensor derived from the vertical component of gravity: a Fourier transform technique, J. Appl. Geophys. 46, 3, 159-174.
• Mooney, W.D., G. Laske, and T.G. Masters (1998), CRUST 5.1: A global crustal model at 5°×5°, J. Geophys. Res. 103, 727-747.
• Novák, P., and E.W. Grafarend (2006), The effect of topographical and atmospheric masses on spaceborne gravimetric and gradiometric data, Studia Geophys. Geod. 50, 4, 549-582.
• Pagiatakis, S.D., and C. Armenakis (1999), Gravimetric geoid modeling with GIS, Int. Geoid Ser. Bull. 8, 105-112.
• Pail, R., G. Plank, and W.-D. Schuh (2001), Spatially restricted data distributions on the sphere: the method of orthonormalized functions and applications, J. Geod. 75, 1, 44-56.
• Pawlowski, B. (1998), Gravity gradiometry in resource exploration, The Leading Edge, 17, 1, 51-52.
• Pawlowski, R., and C. Prieto (1997), Gravity gradiometry in natural resource exploration, IGC Footnote Ser. 4, 1.
• Petrovskaya, M.S., and A.N. Vershkov (2006), Non-singular expressions for the gravity gradients in the local north-oriented and orbital reference frames, J. Geod. 80, 3, 117-127.
• Sébilleau, D. (1998), On the computation of the integrated products of three spherical harmonics, J. Phys. A: Math. Gen. 31, 7157-7168.
• Seitz, K., and B. Heck (2003), Efficient calculation of topographic reductions by the use of tesseroids, Presentation at the joint assembly of the EGS, AGU and EGU, Nice, France, 6-11 April, 2003.
• Simons, F.J., F.A. Dahlen, and M.A. Wieczorek (2006), Spatiospectral concentration on a sphere, SIAM Rev. 48, 3, 504-536.
• Sjöberg, L.E. (2000), Topographic effects by the Stokes-Helmert method of geoid and quasi-geoid determinations, J. Geod. 74, 2, 255-268.
• Sjöberg, L.E. (2004a), The ellipsoidal corrections to the topographic geoid effects, J. Geod. 77, 12, 804-808.
• Sjöberg, L.E. (2004b), The effect on the geoid of lateral topographic density variations, J. Geod. 78, 1-2, 34-39.
• Sjöberg, L.E. (2007), The topographic bias by analytical continuation in physical geodesy, J. Geod. 81, 5, 345-350.
• Sjöberg, L.E., and H. Nahavandchi (1999), On the indirect effect in the Stokes-Helmert method of geoid determination, J. Geod. 73, 87-93.
• Sun, W., and L.E. Sjöberg (2001), Convergence and optimal truncation of binomial expansions used in isostatic compensations and terrain corrections, J. Geod. 74, 9, 627-636.
• Tsoulis, D. (2001), Terrain correction computations for a densely sampled DTM in the Bavarian Alps, J. Geod. 75, 5-6, 291-307.
• Tziavos, I.N., and W.E. Featherstone (2000), First results of using digital den sity data in gravimetric geoids computation in Australia, IAG Symposia, GGG2000, 123, 335-340, Springer Verlag, Berlin, Heidelberg.
• Varshalovich, D.A., A.N. Moskalev, and V.K. Khersonskii (1989), Quantum Theory of Angular Momentum, World Scientific Publ., Singapore.
• Wild, F., and B. Heck (2004a), A comparison of different isostatic models applied to satellite gravity gradiometry, Gravity, Geoid and Space Missions GGSM 2004, IAG International Symposium Porto, Portugal, August 30 – September 3, 2004.
• Wild, F., and B. Heck (2004b), Effects of topographic and isostatic masses in satellite gravity gradiometry, Proc. Second Inter. GOCE User Workshop. The Geoid and Oceanography, ESA-ESRIN, Frascati/Italy, March 8-10, 2004 (ESA SP – 569, June 2004), CD-ROM.
• Xu, Y.L. (1996), Fast evaluation of the Gaunt coefficients, Math. Comp. 65, 1601-1612.