A mathematical model of the bathymetry-generated external gravitational field

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A mathematical model of the bathymetry-generated external gravitational field

The currently available global geopotential models and the global elevation and bathymetry data allow modelling the topography-corrected and bathymetry stripped reference gravity field to a very high spectral resolution (up to degree 2160 of spherical harmonics) using methods for a spherical harmonic analysis and synthesis of the gravity field. When modelling the topography-corrected and crust-density-contrast stripped reference gravity field, additional stripping corrections are applied due to the ice, sediment and other major known density contrasts within the Earth's crust. The currently available data of global crustal density structures have, however, a very low resolution and accuracy. The compilation of the global crust density contrast stripped gravity field is thus limited to a low spectral resolution, typically up to degree 180 of spherical harmonics. In this study we derive the expressions used in forward modelling of the bathymetry-generated gravitational field quantities and the corresponding bathymetric stripping corrections to gravity field quantities by means of the spherical bathymetric (ocean bottom depth) functions. The expressions for the potential and its radial derivative are formulated for the adopted constant (average) ocean saltwater density contrast and for the spherical approximation of the geoid surface. These newly derived expressions are utilized in numerical examples to compute the gravitational potential and attraction generated by the ocean density contrast. The computation is realized globally on a 1 x 1 arc-deg geographical grid at the Earth's surface.

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  • Eshagh M. Sjöberg L. E. 2008: Impact of topographic and atmospheric masses over Iran on validation and inversion of GOCE gradiometric data. J. Earth Space Phys. 34 3 15-30.

  • Eshagh M. Sjöberg L. E. 2009: Atmospheric effect on satellite gravity gradiometry data. J. Geodynamics 47 9-19.

  • Garrison T. 2001: Essentials of Oceanography. Pacific Grove CA: Brooks Cole.

  • Heck B. 2003: On Helmert's Methods of Condensation. J. Geod. 7 155-170 doi: 10.1007/s00190-003-0318-5.

  • Heiskanen W. H. Moritz H. 1967: Physical Geodesy. WH Freeman and Co. San Francisco.

  • Hobson E. W. 1931: The theory of spherical and ellipsoidal harmonics. Cambridge University Press Cambridge.

  • Kaban M. K. Schwintzer P. Tikhotsky S. A. 1999: Global isostatic gravity model of the Earth. Geophys. J. Int. 136 519-536.

  • Kaban M. K. Schwintzer P. 2001: Oceanic upper mantle structure from experimental scaling of Vs. and density at different depths. Geophys. J. Int. 147 199-214.

  • Kaban M. K. Schwintzer P. Artemieva I. M. Mooney W. D. 2003: Density of the continental roots: compositional and thermal contributions. Earth Planet. Sci. Lett. 209 53-69.

  • Kaban M. K. Schwintzer P. Reigber Ch. 2004: A new isostatic model of the lithosphere and gravity field. J. Geod. 78 368-385 doi: 10.1007/s00190-004-0401-6.

  • Makhloof A. A. 2007: The use of topographic-isostatic mass information in geodetic application Dissertation D98 Institute of Geodesy and Geoinformation Bonn.

  • Moritz H. 1980: Advanced Physical Geodesy. Abacus Press Tunbridge Wells.

  • Millero F. J. Poisson A. 1981: Density of seawater and the new International Equation of State of Seawater. 1980. IMS Newsletter 30 Wright (ed.) Special Issue 1981-1982 UNESCO Paris France 3 p.

  • Nahavandchi H. 2004: A new strategy for the atmospheric gravity effect in gravimetric geoid determination. J. Geod. 77 823-828 doi: 10.1007/s00190-003-0358-x.

  • Novák P. 2000: Evaluation of gravity data for the Stokes-Helmert solution to the geodetic boundary-value problem. Technical Report 207 University New Brunswick Fredericton.

  • Novák P. Vaníček P. Martinec Z. Veronneau M. 2001: Effects of the spherical terrain on gravity and the geoid. J. Geod. 75 9-10 491-504 doi: 10.1007/s001900100201.

  • Novák P. Grafarend E. W. 2005: The ellipsoidal representation of the topographical potential and its vertical gradient. J. Geod. 78 11-12 691-706 doi: 10.1007/s00190-005-0435-4.

  • Novák P. Grafarend E. W. 2006: The effect of topographical and atmospheric masses on spaceborne gravimetric and gradiometric data. Stud. Geoph. Geod. 50 4 549-582 doi: 10.1007/s11200-006-0035-7 doi: 10.1007/s11200-006-0035-7.

  • Novák P. 2009: High resolution constituents of the Earth gravitational field. Surveys in Geophysics doi: 10.1007/s10712-009-9077-z.

  • Ramillien G. 2002: Gravity/magnetic potential of uneven shell topography. J. Geod. 76 139-149 doi: 10.1007/s00190-002-0193-5.

  • Sjöberg L. E. 1993: Terrain effects in the atmospheric gravity and geoid correction. Bull. Geod. 64 178-184.

  • Sjöberg L. E. 1998: The atmospheric geoid and gravity corrections. Bollettino di geodesia e scienze affini 4.

  • Sjöberg L. E. 1999: The IAG approach to the atmospheric geoid correction in Stokes's formula and a new strategy. J. Geod. 73 362-366 doi: 10.1007/s001900050254.

  • Sjöberg L. E. Nahavandchi H. 1999: On the indirect effect in the Stokes-Helmert method of geoid determination. J. Geod. 73 87-93 doi: 10.1007/s001900050222.

  • Sjöberg L. E. 2000: Topographic effects by the Stokes-Helmert method of geoid and quasi-geoid determinations. J. Geod. 74 2 255-268 doi: 10.1007/s001900050284.

  • Sjöberg L. E. Nahavandchi H. 2000: The atmospheric geoid effects in Stokes formula. Geoph. J. Int. 140 95-100 doi: 10.1046/j.1365-246x.2000.00995.x.

  • Sjöberg L. E. 2001: Topographic and atmospheric corrections of gravimetric geoid determination with special emphasis on the effects of harmonics of degrees zero and one. J. Geod. 75 283-290 doi: 10.1007/s001900100174.

  • Sjöberg L. E. 2006: The effects of Stokes's formula for an ellipsoidal layering of the earth's atmosphere. J. Geod. 79 675-681 doi: 10.1007/s00190-005-0018-4.

  • Sjöberg L. E. 2007: Topographic bias by analytical continuation in physical geodesy. J. Geod. 81 345-350 doi: 10.1007/s00190-006-0112-2.

  • Sun W. Sjöberg L. E. 2001: Convergence and optimal truncation of binomial expansions used in isostatic compensations and terrain corrections. J. Geod. 74 627-636.

  • Sünkel H. 1968: Global topographic-isostatic models. In: Mathematical and numerical techniques in Physical geodesy (Ed. Sünkel H.) Lecture Notes in Earth Sciences 7 Springer-Verlag 417-462.

  • Tenzer R. 2005: Spectral domain of Newton's integral. Bollettino di Geodesia e Scienze Affini 2 61-73.

  • Tenzer R. Hamayun Vajda P. 2008a: Global secondary indirect effects of topography bathymetry ice and sediments. Contrib. Geophys. Geod. 38 2 209-216.

  • Tenzer R. Hamayun Vajda P. 2008b: Global map of the gravity anomaly corrected for complete effects of the topography and of density contrasts of global ocean ice and sediments. Contrib. Geophys. Geod. 38 4 357-370.

  • Tenzer R. Hamayun Vajda P. 2009a: Global maps of the CRUST 2.0 crustal components stripped gravity disturbances. Journal of Geophysical Research 114 B 05408 doi: 10.1029/2008JB006016.

  • Tenzer R. Vajda P. Hamayun 2009b: Global atmospheric corrections to the gravity field quantities. Contrib. Geophys. Geod. 39 3 221-236.

  • Tsoulis D. 1999: Spherical harmonic computations with topographic/isostatic coefficients. Reports in the series IAPG / FESG (ISSN 1437-8280) Rep. No. 3 (ISBN 3-934205-02-X) Institute of Astronomical and Physical Geodesy Technical University of Munich.

  • Tsoulis D. 2001: A comparison between the Airy-Heiskanen and the Pratt-Hayford isostatic models for the computation of potential harmonic coefficients. J. Geod. 74 9 637-643 doi: 10.1007/s001900000124.

  • Vajda P. Ellmann A. Meurers B. Vaníček P. Novák P. Tenzer R. 2008: Global ellipsoid-referenced topographic bathymetric and stripping corrections to gravity disturbance. Studia Geophys. Geod. 52 19-34 doi: 10.1007/s11200-008-0003-5.

  • Vaníček P. Najafi M. Martinec Z. Harrie L. Sjöberg L. E. 1995: Higher-degree reference field in the generalised Stokes-Helmert scheme for geoid computation. J. Geod. 70 3 176-182 doi: 10.1007/BF00943693.

  • Wild F. Heck B. 2004: Effects of topographic and isostatic masses in satellite gravity gradiometry. Proceedings: Second International GOCE User Workshop GOCE. The Geoid and Oceanography ESA-ESRIN Frascati Italy March 8-10 2004 (ESA SP - 569 June 2004) CD-ROM.

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