Surveys in Geophysics

, Volume 27, Issue 2, pp 257–275 | Cite as

Airborne Gradiometry Error Analysis

  • Christopher Jekeli


Gravity gradiometry is one of the older methods of determining the Earth’s local gravitational field, but lies in the shadow of more conventional static and moving-base gravimeter-based systems. While the static torsion balance appears to have been relegated to the museum, support for the airborne and space-borne differential accelerometer (gradiometer) continues so as to overcome limitations in spatial resolution and accuracy inherent in ordinary moving-base gravimetry. One airborne system exists, building on 30 year old technology concepts, and new technologies (e.g., cold-atom interferometry) promise significant improvements. Concomitant advances are required to measure accurately the angular velocity and angular acceleration of the platform, which inseparably combine (in an absolute sense) with the Earth’s gravitational gradients. A numerical analysis of instrument errors, with simulated aircraft dynamics, shows that navigation-grade gyros are just sufficient to account for these effects in gradiometers with 1E/ \(\sqrt{{\rm Hz}}\) sensitivity. More accurate instruments, with 0.1 E/\(\sqrt{{\rm Hz}}\) sensitivity, require commensurate sensitivity in the gyros, of the order of 0.01°/h/\(\sqrt{{\rm Hz}}\) = 1.5\times10−4 ° \ \(\sqrt{{Hz}}\) for typical survey aircraft dynamics. On the other hand, typical orientation errors in the platform, which are problematic for vector gravimetry, are much less of a concern in gradiometry. They couple to the gradient signals and affect only the very low frequencies of the total gradient error.


airborne gravity gradiometry gradiometer error analysis angular rate errors 


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  1. Bell, R. E., Coakley, B. J., Stemp, R. W. 1991‘Airborne Gravimetry from a Small twin Engine Aircraft over the Long Island Sound’Geophysics5614861493CrossRefGoogle Scholar
  2. Bona, P. and Tiberius, C.: 2000, ‘An Experimental Comparison of Noise Characteristics of Seven High-end Dual Frequency GPS Receiver Sets’, Proc. IEEE PLANS2000, 13–16 March 2000, San Diego, California, pp. 237–244.Google Scholar
  3. Brozena, J. M, Peters, M. F 1994State-of-the-art Airborne GravimetrySünkel, H.Marson, I eds. Gravity and Geoid, IAG Symposia 113SpringerBerlin187197Google Scholar
  4. Chen, J.-H., Lee, S.-C, DeBra, D. B. 1994‘Gyroscope Free Strapdown Inertial Measurement Unit by Six Linear Accelerometers’J. Guidance Control Dyn.17286290CrossRefGoogle Scholar
  5. Dransfield, M.: 1994, Airborne gravity gradiometry, Ph.D. Thesis, Department of Physics, The University of Western Australia.Google Scholar
  6. ESA: 1999, Reports for mission selection, the four candidate Earth explorer core missions, gravity field and steady-state ocean circulation mission. Report SP-1233(1), European Space Agency.Google Scholar
  7. Jekeli, C. 1984‘Analysis of Airborne Gravity Gradiometer Survey Accuracy’Manuscripta Geodaetica9323379Google Scholar
  8. Jekeli, C. 1988‘The Gravity Gradiometer Survey System’EOS Trans. Am. Geophys. Union69116117105CrossRefGoogle Scholar
  9. Jekeli, C. 1993‘A Review of Gravity Gradiometer Survey System Data Analysis’Geophysics58508514CrossRefGoogle Scholar
  10. Jekeli, C. 2000Inertial Navigation Systems with Geodetic ApplicationsW. deGruyterBerlinGoogle Scholar
  11. Jekeli, C.: 2003, Statistical analysis of moving-base gravimetry and gravity gradiometry. Report No.466, Laboratory for Space Geodesy and Remote Sensing Research, Geodetic Science, Ohio State University, Columbus, Ohio.Google Scholar
  12. Jekeli, C.: 2004, ‘High Resolution Gravity Mapping, the Next Generation of Sensors’, in R. S. J. Sparks (ed.), The State of the Planet, Frontiers and Challenges in Geophysics, Geophysical Monograph 150, IUGG Vol. 19, pp. 135–146.Google Scholar
  13. Jekeli, C.: 2005, ‘Precision Free-inertial Navigation with Gravity Compensation by an Onboard Gradiometer’, J. Guidance Control Dynamics, in press.Google Scholar
  14. Kwon, J. H, Jekeli, C. 2001‘A New Approach for Airborne Vector Gravimetry Using GPS/INS’J. Geodesy74690700CrossRefGoogle Scholar
  15. Lemoine F. G., Kenyon, S. C., Factor, J. K., Trimmer, R. G., Pavlis, N. K., Chinn, D. S., Cox, C. M., Klosko, S. M., Luthcke, S. B., Torrence, M. H., Wang, Y. M., Williamson, R. G., Pavlis, E. C., Rapp, R. H., and Olson, T. R.: 1998, The development of the joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) geopotential model EGM96, NASA Technical Paper NASA/TP-1998-206861, Goddard Space Flight Center, Greenbelt.Google Scholar
  16. McGuirk, J. M., Foster, G. T., Fixler, J. B., Snadden, M. J, Kasevich, M. A. 2002‘Sensitive Absolute Gravity Gradiometry Using Atom Interferometry’Phys. Rev. A65033608CrossRefGoogle Scholar
  17. Moody, M. V., Chan, H. A, Paik, H. J. 1986‘Superconducting Gravity Gradiometer for Space and Terrestrial Applications’J. Appl. Phys.6043084315CrossRefGoogle Scholar
  18. Müller, J. 2003‘GOCE Gradients in Various Reference Frames and their Accuracies’Adv. Geosci.13338CrossRefGoogle Scholar
  19. Nettleton, L. L. 1976Gravity and Magnetics in Oil ProspectingMcGraw Hill Inc.New YorkGoogle Scholar
  20. Paik, H.J., Canavan, E. R., and Moody, M. V.: 1997, ‘Airborne/Shipborne SGG Survey System’, in Proceedings of the International Symposium on Kinematic Systems in Geodesy, Geomatics, and Navigation, 3–6 June 1997, Banff, Canada, pp. 565–570.Google Scholar
  21. Pedersen, L. B, Rasmussen, T. M. 1990‘The Gradient Tensor of Potential Field Anomalies – Some Implications on Data Collection and Data Processing of Maps’Geophysics5515581566CrossRefGoogle Scholar
  22. Schwarz, K. P., Colombo, O. L., Hein, G., and Knickmeyer, E. T.: 1992, ‘Requirements for Airborne Vector Gravimetry’, in Proc. Int. Assoc. of Geodesy Symposia, from Mars to Greenland: Charting Gravity with Space and Airborne Instruments, No. 110, pp. 273–283.Google Scholar
  23. Schweitzer, M., Feldman, W. K., Konig, W. F., DiFrancesco, D. J., Sieracki, D. L., and San Giovanni, C. P.: 2000, System and process for optimizing gravity gradiometer measurements. U.S. Patent 6,125,698.Google Scholar
  24. Sünkel, H. (ed.): 2000, From Eötvös to Milligal, ESA Final Report, ESA/ESTEC, contract no. 13392/98/NL/GD, Graz, Austria.Google Scholar
  25. Leeuwen, E. H. 2000‘BHP Develops Airborne Gravity Gradiometer for Mineral Exploration’Leading Edge1912961297CrossRefGoogle Scholar
  26. Wei, M., Schwarz, K. P. 1998‘Flight Test Results from a Strapdown Airborne Gravity System’J. Geodesy72323332CrossRefGoogle Scholar
  27. Zorn, A. H.: 2002, ‘A Merging of System Technologies – All-Accelerometer Inertial Navigation and Gravity Gradiometry. Presented at IEEE Position Location and Navigation Symposium (PLANS) 2002, Palm Springs, California, 15–18 April 2002.Google Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Division of Geodetic Science, Department of Geological SciencesOhio State UniversityColumbusUSA

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