The Use of Gravity Reductions in the Indirect Strapdown Airborne Gravimetry Processing


Strapdown airborne gravimetry (SAG) is one of the most efficient techniques used in geodesy and geophysics for acquiring gravity data on relatively large regions in a faster and cost-effective way or to fill in the gravity data gaps on areas where it is neither practical nor possible to make terrestrial measurements. Recent studies have shown that accuracies of 1 mGal and precision of sub-mGal levels are possible with the strapdown inertial systems modified for gravimetry (e.g., temperature stabilization). Besides the advancements in the instrumentation, data processing and integration algorithms are evolving consistently. This study investigates the contribution of long- and short-wavelength gravity reductions following the remove–restore procedure in the indirect SAG processing, where the gravity disturbance at flight altitude is modeled stochastically as an additional system state in the Kalman filter sense. The proposed method is implemented to the airborne data collected in central Turkey in 2018 with a thermally stabilized strapdown inertial measurement unit of navigation-grade type. The inclusion of the long- and short-wavelength gravity reductions in the SAG processing limits the in-run bias variations of the Z-accelerometer and changes the parameters of the third-order Gauss–Markov gravity state model significantly. Utilization of the reduced gravity disturbance in the processing provides better long-wavelength stability in the solution by reducing the mean bias of about 2.60 to 0.65 mGal between the airborne gravity estimates and a high-resolution global gravity model. Moreover, a remarkable improvement in the internal precision is achieved when the gravity reductions are introduced into the SAG solution. Comparisons at the crossover points demonstrate that the application of gravity reductions yields considerably lower crossover residuals than the standard solution without reductions. The non-adjusted crossover differences of the long- and short-wavelength removed and restored SAG solution result in an RMSE value of 0.79 mGal, that is, 40% better precision than the standard solution.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Availability of Data and Material

The data that support the findings of this study are owned by the Ministry of National Defense, General Directorate of Mapping, Turkey. The author is not authorized to share the data with third parties. To access the data, contact the General Directorate of Mapping at


  1. Ayres-Sampaio D, Deurloo R, Bos M, Magalhães A, Bastos L (2015) A comparison between three IMUs for strapdown airborne gravimetry. Surv Geophys 36(4):571–586.

    Article  Google Scholar 

  2. Becker D (2016) Advanced calibration methods for strapdown airborne gravimetry. Dissertation, Technische Universität Darmstadt, Darmstadt, Germany.

  3. Becker JJ, Sandwell DT, Smith WHF, Braud J, Binder B, Depner J et al (2009) Global bathymetry and elevation data at 30 arc seconds resolution: SRTM30_PLUS. Mar Geodesy 32(4):355–371.

    Article  Google Scholar 

  4. Becker D, Nielsen JE, Ayres-Sampaio D, Forsberg R, Becker M, Bastos L (2015) Drift reduction in strapdown airborne gravimetry using a simple thermal correction. J Geod 89:1133–1144.

    Article  Google Scholar 

  5. Bruton AM, Schwarz KP, Ferguson S, Kern M, Wei M (2002) Deriving acceleration from DGPS: toward higher resolution applications of airborne gravimetry. GPS Solut 5(3):1–14.

    Article  Google Scholar 

  6. Bucha B, Janák J (2014) A MATLAB-based graphical user interface program for computing functionals of the geopotential up to ultra-high degrees and orders: efficient computation at irregular surfaces. Comput Geosci 66:219–227.

    Article  Google Scholar 

  7. Deurloo RA (2011) Development of a Kalman filter integrating system and measurement models for a low-cost strapdown airborne gravimetry system. Dissertation, Faculty of Sciences, University of Porto, Porto, Portugal

  8. Deurloo R, Yan W, Bos M, Ayres-Sampaio D, Magalhães A, Becker M, Becker D, Bastos L (2015) A comparison of the performance of medium-and high-quality inertial systems grades for strapdown airborne gravimetry. In: Rizos C, Willis P (eds) IAG 150 Years. International association of geodesy symposia, vol 143. Springer, Cham, pp 323–329.

    Google Scholar 

  9. Forsberg R (1984) A study of terrain reductions, density anomalies and geophysical inversion methods in gravity field modeling. Report No. 355, Department of Geodetic Science and Surveying, The Ohio State University, Columbus, USA.

  10. Forsberg (1985) Gravity field terrain effect computations by FFT. Bull Géodésique 59(4):342–360.

    Article  Google Scholar 

  11. Forsberg R, Tscherning C (1981) The use of height data in gravity field approximation by collocation. J Geophys Res 86(B9):7843–7854.

    Article  Google Scholar 

  12. Gelb A (1974) Applied optimal estimation. The M.I.T Press, Cambridge. ISBN 0-262-20027-9

    Google Scholar 

  13. Glennie C, Schwarz KP (1999) A comparison and analysis of airborne gravimetry results from two strapdown inertial/DGPS systems. J Geod 73(6):311–321.

    Article  Google Scholar 

  14. Glennie CL, Schwarz KP, Bruton AM, Forsberg R, Olesen AV, Keller K (2000) A comparison of stable platform and strapdown airborne gravity. J Geod 74(5):383–389.

    Article  Google Scholar 

  15. Groves PD (2013) Principles of GNSS, inertial, and multisensor integrated navigation systems, 2nd edn. Artech House, Boston. ISBN 978-1-60807-005-3

    Google Scholar 

  16. Heiskanen WA, Moritz H (1967) Physical geodesy. WH Freeman and Company, San Francisco

    Google Scholar 

  17. Hirt C, Rexer M (2015) Earth 2014: 1 arc-min shape, topography, bedrock and ice-sheet models available as gridded data and degree-10,800 spherical harmonics. Int J Appl Earth Observ Geoinf 39:103–112.

    Article  Google Scholar 

  18. Jekeli C (1994) Airborne vector gravimetry using precise, position-aided inertial measurement units. Bull Géodésique 69(1):1–11.

    Article  Google Scholar 

  19. Jekeli C (2001) Inertial navigation systems with geodetic applications. Walter de Gruyter, Berlin

    Google Scholar 

  20. Jensen TE (2018) Airborne Strapdown Gravity Measurements for Geodesy and Geophysics. Dissertation, Kgs. Lyngby: Technical University of Denmark.

  21. Jensen TE, Forsberg R (2018) Helicopter test of a strapdown airborne gravimetry system. Sensors 18(9):3121.

    Article  Google Scholar 

  22. Jensen TE, Olesen AV, Forsberg R, Olsson PA, Josefsson Ö (2019) New results from strapdown airborne gravimetry using temperature stabilisation. Remote Sens 11(22):2682.

    Article  Google Scholar 

  23. Kvas A, Mayer-Gürr T, Krauss S, Brockmann JM, Schubert T, Schuh W-D, Pail R, Gruber T, Jäggi A, Meyer U (2019) The satellite-only gravity field model GOCO06s. Paper presented at EGU General Assembly 2019, Vienna, Austria.

  24. Kwon JH, Jekeli C (2001) A new approach for airborne vector gravimetry using GPS/INS. J Geod 74(10):690–700.

    Article  Google Scholar 

  25. Moritz H (2000) Geodetic reference system 1980. J Geod 74(1):128–133.

    Article  Google Scholar 

  26. Nagy D (1966) The prism method for terrain corrections using digital computers. Pure appl Geophys 63:31–39.

    Article  Google Scholar 

  27. Nagy D, Papp G, Benedek J (2000) The gravitational potential and its derivatives for the prism. J Geod 74:552–560.

    Article  Google Scholar 

  28. Olson CJ, Becker JJ, Sandwell DT (2016) SRTM15_PLUS: data fusion of Shuttle Radar Topography Mission (SRTM) land topography with measured and estimated seafloor topography (NCEI Accession 0150537)

  29. Pavlis NK, Factor JK, Holmes SA (2007) Terrain-related gravimetric quantities computed for the next EGM. In: Proceedings of the 1st International Symposium of the International Gravity Field Service, Harita Dergisi 18:318-323

  30. Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2008) An Earth gravitational model to degree 2,160: EGM2008. Presented at the 2008 General Assembly of the European Geosciences Union, Vienna, 13-18 April 2008

  31. Rauch HE, Striebel CT, Tung F (1965) Maximum likelihood estimates of linear dynamic systems. AIAA J 3(8):1445–1450.

    Article  Google Scholar 

  32. Sampietro D, Capponi M, Mans AH, Gatti A, Marchetti P, Sansò F (2017) Space-Wise approach for airborne gravity data modelling. J Geod 91:535–545.

    Article  Google Scholar 

  33. Sampietro D, Mansi AH, Capponi M (2018) A new tool for airborne gravimetry survey simulation. Geosciences 8:292.

    Article  Google Scholar 

  34. Schwarz KP (1983) Inertial surveying and geodesy. Rev Geophys 21(4):878–890.

    Article  Google Scholar 

  35. Schwarz KP, Wei M (1990) A framework for modelling kinematic measurements in gravity field applications. J Geod 64(4):331–346.

    Article  Google Scholar 

  36. Schwarz KP, Colombo O, Hein G, Knickmeyer ET (1992) Requirements for airborne vector gravimetry. In: Colombo OL (eds) From Mars to Greenland: Charting gravity with space and airborne ınstruments. International Association of Geodesy Symposia, vol 110. Springer, New York, NY.

  37. Simav M, Becker D, Yildiz H, Hoss M (2020) Impact of temperature stabilization on the strapdown airborne gravimetry: a case study in Central Turkey. J Geod 94:41.

    Article  Google Scholar 

  38. Tomé P (2002) Integration of inertial and satellite navigation systems for aircraft attitude determination. Dissertation, Faculty of Sciences, University of Porto, Porto, Portugal

  39. Tozer B, Sandwell DT, Smith WHF, Olson C, Beale JR, Wessel P (2019) Global bathymetry and topography at 15 arcsec: SRTM15+. Earth Space Sci.

    Article  Google Scholar 

  40. Wei M, Schwarz KP (1998) Flight test results from a strapdown airborne gravity system. J Geod 72(6):323–332.

    Article  Google Scholar 

  41. Yamazaki D, Ikeshima D, Tawatari R, Yamaguchi T, O’Loughlin F, Neal JC, Sampson CC, Kanae S, Bates PD (2017) A high accuracy map of global terrain elevations. Geophys Res Lett 44:5844–5853.

    Article  Google Scholar 

  42. Zingerle P, Pail R, Gruber T, Oikonomidou X (2019) The experimental gravity field model XGM2019e. GFZ Data Services.

    Article  Google Scholar 

Download references


This work is a part of the Turkish Height System Modernization and Gravity Recovery Project supported by the Presidency of Turkey, Directorate of Strategy and Budget, and coordinated by the Turkish General Directorate of Mapping.


This research received no external funding.

Author information




The author has done the whole work by himself.

Corresponding author

Correspondence to Mehmet Simav.

Ethics declarations

Conflict of interest

The author declares that he has no conflict of interests.

Code Availability

The SAG processing software used in the study is owned by the Ministry of National Defense, General Directorate of Mapping, Turkey. The author is not authorized to share it with third parties.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Simav, M. The Use of Gravity Reductions in the Indirect Strapdown Airborne Gravimetry Processing. Surv Geophys (2020).

Download citation


  • Strapdown airborne gravimetry
  • Indirect approach
  • Gravity reductions
  • Global geopotential model
  • Residual terrain modeling
  • Remove–restore