# Space-Wise approach for airborne gravity data modelling

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## Abstract

Regional gravity field modelling by means of remove-compute-restore procedure is nowadays widely applied in different contexts: it is the most used technique for regional gravimetric geoid determination, and it is also used in exploration geophysics to predict grids of gravity anomalies (Bouguer, free-air, isostatic, etc.), which are useful to understand and map geological structures in a specific region. Considering this last application, due to the required accuracy and resolution, airborne gravity observations are usually adopted. However, due to the relatively high acquisition velocity, presence of atmospheric turbulence, aircraft vibration, instrumental drift, etc., airborne data are usually contaminated by a very high observation error. For this reason, a proper procedure to filter the raw observations in both the low and high frequencies should be applied to recover valuable information. In this work, a software to filter and grid raw airborne observations is presented: the proposed solution consists in a combination of an along-track Wiener filter and a classical Least Squares Collocation technique. Basically, the proposed procedure is an adaptation to airborne gravimetry of the Space-Wise approach, developed by Politecnico di Milano to process data coming from the ESA satellite mission GOCE. Among the main differences with respect to the satellite application of this approach, there is the fact that, while in processing GOCE data the stochastic characteristics of the observation error can be considered a-priori well known, in airborne gravimetry, due to the complex environment in which the observations are acquired, these characteristics are unknown and should be retrieved from the dataset itself. The presented solution is suited for airborne data analysis in order to be able to quickly filter and grid gravity observations in an easy way. Some innovative theoretical aspects focusing in particular on the theoretical covariance modelling are presented too. In the end, the goodness of the procedure is evaluated by means of a test on real data retrieving the gravitational signal with a predicted accuracy of about 0.4 mGal.

## Keywords

Gravity Airborne gravimetry Remove-compute-restore procedure Covariance modelling Space-Wise approach## Notes

### Acknowledgements

The authors would like to thank the management of Eni Upstream and Technical Services for the permission to present this work.

## References

- Bell RE, Childers VA, Arko RA, Blankenship DD, Brozena JM (1999) Airborne gravity and precise positioning for geologic applications. J Geophys Res Sol Earth 104(B7):15281–15292CrossRefGoogle Scholar
- Boumann J, Ebbing J, Meekes S, Fattah RA, Gradmann S, Bosch W (2015) GOCE gravity gradient data for litospheric modeling. Int J Appl Earth Obs 35:16–30CrossRefGoogle Scholar
- Brockmann JM, Zehentner N, öck E, Pail R, Loth I, Mayer Gürr T, Schuh WD (2014) EGM_TIM_RL05: an independent geoid with centimeter accuracy purely based on the GOCE mission. Geophys Res Lett 41(22):8089–8099CrossRefGoogle Scholar
- Bruton AM (2000) Improving the accuracy and resolution of SINS/DGPS airborne gravimetry, Phd Thesis, University of Calgary, Calgary CanadaGoogle Scholar
- CarbonNet Project Airborne Gravity Survey (2012) Gippsland Basin Nearshore Airborne Gravity Survey, Victoria, Australia. Victoria: Department of primary industries, Victoria State GovernmentGoogle Scholar
- Davis PJ (1975) Interpolation and approximation. Courier Corporation, New YorkGoogle Scholar
- de Saint-Jean B, Verdun J, Duquenne H, Barriot JP, Melachroinos S, Cali J (2007) Fine analysis of lever arm effects in moving gravimetry. Int Assoc Geod Symp 130:809–816CrossRefGoogle Scholar
- Drinkwater MR, Floberghagen R, Haagmans R, Muzi D, Popescu A (2003) GOCE: ESA’s first Earth Explorer Core mission. Space Sci Ser ISSI 17:419–432CrossRefGoogle Scholar
- Forsberg R, Olesen A, Bastos L, Gidskehaug A, Meyer U, Timmen L (2000) Airborne geoid determination. Earth Planets Space 52(10):863–866CrossRefGoogle Scholar
- Förste C, Bruinsma SL, Abrikosov O, Lemoine JM, Schaller T, Götze HJ, Ebbing J, Marty JC, Flechtner F, Balmino G, Biancale R (2014) EIGEN-6C4 The latest combined global gravity field model including GOCE data up to degree and order 2190 of GFZ Potsdam and GRGS Toulouse. In: Presented at the 5th GOCE User Workshop, Paris, 25–28 Nov 2014Google Scholar
- Gatti A, Reguzzoni M, Sansó F, Venuti G (2013) The height datum problem and the role of satellite gravity models. J Geodesy 87(1):5–22CrossRefGoogle Scholar
- Gilardoni M, Menna M, Pulain PM, Reguzzoni M (2013) Preliminary analysis on GOCE contribution to the Mediterranean Sea circulation. ESA Spec Publ 722:206Google Scholar
- Gilardoni M, Reguzzoni M, Sampietro D (2016) GECO: a global gravity model by locally combining GOCE data and EGM2008. Stud Geophys Geod 60(2):228–247CrossRefGoogle Scholar
- Glennie CL, Schwarz KP, Bruton AM, Forsberg R, Olesen AV, Keller K (2000) A comparison of stable platform and strapdown airborne gravity. J Geodesy 74(5):383–389CrossRefGoogle Scholar
- Hamilton AC, Brul BG (1967) Vibration-induced drift in LaCoste and Romberg Geodetic Gravimeters. J Geophys Res 72(8):2187–2197CrossRefGoogle Scholar
- Harlan RB (1968) Eotvos corrections for airborne gravimetry. J Geophys Res 73(14):4675–4679CrossRefGoogle Scholar
- Hinze WJ, Von Frese RR, Saad AH (2013) Gravity and magnetic exploration: principles, practices, and applications, 512. Cambridge University Press, New YorkCrossRefGoogle Scholar
- Hirt C, Kuhn M, Featherstone WE, Göttl F (2012) Topographic/isostatic evaluation of new-generation GOCE gravity field models. J Geophys Res Sol Earth 117(B5):B05407CrossRefGoogle Scholar
- Knudsen P, Bingham R, Andersen O, Rio MH (2011) A global mean dynamic topography and ocean circulation estimation using a preliminary GOCE gravity model. J Geodesy 85(11):861–879CrossRefGoogle Scholar
- Kreh M (2012) Bessel functions. Lecture notes, Penn StateGöttingen summer school on number theoryGoogle Scholar
- Lambeck K (1990) Aristoteles: an ESA mission to study the earth’s gravity field. ESA J 14:1–21Google Scholar
- Lawson CL, Hanson RJ (1974) Solving least squares problems, Englewood Cliffs. Prentice-Hall, Upper Saddle RiverGoogle Scholar
- Mariani P, Braitenberg C, Ussami N (2013) Explaining the thick crust in Paran basin, Brazil, with satellite GOCE gravity observations. J S Am Earth Sci 45:209–223CrossRefGoogle Scholar
- Menna M, Poulain PM, Mauri E, Sampietro D, Panzetta F, Reguzzoni M, Sansó F (2013) Mean surface geostrophic circulation of the Mediterranean Sea estimated from GOCE geoid models and altimetric mean sea surface: initial validation and accuracy assessment. B Geofis Teor Appl 54(4):347–365Google Scholar
- Pavlis NA, Holmes SA, Kenyon SC, Factor JK (2012) The development and evaluation of the Earth Gravitational Model 2008 (EGM2008), J Geophys Res-Sol Earth 117(B4):4406. doi: 10.1029/2011JB008916
- Reguzzoni M, Sampietro D (2015) GEMMA: an Earth crustal model based on GOCE satellite data. Int J Appl Earth Obs 35:31–43CrossRefGoogle Scholar
- Reguzzoni M, Tselfes N (2009) Optimal multi-step collocation: application to the space-wise approach for GOCE data analysis. J Geodesy 83(1):13–29CrossRefGoogle Scholar
- Sansó F, Sideris MG (eds) (2013) Geoid determination: theory and methods. Springer, BerlinGoogle Scholar
- Sampietro D, Capponi M, Triglione D, Mansi AHH, Marchetti P, Sansó F (2016) GTE: a new software for gravitational terrain effect computation: theory and performances. Pure Appl Geophys 173(7):1–19Google Scholar
- Schwarz KP, Li Z (1997) An introduction to airborne gravimetry and its boundary value problems. Lecture notes in Earth sciences 65:312–358Google Scholar
- Schwarz KP, Sideris MG, Forsberg R (1990) The use of FFT techniques in physical geodesy. Geophys J Int 100(3):485–514CrossRefGoogle Scholar
- Schwarz KP, Li Y (1996) What can airborne gravimetry contribute to geoid determination? J Geophys Res 101(B8):873–881CrossRefGoogle Scholar
- Smit M, Koop R, Visser P, van den IJssel J, Sneeuw N, Muller J, Oberndorfer H (2000) GOCE End-to-End Performance Analysis, Final Report, ESTEC Contract No. 12735/98/NL/GDGoogle Scholar
- Térmens A, Colomina I (2005) Network approach versus state-space approach for strapdown inertial kinematic gravimetry. Int Assoc Geod Symp 129:107–112CrossRefGoogle Scholar
- Tscherning CC, Rubek F, Forsberg R (1998) Combining airborne and ground gravity using collocation. Int Assoc Geod Symp 119:18–23CrossRefGoogle Scholar
- Vermeersen LLA (2003) The potential of GOCE in constraining the structure of the crust and lithosphere from post-glacial rebound. Space Sci Rev 108(1–2):105–113CrossRefGoogle Scholar
- Voigt C, Denke H (2015) Validation of GOCE gravity field models in Germany. Newton’s Bull 5:37–49Google Scholar
- Watson GN (1995) A treatise on the theory of bessel functions. Cambridge University Press, MontpelierGoogle Scholar
- Whiteway TG (2009) Australian bathymetry and topography grid. Geoscience Australia, CanberraGoogle Scholar
- Wiener N (1949) Extrapolation, interpolation, and smoothing of stationary time series. MIT Press, CambridgeGoogle Scholar