# A New Tool for Airborne Gravimetry Survey Simulation

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

^{2}) at a spatial resolution of 5–6 km [1]. Thanks to this technological advancement, apart from the classical stabilized platform system, various measuring systems started to be deployed like the Strapdown Inertial Navigation System, which is based on a set of three orthogonal accelerometers and three gyroscopes or the system based on a combination of GPS and Inertial Measurement Units, used to determine all the components of the gravity vector [5,6,7,8]. Nowadays, even if different research groups were able to show that strapdown systems can basically produce the same gravity quality of the stabilized platform one [1,9,10] (also for production-oriented campaigns under challenging conditions), the latter is still considered as the standard technique, especially for geophysical applications.

## 2. Methodology

^{3}kg

^{−1}s

^{−2}, M is the Earth mass ($5.972\times {10}^{24}$ kg), a is the Earth semi-major axis (taken here equal to 6,378,137 m), ${P}_{\ell m}$ is the fully normalized associate Legendre function of degree m and order ℓ, and $\left(\right)$ are the geocentric coordinates of the point in which $\delta {g}_{GGM}$ should be computed.

- observation along the same flight line are correlated, while observations of different flight lines are supposed to be independent;
- the observation noise is zero mean and stationary, namely ${\mu}_{\nu}=0$ and ${C}_{\nu \nu}={C}_{\nu \nu}\left(d\right)$, where d is the distance between two points on the same flight line.

## 3. Numerical Tests

^{2}and a correlation length of about $0.05\xb0$ corresponding to $5.2$ km.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Forsberg, R.; Olesen, A.V. Airborne gravity field determination. In Sciences of Geodesy-I; Springer: Berlin, Germany, 2010; pp. 83–104. [Google Scholar]
- Brozena, J.M. Airborne gravimetry. In Handbook of Geophysical Exploration at Sea; CRC Press: Boca Raton, FL, USA, 2018; pp. 117–136. [Google Scholar]
- Forsberg, R.; Kenyon, S. Gravity and geoid in the Arctic Region—The Northern Polar Gap now filled. In Proceedings of the 2nd GOCE User Workshop, Frascati, Italy, 8–10 March 2004; Volume 569. [Google Scholar]
- Forsberg, R.; Olesen, A.V.; Yildiz, H.; Tscherning, C.C. Polar gravity fields from GOCE and airborne gravity. In Proceedings of the 4th International GOCE User Workshop, Munich, Germany, 31 March–1 April 2011. [Google Scholar]
- Kwon, J.H.; Jekeli, C. A new approach for airborne vector gravimetry using GPS/INS. J. Geodesy
**2001**, 74, 690–700. [Google Scholar] [CrossRef] - Jekeli, C.; Li, X. INS/GPS Vector Gravimetry along Roads in Western Montana; Technical Report; Division of Geodetic Science, Ohio State University: Columbus, OH, USA, 2006. [Google Scholar]
- Li, X. Strapdown INS/DGPS airborne gravimetry tests in the Gulf of Mexico. J. Geodesy
**2011**, 85, 597. [Google Scholar] [CrossRef] - Jekeli, C. Inertial Navigation Systems with Geodetic Applications; Walter de Gruyter: Berlin, Germany, 2012. [Google Scholar]
- Glennie, C.; Schwarz, K.; Bruton, A.; Forsberg, R.; Olesen, A.V.; Keller, K. A comparison of stable platform and strapdown airborne gravity. J. Geodesy
**2000**, 74, 383–389. [Google Scholar] [CrossRef] - Becker, D.; Becker, M.; Leinen, S.; Zhao, Y. Estimability in strapdown airborne vector gravimetry. In IGFS 2014; Springer: Berlin, Germany, 2015; pp. 11–15. [Google Scholar]
- Forsberg, R.; Olesen, A.; Einarsson, I. Airborne gravimetry for geoid determination with Lacoste Romberg and Chekan gravimeters. Gyrosc. Navigat.
**2015**, 6, 265–270. [Google Scholar] [CrossRef][Green Version] - Rummel, R.; Balmino, G.; Johannessen, J.; Visser, P.; Woodworth, P. Dedicated gravity field missions— Principles and aims. J. Geodynam.
**2002**, 33, 3–20. [Google Scholar] [CrossRef] - Scheinert, M.; Ferraccioli, F.; Schwabe, J.; Bell, R.; Studinger, M.; Damaske, D.; Jokat, W.; Aleshkova, N.; Jordan, T.; Leitchenkov, G.; et al. New Antarctic gravity anomaly grid for enhanced geodetic and geophysical studies in Antarctica. Geophys. Res. Lett.
**2016**, 43, 600–610. [Google Scholar] [CrossRef] [PubMed][Green Version] - Li, X. Using radial basis functions in airborne gravimetry for local geoid improvement. J. Geodesy
**2018**, 92, 471–485. [Google Scholar] [CrossRef] - Sampietro, D.; Capponi, M.; Mansi, A.; Gatti, A.; Marchetti, P.; Sansò, F. Space-Wise approach for airborne gravity data modelling. J. Geodesy
**2017**, 91, 535–545. [Google Scholar] [CrossRef] - Heiskanen, W.A.; Moritz, H. Physical geodesy. Bull. Géodésique (1946–1975)
**1967**, 86, 491–492. [Google Scholar] [CrossRef] - Forsberg, R. Gravity field terrain effect computations by FFT. Bull. Géodésique
**1985**, 59, 342–360. [Google Scholar] [CrossRef] - Kaula, W.M. Tests and combination of satellite determinations of the gravity field with gravimetry. J. Geophys. Res.
**1966**, 71, 5303–5314. [Google Scholar] [CrossRef] - Sampietro, D.; Capponi, M.; Triglione, D.; Mansi, A.; Marchetti, P.; Sansò, F. GTE: A new software for gravitational terrain effect computation: Theory and performances. Pure Appl. Geophys.
**2016**, 173, 2435–2453. [Google Scholar] [CrossRef] - CarbonNet Project Airborne Gravity Survey (2012) Gippsland Basin Nearshore Airborne Gravity Survey; Technical Report; Department of Primary Industries, Victoria State Government: Victoria, UK, 2012.

**Figure 2.**The proposed processing scheme to estimate the final predicted accuracy of a simulated airborne survey.

**Figure 4.**Empirical covariance retrieved from the CarbonNet dataset by means of the crossover analysis (red points), and theoretical covariance used to simulate data (light blue solid line).

**Figure 5.**Reference field (

**left**) and simulated observations (

**right**).The black line represents the shoreline, where the land is located in the northwest and the sea in the south. Unit [mGal].

**Figure 6.**Difference between the estimated field and the reference one (

**left**) and predicted accuracy from the simulated data (

**right**). The black line represents the shoreline, where the land is located in the northwest and the sea in the south. Unit [mGal].

**Figure 7.**Signal power spectrum (green line), compared with the theoretical power spectrum of a white noise with standard deviation equal to $0.67$ mGal (red line), 1 mGal (blue line), and $1.4$ mGal (black line).

Test ID | Aircraft Velocity [m/s] | Traverse Lines Spacing [m] | Control Lines Spacing [m] | Flight Time Time [h] | Accuracy Mode Mode [mGal] |
---|---|---|---|---|---|

1 | 50 | 1000 | 10,000 | 52.9 | 0.67 |

2 | 65 | 1000 | 10,000 | 40.5 | 0.95 |

3 | 75 | 1000 | 10,000 | 35.1 | 0.96 |

4 | 85 | 1000 | 10,000 | 30.9 | 1.05 |

5 | 100 | 1000 | 10,000 | 26.3 | 1.03 |

6 | 50 | 2500 | 10,000 | 22.7 | 1.10 |

7 | 50 | 5000 | 10,000 | 12.6 | 1.22 |

8 | 50 | 7500 | 10,000 | 9.2 | 1.37 |

9 | 50 | 10,000 | 10,000 | 7.5 | 1.44 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sampietro, D.; Mansi, A.H.; Capponi, M.
A New Tool for Airborne Gravimetry Survey Simulation. *Geosciences* **2018**, *8*, 292.
https://doi.org/10.3390/geosciences8080292

**AMA Style**

Sampietro D, Mansi AH, Capponi M.
A New Tool for Airborne Gravimetry Survey Simulation. *Geosciences*. 2018; 8(8):292.
https://doi.org/10.3390/geosciences8080292

**Chicago/Turabian Style**

Sampietro, Daniele, Ahmed Hamdi Mansi, and Martina Capponi.
2018. "A New Tool for Airborne Gravimetry Survey Simulation" *Geosciences* 8, no. 8: 292.
https://doi.org/10.3390/geosciences8080292