# Deflections of the vertical from full-tensor and single-instrument gravity gradiometry

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## Abstract

Gravity gradiometry on a moving platform, whether ground or airborne, has the potential to offer an efficient and accurate determination of the deflection of the vertical by simple line integration. A significant error in this process is a trend error that results from the integration of systematic gradient errors. Using an airborne full-tensor gradiometry data set of regularly spaced and intersecting tracks over a 10 km square region and the USDOV2012 vertical deflection model to calibrate these long wavelength errors, it is shown that the gradient-derived deflections agree with the USDOV2012 model at the level of 0.6–0.9 arcsec. Moreover, it is shown by graphical inspection that these differences represent high-frequency signal rather than error. Another data processing technique is examined using only (simulated) single-gradiometer instrument data, i.e., the local differential curvature components, \((\varGamma _{{ yy}} - \varGamma _{{ xx}})/2\) and \(\varGamma _{{ xy}}\), of the gravity field. While in theory these data can yield deflection components using two parallel data tracks, the results in the tested case are unsatisfactory due to implicit additional cross-track integration errors that accumulate systematically. The analysis thus demonstrates the importance of using the individual horizontal gradient components, \(\varGamma _{{ xx}}\), \(\varGamma _{{ yy}}\), to derive the deflection of the vertical.

## Keywords

Deflection of the vertical Gravity gradiometry Torsion balance Line integration## Notes

### Acknowledgements

The work described in this report was supported by the Oak Ridge Institute for Science and Education (ORISE) through an interagency agreement between NGA and the U.S. Department of Energy (DOE) and under their NGA Visiting Scientist Program. Special thanks are also due Bell Geospace, Inc., for providing their airborne gradiometry data from the Parkfield survey.

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