On the Detectability of Synthetic Disturbances in FG5 Absolute Gravimetry Data Using Lomb-Scargle Analysis

Publication: GEOMATICA
1 January 2012


An instrumental or environmental disturbance (signal plus noise) in FG5 absolute gravimetry observations becomes visible by analyzing the residuals, which represent the misfit from the theoretical acceleration parabola. While spectral analysis of FG5 residuals via classical discrete Fourier transform (DFT) is limited by the non-equispaced nature of the FG5 observations, the Lomb-Scargle periodogram can analyze nonequispaced observations and estimate (detect) signals in FG5 residuals. We investigate the detectability of synthetically introduced disturbances in FG5 residuals using Lomb-Scargle periodogram analysis. The sensitivity of the FG5 measurement and adjustment process is a function of disturbance frequency, amplitude, phase, and signal-to-noise ratio (SNR). We conclude that the used drop length and the transfer function of the instrument can significantly alter the estimated gravity values. Further, we establish a sensitivity function called LOFSMAP which depends on the disturbance parameter space of amplitude, frequency, phase and SNR.


Une perturbation attribuable aux instruments ou à l’environnement (signal et bruit) dans les observations du gravimètre absolu FG5 devient visible en analysant les résiduelles, qui représentent les écarts relativement à la parabole d’accélération théorique. Même si l’analyse spectrale des résiduelles du FG5 par la transformée de Fourier discrète (TFD) classique est limitée par la nature inégale de l’espacement des observations par FG5, le périodogramme Lomb-Scargle peut analyser des observations inégalement espacées et estimer (détecter) des signaux dans les résiduelles du FG5. Nous étudions le caractère détectable des perturbations introduites synthétiquement dans les résiduelles du FG5 au moyen de l’analyse du périodogramme Lomb-Scargle. La sensibilité du processus de mesure et d’ajustement du FG5 est fonction de la fréquence, de l’amplitude, de la phase et du rapport signal-bruit (S/B) des perturbations. Nous concluons que la longueur de chute libre utilisée et la fonction de transfert de l’instrument peuvent modifier considérablement les valeurs de gravité estimées. En outre, nous établissons une fonction de sensibilité appelée LOFSMAP, qui dépend de l’espace de paramètre de la perturbation que sont l’amplitude, la fréquence, la phase et le rapport S/B.

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van Camp M., Williams S.D.F.P., and Francis O. Uncertainty of absolute gravity measurements Journal of Geophysical Research 2005 110 B05406 9
Charles K. and Hipkin R. Vertical gradient and datum height corrections to absolute gravimeter data and the effect of structured fringe residuals Metrologia 1995 32 193
Eichenberger A., Jeckelmann B., and Richard P. Tracing Planck’s constant to the kilogram by electromechanical methods Metrologia 2003 40 6 356 365
Francis O, Niebauer T.M., Sasagawa G., Klopping F., and Gschwind J. Calibration of a superconducting gravimeter by comparison with an absolute gravimeter FG5 in Boulder Geophysical Research Letters 1998 25 7 1075 1078
Klopping F.J., Peter G., Robertson D.S., Berstis K.A., Moose R.E., and Carter W.E. Improvements in Absolute Gravity Observations Journal of Geophysical Research 1991 96 B5 8295 8303
Lambert A., Courtier N., and James T.S. Long-term monitoring by absolute gravimetry: tides to postglacial rebound Journal of Geodynamics 2006 41 1-3 307 317
de Linage C., Hinderer J., and Rogister Y. A search for the ratio between gravity variation and vertical displacement due to a surface load Geophysical Journal International 2007 171 3 986 994
Lomb N.R. Least-squares Frequency Analysis of Unequally Spaced Data Astrophysics and Space Science 1976 39 447 462
Mazzotti S., Lambert A., Courtier N., Nykolaishen L., and Dragert H. Crustal uplift and sea level rise in northern Cascadia from GPS, absolute gravity, and tide gauge data Geophysical Research Letters 2007 34 15 5
MicroG-Lacoste. 2008. FG5 g8 User’s Manual / Software. MicroG-Lacoste, Erie, Colorado, USA
Mitra, S.K., and J.F. Kaiser (eds). 1993 Handbook for Digital Signal Processing. Wiley-Interscience
Niebauer, T.M. 1987. New absolute gravity instruments for physics and geophysics. PhD thesis, Colorado University, Boulder
Niebauer T.M., Sasagawa G.S., Faller J.E., Hilt R., and Klopping F. A new generation of absolute gravimeters Metrologia 1995 32 3 159 180
Niebauer T.M., Billson R., Ellis B., Mason B., van Westrum D., and Klopping F. Simultaneous gravity and gradient measurements from a recoilcompensated absolute gravimeter Metrologia 2011 48 3 154 163
Niemeier, W. 2002. Ausgleichsrechnung, 1st edn. Walter de Gruyter - Berlin - New York
Oppenheim, A., and R. Schafer. 1989. Discrete-Time Signal Processing. Prentice-Hall Inc.
Orlob, M. 2004. Beurteilung von Schweremessungen verschiedener Absolutgravimeter FG5. Master’s thesis, Institut für Erdmessung, Gottfried Wilhelm Leibniz Universität Hannover
Press W.H. and Teukolsky S. Search algorithm for weak periodic signals in unevenly spaced data Computers in Physics 1988 2 6 77, 80 82
Press, W.H., S. Teukolsky, W. Vetterling, and B. Flannery. 2003. Numerical Recipes in C++ The Art of Scientific Computing Second Edition. Cambridge University Press
Röder, R. 1994. Zum Einsatz des Absolutgravimeters JILAG-3 in Präzisionsschwerenetzen—wis-senschaftliche Arbeiten der Fachrichtung Vermessungswesen der Universität Hannover. PhD thesis, Institut für Erdmessung, Gottfried Wilhelm Leibniz Unversität Hannover
Rundle J.B. Viscoelastic crustal deformation by finite, quasi-static sources Journal of Geophysical Research 1978 83 B12 5937 5945
Scargle J.D. Studies in Astronomical Time Series Analysis. II. Statistical Aspects of Spectral Analysis of Unevenly Spaced Data The Astrophysical Journal 1982 263 835 853
Schwarz J.P., Robertson D.S., Niebauer T.M., and Faller J.E. A Free-Fall Determination of the Newtonian Constant of Gravity Science 1998 282 5397 2230 2234
Steiner R.L., Williams E.R., Liu R., and Newell D.B. Uncertainty Improvements of the Nist Electronic Kilogram. Instrumentation and Measurement IEEE Transactions on 2007 56 2 592 596
Timmen, L. 1994. Untersuchung zur Modellbildung bei der Auswertung absoluter Schweremessungen - wis-senschaftliche Arbeiten der Fachrichtung Vermessungswesen der Universität Hannover. PhD thesis, Institüt fur Erdmessung, Gottfried Wilhelm Leibniz Unversität Hannover
Timmen L., Röder R., and Schnüll M. Absolute gravity determinations with JILAG-3—improved data evaluation and instrumental technics Bulletin Geodesique 1993 67 71 81
Torge, W. 1989. Gravimetry. Walter de Gruyter— Berlin—New York.
Wahr J., Han D., and Trupin A. Predictions of vertical up-lift caused by changing polar ice volumes on a viscoelastic earth Geophysical Research Letters 1995 22 8 977 980
Wenzel, G. 2001. Gravimetrie 1-Überarbeiteter Nachdruck des Orignalvorlesungsskripts von Univ. Prof. Dr.-Ing. habil. Georg Wenzel. Institut für Erdmessung, Gottfried Wilhelm Leibniz Unversität Hannover.
Williams S.D.P., Baker T.F., and Jeffries G. Absolute gravity measurements at UK tide gauges Geophysical Research Letters 2001 28 12 2317 2320

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Published In

cover image GEOMATICA
Volume 66Number 2June 2012
Pages: 113 - 124


Published online: 1 January 2012


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Martin Orlob
Department of Geosciences, University of Texas at Dallas, Texas, USA
Alexander Braun
Department of Geosciences, University of Texas at Dallas, Texas, USA


Martin Orlob, E-mail: martin.orlob@alumnimail.utdallas.edu
Alexander Braun, E-mail: braun@utdallas.edu

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1. Impact Estimation and Filtering of Disturbances in FG5 Absolute Gravimeter Observations

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