One of the most important operating procedures after the installation of a superconducting gravimeter (SG) is its calibration. The calibration process can identify and evaluate possible time variability in the scale factor and in the hardware anti-aliasing filter response. The SG installed in Cantley, Canada is calibrated using two absolute gravimeters and the data are analysed in the time and frequency domains to estimate the SG scale factor. In the time domain, we use the weighted linear regression method whereas in the frequency domain we use the least squares response method. Rigorous statistical procedures are applied to define data disturbances, outliers, and realistic data noise levels. Using data from JILA-2 and FG5-236 separately, the scale factor is estimated in the time and frequency domains as ？μGal/V and ？μGal/V, respectively. The relative accuracy in the time domain is 0.015%. We cannot identify any significant periodicity in the scale factor. The hardware anti-aliasing filter response is tested by injecting known waves into the control electronics of the system. Results show that the anti-aliasing filter response is stable and conforms to the global geodynamics project standards. 1. Introduction and Background Nowadays, most systems and devices are controlled by digital computers where digital output is the norm. The superconducting gravimeter (SG) is no exception; its output is digitized by an A/D converter. The SG is a relative gravimeter and must be calibrated accurately to estimate its scale factor before further use of its records and data interpretation. The voltage output from the SG has no physical meaning until it is converted to the proper units of Gal by using specific calibration techniques. Therefore, physical experiment or externally induced acceleration can be used to represent or simulate the input or the physics (gravity changes) behind this voltage variation. Reference [1] reported that a highly accurate scale factor is essential to constrain mantle anelasticity. In [2], it is mentioned that an accurate scale factor is needed, for ocean tide loading, removal of synthetic tide, and amplitude determination of the Earth's normal modes in the sub-seismic band. To meet the above-mentioned application requirements, it is very important to estimate the scale factor with relative accuracy of less than 0.1% [3]. However, it is really a challenge to calibrate a device using another one, which is much less precise: the absolute gravimeter (AG) precision is at the Gal level while the SG is at the nGal level. In other words, the SG
References
[1]
T. Sato, M. Ooe, K. Nawa, K. Shibuya, Y. Tamura, and K. Kaminuma, “Long-period tides observed with a superconducting gravimeter at Syowa Station, Antarctica, and their implication to global ocean tide modeling,” Physics of the Earth and Planetary Interiors, vol. 103, no. 1-2, pp. 39–53, 1997.
[2]
J. Hinderer, D. Crossley, and R. Warburton, “Superconducting gravimetry,” in Treatise on Geophysics, T. Herring and G. Schubert, Eds., vol. 3, Elsevier, Amsterdam, The Netherlands, 2007.
[3]
J. Hinderer, N. Florsch, J. Makinen, H. Legros, and J. E. Faller, “On the calibration of a superconducting gravimeter using absolute gravity measurements,” Geophysical Journal International, vol. 106, no. 2, pp. 491–497, 1991.
[4]
M. Amalvict, J. Hinderer, J. Boy, and P. Gegout, “A three year comparison between a superconducting gravimeter (GWR C026) and an absolute gravimeter (FG5 206) in Strasbourg (France),” Journal of the Geodetic Society of Japan, vol. 47, pp. 410–416, 2001.
[5]
O. Francis, “Calibration of the C021 superconducting gravimeter in membach (Belgium) using 47 days of absolute gravity measurements, gravity, geoid and marine geodesy,” in Proceedings of the International Association of Geodesy Symposia, vol. 117, pp. 212–219, 1997.
[6]
O. Francis and T. Van Dam, “Evaluation of the precision of using absolute gravimeters to calibrate superconducting gravimeters,” Metrologia, vol. 39, no. 5, pp. 485–488, 2002.
[7]
O. Francis, T. M. Niebauer, G. Sasagawa, F. Klopping, and J. Gschwind, “Calibration of a superconducting gravimeter by comparison with an absolute gravimeter FG5 in Boulder,” Geophysical Research Letters, vol. 25, no. 7, pp. 1075–1078, 1998.
[8]
T. Sato, Y. Tamura, S. Okubo, and S. Yoshida, “Calibration of scale factor of superconducting gravimeter at Esashi using an absolute gravimeter FG5,” Journal of the Geodetic Society of Japan, vol. 42, pp. 225–232, 1996.
[9]
M. Amalvict, H. McQueen, and R. Govind, “Absolute gravity measurements and calibration of SG-CT031 at Canberra, 1999-2000,” Journal of the Geodetic Society of Japan, vol. 47, pp. 334–340, 2001.
[10]
Y. Imanishi, T. Higashi, and Y. Fukuda, “Calibration of the superconducting gravimeter T011 by parallel observation with the absolute gravimeter FG5 #210—a Bayesian approach,” Geophysical Journal International, vol. 151, no. 3, pp. 867–878, 2002.
[11]
Y. Tamura, T. Sato, Y. Fukuda, and T. Higashi, “Scale factor calibration of a superconducting gravimeter at Esashi Station, Japan, using absolute gravity measurements,” Journal of Geodesy, vol. 78, no. 7, pp. 481–488, 2004.
[12]
R. Falk, M. Harnisch, G. Harnisch, I. Nowak, B. Richter, and P. Wolf, “Calibration of superconducting gravimeters SG103, C023, CD029, and CD030,” Journal of the Geodetic Society of Japan, vol. 47, no. 1, pp. 22–27, 2001.
[13]
R. Warburton, C. Beaumont, and J. Goodkind, “The effect of ocean tide loading on tides of the solid earth observed with the superconducting gravimeter,” Geophysical Journal of the Royal Astronomical Society, vol. 43, pp. 707–720, 1975.
[14]
V. Achilli, P. Baldi, G. Casula et al., “A calibration system for superconducting gravimeters,” Bulletin Géodésique, vol. 69, no. 2, pp. 73–80, 1995.
[15]
B. Richter, “Calibration of superconducting gravimeters,” in Proceedings of the Workshop on Non Tidal Gravity Changes Intercomparison between Absolute and Superconducting Gravimeters, vol. 3, pp. 99–107, Conseil de l'Europe, Cahiers du Centre Europeen de Geodynamique et de Seismologie, Luxembourg, 1991.
[16]
D. Bower, J. Liard, D. Crossley, and R. Bastien, “Preliminary calibration and drift assessment of the superconducting gravimeter GWR12 through comparison with absolute gravimeter JILA2,” in Proceedings of the Workshop on Non Tidal Gravity Changes Intercomparison between Absolute and Superconducting Gravimeters, vol. 3, pp. 129–142, Conseil de l'Europe, Cahiers du Centre Europeen de Geodynamique et de Seismologie, Luxembourg, 1991.
[17]
J. Merriam, S. Pagiatakis, and J. Liard, “Reference level stability of the Canadian superconducting gravimeter installation,” Journal of the Geodetic Society of Japan, vol. 47, no. 1, pp. 417–423, 2001.
[18]
M. Abd El-Gelil, S. Pagiatakis, and A. El-Rabbany, “Frequency-dependent atmospheric pressure admittance of superconducting gravimeter records using least squares response method,” Physics of the Earth and Planetary Interiors, vol. 170, no. 1-2, pp. 24–33, 2008.
[19]
P. Vaní？ek, “Approximate spectral analysis by least-squares fit—successive spectral analysis,” Astrophysics and Space Science, vol. 4, no. 4, pp. 387–391, 1969.
[20]
P. Vaní？ek, “Further development and properties of the spectral analysis by least-squares,” Astrophysics and Space Science, vol. 12, no. 1, pp. 10–33, 1971.
[21]
M. Craymer, The least squares spectrum, its inverse transform and autocorrelation function: theory and some applications in geodesy [Ph.D. thesis], University of Toronto, Toronto, Canada, 1998.
[22]
S. D. Pagiatakis, “Stochastic significance of peaks in the least-squares spectrum,” Journal of Geodesy, vol. 73, no. 2, pp. 67–78, 1999.
[23]
S. Pagiatakis, “Application of the least-squares spectral analysis to superconducting gravimeter data treatment and analysis,” in Proceedings of the workshop on High precision gravity measurements with application to geodynamics and Second GGP, vol. 17, pp. 103–113, Cahiers Du Centre Europeen De Geodynamique et de Seismologie (ECGS), 2000.
[24]
P. Vaní？ek, Geodesy: The Concepts, North Holland, Amsterdam, The Netherlands, 1986.
[25]
H. Yin and S. Pagiatakis, “Least squares spectrum analysis and its application to superconducting gravimeter data analysis,” Geo-Spatial Information Science, vol. 7, no. 4, pp. 279–283, 2004.
[26]
S. D. Pagiatakis, H. Yin, and M. A. El-Gelil, “Least-squares self-coherency analysis of superconducting gravimeter records in search for the Slichter triplet,” Physics of the Earth and Planetary Interiors, vol. 160, no. 2, pp. 108–123, 2007.
[27]
R. V. Hogg and A. T. Craig, Introduction to Mathematical Statistics, Prentice-Hall, Upper Saddle River, NJ, USA, 6th edition, 2005.
[28]
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover Publications, 1965.
[29]
J. B. Merriam, “An ephemeris for gravity tide predictions at the nanogal level,” Geophysical Journal International, vol. 108, no. 2, pp. 415–422, 1992.
[30]
M. Van Camp, H. G. Wenzel, P. Schott, P. Vauterin, and O. Francis, “Accurate transfer function determination for superconducting gravimeters,” Geophysical Research Letters, vol. 27, no. 1, pp. 37–40, 2000.
