In autumn 2007 the superconducting gravimeter GWR C025 was transferred from Vienna (VI) to the new Conrad observatory (CO) 60 km SW of Vienna. It is one of few instruments which were operated at different stations. This aspect motivated a reanalysis of all calibration experiments at VI and CO, focused on drift and noise effects. Considering the drift even of absolute gravimeters in a common adjustment reduces the root mean square error of the averaged calibration factor essentially. Also spring type gravimeters have some potential to contribute to the SG calibration factor determination. The calibration factor of GWR C025 did not significantly change during the transfer from VI to CO. The final calibration factor is calculated as weighted average over in total 9 JILAg and FG5 experiments with an accuracy of better than
Currently, the superconducting gravimeter (SG) is the most precise instrument for investigating temporal gravity variations both in the time and the frequency domain. SGs exhibit an extremely small instrumental drift that can be modeled by either a linear or exponential function of time [
Location of SG sites in Vienna (VI: 48.2489°N, 16.3565°E, 192.74 m a.s.l.) and Conrad observatory (CO: 47.9283°N, 15.8598°E, 1044.12 m a.s.l.) (maps modified after
The gravity time series in CO currently extends over more than 4 years and allows now safely comparing the tidal analysis results for VI and CO as well as validating the most recent body-tide models [
Presently, the most common method of SG calibration is based on colocated gravity observation by using absolute gravimeters (AG) [
The calibration method relies on the basic assumption, that observation errors follow a Gaussian distribution, and that both the SG and AG sensor experience exactly the same gravity variation. Actually, this assumption is never perfectly true, as the signal composition of both sensors differs due to following reasons (e.g., [ instrumental noise, ground noise response, spatial separation of both sensors, transfer function introducing different time lags, preprocessing filter response, response on air pressure variations (e.g., non-compensated Archimedean forces in spring gravimeters), instrumental drift.
Kroner [
Spatial separation of the SG and colocated gravimeter sensors.
Sensor separation (m) |
|
|||
---|---|---|---|---|
Horizontal | Vertical | |||
VI | FG5 | 2.1 | 0.98 | 0.186 |
JILAg | 2.1 | 0.68 | 0.139 | |
CG5 | 1.2 | −0.05 | 0.098 | |
| ||||
CO | FG5 | 3.4 | 0.98 | 0.051 |
JILAg | 3.4 | 0.68 | 0.050 | |
CG5 | 1.4 | −0.05 | 0.014 |
A systematic error arises when one or both sensors are influenced by instrumental drift [
A performance study by [
For calibration both different AGs and a well-calibrated Scintrex Autograv CG5 have been used. The calibration factor is calculated by linear adjustment of the gravity data acquired by the SG and the gravimeter used as reference (either the AG or the spring gravimeter). Acquisition and processing procedures are described in the following chapter.
The raw 1s SG data is filtered by convolution with the GGP filter g1s1m (
Three methods are applied in this study. In the first approach, each single AG drop is used. The corresponding SG data is extracted from the filtered 1s SG time series. The SG time lag is taken into account. Outliers are removed by applying either the
An alternate procedure, proposed for example, by [
This method is slightly changed in a third procedure. Both SG and AG data is averaged by applying a moving window. The window length corresponds to the duration of one AG drop set. Then the standard deviation of the AG residuals within each window is determined. Like in the second method, the scatter of the averaged gravity is drastically reduced compared with the drop-to-drop scatter, but the number of data pairs entering the adjustment remains comparable with that of the first method.
In this study, a commercial Scintrex CG5 Autograv has been used (SN 40236). This instrument has been carefully calibrated twice a year on the Hochkar calibration line (HCL). The latter is located within the Northern Calcareous Alps of Austria and covers a gravity difference of 1980
Repeated observations on HCL show that the CG5 scale factor varies linearly with time and decreased by 0.5‰ within 3.5 years (Figure
Scale factor determination of the Scintrex Autograv CG5, SN 40236. The grey and black dots refer to results taking only one specific gravity difference into account; the red triangles denote the results achieved by weighted averaging over all possible gravity differences along the Hochkar calibration line.
The Scintrex Autograv CG5 samples both gravity and tilt data with 6 Hz during a selectable time interval. The final gravity reading corresponds to the average over this interval (typically 1 or 2 min), automatically corrected for tilt effects. The filtered 1s SG data is extracted and averaged over the same period. Optionally the CG5 readings can also be corrected for the tides. However, the CG5 acquisition software stores all results with a limited resolution of 10 nms−2. Round off errors are produced later on, when the tides are restored, and affect the calibration result systematically. Therefore, this option is not recommendable for SG calibration. In this study, gravity measurements were performed in the auto-repeat mode with 2 min duration during a few months.
Calibration factor and drift function are determined in a common adjustment process as proposed by, for example, [
The AG drop-to-drop scatter of free fall observations depends on the typical site noise and consequently limits the calibration accuracy. Depending on the microseismic activity, the standard deviation of the AG residual typically varies between 50 and 300nms−2. The large ground noise in Vienna (VI) hampers achieving a calibration accuracy better than 2‰ for a single experiment. However, getting a reliable calibration factor for the VI time series is crucial for comparing tidal analysis results. Even in case of random noise, the calibration factor does not necessarily converge or does not converge to the correct number even when a high amount of data pairs is available. This is shown by the following study.
We use synthetic body tides as reference and compare with an identical time series to which Gaussian noise has been added. The noise-standard deviation was defined by multiplying the AG drop set standard deviations taken from a real calibration experiment by the factors 0.1, 1, 3, and 5, resulting to a noise sigma between 10 and 600nms−2. 25 data sets with different random noise models have been compiled for each multiplication factor. Similarly as in the calibration experiments, the 3 sigma criterion has been applied to remove outliers before the linear adjustment. Figure
(a) Regression factor for synthetic data sets which combine synthetic tides without and with random noise of different standard deviation. For each noise-standard deviation, 25 data sets have been compiled. Without noise, the regression factor would be equal to 1 as expected. This is not shown on the view graph for simplicity. (b) Maximum deviation of the resulting regression coefficients from the value expected for noise-free data in dependence on the noise-standard deviation and on the number of data pairs entering the adjustment.
This behavior is due to the fact, that the even rather large number of data pairs still violates the “law of large numbers” principle of statistics. Consequently, it obviously happens in some cases, that the noise is weakly correlated with the tidal signal. The error range (maximum of the absolute deviation from expectation) increases almost linearly with the noise standard deviation (Figure
Absolute gravimeters are obviously not free from systematic errors due to instrumental reasons. The drop set results generally should be randomly distributed, but often a systematic trend is visible in the residuals obtained by subtracting the tides and atmospheric effects while almost no trend is detectable in the SG record. Figure
Gravity residual (running average) of SG (red) and AG (blue) during the calibration experiment at Conrad observatory in December 2008 (GWR C025/JILAg-6, (a)) and in June 2011 (GWR C025/FG5 242, (b)). The difference (green) is used to model the drift (dashed line).
Drift effects like those presented in Figure
SG/AG comparison experiment at Conrad observatory in December 2008 (upper panels) and June 2011 (lower panels). (a) Calibration factor plotted against the number of data pairs used in the linear adjustment. No (black) or linear (red) drift has been adjusted. (b) Calibration factor (black) and RMS of the residual (grey) plotted against the polynomial degree selected for AG drift adjustment. The ±1‰ error range is displayed as grey box.
The situation is completely different for spring gravimeters because of their much stronger and irregular drift, which cannot be approximated simply by linear functions. In the following the calibration experiment performed at Conrad observatory between July 13, 2010 and September 22, 2010 is discussed, when the SG GWR C025 monitored site by site with a Scintrex Autograv CG5. Figure
SG/CG5 comparison experiment at Conrad observatory (July 13, 2010 to September 22, 2010). (a) Calibration factor plotted against the number of data pairs used in the adjustment and for different drift polynomials. As best choice, a drift polynomial of degree 8 has been selected (dashed red line). (b) Calibration factor (black) and RMS of the residual (grey) plotted against the polynomial degree selected for AG drift adjustment. The ±1‰ error range is displayed as grey box.
Since the SG GWRC025 has been operating in VI and CO, numerous calibration experiments have been performed, involving JILAg and FG5 absolute gravimeters as well as the Scintrex Autograv CG5 SN 40236. All results are presented in Figure
Calibration factors determined by adjusting colocated gravity observations with SG GWR C025 and FG5 (red dots), JILAg-6 (green dots), and Scintrex Autograv CG5 SN 40236 (blue dots). The differential drift of the reference gravimeter has been adjusted by polynomial functions. Dark grey dots indicate the results obtained for the zero drift assumption. The ±1‰ error range is displayed as grey box. The dotted lines indicate the calibration factors resulting from the CG5 (−779.1628 nms−2/V, blue) and AG (−779.4732 nms−2/V, red) experiments. (a) All calibration experiments performed in Vienna (VI) and Conrad observatory (CO). (b) Zoom of the experiments performed at Conrad observatory (CO).
Due to the high noise level at the VI station the calibration experiments using the JILAg type absolute gravimeter are much less accurate than those using FG5s in 2005 and 2006. Under low noise level conditions like at CO, both AG types provide a comparable accuracy. Tables
Weighted average
Vienna | |||||||
---|---|---|---|---|---|---|---|
Method | Single drop | ||||||
Outlier detection | 3 |
modified |
|
||||
|
|
|
|
|
|
||
FG5 + JILAg |
−779.5978 |
0.5272
|
2.3008
|
−779.6254 |
0.5278
|
2.4234 |
6 |
FG5 + JILAg |
−779.6828 |
0.5272
|
2.8414
|
−779.7127 |
0.5278
|
2.8677 |
6 |
| |||||||
Vienna | |||||||
Method | Set mean | Running average | |||||
Outlier detection | modified |
modified |
|
||||
|
|
|
|
|
|
||
| |||||||
FG5 + JILAg |
−779.7295 |
7.0139
|
2.3820
|
−779.5454 |
0.5297
|
2.7151
|
6 |
| |||||||
Conrad observatory | |||||||
Method | Single drop | ||||||
Outlier detection | 3 |
modified |
|
||||
|
|
|
|
|
|
||
| |||||||
CG5 |
|
0.2295 |
0.5392 |
10 | |||
FG5 + JILAg |
−779.4676 | 0.1774 |
0.5268 |
−779.4566 | 0.1746 |
0.3721 |
7 |
FG5 + JILAg |
−779.6434 | 0.1774 |
1.0058 |
−779.6230 | 0.1746 |
0.9890 |
7 |
| |||||||
Conrad observatory | |||||||
Method | Set mean | Running average | |||||
Outlier detection | modified |
modified |
|
||||
|
|
|
|
|
|
||
| |||||||
FG5 + JILAg |
−779.4982 |
1.9087
|
0.3584
|
−779.4620 |
0.1756
|
0.3875 |
7 |
Weighted average
VI + CO | |||||||
---|---|---|---|---|---|---|---|
Method | Single drop | ||||||
Outlier detection | 3 |
modified |
|
||||
|
|
|
|
|
|
||
FG5 + JILAg since 2005 |
−779.4537 |
0.1692
|
0.5432
|
|
0.1667
|
0.4476
|
9 |
FG5 + JILAg since 2005 |
−779.6221 |
0.1692
|
0.9255
|
−779.6055 |
0.1667
|
0.9161
|
9 |
Both tables present the weighted average of the calibration factor
The difference between the mean calibration factors obtained with and without common AG drift adjustment amounts to about 0.6‰ at CO. Also the rms deviation
The difference between the results (modified
The results obtained by colocated observation with the Scintrex Autograv CG5 SN 40236 fit very well to those obtained by AGs (difference: 0.38‰). In particular, they do not indicate a significant change of the calibration factor, which might be caused by the transfer from VI to CO. The result shows also, that even spring gravimeters can support valuable information on the SG calibration factor provided they are carefully calibrated and their irregular drift is properly modeled in the adjustment process.
The SG phase calibration has been performed by applying the step response method [
Time lag of the SG GWR C025 at stations VI and CO.
Site | VI | CO | |||
---|---|---|---|---|---|
Date | 1995 08 | 1997 09 | 1999 12 | 2004 04 | 2007 11 |
Time lag (s) | 16.995 | 9.345 | 10.040 | 9.131 | 8.702 |
Error (s) | 0.005 | 0.027 | 0.047 | 0.066 | 0.026 |
Before tidal analysis, spikes and short-term disturbances present in the 1 Hz raw SG data (e.g., due to earthquakes or maintenance) were carefully removed by applying the software packages ETERNA v3.4 [
Table
Tidal analysis results of the VI and CO gravity time series corrected for ocean load based on load vectors provided by [
Ocean model | CO | VI | Difference CO-VI | |||
---|---|---|---|---|---|---|
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| |
No corr. |
|
|
|
|
|
|
CSR4.0 | 1.15319 | −0.0186 | 1.15315 | −0.0131 | 0.00004 | −0.0055 |
DTU10 | 1.15322 | −0.0217 | 1.15316 | −0.0149 | 0.00006 | −0.0068 |
EOT11a | 1.15330 | −0.0219 | 1.15324 | −0.0151 | 0.00006 | −0.0068 |
FES2004 | 1.15369 | −0.0040 | 1.15364 | 0.0029 | 0.00005 | −0.0069 |
GOT00.2 | 1.15341 | −0.0139 | 1.15338 | −0.0081 | 0.00003 | −0.0058 |
HAMTIDE | 1.15359 | −0.0120 | 1.15354 | −0.0054 | 0.00005 | −0.0066 |
TPXO.7.2 | 1.15347 | −0.0098 | 1.15343 | −0.0050 | 0.00004 | −0.0048 |
Ave |
|
|
|
|
|
|
Stddev | 0.00019 | 0.0066 | 0.00019 | 0.0066 | 0.00001 | 0.0008 |
Max–min | 0.00050 | 0.0179 | 0.00049 | 0.0180 | 0.00003 | 0.0021 |
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Ocean model | CO | VI | Difference CO-VI | |||
|
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| |
| ||||||
No corr. |
|
|
|
|
|
|
CSR4.0 | 1.16224 | 0.0256 | 1.16217 | 0.0334 | 0.00007 | −0.0078 |
DTU10 | 1.16193 | 0.0244 | 1.16187 | 0.0294 | 0.00006 | −0.0050 |
EOT11a | 1.16212 | 0.0074 | 1.16205 | 0.0123 | 0.00007 | −0.0049 |
FES2004 | 1.16310 | 0.0403 | 1.16301 | 0.0469 | 0.00009 | −0.0066 |
GOT00.2 | 1.16192 | 0.0125 | 1.16182 | 0.0194 | 0.00010 | −0.0069 |
HAMTIDE | 1.16206 | 0.0041 | 1.16195 | 0.0110 | 0.00011 | −0.0069 |
TPXO.7.2 | 1.16174 | 0.0030 | 1.16161 | 0.0128 | 0.00013 | −0.0098 |
Ave |
|
|
|
|
|
|
Stddev | 0.00045 | 0.0138 | 0.00045 | 0.0135 | 0.00003 | 0.0017 |
Max–min | 0.00136 | 0.0373 | 0.00140 | 0.0359 | 0.00007 | 0.0049 |
The averaged amplitude factors rather fit better to the nonhydrostatic models DDW/NHi [
Comparison of the corrected amplitude factor (average over all ocean models applied at VI and CO) with the DDW [
DDW/H [ |
DDW/NHi [ |
MAT01/NH [ |
WEN [ |
Ave (CO, VI) | Dev DDW/H | Dev DDW/NHi | Dev MAT01/NH | |
---|---|---|---|---|---|---|---|---|
|
1.1528 | 1.1543 | 1.1540 | 1.1534 | 1.1534 | 0.0006 | −0.0009 | −0.0006 |
|
1.1324 | 1.1345 | 1.1349 | 1.1353 | 1.1351 | 0.0027 | 0.0006 | 0.0002 |
|
1.1605 | 1.1620 | 1.1616 | 1.1621 | 1.1621 | 0.0016 | 0.0001 | 0.0005 |
The scatter of the calibration factors derived from single experiments (Figure
(a) Tidal analysis results from overlapping 1-year interval (black dots: amplitude factor, blue dots: phase). Ocean load correction [
The air pressure admittance factor is systematically higher at CO (−3.35 nms−2/hPa) than in VI (−3.54 nms−2/hPa). Because the distance between both stations is small (about 60 km), the deformation part is expected to be similar at both sites. However, the Newtonian part is different, as both stations are located in different altitudes (VI: 190 m, CO: 1045 m). The admittance factors differ by 0.19 nms−2/hPa roughly. This number matches fairly well the Newtonian effect due to the elevation difference calculated in flat approximation for a hydrostatic atmosphere.
The amplitude factors of O1 and M2 do not vary consistently, that is, the correlation is not significant on the 95% confidence level. The overall variation is as small as less than ±0.2‰. In contrast, the phases of O1 and M2 show a statistically significant correlation (Figure
Temporal variation of the regression factor and the time lag obtained by adjusting synthetic tides based on tidal parameters obtained from 1-year interval analyses to synthetic body tides using tidal parameters obtained from analyzing the entire time series.
By this way, time dependant regression factors and time lags are obtained that can be interpreted as temporal calibration factor variation provided the tidal parameters are assumed not to change with time. Of course, this is not necessarily a valid assumption. Figure
For spring type gravimeters it is mandatory to consider the irregular drift in the adjustment of the calibration factor. The calibration experiments performed in VI and CO show, that even the drift of the AG should be considered in a common adjustment of the calibration factor. Though the systematic effect is small, the root mean square error of the averaged calibration factor is essentially reduced. Calibration results are biased not only by drift effects, but also by even random noise which limits the accuracy of the calibration experiment. Therefore the calibration experiment should be repeated several times. Spring type gravimeters have some potential to contribute to the SG calibration factor determination provided the drift is carefully modeled, for example, by higher degree polynomial functions, and the spring gravimeter is accurately calibrated. The dependence of the root mean square error of the adjustment on the polynomial degree of the drift function may serve as selection criterion for an appropriate drift model.
The reanalysis of the calibration experiments performed in VI and CO proves that the calibration factor of GWR C025 remained unchanged during the transfer from VI to CO. The SG/CG5 experiments fully support this statement and turn out to be a valuable extension to the SG/AG comparisons. A final calibration factor has been calculated as weighted average over in total 9 JILAg and FG5 experiments. Based on the root mean square deviation from the average, the accuracy estimate amounts to 0.5‰, while the formal error of the calibration factor is even smaller (0.2‰). The calibration factor turns out to be temporarily stable. A regression analysis shows that temporal variations, if present, are below ±0.1‰.
The reanalysis of the calibration experiments enables a direct comparison of the tidal parameters obtained in VI and CO. The amplitude factors O1, K1, and M2 agree almost perfectly after correcting for ocean loading effects and fit closely to the nonhydrostatic body tide models calculated by [
Close cooperation with ZAMG (Austria), the owner of Conrad observatory, and the GWR C025, are gratefully acknowledged as well as all the efforts of the operators of the JILAg and FG5 absolute gravimeters D. Ruess, Ch. Ullrich (both BEV, Vienna), O. Francis (University of Luxembourg), and V. Pálinkáš (Research Institute of Geodesy, Topography and Cartography, Department of Geodesy and Geodynamics). Two anonymous reviewers made valuable suggestions improving the paper. The author of the paper has no direct financial relations with the commercial identities mentioned in the paper that might lead to a conflict of interest for the author.