Journal of Geodynamics 41 (2006) 14–22
Precise tidal measurements by spring gravimeters
at the station Pecný
Vojtech Pálinkáš ∗
Research Institute of Geodesy, Topography and Cartography, Geodetic Observatory Pecný, 25165 Ondřejov 244, Czech Republic
Accepted 30 August 2005
Abstract
The tidal measurements at the Geodetic Observatory Pecný began in 1970. After continuous methodological and instrumental
improvements new gravity tide records have been made by the LaCoste & Romberg G No. 137 (LCR 137) equipped with the
maximum voltage retroaction (MVR) feedback and by Askania Gs 15 No. 228 (ASK 228) equipped with an electromagnetic
feedback in the refurbished tidal laboratory Pecný since August 2002. The standard deviation of the observed hourly ordinate was
0.6 nm/s2 and 2.0 nm/s2 , respectively.
The air temperature and relative humidity are stabilized within the range of 0.2 ◦ C and 3%, respectively, during a year. A significant
linear correlation between the gravimeter drift of the LCR 137 and the humidity was found from experimental investigations of the
temperature and humidity effects on this instrument.
The repeated absolute gravity measurements with the FG5 No. 215 gravimeter at the observatory Pecný were used for computing
calibration factors of the tidal gravimeters ASK 228 and LCR 137. From 3-day simultaneous measurements during tidal variations
of about 2.5 ␮m/s2 the calibration coefficients were determined with a precision of 0.05%. The scales of the tidal gravimeters were
determined from 28 absolute campaigns with the accuracy of 0.04%.
© 2005 Elsevier Ltd. All rights reserved.
Keywords: Tidal gravimeters; FG5; Calibration; Humidity
1. Introduction
In present, the most precise tidal gravimetric measurements are collected using superconducting gravimeters (SG).
Of course, spring gravimeters due to their availability are still used at many tidal stations. Results of measurements
by this “old technology” cannot be considered as unimportant. Precision of tidal parameters for diurnal and semidiurnal frequencies determined from measurements of spring gravimeters can be better than precision of older types of
superconducting gravimeters (Ducarme et al., 2002). Results of these measurements are important in many cases, e.g.:
• Accurate determination of the gravimetric earth tide correction. Tidal corrections have to be determined with the
accuracy better than 5 nm/s2 mainly for precise absolute gravity measurements when the measurements do not cover
uniformly a whole day.
∗
Tel.: +420 323 649 235; fax: +420 323 649 236.
E-mail address: [email protected].
0264-3707/$ – see front matter © 2005 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jog.2005.08.013
V. Pálinkáš / Journal of Geodynamics 41 (2006) 14–22
15
• Testing of various body tide and ocean tide models.
• Time variations of the tidal signal due to tectonic processes.
The use of results depends on correct determination of the scale of tidal records which should have relative accuracy
better than 0.1%. The most frequent method for calibration of spring gravimeter records is the calibration with the help
of their measuring screw. This method is characteristic by high precision but it can often be affected by systematic
errors. Thanks to the absolute gravimeter FG5 No. 215, the results of screw calibrations were compared with results of
the absolute gravimeter (AG) calibration at the station Pecný. The method based on parallel records of the AG and tidal
gravimeters is mainly used for calibration of SG records. This method naturally can be used also for spring gravimeters
where more or less-regular gravimeter drift than for the SG must be considered.
2. Tidal station Pecný
The tidal station Pecný is located in the hilly region in the central part of the Bohemian Massif in Central Europe.
From the geological point of view this region is very stable. The first tidal measurements at the Pecný station were
made with the Askania Gs 11 No. 131 gravimeter in 1970. In the catalogue of the International Centre of the Earth
Tides the station has the number 0930.
Today two continually recording gravimeters operate at the station. The main instrument, which has been operated
here since 1975, is the gravimeter Askania Gs 15 No. 228 (ASK 228). In 2000, this instrument was equipped with a
digital electromagnetic feedback system (Brož et al., 2002). This digital feedback system does not cause any disturbing
heating effects. The instrumental phase lag of ASK 228 is 0 s at tidal frequencies. Next advantage of the ASK 228 is
a very stable calibration factor which has not changed since 2000. The sampling rate of 25 Hz of the feedback signal
is resampled to 5 s and 1 min averages. The second instrument operated at the station since 2001 is the gravimeter
LaCoste & Romberg G No. 137 (LCR 137). This instrument is equipped with an electrostatic feedback maximum
voltage retroaction (MVR) (van Ruymbeke, 1989) which is characterized by strong damping of the output signal
(instrumental phase lag is 41 s at tidal frequencies) and, unfortunately, by an unstable calibration factor (Pálinkáš,
2003). The sampling rate of the feedback signal is 1 Hz.
Besides feedback signals from the gravimeters the following data are also recorded:
• tilt of the gravimeters;
• air pressure, temperature and relative humidity at the station;
• meteorological and hydrological parameters like precipitation, height of the ground water level and soil moisture
near to the station.
The results presented below refer to the tidal observations carried out in the refurbished tidal laboratory since
September 2002. The main benefit of the improvement is a control of the relative air humidity at the station. The
humidity is kept on the level of 40% with a precision of ±1% using a dryer–humidifier system, see Fig. 1. The
Fig. 1. Temperature and relative humidity variations at the station Pecný.
V. Pálinkáš / Journal of Geodynamics 41 (2006) 14–22
16
temperature is controlled by a contact thermometer, air conditioning device and heating fans to 28 ◦ C with a precision
of ±0.1 ◦ C.
3. Calibration
Two methods are used for calibration of the tidal gravimeter records at the Pecný station. The first method is the
calibration with the help of measuring screws and the second one is the calibration by comparison with simultaneous
absolute gravity measurements (Hinderer et al., 1998), (Francis and van Dam, 2002).
3.1. Calibration with the help of measuring screw
The scales of measuring screws of the LCR 137 and ASK 228 were determined by calibration measurements on the
Czech national main calibration line (gravity difference of 3.1 mm/s2 ).
The calibration of the ASK 228 is based on step changes of the feedback signal caused by resetting the measuring
screw by about 50 ␮m/s2 (Brož et al., 2002). Since 2000, when the ASK 228 was equipped with a feedback system,
the calibration factor has been represented by the relation:
bM = 3.2932 ± 0.0005 nm/s2 /DU
(DU, digital unit).
The calibration method of the LCR 137 is based on re-settings of the micrometric screw of the gravimeter in the range
of 2 CU (1 CU = 1 rotation of the Model G dial) with steps of 0.2 CU every 5 min for the first time in clock-wise and for
the second time in counter clock-wise direction with backlash compensation (Pálinkáš, 2003). During the calibration
procedure 22 measured values from feedback system is collected. The feedback calibration function is approximated
by a third-order polynomial the coefficients of which change with time. The variation of the linear calibration term
since September 2002 is shown in Fig. 2. The time variations of the quadratic and cubic terms are within the range of
35 × 10−6 to 50 × 10−6 nm/s2 /DU2 and −20 × 10−9 to 20 × 10−9 nm/s2 /DU3 , respectively.
3.2. Calibration by comparison with absolute gravity measurements
The absolute gravimeter FG5 No. 215 has been used for repeated AG measurements at the Geodetic Observatory
Pecný since August 2001 (Pálinkáš and Kostelecký, 2003). Till June 2004 altogether 56 AG measurements with
minimum duration 24 h (100–150 drops per hour) were carried out at this absolute station. The calibration factors of
the tidal gravimeters ASK 228 and LCR 137 were computed from 26 and 23 repeated AG measurements, respectively.
It represents the total of 43 days of simultaneous measurements for ASK 228 and 36 days for LCR 137. The calibration
factor bA (nm/s2 /DU) was determined from the regression line
yi = a + b A x i ,
(1)
Fig. 2. Variation of the linear calibration term of the LCR 137.
V. Pálinkáš / Journal of Geodynamics 41 (2006) 14–22
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Table 1
Results of AG calibrations of the LCR 137 and ASK 228 for minimum 2-day simultaneous measurements
Date
Duration (day)
28 January 2002
8 August 2002
5 December 2002
15 June 2003
26 November 2003
20 January 2004
3 June 2004
5.9
3.2
2.0
3.3
3.0
2.4
2.6
Tidal var.
(␮m/s2 )
2.49
2.33
2.42
2.53
2.60
2.54
2.62
LCR 137
bA
(nm/s2 /DU)
–
10.1361
10.0443
9.9944
9.9748
9.9654
–
ASK 228
σ(bA )
(nm/s2 /DU)
–
0.0051
0.0060
0.0050
0.0050
0.0050
–
bA (nm/s2 /DU)
σ(bA ) (nm/s2 /DU)
3.2975
3.2988
3.3010
3.2928
3.3036
3.3015
3.3040
0.0019
0.0016
0.0020
0.0017
0.0016
0.0016
0.0015
where
• yi (nm/s2 ) is the free-fall acceleration measured by the FG5 No. 215 corrected for the effects of the atmospheric pressure variations (using regression coefficient −3.0 nm/s2 /hPa) and polar motion (using International Earth Rotation
and Reference System Service data) in which no tidal corrections are applied,
• xi (DU) is the corresponding output value from the feedback of a relative gravimeter at the moment of i-th free fall
including corrections for atmospheric pressure variations (using regression coefficients from tidal analysis), for the
tilt and for instrumental drift which includes also the effect of the polar motion. The instrumental drift was computed
from the residual curve of the gravimeter record (corrected for tides and air pressure variations) for of about 2 days
longer period than duration of absolute measurements.
Results of AG calibrations of the LCR 137 and ASK 228 for minimum 2-day simultaneous measurements are in
Table 1. From these results we can conclude that from 3-day simultaneous measurements carried out during tidal
variations of about 2.5 ␮m/s2 the calibration factors can be determined with a precision of 0.05%. Unfortunately, this
high precision describe only a formal error of the calibration method. The calibration accuracy have to be determined
from the dispersion between repeated AG calibrations.
The evolution of the AG calibration results for the ASK 228 is shown in Fig. 3. Considering the stable calibration
factor of the ASK 228, results of simultaneous observations prior the analyzed period (September 2002–April 2004)
were also used. Weights of individual AG calibrations were computed by the expression wi = 1/σ(bA )2 , where σ(bA )
is the standard deviation of the calibration factor computed from Eq. (1). The weighted mean of the calibration factor
of the ASK 228 is
bM = 3.2990 ± 0.0012 nm/s2 /DU.
Fig. 3. Evolution of ASK 228 calibration factors determined using absolute gravity measurements. The error bars represent the precision characterised
by standard deviation of the calibration factor computed from Eq. (1). The highlighted results were obtained from minimum 2-day simultaneous
measurements.
V. Pálinkáš / Journal of Geodynamics 41 (2006) 14–22
18
Fig. 4. Differences between calibration
factors determined using absolute gravity measurements bA and screw calibration bM for LCR 137. The
error bars represent the precision 100 σ(bA )2 + σ(bM )2 /bM in percent, where σ(bA ) and σ(bM ) are the precision of AG and screw calibration,
respectively. The highlighted results were obtained from minimum 2-day simultaneous measurements.
It means that the relative difference between calibration factors estimated from the AG and screw calibration is
0.176 ± 0.039%.
The application of the AG calibration results for the LCR 137 differed from those of the ASK 228 due to a
varying sensitivity of the MVR feedback system. The adjusted calibration function of the LCR 137, see Fig. 2, was
determined from results of highly-precise screw calibrations. Objects of the final computation were the differences
between calibration factors computed from this function and from the AG calibration, see Fig. 4. Weights of these
differences were computed from the relation wi = 1/(σ(bA )2 + σ(bM )2 ), where σ(bM ) = 0.004 nm/s2 /DU is the precision
of the screw calibration. The weighted mean of differences between the calibration factors bA and bM for the LCR 137
is
bA − bM = 0.035 ± 0.040%.
The achieved calibration accuracy of about 0.04% for both tidal gravimeters is an important result of the AG
calibrations. This high accuracy was achieved using 43-day simultaneous measurements for the ASK 228 and 36-day
measurements for the LCR 137 during tidal variations of at least 1.7 ␮m/s2 . The relation between accuracy (computed
from the dispersion of individual AG calibrations) and precision (formal error computed from Eq. (1)) was estimated
by the factor 2.2. From this result we can assume that the required calibration accuracy of 0.1% can be achieved from
two 3-day absolute campaigns with the FG5 No. 215 during tidal variations of about 2.5 ␮m/s2 at the station Pecný.
4. Tidal analysis
The tidal analysis was carried out by the program ETERNA 3.4 (Wenzel, 1996) for the period September 2002–April
2004. The results of tidal analysis are in Table 2. For O1, K1 and M2 waves, the agreement is better than 0.05% and 0.05◦
for both gravimeters. The most important discrepancy between the tidal waves was found for S2, where the difference
is 0.15% for the delta factor and 0.11◦ for the phase lag. The air pressure regression coefficients of −3.0 nm/s2 /hPa
for LCR 137 and of −4.8 nm/s2 /hPa for ASK 228 demonstrate a good air pressure compensation for both gravimeters.
High precision of both tidal gravimeters is evident from standard deviation of the observed hourly ordinate that is better
than precision of older type of superconducting gravimeters.
Results of the tidal analysis for measurements with the ASK 228 and LCR 137 at the station Pecný since 1976
are in Table 3. The increase of amplitude factors of about 0.15% for the period September 2002–April 2004 is
evident from a comparison of results in Table 3. This change is obvious mainly from results achieved since 1997
when the ASK 228 was equipped by the feedback system. The reason of this amplitude factor increase is the
change of the calibration method for the ASK 228 since 2002. The detected difference of 0.18% between the
AG and screw calibration had to increase the amplitude factors. We can suppose, that the tidal measurements carried out till 2002 with the ASK 228 equipped with the feedback system are affected by the calibration error of
about 0.18%.
Table 2
Results of tidal measurements (September 2002–April 2004) at the station Pecný
V. Pálinkáš / Journal of Geodynamics 41 (2006) 14–22
19
20
Table 3
Comparison of the results of tidal measurements with ASK 228 and LCR 137 at the station Pecný
ASK 228
analog
–
ASK 228
digital
–
ASK 228
digital
analog
ASK 228
digital
digital
ASK 228
digital
digital
LCR 137
digital
MVR
Period
Days
Analysis
Calibration
76 04–95 03
4555
ETERNA 2.1
screw
95 12–96 09
284
ETERNA 3.20
screw
97 10–99 01
412
ETERNA 3.20
screw
00 04–02 03
671
ETERNA 3.20
screw
02 09–04 04
551
ETERNA 3.40
AG
02 09–04 04
522
ETERNA 3.40
AG
δ ± σδ
κ ± σκ
δ ± σδ
κ ± ␴␬
δ ± σδ
κ ± σκ
δ ± σδ
κ ± σκ
δ ± σδ
κ ± σκ
δ ± σδ
κ ± σκ
1.1479
2
−0.01
0.01
1.1491
2
0.09
0.01
1.1490
1
0.09
0.01
1.1482
1
0.13
0.00
1.1503
2
0.12
0.01
1.1500
1
0.10
0.00
K1
1.1348
2
0.06
0.01
1.1354
1
0.18
0.01
1.1364
1
0.15
0.00
1.1351
0
0.16
0.00
1.1375
1
0.19
0.01
1.1370
1
0.15
0.00
M2
1.1849
2
1.03
0.01
1.1839
1
1.22
0.01
1.1840
1
1.20
0.00
1.1827
1
1.22
0.00
1.1853
1
1.23
0.01
1.1846
1
1.21
0.00
S2
1.1798
3
0.14
0.01
1.1807
2
−0.04
0.01
1.1799
2
−0.01
0.01
1.1771
1
0.08
0.01
1.1802
3
−0.01
0.01
1.1820
1
0.10
0.01
Wave
O1
σ (nm/s2 )
4.74
1.49
0.91
0.99
1.96
0.63
V. Pálinkáš / Journal of Geodynamics 41 (2006) 14–22
Gravimeter
Record
Feedback
V. Pálinkáš / Journal of Geodynamics 41 (2006) 14–22
21
Fig. 5. Relative air humidity and gravimeter drift variations.
5. Gravimeter drift versus relative air humidity
Stabilization of climatic conditions at a tidal station is necessary for achieving high precision tidal measurements.
First and often the last step is the stabilization of the air temperature. The relative air humidity is an important parameter
which is often neglected. The correlations between the relative air humidity and gravimeter drift were detected at
different tidal stations (El Wahabi et al., 2000, 2001).
The effects of the relative air humidity changes for the LCR 137 and ASK 228 were studied during their re-installation
in the refurbished tidal station Pecný. After the humidity change of about 25% the temperature was stabilised with the
precision of 0.2 ◦ C. The relative air humidity and the drift of both gravimeters (derivation of residuals) can be seen from
Fig. 5. The linear correlation between the drift of the LCR 137 and the relative air humidity is evident. The regression
coefficient is 9.38 ± 0.005 nm/s2 /day/% and the correlation coefficient is 0.98. No time delay between the response of
the gravimeter drift to the humidity change was found. The humidity change is followed by a drift change within 2 h.
A similar correlation between the drift of the ASK 228 and the humidity change was not found. Different responses
of both gravimeters to the humidity changes are probably caused by different construction types of gravimeters and of
their feedback systems.
Stabilization of the relative humidity for diurnal and semi-diurnal frequencies is the most important for the LCR
137. Possible humidity variations at these frequencies can affect the result of tidal measurements.
6. Conclusion
The calibration of tidal records is of primary importance for high-quality tidal measurements. The calibration
accuracy of about 0.04% was obtained at the station Pecný by comparison of tidal records with simultaneous absolute
gravity measurements by the FG5 No. 215. This high accuracy (computed from the dispersion of individual AG
calibrations) was achieved from 43 days of simultaneous measurements for the ASK 228 and 36 days for the LCR
137 during tidal variations of at least 1.7 ␮m/s2 . We can assume that the required calibration accuracy of 0.1% can be
achieved from two 3-day absolute campaigns during tidal variations of about 2.5 ␮m/s2 with the precise FG5 gravimeter
at the quite station like Pecný. The calibration based on the AG measurements is very useful not only for SG but also
for spring gravimeters. This calibration method can identify some systematic errors in the screw calibration method
that is often used for spring tidal gravimeters.
A significant linear correlation between the gravimeter drift of the LCR 137 and the relative air humidity was
estimated by the analysis of tidal records after the induced humidity change of about 25%. The stabilization of the
relative humidity at the tidal station can improve the quality of tidal observation especially when the spring gravimeter
is equipped with an electrostatic feedback system.
The results of tidal parameters for the period September 2002–April 2004 are in a good agreement for both tidal
gravimeters at the station Pecný. The standard deviation of the observed hourly ordinate is 0.6 nm/s2 and 2.0 nm/s2
for the LCR 137 and ASK 228, respectively. It means that the precision of both tidal gravimeters is for diurnal and
semi-diurnal frequencies better than the precision of older types of superconducting gravimeters.
22
V. Pálinkáš / Journal of Geodynamics 41 (2006) 14–22
Acknowledgement
This presentation is based on the research carried out within the project “Experimental Research of the Dynamics
of the Earth and Its Surface” No. LN00A005 supported by the Ministry of Education, Youth and Sports of the Czech
Republic. The gravimeter LCR 137 was kindly made available as a long term loan by the NIMA (today NGA), DoD,
USA. All this support is gratefully acknowledged.
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