Luck

J Ferhat

M Hinderer

P Amalvict

B Gegout

S Rosat

J.-P Boy

G Ferhat

J Hinderer

M Amalvict

P Gegout

& B Luck

Analysis of a ten-year (1997-2007) record of time-varying gravity in Strasbourg using absolute and superconducting gravimeters: new results on the calibration and comparison with GPS height changes and hydrology

Keywords: SG calibration, inter-comparison of geodetic techniques, global hydrology model, GPS

    Analysis of a ten-year (1997-2007) record of time-varying gravity in Strasbourg using absolute and superconducting gravimeters: new results on the calibration and comparison with GPS height changes and hydrology

Introduction

Since July 1996 the superconducting gravimeter (SG) GWR C026 is recording the timevarying gravity at the French J9 observatory in Strasbourg in the framework of the Global Geodynamics Project (GGP) (Crossley et al., 1999;[START_REF] Hinderer | Scientific achievements from the first phase (1997-2003) of the Global Geodynamics Project using a worldwide network of superconducting gravimeters[END_REF]), although we are using here only gravity records since March 1997, after the upgrade of the acquisition system. In parallel to the SG measurements, absolute gravity (AG) measurements are performed routinely several A c c e p t e d M a n u s c r i p t 2 times per year using the ballistic instrument FG5 #206. It is well-established in the gravimetric community that parallel AG measurements with the continuous SG records are primordial to estimate and check the long-term stability of the SG instrumental drift. Besides, intensive AG recording during several days are regularly performed to estimate the calibration factor of the SG and to check its stability in time. The 10-year SG records now available at the J9 site highlight the presence of seasonal effects that we will interpret in terms of hydrology. Next, the long-term effects and the seasonal variations are investigated in the vertical displacement given by GPS data. The permanent GPS that belongs to the French geodetic network has been recorded since 1999 right on the top of the building of the gravity station. The collocated GPS height changes help in separating the gravity variation due to the vertical motion of the station from the variation due to the mass redistribution.

SG calibration

The scale factor calibration of a relative SG can be done in several ways: 1/ by monitoring the tides for a long period (2-3 years) and then use a well-known tidal amplitude (e.g. the diurnal wave O 1 ) to calibrate the SG [START_REF] Melchior | A new data bank for tidal gravity measurements (DB92)[END_REF]; 2/ the use of a calibration platform [START_REF] Falk | Calibration of the superconducting gravimeters SG103, C023, CD029 and CD030[END_REF]; 3/ by moving an external mass (Achilli et al., 1995); 4/ by comparison with a reference instrument, especially an absolute gravimeter [START_REF] Hinderer | On the calibration of a superconducting gravimeter using absolute gravity measurements[END_REF]. Comparison with an absolute gravimeter is the most widely used method (e.g. [START_REF] Imanishi | Calibration of the superconducting gravimeter T011 by parallel observation with the absolute gravimeter FG5 #210-a Bayesian approach[END_REF][START_REF] Fukuda | Calibration of the superconducting gravimeter CT#043 with an absolute gravimeter FG5#210 at Syowa Station, Antarctica[END_REF] to calibrate a relative gravimeter as it does not disturb the observational series of the SG and it also enables the investigation of the long-term drift of the SG [START_REF] Francis | Calibration of a superconducting gravimeter by comparison with an absolute gravimeter FG5 in Boulder[END_REF]. Since 1997, several calibration campaigns were performed at the J9 site. The time-length of the parallel registrations must be long enough (at least 5 days) to reach a reasonable accuracy on the scale factor estimate [START_REF] Francis | Evaluation of the precision of using absolute gravimeters to calibrate superconducting gravimeters[END_REF]. Therefore only the intensive campaigns, meaning at least 5 days of continuous AG measurements, are considered as useful for the scale-factor determination. The

i i bx a y + = , (1)
where y i stands for the AG data and is expressed in nm/s 2 , x i for the SG feedback output in volt (V), b is the scale-factor expressed in nm/s 2 /V and a is the offset in nm/s 2 . As the fit is better on high gravity signals, the tides are not removed from the signals. We use the set gravity values of the AG resulting from a statistical processing of the drop gravity values; a rejection criterion of outlier sets is applied at 1σ (standard deviation), prior to the calibration. From the 1-min sampled SG records, we derive the SG value corresponding to the central time of the AG set before applying the linear least-squares method is applied. The raw SG records must have been corrected for any earthquake occurring at the time of calibration. AG set values are not perfect but contain some errors that we computed from the drop scatter. These standard deviations are used in the least-squares inversion in order to take into account the AG measurement errors; some clock problems can occur during the calibration experiments for instance that generate an error around 1 nm/s 2 [START_REF] Van Camp | Uncertainty of absolute gravity measurements[END_REF].

The estimated scale factors for the various calibration campaigns are plotted in Fig. 1 for the period September 2002 -May 2008. As expected, the scale factor is stable in time, as there should be no changes in the magnetic fields of the upper and lower coils inducing the levitation of the niobium sphere inside the SG.

Note that because of the low instrumental drift of the SG (less than 15 nm/s 2 per year; see next part) and the short duration of each calibration campaign (the longest one was 12 days), this instrumental drift does not need to be removed for the linear regression fitting. The induced error lies within the error bars of the scale factors.

The weighted mean value leads to a scale factor of -790.7 +/-2.6 nm/s 2 /V, corresponding to a relative precision of 0.3 %. We have checked the decrease of the relative calibration error with the number of days of parallel AG measurements in Fig. 2 for the December 2004 campaign. Note that this calibration campaign was performed before the occurrence of the Sumatra earthquake. After 7

A c c e p t e d M a n u s c r i p t 4 days of parallel measurements, the uncertainty merely does not decrease any more and tends to 0.7 % for this specific campaign.

If we do not take into account the AG drop standard deviations, we obtain a value of -791.5

+/-0.5 nm/s 2 /V for the calibration factor which corresponds to a relative uncertainty of 0.06 %. In 1998) and [START_REF] Baker | Validating Earth and ocean tide models using tidal gravity measurements[END_REF].

SG instrumental drift

The SGs are known to be stable in time, as confirmed by the previous session, and to have a low drift. They are therefore useful instruments to record long-period geophysical signals (e.g. [START_REF] Richter | From Chandler wobble to free oscillations: comparison of cryogenic gravimeters and other instruments in a wide period range[END_REF]. By superposition with AG measurements, we can retrieve the purely instrumental part of the observed SG trend. This instrumental drift is defined as the total SG trend minus the observed trend in AG measurements. The AG trend is interpreted as a geophysical signal that could correspond to some long term deformations. [START_REF] Amalvict | Long-term and seasonal gravity changes at the Strasbourg station and their relation to crustal deformation and hydrology[END_REF] have shown that the gravity was increasing in time at a rate of about 15.7 nm/s 2 /yr from the beginning of 1997 to the end of 2002. In this paper, our data are spanning from the beginning of 1997 to the end of 2007, and the gravity increase observed in AG measurements is about 13.3 nm/s 2 /yr, while the SG instrumental drift is deduced to be 13.9 nm/s 2 /yr. In Fig. 3 processes must be applied to both datasets for a rigorous comparison. The SG data were calibrated using a scale factor of -792 nm/s 2 /V, based on the previous AG calibration campaigns and were first corrected for major instrumental perturbations such as gaps, spikes or offsets following the classical procedure [START_REF] Crossley | A slew rate detection criterion applied to SG data processing[END_REF]) and were decimated to hourly samples using a low-pass filter with a cut-off frequency of 12 cycles per day.

As we can observe on these plots, the gravity is smoothly increasing during the year 2001 and the observed drift seems to be different before and after 2001. This kind of feature could suggest that the SG instrumental drift would be better modeled by an exponential function of time as suggested previously by [START_REF] Van Camp | Is the instrumental drift of superconducting gravimeters a linear or exponential function of time?[END_REF]. However, when looking at the observed gravity increase in the AG data, we can notice that the gravity rate is also different before and after April 2001.

Before April 2001, the observed gravity increase from the AG measurements is 11.7 nm/s 2 /yr leading to an SG linear instrumental drift of 13.1 nm/s 2 /yr. From the beginning of 2002 to the end of 2007, the observed gravity increase is only 1 nm/s 2 /yr and the SG instrumental drift is 8.4 nm/s 2 /yr. From before and after 2001, the gravity increase rate has dropped by a factor 10. The reason for this change of behavior has not been explained yet. Some local effects have to be investigated like, for instance, the local hydrology impact in 2001.

Seasonal effects

Besides the long-term drift of the time-varying gravity, the seasonal effects clearly appear in the SG residuals plotted in Fig. 4 (a) and (b). These seasonal effects can mostly be explained by the global hydrology loading as the contribution of the continental water storage changes (soil-moisture and snow) to gravity variations is one of the largest signal at seasonal timescales [START_REF] Boy | Study of the seasonal gravity signal in superconducting gravimeter data[END_REF]. Contrary to the part 3 when comparing SG with AG with the use of a constant barometric admittance, here we correct gravity variations for global atmospheric and induced non- barotropic ocean model [START_REF] Carrere | Modeling the barotropic response of the global ocean to atmospheric wind and pressure forcing -comparison with observations[END_REF] with a resolution of 0.5 degree and a temporal sampling of 6 hours. In Fig. 5 we have superimposed the obtained SG residuals with the global hydrology effects estimated from two different global models: ECMWF with temporal sampling of 6 hours and changing spatial sampling with the upgrades of the model (from 1.125 degree in 1997 to less than 0.25 after 2006), and GLDAS/Noah (Global Land Data Assimilation System) [START_REF] Rodell | The global land data assimilation system[END_REF] with spatial sampling of 0.25 degree and temporal sampling of 3 hours. The outputs of these models consist in soil moisture content, in equivalent snow height, and to a smaller extend canopy water for GLDAS model. The hydrology effect is modeled as a thin-layer process acting on a spherical Earth surface for which we model the direct Newtonian attraction and the elastic loading. The local Newtonian contribution will have a sign different whether the station is buried in the ground or if the station is located at the surface. In the case of the J9 SG site, the station is below the ground, so an excess of water mass will decrease the gravity. Note that the local Newtonian attraction could be improved by taking into account the local topography of the site [START_REF] Longuevergne | Contribution à l'hydrogéodésie[END_REF].

There is a correlation between our SG residuals and these estimated continental water storage loading effects. The correlation with the ECMWF model is of 42 % for the period March than GLDAS model. The difference between both hydrology models is as large as the difference between the computed hydrological effect and the gravity residuals. These discrepancies may be associated with local hydrology effects (see [START_REF] Longuevergne | Contribution à l'hydrogéodésie[END_REF], which are not taken into account in global models. The atmospheric loading contribution should also be modeled using a

A c c e p t e d M a n u s c r i p t 7 three-dimensional model [START_REF] Neumeyer | Gravity reduction with threedimensional atmospheric pressure data fro precise ground gravity measurements[END_REF] of air masses attraction in the neighborhood of the gravimeter and a two-dimensional model of air masses attraction [START_REF] Boy | Reduction of surface gravity data from global atmospheric pressure loading[END_REF] far from the station.

GPS height changes

We can explain most of the observed seasonal effects in gravity using a global hydrology model. Besides the purely Newtonian attraction, the global water masses contribute to elastically deform the Earth's surface. Such a vertical displacement should be visible by GPS. Above the SG instrument at Strasbourg J9 site, a GPS antenna has been recorded since 1999.

Generally, the hydrological loading caused by an excess in the soil water content leads to a decrease in height (subsidence) observable by GPS and to an increase in gravity observable by SGs. Hence the ratio of gravity change versus height change is always negative for this type of load [START_REF] De Linage | A search for the ratio between gravity variation and vertical displacement due to a surface load[END_REF]).

However since the Strasbourg SG station is below the ground, any excess of local water mass due to rain for instance will in fact decrease the gravity since the Newtonian local contribution dominates (see [START_REF] Boy | Study of the seasonal gravity signal in superconducting gravimeter data[END_REF][START_REF] Longuevergne | Contribution à l'hydrogéodésie[END_REF]. This is why the signs of height and gravity are expected to be the same for our station (see Fig. 6).

We analyzed the GPS data from J9 site as well as other French (RENAG, webrenag.unice.fr) sites and European stations from the International Global Navigation Satellite System Service (IGS) network. We analyzed the GPS vertical displacement using the version 10.33 of GAMIT software. GPS Daily solutions are then combined using GLOBK software [START_REF] Herring | Introduction to GAMIT/GLOBK[END_REF] to obtain times series of positions in an International reference frame, ITRF2005 [START_REF] Altamimi | ITRF2005: A new release of the International Terrestrial Reference Frame based on time series of station positions and Earth Orientation Parameters[END_REF].We have not applied any loading correction in order to compare the obtained displacements with our gravity residuals as obtained in section 3.

Before 2001, the GPS vertical displacement is very noisy, so we compare the GPS height changes with the SG residuals from 2002 only. They are superimposed in Fig. 6 where the daily

Conclusion

The calibration factor of SG C026 in Strasbourg is very stable in time and has been determined to be -791.8 +/-0.25 nm/s 2 /V (0.03 % relative precision) for the period March 1997-May 2008. From the beginning of 1997 to the end of 2007, the SG instrumental drift is equal to 13.9 nm/s 2 /yr. The observed AG gravity trend is different before and after April 2001, respectively of 11.7 nm/s 2 /yr and 1 nm/s 2 /yr, suggesting that some unexplained local effects occurred during this period. In addition to long term trends, there are seasonal effects observed in the gravity residuals site which are mostly due to the local hydrological Newtonian effects, while the elastic effect of the continental water storage prevails in the observed seasonal GPS height changes at J9. The 2001 gravity increase cannot be explained by the global hydrological effects. Some other local effects must be investigated.

  estimate the calibration factor is by least-squares fitting of the SG records to the AG data points according to:

  the past,[START_REF] Amalvict | A three year comparison between a superconducting gravimeter (GWR C026) and an absolute gravimeter (FG5#206) in Strasbourg (France)[END_REF] performed estimates of the SG scale factor for the period March 1997 -April 2000. By combining their values with ours, we obtain the scale factors plotted in Fig.1(b) and the averaged value for the 10 years is -791.8 +/-0.25 nm/s 2 /V. This relative uncertainty is smaller than the 0.1 % accuracy required for a number of geophysical studies (nearly diurnal free wobble, ocean and atmospheric loading, polar motion, anelasticity and tides…) as stated byFrancis et al. (

  we show the superposition of AG measurements with the SG record at Strasbourg from 1997 to 2007 before and after removal of the SG instrumental drift. Both AG and SG records have been corrected for the local tides, local atmospheric pressure using a barometric admittance of -3 nm/s 2 /hPa and for the polar motion effect. The pole tide, induced by polar motion and length-of-day variations, is modeled using daily Earth orientation A c c e p t e d M a n u s c r i p t 5 parameters provided by the International Earth Rotation Service (EOPC04 series). The same

  effects[START_REF] Boy | Reduction of surface gravity data from global atmospheric pressure loading[END_REF][START_REF] Boy | High-frequency non-tidal ocean loading effects on surface gravity measurements[END_REF] using global surface pressure field provided by the European Centre for Medium-range Weather Forecasts (ECMWF), and seasurface height from the Toulouse Hydrodynamic Unstructured Grid Ocean model(HUGO-m)

1997-

  April 2001 and is of 64 % for the period November 2001 -November 2007. The correlation with GLDAS model is 46 % for the period March 2000 -April 2001 and 37 % for the period November 2001 -December 2006. The ECMWF hydrological model better fits the SG residuals

  smoothed using an FFT filtering method. As expected, the seasonal effects are also observed in the GPS height changes with a positive correlation between vertical displacement and gravity.If the seasonal effects observed in GPS height changes are due to the global hydrology loading, there must be a correlation between the elastic loading effect in gravity and the vertical displacement. We have plotted both signals in Fig.7. The gravity contribution due to elastic hydrology loading has been computed using GLDAS global model. This purely elastic gravity effect has been converted into vertical displacement based on the ratio -2 nm/s 2 /mm which is a mean value of the ratio over a large spectral range (see Fig.5of[START_REF] De Linage | A search for the ratio between gravity variation and vertical displacement due to a surface load[END_REF]). The seasonal variations observed in the GPS height changes are hence mostly explained by the elastic loading of the continental water masses.

Fig. 1

 1 Figure caption

Fig. 5

 5 Fig. 5 SG gravity residuals and global hydrology effects at Strasbourg, J9 site before (left-hand) and

  Fig. 6 SG gravity residuals (in black) and GPS height changes (in blue) observed at Strasbourg, J9

  Fig.1 (a)

  Fig. 4

  Fig. 7

Acknowledgments


Keywords: superconducting gravimeter, calibration, absolute gravimeter, absolute gravity database

Abstract. A new database for absolute gravity (AG) measurements has been implemented at BGI and BKG and is operational now for storing absolute gravity data either in the form of metadata or as detailed measurement results. The database development was proposed by the IGFS (International Gravity Field Service) and is expected to have a great importance for the GGOS (Global Geodetic Observing System) initiative. This database will provide an overview about AG stations and observations and by this improve the cooperation between gravity groups and foster the combination with other geodetic observation techniques. The international community of absolute gravimeter users is asked to contribute to this database.

In addition to its primary purposes, demonstration of the global site distribution and information about available observations, the database could also provide an important contribution to the Global Geodynamics Project (GGP). Precise repeated absolute gravity measurements at the superconducting gravimeter (SG) sites are necessary for the determination of SG drift parameters and can be used for checking SG instrument calibration factors. The AGrav database is capable of storing the necessary AG observations at the SG location in detail up to the "single drop level" and provide this information for the combination with SG time series. An example for a selected station is presented. It is proposed to establish an interface between the AGrav and GGP databases. Introduction

Studies of superconducting gravimeter (SG) time series for geophysical and geodetic applications require precise knowledge of the instrumental drift behaviour and the calibration parameters. Repeated absolute gravimeter (AG) measurements at the SG's location can be used to determine the SG instrumental drift function and by this enable to distinguish between instrumental drift and gravity changes caused by geophysical processes. [START_REF] Hinderer | On the calibration of a superconducting gravimeter using absolute gravity measurements[END_REF] and Francis, van Dam (2002) demonstrated that by the combination of SG time series and repeated AG measurements precise calibration factors can be determined with their uncertainty estimates. Further studies by [START_REF] Wziontek | Precise gravity time series and instrumental properties from combination of superconducting and absolute gravity measurements[END_REF] showed that in a combined procedure SG and AG measurements can be used to determine SG drift and calibration

A c c e p t e d M a n u s c r i p t together with the offset checks for the contributing absolute gravimeters. With data over a longer period offset changes for the AG e.g. after maintenance works can be detected. Since 1993 the community of SG users has been organised in the Global Geodynamics Project (GGP) (Hinderer and Crossley, 2003) and most of their observations are stored in a common database which advances cooperation and investigations with regional and global applications.

International comparisons of absolute gravimeter are organised in four-yearly intervals at BIPM in Sevres by the "Consultative Committee for Mass and Related Quantities (CCM), Working Group on Gravimetry" and the "IAG Study Group on the Comparison of Absolute Gravimeters" (e.g. [START_REF] Vitushkin | Results of the Sixth International Comparison of Absolute Gravimeters, ICAG-2001[END_REF]. Still, a comparable status of organisation has not yet been achieved for the community of absolute gravimeter users as concerns the cooperation in measurement projects, the harmonisation of processing standards and the sharing of observation results.

Absolute Gravity Database AGrav

The growing number of AG instruments, together with the understanding that the absolute gravity measurements have a high importance in their timely and geographical distribution, encourage the development of an international database for absolute gravity observations. This database under the umbrella of the International Gravity Field Service (IGFS) [START_REF] Forsberg | The gravity field and GGOS[END_REF] was developed by the Bundesamt für Kartographie und Geodäsie (BKG) and put into operation together with the Bureau Gravimétrique International (BGI). This new database not only improves the propagation and notice of the AG observations and by this enhance the use of gravity data, but will also encourage cooperation in regional and global gravity projects. Work has begun to develop common standards for AG measurements and data evaluation procedures using consistent parameters and models.

The system was set into operation at two mirrored servers with web-based frontend located at BGI: http://bgi.dtp.obs-mip.fr/agrav-meta/ and at BKG: http://agrav.bkg.bund.de/agrav-meta/. Fig. 1 shows the AGrav database graphical web interface. With this realization the database pursues the following aims:

• to reach a better dissemination of information on the AG technique and existing observations • to provide a means for the coordination of activities • to facilitate cooperation between AG user groups • to assist the combination of gravity data with other techniques • to make the observed gravity data comparable • to provide secure storage of AG observations for long-term availability • to improve the scientific usability of the AG measurements. The AGrav database informs about station location, observation epoch, instrument type and serial number, instrument owner or user respectively and measurement results. Accordingly, the basic structure of the relational database is composed by four tables to store information about the stations, instruments, measurement epochs, and involved institutions, which are linked to each other. Other details can be stored in supplemental tables. In this way, storage of redundant information is avoided and a flexible adaption to future needs is possible.

A c c e p t e d M a n u s c r i p t

Concerning observation epochs for instance, it is possible just to store time and date of the observation up to complete processing results, including single drop observations. The database concept distinguishes two basic features:

• It can inform with meta data about measurements and, where the details are available, about results, but with limited accuracy. This service is freely available without access restrictions.

• It can store the measurement results including all corrections and processing details.

Here, restrictions are applied, access is granted only to users, who have contributed own data.

By this design, meta data and detailed data share the same database. Dependent on task and authentication, meta information only or complete datasets are provided. In this way it is possible just to inform other interested groups about the existence of the stations and observations or to store the data for projects, publications and cooperation. The latter case with the complete observation results would be very helpful for cooperation between groups or if the database is used as permanent repository. In any case, the user retains control over the data, which means, later editing of submitted data is possible at any time Stored gravity data can differ in their resolution and level of detail. To facilitate the upload of new data into the database, a format standard was chosen which is based upon the so-called "project file", a file which is generated automatically by the FG5-or A10-type gravimeter and its standard processing software "g" (Micro-g Lacoste Inc. 2007) during data taking or reprocessing. This software is applied by the majority of AG users. Due to a simple format structure, conversions can be made to include also data from other instruments and processing formats. To provide station descriptions or additional information to instruments or observations, additional documents of arbitrary format can be uploaded and linked to the primary data. Table 1 shows the information uploaded from the "project file" into the AGrav database structure.

Additional information about the processing results as, e.g. tidal models or laser frequencies, are documented in a copy of the complete project file. Information about the institution needs to be entered manually during the upload procedure.

For the proposed application only the measurements at the GGP sites are of interest. If the SG drift function is searched for, only those AG observations, which are processed consistently with respect to reduction models for tides, atmosphere and polar motion can be used.

When the calibration factor should also be determined, it is necessary to go back to the uncorrected observations with SG and AG. If data from more than one AG are included in the analysis the offset between AG instruments also needs to be determined or must be known from an earlier independent analysis.

Table 1: Content of the g-Software "Project" file transferred into the AGrav database structure

The Combination of AG and SG observations

The complementary characteristics of the superconducting gravimeter (SG), a relative sensor with low noise level of 0.1 nm/s² and very stable instrumental drift on the order of a few A c c e p t e d M a n u s c r i p t 10 nm/s² per year, and the absolute gravimeter (AG), a drift-free sensor due to its direct reference to physical standards with a measurement uncertainty of a few 10 nm/s² for single drop, lead to the development of an evaluation procedure by which observations of both instrument types at the same station are combined and SG drift parameters and calibration factors are determined in one least squares solution together with the offsets of the participating AG. Fig. 2 shows the main features of both gravimeter types and the principle of the combination procedure. In parallel repeated absolute gravity measurements were performed with in total 8 instruments operated by BKG and visiting institutions. The two graphs in fig. 3 show the input data, SG residuals curve after reduction of tides, atmospheric influence and polar motion, together with the results of 175 AG measurements after applying the same reductions. (Each AG measurement consists of at least 6 (in general 24) sets of 150 drops each every 10 seconds.) The adjustment result shows the gravity residual curve (in red) after the instrumental drift is removed and calibration is improved. The AG results could be improved further by including instrumental offsets in the range of a few 10 nm/s². Due to this relatively long comparison period with a large number of observations even smaller but significant offset changes for single AG could be detected. These changes could be related to maintenance works [START_REF] Wziontek | Precise gravity time series and instrumental properties from combination of superconducting and absolute gravity measurements[END_REF].

Benefit for the GGP community

Which role can the AG database AGrav play for the GGP? AGrav is an operational database in which AG measurements can be stored with the required resolution. With contributions from the AG community the data could be used by the members of GGP to link this information to the SG time series. Apart from the more simple approach of using one absolute gravity value per occupation with the AG, it is also possible to extend the comparison between both instrument types to the AG single drop level. This enables more detailed investigations of the SG calibration factor and the uncertainty of the combination of both measurement series. The next necessary steps for the adaptation of the AGrav database to the proposed GGP application would be to implement a user interface for the upload of AG drop data for the AG community and a similar interface for the SG community to retrieve these data for a selected SG site.

Conclusions

A c c e p t e d M a n u s c r i p t

A direct cooperation between the SG and AG communities is proposed which includes the link of the two databases, GGP and AGrav. The benefit would be the possibility to determine SG drift and calibration parameters and by this to create a combined verified gravity signal. The AGrav database foresees the storing of AG occupation results and AG drop data at the sites of the GGP network. For the successful combination of both data types it is necessary to ensure consistent AG gravity measurements together with agreed standards for the analysis of both types of gravity data. In addition it will be necessary to adapt the AGrav database with an additional interface which supports the upload and retrieval of single drop AG measurements.

A c c e p t e d M a n u s c r i p t

  a * , H. Wziontek a , R. Falk a , S. Bonvalot b a Bundesamt für Kartographie und Geodäsie (BKG), Richard-Strauss-Allee 11, D-60598 Frankfurt a.M., Germany b Bureau Gravimétrique International (BGI), Observatoire Midi-Pyrénées, 14-16 Avenue Edouard Belin, F-31401 Toulouse Cedex 4, France

Figure 1 :

 1 Figure 1: Layout of the AGrav database web interface (status 2008)

Figure 2 :

 2 Figure 2: Features of superconducting and absolute gravimeters

Figure 3 :

 3 Figure 3: Example for the combination of AG and SG observations at the station Bad Homburg (Germany); upper graph: SG-30 residual gravity function (black) and AG measurement results of 8 AG, symbols in selected colours; lower graph: SG and AG observations prior (black/upper curve) and after combination (red/lower curve); AG measurement results show smaller residuals after offset determination for the individual AG.

Figure 1 :Figure 2 :Figure 3 :

 123 Figure 1: Layout of the AGrav database web interface (status 2008)

  Figure 1

  Figure 3

Table 1 :

 1 Content of the g-Software "Project" file transferred into the AGrav database structure

Table 1 :

 1 Content of the g-Software "Project" file transferred into the AGrav database structure

	Station	Name
	Information	Site Code
		Longitude
		Latitude
		Height
	Instrument	Meter Type
	Information	Meter Serial
	Observation	Reference Date/Time
	Epoch	Gravity *
		Total Uncertainty *
		Measurement Precision *
		Transfer Height
		Laser
		Number of Sets Collected
		Number of Drops per Set
		Operator
		* not updated automatically
	Processing	Processing Date/Time
	Results	Project Name
		Gravity
		Set Scatter
		Measurement Precision
		Total Uncertainty
		Acquisition Version
		Processing Version
		Setup Height
		Transfer Height
		Factory Height
		Gradient
		Barometric Admittance Factor
		Polar Motion Coordinates
		Nominal Air Pressure
		Fringe Start
		Processed Fringes
		Rubidium Frequency
		Modulation Frequency


Tilt Effects on GWR Superconducting Gravimeters

Keywords: Superconducting gravimeter, Tilt output Calibration, Gravity

The superconducting gravimeters (SGs) are the most sensitive and stable gravity sensors currently available. The low drift and high sensitivity of these instruments allow to investigate several geophysical phenomena inducing small and long-period gravity changes. In order to study such topics, any kind of disturbance of instrumental origin has to be identified and possibly modelled. A critical point in gravity measurement is the alignment of the gravimeter to the local vertical. In fact a tilt of the instrument will lead to an apparent gravity change and can affect the instrumental drift. To avoid these drawbacks, SGs are provided with an "Active Tilt Feedback System" (ATFS) designed to keep the meter aligned to the vertical. We analyze tilt and environmental parameters collected near Strasbourg, France, since 1997 to study the source of the tilt changes and check the capability of the ATFS to compensate them. We also present the outcomes of a calibration test applied to the ATFS output to convert the Tilt Power signals into angles. We find that most of the observed signal has a thermal origin dominated by a strong annual component of about 200 µrad. Nevertheless, our analysis shows that even the tilt due to different geophysical phenomena, other than the thermal ones, can be detected. A clear tidal signal of about 0.05 µrad is detectable thanks to the large data stacking (> 11 years). We conclude that (i) the ATFS device compensates the tilt having a thermal origin or coming from any sources and (ii) no significant tilt changes alter the gravity signal, except for the high-frequency (> 1 mHz) perturbations.

A c c e p t e d M a n u s c r i p t

Introduction

The superconducting gravimeters (SGs) are the most sensitive and stable gravity sensors currently available for ground-based measurements. The inherent stability of the SGs enables them to detect signals from a sampling time of 1 s up to several years with a time-domain accuracy of 1nm/s 2 = 0.1 μGal or better [START_REF] Richter | From Chandler wobble to free oscillations: comparison of cryogenic and other instruments in a wide period range[END_REF][START_REF] Rosat | Performance of superconducting gravimeters from long-period seismology to tides[END_REF] and down to 0.5 nm/s² in the frequency domain [START_REF] Rosat | Performance of superconducting gravimeters from long-period seismology to tides[END_REF]. The SG is a device that uses magnetic levitation of a superconducting sphere instead of a mechanical spring as in the case of a classical gravimeter. The sensitivity of SG approaches one nGal (10 -11 ms -2 ), which corresponds to 10 -12 of the surface gravity, and drift rates are as low as a few µGal per year. These features allow us to study many geophysical phenomena inducing gravity changes over a broad time-scale range, such as seismic free oscillations, earth tides, ocean and atmospheric loads, post-glacial rebound, seasonal water storage variations and so on [START_REF] Hinderer | Time Variations and Inferences on the Earth's Structure and Dynamics[END_REF][START_REF] Letellier | Etude des ondes de marée sur les plateux continentaux. Thèse doctorale[END_REF]. In order to match such topics, any kind of disturbance of instrumental origin has to be modelled and subtracted from the raw gravity signal. It is of central importance in gravity measurement to align the gravimeter to the local vertical. In fact a tilt of the instrument will lead to an apparent gravity change and can affect the instrumental drift. This effect could deteriorate the quality of the collected data and hide real gravity changes. In principle, all of the aforementioned geophysical sources induce elasto-gravitational deformation of the Earth, and, therefore, a tilt of the ground (e.g. [START_REF] Rerolle | L'inclinométrie, un nouvel outil pour le suivi temporel des aquifères?[END_REF][START_REF] Jahr | Monitoring fluid induced deformation of the earth's crust: A large scale experiment at the KTB location/Germany[END_REF]. Also the daily and seasonal temperature variations produce thermal waves which propagate into the ground and produce the well known thermo-elastic deformation [START_REF] Berger | A Note on Thermoelastic Strain and Tilts[END_REF]. Besides these natural sources, the ambient conditions in the laboratory have to be taken into account. For instance temperature-related tilt signals may be caused by the periodic turning on and off of the air conditioning system. Moreover, air drafts on the dewar can produce rapid variations in horizontal pressure, while temperature changes cause unequal thermal expansion of the dewar walls. Either will produce tilt by causing the top of the dewar to move slightly. In order to avoid all these effects, SGs are provided with an "Active Tilt Feedback System" (ATFS) designed to keep the meter aligned to the vertical to better than a few µradians (GWR Instruments Inc., 1985).

If a gravimeter is tilted by an angle φ, from the local vertical, it measures the component of gravity g cosφ , along its axis. For φ is small, the difference between the gravity g and the projection g cosφ of g onto the gravimeter axis is gφ 2 /2, to the second order in φ. Of course, the apparent gravity g cosφ, which is measured by the gravimeter, is smaller than g. The apparent decrease in the gravity is about -4.9 x 10 -3 nm s -2 µrad -2 . However, for the SGs, there is an apparent increase in the measured A c c e p t e d M a n u s c r i p t 3 gravity. The tilt sensitivity of the SG is opposite to that of the ideal gravimeter because of the geometry of the magnetic field that levitates the sphere. When the SG is tilted, the horizontal component of gravity pushes the sphere away from the axis of the coil. Since the vertical force due to the magnetic field decreases radially from the axis, the sphere falls down as the instrument deviates from the vertical, resulting in an apparent increase in gravity. Thus the gravimeter outputs a minimum value of gravity when it is properly levelled (GWR Instruments Inc., 1985).When the meter is properly levelled, we reach what is called the "Tilt Insensitive Position" (TIP). It is a very important parameter because it measures the extent to which instrumental tilts will induce spurious gravity signals. To reduce this effect, it is recommended that the levelling of the SG be annually checked [START_REF] Warburton | Optimizing the performance of the SG during the GGP[END_REF].

The ATFS consists of: 1) tiltmeters, 2) tilt electronics, 3) thermal levellers (TLs), 4) support frame. Tilt variation of the gravimeter is detected by two tiltmeters, which are orthogonally positioned just above gravity sensing unit at 4K and corresponding analog voltages are sent to the tilt control electronics (GEP-2). Users can record these signals (X, Y "Tilt Balance"). In an active feedback operation, the balance signals generate feedback currents (Left, Right "Tilt Power") for the TLs. Heat expansion elements inside the TLs expand or shrink according to supplied power and keep the Tilt Balance signals nulled to zero. The TLs mechanically tilt the gravimeter through the support frame. They are designed to control only long-period tilt signals -down to about 15 minutes. This implies that the influence of tilt on the seismic band is not accounted for. Higher frequency tilt signals, as those related to earthquakes, are not compensated and they will appear on both the X and Y Tilt Balance signals and gravity. The TLs also have a manual height adjustment element; the gravimeter is tilted by rotating the micrometer head on top of the TL assembly. This device is used for coarse levelling and fine adjustment of the TIP.

There are two types of ATFS-geometries used in SGs: one model is suspended from the top by the support frame while the other is mounted on the base [START_REF] Iwano | Superconducting gravimeter observations without a tilt compensation system[END_REF]. Both types have the same mechanism in which the support frame has three legs, one is fixed and the others are controlled by the TLs. The two axes of the support frame are linked to two tiltmeters. For the topmounted type (old ones with a big dewar) the support frame is a right isosceles triangle and its orthogonal axes are aligned with the tiltmeter axes. For the bottom-mounted type ("SG C type", having a Compact dewar and most recent "OSG" meters), the support frame is an equilateral triangle and the directions of the support frame and tiltmeters axes are not aligned. The SG C-026 at the J9 station in Strasbourg is of the bottom-mounted type; the geometry and orientation of its tilt frame are illustrated in Fig. 1. The advantage of the isosceles support frames (top-mounted type) is that the left and right axes are orthogonal and the two tiltmeters can be aligned with these axes. For In order to study the tilt changes at J9, we analyzed more than eleven years of Tilt Power and environmental parameters, namely temperature and humidity, collected since 1997. We evaluate the capability of the ATFS to compensate the tilt changes preserving the verticality of the meter and detect and study the "sources" of the observed tilt changes.

As the scale factors for the SGs ATFS are not provided by the manufacturing company (GWR Instruments Inc.), we face the problem of the TLs output calibration. Here we present a calibration test applied to the Tilt Power signal from the ATFS and its validation by using different methodological approaches.

Data analysis and results

The J9 gravity station hosts the superconducting gravimeter C026 (SG-C026) in a bunker 15 km from Strasbourg, where it has been operating since July 1996. The meter has a compact dewar (volume: 125 l) and a tilt frame sizing 28 inches (711.2 mm). It is the bottom mounted type; the geometry and orientation of its tilt frame are illustrated in Fig. 1. The meter is located in a separate gravity room that is somewhat thermally separated from the rest of the equipment, including the devices for the room temperature control and the helium compressor. To decouple mechanically the SG from the building it operates on a concrete pillar that is isolated from the floor and connected to the bedrock. This should minimize the disturbances transmitted from environmental noise or human activity in the building. . In November 1999 an air dryer device was installed to control the room temperature and humidity; it has a switching cycle on/off triggered by a set humidity value and uses fans to distribute the air. The meter is shielded with a styrofoam panel to avoid direct air drafts on the dewar. The SG-C026 is routinely calibrated, 6 times per year on the average, by means of parallel recording with the absolute gravimeter FG5 #206 [START_REF] Amalvict | A 3 years comparison between a superconducting gravimeter (GWR C026) and an absolute gravimeter (FG5-206) in Strasbourg (France)[END_REF][START_REF] Amalvict | Is the calibration factor stable in time? paper presented at First Asian Workshop on SGs[END_REF]. A maintenance experiment, aimed at checking the tilt compensation system, was rate of about 20 μrad/year is obtained. A similar offset from the true vertical was found by [START_REF] Camp | Is the instrumental drift of superconducting gravimeters a linear or exponential function of time?[END_REF] at Membach (Belgium) station after 10 years of operation. Accounting for the typical accuracy (0.3 mils) for the TIP setting, we can conclude that only small changes affected the SG verticality in more than 11 years. This experiment was only performed twice to avoid instrumental disturbances.

To study the tilt changes at J9, a 4116-days long (more than 11 years) data-set has been analysed (Fig. 2). The collected signals are the "Tilt Power" outputs from Left and Right TLs (Figs. 2a and2b) and environmental data (temperature and humidity of the SG room) (Figs. 2c and2d) from 1997 February 22 nd to 2008 June 3 rd . A strong negative correlation between Tilt Power and temperature is quite evident (Fig. 2). The TLs are activated by heat, so it is expected that the tilt control voltages will correlate very well with the room temperature. Fig. 2d clearly displays that the ambient conditions at the J9 gravity station sharply changed after the setup of the air dryer device at the end of 1999; the mean humidity in the room falls down from 75% to 40%. The drawback of this installation is that the air dryer has "coloured" the ambient noise with a characteristic spectral signature due to the cycling switching on/off triggered by a temperature sensor. The spectral signature consists in a main peak at the frequency 24 cycles/day (cpd) [period = 1hour] and higher harmonics (48 cpd, 72 cpd, 96 cpd). These spectral features appeared since the time of the air dryer setup; almost all of the geophysical instruments installed in J9 are affected by this background noise. Moreover the room temperature (Fig. 2c) has been strongly influenced by a massive tree cutting above and around the building in February 1999 to install a permanent GPS antenna. As a consequence, the seasonal variation of the room temperature increases from 4°C to 6°C peak-to-peak. This is likely because the shadowing of the woody cover has disappeared. Since 2007 a further remarkable step-like increase (about 2.4°C peak-to-peak) in the room temperature has to be pointed out; this is imputable to the increase of the heating sources coming from new equipments (data acquisition system for SG and a weather station).

Calibration of the Thermal Levellers output

Because the scale factors for the ATFS are not provided by the manufacturing company, we apply a calibration procedure to the TLs to convert the tilt voltages into angles. We perform the calibration of the TLs' output voltages by inducing variations in the height of the free legs of the support frame through a known micrometer turn; the units of the micrometer dial are "mils". The ,4c) and peaks in the solar bands at 1 cpd, 2 cpd and harmonics (Figs. 4a,4b). Zooming in on the frequency range 0 -4 cpd (Fig. 4b), we see that the temperature spectrum displays a single peak at 2cpd, as expected, and the spectra of the Tilt Power are characterized by a double peak: the first one at the thermal frequency of 2 cpd and the second one at a frequency of 1.93 cpd, in the range of the M2 tidal band. To separate the spectral components having a thermal origin from the tidal ones, a coherence analysis has been performed (Fig. 5). Actually we use an approach slightly different from the classic cross-spectral analysis in defining coherence function . We computed a set of frequencydependent cross-correlation factors. The procedure, described by [START_REF] Riccardi | On the Efficiency of Barometric Arrays to Improve the Corrections of Atmospheric Effects on Gravity Data[END_REF], can be summed up as follows: first, we filter the time-series by means of a set of pass-band filters with a narrow bandwidth (0.01 cpd), then we apply a regression analysis to the filtered signals and account for the correlation factors in each frequency band. Considering that the "coherence function" is a cross-correlation in the frequency domain, our procedure is equivalent to the classic one. The main advantage of this approach is that it provides the sign of the coherence to investigate whether there is an inverse or direct correlation in each frequency band, summing up the information coming from both the amplitude and phase cross-spectrum. We apply this analysis to, first, the Tilt Power and background level scattering around a mean value -0.5 and (ii) a line spectrum at the harmonics of the day (1 cpd, 2 cpd) owing to the effect of the solar heating; there is no line at the M2 frequency.

On the contrary, the coherence between the TL and body tide shows a background scattering around 0 and a line spectrum at the harmonics (0.93 cpd, 1 cpd, 1.93 cpd, 2 cpd), which include highamplitude tidal waves O1, PSK1, and M2. So, we conclude that the spectral peak at 1.93 cpd has a tidal origin. It is noteworthy that the sensitivity of the ATFS is good enough to detect the tilt associated to the solid Earth tides, provided that the time-series of the Tilt Power are sufficiently long to allow a suitable stacking of the "weak" tidal signal.

Consequently, we use the theoretical tides to calibrate the TL outputs. We compute the tilt due to both the body tides, for the Wahr-Dehant (WD) Earth model, [START_REF] Dehant | Tides for a convective Earth[END_REF] and the ocean tide loading (OTL) [START_REF] Boy | A comparison of tidal ocean loading models using superconducting gravimeter data[END_REF] according to model FES04 [START_REF] Letellier | Etude des ondes de marée sur les plateux continentaux. Thèse doctorale[END_REF][START_REF] Lyard | Modelling the global ocean tides: Modern insights from FES2004[END_REF]. We obtain the scale factors from the ratio between the spectral amplitudes of the theoretical tidal signal and Tilt Power: the results are listed in Tab. I. As the OTL effect is only available for North-South and East-West directions, we applied this correction exclusively to the Right TL, which is almost East-West oriented (ref. Fig. 1). The results obtained in the frequency domain match pretty well those collected by the micrometer manipulations; they deviate less than 10% from each other.

Still willing to validate the calibration factors, we make a tidal analysis [START_REF] Wenzel | The nanogal software: Earth tide data processing package ETERNA 3.30[END_REF] of the Tilt Power signals calibrated by using the factors coming from the calibration test. For the M2 tidal wave, we obtain a tidal tilt factor (γ) and a phase in agreement with the Earth models (Tab. II) [START_REF] Wenzel | The nanogal software: Earth tide data processing package ETERNA 3.30[END_REF]d'Oreye, 2003;[START_REF] Jahr | Monitoring fluid induced deformation of the earth's crust: A large scale experiment at the KTB location/Germany[END_REF].

Analyses of the calibrated Tilt Power signal

In order to get insight into the possible sources of the observed tilt changes, we filter out the different components (Fig. 6) of the signal to make a better correlation analysis between the Tilt Finally, we tried to address the question whether uncompensated tilts can affect the observed gravity changes. We compute the gravity variation due to the observed tilt changes (Fig. 8a) accounting for the previously mentioned tilt dependence of 4.9 × 10 -3 nm/s 2 /μradian 2 .

In case the SG should operate without the ATFS, which keep the meter vertical, tilt changes would induce a huge gravity signal; it would be as large as the solid Earth tides, making the meter unusable for gravity record. Moreover we check whether only the non-thermal tilt was uncompensated by the ATFS. To separate the thermal and non-thermal Tilt Power signals, we use the frequency dependent admittance coefficients as parameters for the transfer function of the temperature influence on the Tilt Power. The Tilt Power signal reduced for the thermal effect is drawn in the Fig. ( 8b) and (8c). The high amplitudes of the residual signal from 1997 till 2000 show that the transfer function of the thermal effect computed by means of the admittance coefficients is inefficient in the first part of the time series; this is probably because we have neglected the time variation of the amplitude of the thermal effects. The temperature variations in the room were actually larger before the installation of the device for the temperature control in November 1999.

That was also the case in 2002, when the air dryer was switched off during about two months to study the noise it generates. 8d) displays the gravity variation induced by the non-thermal tilt changes. Just for having a comparison between a well known gravity signal and the gravity effect due to the nonthermal tilt changes, we also plot the gravity variation associated to the polar motion. This enables us to have an idea of the amount of the gravity signal that could be induced if the observed tilt was uncompensated. To answer definitely the question whether any inefficiency of the ATFS could alter the gravity signal, we compare the residual gravity changes (Fig. 8e) and the equivalent gravity effect due to the non-thermal tilt changes; they look uncorrelated. This means there is no obvious significant gravity variation due to uncompensated tilt.

Conclusions

To quantify the tilt sensed by superconducting gravimeter C-026, located 10 km north of Strasbourg, France, we have calibrated the Thermal Levellers (TLs) of the Active Tilt Feedback System (ATFS). As the TLs are activated by heat, the Tilt Power signals have mainly a thermal origin so it's not supposed to be real tilt. However our analysis shows that the tilt due to different geophysical phenomena, other than the thermal ones, can affect the collected Tilt Power signals.

Actually a clear tidal signal sticks out from the time series; anyway it is hard to separate in the Tilt Power signal the real tilt from the pure thermal effect. Three simultaneous sources actually contribute to the recorded Tilt Power signals. The biggest one is the direct reaction of the TL to the room temperature changes; in that case the TLs behave as thermometers, but with a characteristic phase lag as long as 20 min. Furthermore feedback currents are generated by the tiltmeters in response to the tilt of the SG, which could be due to geophysical phenomena, e.g. the body tides; hydrology, ground deformation and to the thermo-elastic deformation due to the propagation of thermal waves into the building and surrounding ground. In fact the thermal expansion and contraction in response to daily and seasonal temperature fluctuations generate real movements of the building and pillar hosting the SG that are detected by the tiltmeters and other sensors. Even if the room temperature did not vary, real tilts up to several microradians would occur because of the daily heating and cooling of the pillar and building.

As expected we find that most of the observed Tilt Power signal has a thermal origin.

In summary, we detect: Thus we can conclude the efficiency of the ATFS device is at a suitable level to guarantee high accuracy gravity measurements and inherent time stability. TLs are very sensitive to the room temperature, but any changes in temperature or coming from whatever sources are correctly balanced, except for the high-frequency perturbations (period < 15 min) so that no significant tilt changes alter the gravity signal. It follows that it is not recommended to let the meter operate without this tilt compensation system, because the tilt changes would remarkably affect the measured local gravity as a whole and the long-term trend signal (drift) too.

  the usual procedure of levelling of the gravimeter this means, in the SETUP mode, that a change of the X (or Y) micrometer does not affect the null position measured by the other micrometer.

  performed in 2007 by the GWR Instruments Inc. staff. It was developed in two phases: a) gravimeter levelling by means of micrometer changes; b) fine adjustment of the levelling through electronic reset changes. The data allowed us to check the stability of the TIP coordinates;they were slightly different from the values measured when the gravimeter was installed in 1996. Indeed, during more than 11 years the tilt has changed by about 6.5 mils (equivalent height change = 0.16 A c c e p t e d M a n u s c r i p t 5 mm), which represents about 225 μrad for the J9 support frame; assuming a linear time change, a

  by GWR is that 4 complete dial revolutions (= 100 mils) correspond to a height change of 2.54 mm. Knowing the length of the support frame, we convert the micrometer mils into angles. The calibration test is done by setting the tilt electronics GEP-2 in the RUN mode to activate feedback on any tilt changes. When the tilt levelling system is operating in tilt feedback, the ATFS responds to the frame tilting by adjusting the power to the TLs to keep the tiltmeter reading (Tilt Balance) at a null voltage. Starting with the left micrometer we perform the calibration by inducing several step-like changes in the TL height through precise dial turning and operating on the micrometers one by one. To avoid possible sources of systematic errors and remove any backlash out of the micrometer, we first overshot the targeted dial value, then turn down to it. The elapsed time between two steps is about 30 minutes so that the disturbance fades out. The TLs output during the calibration test is shown in Fig.3. After the signal is stabilized, we fit the data to the micrometer changes, the latter being converted into angle units. A least-square fit(Figs. 3b, 3d) provides the scale factors to convert TL voltages into angles (Tab. 1).We setup a validation test to check the calibration obtained by means of the micrometer manipulations. The spectral features of the available data-set allow us to use a different methodological approach to calibrate the Tilt Power signal. The amplitude spectra of the hourly decimated Tilt Power and room temperature are drawn in Fig. 4; only the long-term polynomial trend is removed from the signals. The spectra clearly show the existence in both the temperature and Tilt Power signals of an annual harmonic component (frequency = 0.00273 cpd) (Figs. 4a

  , next, the Tilt Power and theoretical tilt due to the solid Earth tide. As expected, the correlation between TL and temperature signals is characterized by two features: (i) a

  Power and temperature in different spectral bands. In fact, the Tilt Power and temperature time series show common features at different frequencies: a polynomial long-term trend and an annual periodic signal. The detrended and low-pass filtered (cut-off frequency = 0.01 cpd) time series are plotted in Figs. (6a), (6b) and (6c). By subtracting them from the raw signals, we obtain the highfrequency components shown in Figs (6d), (6e) and (6f). We apply the frequency dependent A c c e p t e d M a n u s c r i p t 8 correlation analysis to the filtered data to investigate the linearity of the temperature influence on the Tilt Power signal and recover the thermal admittance function (Fig. 7). To better define the transfer function of the temperature effect on Tilt Power, we compute a frequency dependent admittance. Both the correlation function and admittance have the smallest negative values at low frequency (< 0.5 cpd) and at the frequency of the thermal harmonics (1 cpd, 2 cpd...). This implies that the Tilt Power and temperature are almost perfectly anti-correlated and that most of the TL signal has a thermal origin. The good coherence at low frequencies comes from the annual variation of both the temperature and Tilt Power, which dominates the signals. The behaviour of the admittance function in the frequency domain confirms these results (Fig. 7); in fact, the thermal influence on Tilt Power in the different spectral bands closely follows the correlation function.

Fig. (

  Fig. (8d) displays the gravity variation induced by the non-thermal tilt changes. Just for

  term trend of about 20 µrad/year, (ii) a strong annual component of about 200 µrad peak-to-peak, (iii) a diurnal component having an amplitude of 0.3 µrad, (iv) a semi-diurnal component of about 0.1µrad (the harmonics S3 and S4 are also evident), (v) a clear tidal component as large as 0.05 µrad in the semi-diurnal band. The tidal effects clearly appear thanks to the large data stacking (> 11 years); moreover they provide us with a tool to validate the results of the TLs calibration made by means of the micrometer height changes. It is noteworthy that Tilt Power signals contain not only the temperature changes, but even low amplitude tidal tilt signals. The tidal signals are likely detected by the tiltmeters inside the gravity sensing unit and routed to the TLs as feedback currents. Anyway it is hard to separate one signal from the other, namely recognizing which device senses the tilt A c c e p t e d M a n u s c r i p t 10 changes. A step ahead would consist in installing an independent tilt sensor, for instance a bi-axial tiltmeter, aligned with the internal SG tiltmeters. This would enable us to better discriminate between the thermal signal and the real tilt.

  Results of the TLs' output calibration through micrometer changes and its validation in the frequency domain. The values of the ratio between the spectral amplitudes of the theoretical tidal signal and Tilt Power are listed in the last two columns; the last ones have been computed for an ocean-less Earth (WD = Wahr-Dehant Earth model) and also accounting for the OTL effect (FES04).

Figure 1 :

 1 Figure 1: Geometry and orientation of the tilt support frame and internal tiltmeters for the SG-C026 meter operating in Strasbourg gravity station J9.

Figure 2 :

 2 Figure 2: The Strasbourg hourly data sets from February 1997 until June 2008: (a) Left Tilt Power; (b) Right Tilt Power; (c) room temperature; (d) room humidity. A polynomial fitting is plotted to emphasize the existence of a long-term parabolic trend in both the Tilt Power and temperature signals.

Figure 3 :

 3 Figure 3: Output signals collected during the calibration test and fit results: (a, c) Left and Right Tilt Power outputs; (b, d) results of the least square fit; the values in the inset represent the micrometer changes expressed in mils.

Figure 4 :

 4 Figure 4: Amplitude spectrum of the Tilt Power signals and room temperature (a); detail focused on the tidal bands (b); detail focused on the lowest frequencies (c) to emphasize the annual peak.

Figure 5 :

 5 Figure 5: Correlation coefficients coming from a frequency-dependent regression analysis of the Left TL output versus both theoretical tilt tide and temperature.

Figure 6 :

 6 Figure 6: De-trended and filtered Tilt Power and temperature: (a)-(c) signals de-trended by means of a polynomial fitting (grey curve) and low-pass filtered ones (black curve); (d)-(f) highpass filtered signals.

Figure 7 :

 7 Figure 7: Correlation coefficients resulting from a frequency-dependent regression between Tilt Power signals and temperature; the thermal admittance is plotted too.

Figure 8 :

 8 Figure 8: Modelling of the equivalent gravity effect due to the tilt changes: (a) gravity effect due to the tilt changes (black curve); the solid Earth tide is plotted for the sake of comparison (grey curve). (b, c) Residual Left and Right Tilt Power signals reduced for thermal effect; (d) equivalent gravity effect induced by tilt signal plotted in (b) and (c); The gravity changes due to the Polar Motion (grey curve) is also drawn to have a reference; (e) Residual gravity computed for J9 station.

  Figure 1

Table II :

 II Parameters (γ and phase) for M2 tidal wave determined by means of harmonic analyses on Tilt Power signals; in the last two lines the theoretical values are given as a reference.

Table I Micrometer changes Spectral Ratio TLs mils/V mm/V µrad/V WD

 I (µrad/V) WD+FES04 (µrad/V) Left 16.8 ± 0.2 0.427 ± 0.003 200 ± 2

				182	Undetermined
	Right	15.05 ± 0.08 0.382 ± 0.002 179 ± 1	162	170 ± 11
			Table II
			γ	Phase (°)
		Right_TL	0.84 ± 0.09	1.48 ± 6.0
		Left_TL	0.77 ± 0.06	-174.3 ± 4.5
		WD	0.70	0
		WD+FES04	0.81	2.1

Acknowledgements

The authors thank W. Zürn and T. Jahr for their valuable comments that significantly improved the paper.