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Germany
Journal of Geodynamics 38 (2004) 263–280
Results from 44 months of observations with a superconducting gravimeter at Moxa/Germany C. Kroner∗ , Th. Jahr, G. Jentzsch Institut f¨ur Geowissenschaften, Friedrich-Schiller-Universit¨at Jena, Burgweg 11, D-07749 Jena, Germany Received 4 November 2003; received in revised form 2 June 2004; accepted 9 July 2004
Abstract Results for more than 42 months of observations with the superconducting gravimeter CD-034 at the Geodynamic Observatory Moxa are discussed. Moxa observatory is one of the newer stations within the ‘Global Geodynamics Project’ (GGP). A special feature of the gravimeter at Moxa is its dual sensor system; differences in the results obtained from the two sensor recordings are generally well within the standard deviations of the tidal analysis. One significant difference concerns the slightly different drift rates of 31 and 49.5 nm/s2 per year for upper and lower sensor; both sensor drifts can be fitted by a linear function. We find that the noise levels are close to the ‘New Low Noise Model’ for the seismic-modes and are also low in the tidal bands. Due to this low noise, Moxa is a station well suited to search for small geodynamic signals. The long-period variation in the gravity residuals correlates well with the polar motion. The difference signal between the two sensor recordings has a peak-to-peak amplitude of about 6 nm/s2 and shows systematic variations. Its spectrum is characterised by instrumental noise between 0.2 and 0.4 cph. The noise level of the difference and of the sum of the two residual datasets are clearly lower, respectively, higher than the noise contents of the gravity residuals themselves. This is a strong indication for the existence of broadband signals common to the two residual datasets, leading to the conjecture that the reduction of environmental effects is still not sufficient. Our results once more emphasize the necessity to correct the data for barometric pressure effects when analyzing the data for seismic modes. The reduction visibly increases the signal-to-noise ratio in the low frequencies of the mode band and helps to avoid misinterpreations of peaks. Besides the well known barometric pressure influence we can establish hydrological effects in the data which are probably caused by soil moisture and groundwater table variations as well as by batch-wise water movement within the weathering layer. As the major part of the observatory surroundings is above gravimeter level, an anticorrelation between hydrological and gravity changes is observed. In addition, it can be shown that global hydrological effects reach an order of magnitude that makes it necessary ∗
Corresponding author. Tel.: +49 3641 948611; fax: +49 3641 948662. E-mail addresses: [email protected] (C. Kroner), [email protected] (Th. Jahr), [email protected] (G. Jentzsch). 0264-3707/$ – see front matter © 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jog.2004.07.012
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to consider these effects when analyzing long-period signals like polar motion. Vice versa these effects are large enough to be detectable in the gravity data. A first joint analysis of five datasets from the GGP network shows no indications for signals related to the Slichter triplet or core modes. © 2004 Elsevier Ltd. All rights reserved.
1. Introduction Temporal changes in earth’s gravity field express deformations of the earth’s solid body and mass transfers in the geosphere. The study of gravity field variations yields information about the earth’s dynamic properties and processes as well as interactions between the atmosphere, hydrosphere and solid body. In the last 20 years, superconducting gravimeters (SG) have been increasingly used for long-term gravity observations. Besides long-term stability, this type of instrument has the advantage of a wide bandwidth of observation which covers the frequencies of the earth’s free oscillations just as well as the polar motion. The results presented in this paper concern gravity observations carried out with a SG installed at the Geodynamic Observatory Moxa in 1999. Moxa observatory, which started as a pure seismological station in 1964 is located about 30 km south of Jena (Fig. 1) at the rim of the Thuringian Slate Mountains (Jahr et al., 2001). It is partly built into a hill in order to reduce environmental noise. The surroundings consist of slate and graywacke of Lower Visean age. The observatory with the SG CD-034 is part of the ‘Global Geodynamics Project’ (Crossley et al., 1999) dedicated to the study of global geodynamic signals such as earth tides, polar motion, core and the Slichter modes, as well as hydrology-related phenomena. 2. Instrument The SG CD-034 installed at Moxa observatory is a dual sensor instrument. About 20 cm above the ‘lower’ sensor a second ‘upper’ sensor unit is built in. Originally, the dual sensor gravimeter was developed in order to detect and correct instrument-induced offsets of some nm/s2 in the gravity data; this was a problem with some of the older generation gravimeters (Warburton and Brinton, 1995). Up to now, no single-sensor offsets were found in the recordings of the instrument at Moxa. Comparisons of the upper and lower datasets give information about instrumental effects as well as the efficiency of reductions of environmental effects applied to the datasets. The gravimeter is installed on a pillar in a temperature-stabilized room that is separated from the rest of the observatory. A long-term temperature stability of ±0.5◦ C is achieved by heating panels beneath the ceiling. The gravimeter chamber directly borders to the hill into which the observatory is built, and the area above the room is covered by an about 3 m thick layer of gravel and clay for additional screening. Conditions inside and around the gravimeter/observatory such as air/He temperature, air/He pressure, wind, precipitation, and tilt compensation are continuously monitored. In a 50 m deep borehole in front of the observatory buildings, groundwater table fluctuations are observed. The water level is about 2–3 m below the well head. The gravimeter was installed at Moxa at Easter 1999. At the end of that year, the data acquisition system was replaced. Due to this and a number of maintenance events during the first months of operation a more extensive analysis of the gravity data did not start until mid-December 1999. The instrument
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Fig. 1. Location of Moxa observatory and other European SG stations.
was amplitude calibrated to ± 0.1% by three 2–3-day long parallel recordings with a FG5 absolute gravimeter of the Federal Agency for Cartography and Geodesy (BKG, Frankfurt). An accurate phase lag determination was not done yet. Therefore, we use a value of 0 s, but we are aware that the SG CD-034 has a time lag of about 5–7 s.
3. Data treatment The gravity data are recorded in 1 s samples. After filtering to 1 min samples and provisional subtraction of earth tides and barometric pressure effects data disturbances such as spikes, offsets, and earthquakes
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are removed. Processing of the minute data is sufficient as there is only a small number of disturbances in the data. Data gaps up to a maximum of 4 h are filled by linear interpolation. For the data processing the interactive graphic software PREGRED of the ETERNA software package is used (Wenzel, 1996). The gravity data then are filtered to hourly values. Barometric pressure data used for reductions are recorded at both 1 and 10 s samples. The other environmental parameters are monitored in 10 s or 1 min intervals. All these data are processed in their original sampling interval and then decimated to 1 h samples. Barometric pressure is additionally resampled to 1 min intervals.
4. Earth tides For the study of small geodynamic signals, it is necessary to remove the earth tides from the gravity data. In order to eliminate the tides in the data, tidal parameters were derived from the 44-month long dataset (1 January 2000–31 August 2003) reduced with regard to barometric pressure and hydrological effects. The local tidal parameters (amplitude factor δ, phase ∆) were determined with the tidal analysis software ETERNA 3.4 (Wenzel, 1996) using the tidal potential HW95 (Hartmann and Wenzel, 1995). The tidal analysis was carried out several times: in a first run a priori tidal parameters were estimated in order to be able to remove the tides from the data for the treatment. After the treatment, the tidal analysis was redone. Generally, short-period tides up to 0.5 cpd and the longer-period ones were separately adjusted. For the short periods all components below 0.5 cpd were eliminated by filtering. Before the parameters of the long-period tides were determined, a linear drift was removed from the datasets. The final results for the lower sensor are given in Table 1 assuming a time delay of 0 s. Besides ter-diurnal waves several diurnal and semi-diurnal wave groups derived from the third degree potential are separated. Tidal constituents with frequencies lower than wave group MSM were not adjusted because the datasets are still not long enough to give reliable results and additional long-term signals (especially annual) interfere with the long-period tides from Sta to Sa. In Fig. 2, the tidal parameters for the principle long- and short-period waves obtained for lower and upper sensors and the Wahr–Dehant–Zschau earth model (Dehant, 1987) are compared. The results for the two sensors are either identical or differ within the standard deviations of the tidal parameters which is determined by a least squares adjustment. Single exception is the amplitude factor of S2 which shows a discrepancy of 0.02%. The standard deviations explain only a discrepancy of 0.01%. A good correspondence is also observable between observed and modelled values. The differences in the short periods between model and observation are mainly due to oceanic loading. The biggest deviations between the two sensors as well as between observation and model exist for the long periods. Upper and lower sensor differ at maximum about 0.2% for the tide MF. A maximum difference between observation and model of about 3% occurs for MTM. The larger deviations for the long periods are due to the short length of the datasets for these periods and hydrological effects still present in the data (Section 6). In Table 2, ocean loading effects for the principle tides calculated with the ocean tidal models CRSN 3.0 (Eanes, 1994), FES95 (Le Provost et al., 1995), and SCW80 (Schwiderski, 1980a,b) are summarized. The loading effects were calculated with the software LOAD89 supplied by O. Francis (ECGS, Luxembourg). The best ocean loading reduction in terms of closest result of observed tidal parameters to modelled ones is obtained when using the CRSN 3.0 model.
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Table 1 Tidal parametersa for Moxa (SG, lower sensor), 1 January 2000–31 August 2003 From (cpd)
To (cpd)
Wave group
δ
0.025812 0.033407 0.060132 0.072436 0.096423 0.106137 0.130596 0.721500 0.851183 0.860896 0.892331 0.892950 0.895216 0.921941 0.934245 0.958085 0.965843 0.966299 0.968565 0.989049 0.996968 0.999853 1.001825 1.005329 1.007595 1.028550 1.036292 1.039324 1.039795 1.075174 1.099161 1.719381 1.825518 1.858777 1.859543 1.863634 1.888387 1.895363 1.895674 1.900529 1.923766 1.958233 1.968271 1.968875 1.969169 1.999706 2.003032 2.031287
0.031744 0.044653 0.070611 0.080797 0.104931 0.115411 0.249951 0.833113 0.859690 0.892184 0.892935 0.894010 0.906315 0.932893 0.940487 0.965827 0.966284 0.966756 0.974188 0.995143 0.998028 1.000147 1.003651 1.005623 1.013689 1.034467 1.039192 1.039649 1.073349 1.080944 1.216397 1.823399 1.856953 1.859381 1.862428 1.872142 1.895069 1.895673 1.898720 1.906462 1.942753 1.966593 1.968727 1.969037 1.998287 2.002885 2.013689 2.047391
MSM MM MSF MF MSTM MTM MSQM SMQ1 2Q1 SIG1 3MK1 Q1 RO1 O1 TAU1 499 M1 M1 CHI1 PI1 P1 S1 K1 PSI1 PHI1 THE1 J1 3MO1 SO1 OO1 NY1 3N2 EPS2 3MJ2 2N2 MY2 839 N2 N2 NY2 M2 LMB2 L2 L2 T2 S2 K2 ETA2
1.20815 1.15744 1.12676 1.14466 1.09440 1.13411 1.18233 1.14899 1.15075 1.15048 1.08306 1.14625 1.14726 1.14925 1.14634 1.15267 1.08438 1.15189 1.14842 1.15371 1.14974 1.19618 1.13685 1.26528 1.17742 1.15653 1.15524 1.08645 1.14922 1.15528 1.14802 1.13231 1.14764 1.07582 1.16347 1.16016 1.17474 1.05885 1.17746 1.17905 1.18637 1.18318 1.16930 1.08097 1.18954 1.18504 1.18720 1.18156
∆ (◦ ) 0.10350 0.01706 0.05270 0.00402 0.07004 0.01400 0.05180 0.00613 0.00181 0.00157 0.00887 0.00039 0.00141 0.00005 0.00391 0.00391 0.00655 0.00141 0.00365 0.00205 0.00012 0.00707 0.00004 0.00502 0.00275 0.00360 0.00101 0.00823 0.00383 0.00102 0.00525 0.00833 0.00389 0.00803 0.00174 0.00099 0.01654 0.00229 0.00024 0.00084 0.00003 0.00406 0.00159 0.00255 0.00106 0.00006 0.00022 0.00357
1.1995 0.7811 2.1155 0.1646 −0.6194 −1.4541 0.8558 −0.2640 −0.6718 −0.5902 1.9463 −0.2144 −0.2437 0.0793 −0.0617 0.1008 0.3554 0.0637 0.5705 0.2187 0.1323 3.3783 0.1748 0.2617 −0.0456 0.0778 0.1076 −0.2934 0.1937 0.0321 0.2706 1.7333 1.4830 −0.6725 2.6036 2.3112 1.8988 0.1518 2.0719 1.9845 1.4881 0.8153 1.4781 −2.1976 0.2359 0.2725 0.4493 0.0615
4.8601 0.8352 2.6672 0.2014 3.6601 0.7084 2.5163 0.3056 0.0901 0.0783 0.4691 0.0193 0.0703 0.0025 0.1955 0.1944 0.3461 0.0703 0.1819 0.1020 0.0060 0.3386 0.0020 0.2272 0.1336 0.1783 0.0501 0.4341 0.1911 0.0506 0.2620 0.4215 0.1943 0.4277 0.0854 0.0488 0.8067 0.1241 0.0114 0.0409 0.0014 0.1965 0.0780 0.1351 0.0509 0.0030 0.0105 0.1731
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Table 1 (Continued) ∆ (◦ )
From (cpd)
To (cpd)
Wave group
δ
2.067579 2.753244 2.892641 2.927107 2.965990
2.182843 2.869713 2.903886 2.940325 3.081254
2K2 MN3 M3 ML3 MK3
1.18059 1.06129 1.06989 1.07806 1.07689
a
−0.3605 0.6139 0.2768 1.7446 0.3142
0.01101 0.00542 0.00152 0.03057 0.01094
0.5342 0.2924 0.0816 1.6246 0.5819
Standard deviations from least squares adjustment by ETERNA 3.4.
Fig. 2. Tidal parameters obtained for lower sensor (∗), upper sensor (), and Wahr–Dehant–Zschau earth model (•), 1 January 2000–31 August 2003. Table 2 Ocean loading for Moxa observatory Wave group
Ocean tidal model CRSN 3.0
FES95
O1 K1 M2 S2
◦
SCW80
Amplitude (nm/s )
Phase ( )
Amplitude (nm/s )
Phase ( )
Amplitude (nm/s2 )
Phase (◦ )
1.41 2.05 12.16 4.08
147.585 78.169 55.442 28.058
1.27 2.01 11.82 3.61
151.134 59.759 53.398 25.481
1.39 1.41 13.02 4.14
159.168 64.984 49.553 21.890
2
2
◦
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5. Long-term variations One of the main reasons to develop a gravimeter with long-term stability was interest in the gravity signal of polar motion. For studies of long-term variations, tides and environmental influences need to be removed from the gravity data to obtain the gravity residuals. For the subtraction of the tidal waves, Sa and Ssa model tidal parameters (δ = 1.16545, ∆ = 0◦ ) were used. 5.1. Instrumental drift For studies of the drift behaviour the polar motion signal δgpol was additionally eliminated from the gravity residuals according to δgpol = 3.9 × 10−8 sin2 2θ[m1 cos λ − m2 sin λ]
(nm/s2 )
(1)
(Wahr, 1985; Crossley and Xu, 1998). In this m1 and m2 are the polar motion parameters in radians and θ and λ the colatitude and longitude of the observatory. Usually a linear or exponential function is assumed for the drift. At Moxa, a linear drift (as the simpler of the two drift models) was fitted. It yields a value of 49.5 nm/s2 /a for the lower sensor and 31 nm/s2 /a for the upper sensor. Absolute gravity measurements carried out at Moxa between December 2000 and May 2003 showed no significant change in the absolute gravity value (Falk, personal communication). Therefore, the drift should be instrumental. A reliable explanation of the drift behaviour of the two sensors is still missing. 5.2. Polar motion For the calculation of the polar motion signal smoothed 1-day polar motion data provided by the International Earth Rotation Service (IERS) on its webpage were used. In Fig. 3, the gravity residuals of both sensors (earth tides, environmental effects, drift subtracted) and the modelled polar motion signal are plotted. The two residual curves are identical within a few nm/s2 . All three curves show a very good agreement. A fit between the lower and upper sensor data to the polar motion signal yields an amplitude factor of 1.11 for the lower sensor and of 1.12 for the upper sensor.
Fig. 3. Gravity residuals and polar motion (model curve slightly shifted), 1 January 2000–31 August 2003. The curves of lower and upper sensor are practically not distinguishable.
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A phase shift could not be detected. The fitting of two harmonic functions having periods of 365.25 and 432 days to the data makes it possible to separately determine parameters for the annual and the Chandler wobble avoiding the necessity of 6.5 years long time series for the separation of the two polar motion components. This estimate yields annual wobble: Chandler wobble:
lower sensor, δ = 1.00, ∆ = 2.3◦ ; lower sensor, δ = 1.16, ∆ = 3.1◦ ;
upper sensor, δ = 0.98, ∆ = −0.1◦ , upper sensor, δ = 1.17, ∆ = 5.9◦ .
The results for the two sensors show a good correspondence and are in the same range as the theoretically favored amplitude factor of about δ = 1.18 (Loyer et al., 1999). The low δ-factor of the annual component can be explained by additional signals present in the data such as long-period ocean loading, hydrological influences and other seasonal effects in the gravity residuals not yet modelled.
6. Environmental influences A part of the variations a gravimeter observes is of atmospheric and hydrologic origin. As these effects significantly enhance the noise contents in the data and thus cover small geodynamic signals, they need to be removed. Barometric pressure fluctuations produce effects in the order of magnitude of 200– 300 nm/s2 . Hydrological effects generated by groundwater table and soil moisture changes can reach an order of magnitude of several 10 nm/s2 . The barometric pressure influence was removed using a complex admittance as discussed by Warburton and Goodkind (1977), Crossley et al. (1995), Kroner and Jentzsch (1999). The importance of the barometric pressure reduction even for the higher frequencies becomes clear when looking at seismic normal-mode spectra. The low-frequency section of the normal-mode spectrum of the Peru earthquake, 23 June 2001, depth 33 km, Mw 8.4, observed at Moxa observatory is given in Fig. 4. As shown before by Z¨urn and Widmer (1995), van Camp (1999) the pressure reduction significantly improves the signal-to-noise ratio, in this example by a factor of 2 for frequencies below 0.7 mHz. Additionally, some of the signals that could be interpreted as free oscillations, especially as Coriolis coupled modes (Z¨urn et al., 2000) are partly pressure-induced in this case. The pressure correction therefore is necessary to avoid misinterpretations. The second environmental influence known at Moxa observatory is hydrology-related. A large portion of the observatory surroundings in which soil moisture variations and changes in the amount of water in the weathering layer occur is above gravimeter level (Kroner, 2001). This hydrological influence is only partly compensated by soil moisture and groundwater table fluctuations below the gravimeter. Due to this we observe an anticorrelation between the gravity residuals and i.e. precipitation (Fig. 5). Additionally geology as well as signatures in the gravity data indicate the occurrence of a batch-wise water movement downhill towards the gravimeter location some time after a rain event. The hydrological changes in the observatory area are largely reflected in the groundwater table variations, thus making it possible to use these data to remove part of the hydrological influence from the gravity residuals. Depending on the time-scale the vertical distance and the dimension of the area involved in producing noticeable hydrological effects at the gravimeter site vary. Seasonal soil moisture variations e.g. affect a larger area and deeper layers than short-term soil moisture changes. Besides, groundwater table and soil moisture variations show similarities as they both originate from precipitation, but there are distinct
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Fig. 4. Section of the seismic normal-mode spectrum (lower sensor) from the Peru earthquake, 23 June 2001, without and with barometric pressure reduction.
differences and phase shifts which could be shown by first test measurements. Due to the fact that at present only the groundwater table measurements can be used for a correction these effects are taken care of by applying a slightly frequency-dependent hydrological reduction. For the long periods (e.g. annual), the coefficient is 0.06 nm/s2 /mm, for the periods of the diurnal to ter-diurnal tides and shorter the coefficient is 0.055 nm/s2 /mm. In between the value changes gradually. For the phase a constant value of 180◦ is applied. The hydrological correction used is given in Fig. 6. A more extensive regime of measurements and a more sophisticated correction are presently being developed. An additional hydrological effect occurs due to large-scale soil moisture changes and sea surface height anomalies. The significance of these effects was addressed by van Dam et al. (2001) and Sato et al. (2001). A similar estimate to that of these two groups of the composed effect of global soil moisture, snow depth and sea surface height variations for Moxa for the years 1987–1988 yields an order of magnitude of 20– 30 nm/s2 for this influence that has seasonal characteristics (Fig. 7). The data used for the computation were taken from the webpages provided by the ‘Global Soil Wetness Project’, the ‘NASA Physical Oceanography Distributed Active Archive Center’ at the Jet Propulsion Laboratory, California Institute of Technology, and the ‘National Oceanographic and Atmospheric Administration’. In the estimate changes in groundwater table and surface water were neglected. Calculations for more recent time spans are not possible yet due to the lack of availability of global hydrological data. This global hydrological influence
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Fig. 5. Gravity residuals lower sensor (a), accumulated precipitation (per hour) (b), and groundwater table variations (c), 18 April–2 May 2000.
Fig. 6. Hydrological reduction, 1 January 2000–31 August 2003.
Fig. 7. Estimated effect of global hydrological variations on gravity, January 1987–January 1989.
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Fig. 8. Typical mean power spectral density observed at Moxa and compared to the NLNM (a), and mean power spectral density of difference between the two sensors (b).
is sufficiently large that it needs to be considered when looking at long-period phenomena like polar motion. On the other hand the scale of the effect is such that it should be detectable in the gravity data.
7. Residuals Gravity data reduced for all known signals (earth tides, drift, polar motion, barometric pressure and hydrological effects) can be analyzed for residual noise levels. The noise contents between 0.1 and 50 mHz was estimated according to Banka and Crossley (1999), but instead of the five quietest days five arbitrary days (arbitrary so far as only days with earthquakes M > 5 were omitted) were used to calculate the mean power spectral density (Fig. 8a). Thus we get an idea what the typical noise level looks like one encounters in the Moxa data. For comparison, additionally the curve of the ‘New Low Noise Model’ (Peterson, 1993) is given. This model describes the mean minimum noise level observed with long-period seismometers worldwide. Though we did not select the quietest days, the curves obtained for Moxa are still quite close to the model. The noise contents of upper and lower sensor is almost identical. The peak at 27 mHz in the spectrum of the lower sensor and at 23 mHz in the one of the upper sensor are due to the parasitic mode of the superconducting sensor spheres (GWR, personal communication). Other peaks in the spectra cannot be explained yet. The descending of the observed noise level below the model curve at frequencies below 0.7 mHz is primary due to the fact that pressure effects removed before the analysis while the noise model contains these effects. Rosat et al. (2002) carried out similar calculations for Moxa and other GGP stations. They could also confirm the low noise contents of the Moxa data.
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Fig. 9. Gravity residuals (lower sensor) (a), difference signal between the sensors (b) and groundwater table variations (c), 1 January 2000–31 August 2003.
In Fig. 8b, the spectrum of the difference between upper and lower sensor is plotted. Its overall noise level is slightly below that given in Fig. 8a showing that the datasets of the two sensors still contain identical signals. This is confirmed when the cross spectrum between the two datasets is computed. The constant level between 0.5 and 15 mHz indicates that the difference data is dominated by instrumental noise in this frequency range. The gravity residuals, in Fig. 9a shown for the lower sensor, have a peak-to-peak amplitude of 60 nm/s2 over the 44 months of observation. The residual signal is partly due to remaining hydrological effects in the data (Fig. 9c). This can be shown by comparison of the gravity residuals with barometric pressure, rain events, and groundwater table variations. The difference of the recordings of upper and lower sensor (Fig. 9b) varies about 6 nm/s2 and shows some kind of systematic changes which is probably also related to the hydrological influence (Kroner, 2001; Kroner et al., 2001). The difference curve was directly computed between the hourly values, only taking into account the different drift behaviour. The residual power spectra of lower and upper sensor of Fig. 10 are nearly undistinguishable. Higher amounts of energy remain in the curves of Fig. 10a at tidal frequencies. The difference spectrum (Fig. 10b) is characterised by similar peaks at tidal frequencies. These peaks occur due to the fact that the two sensors are independent units. This means they react slightly differently to disturbances due to earthquakes, maintenance works or other instrumental/non-environmental effects resulting in slightly different length of gaps and external influences such as hydrology. This affects the signals at tidal frequencies. In general, the noise level of the difference spectrum is one to two orders of magnitude below the level in Fig. 10a.
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Fig. 10. Power spectral density lower and upper sensor (a), and difference and sum of the residuals (b), 1 January 2000–31 August 2003.
The noise level of the spectrum of the sum of the residuals (Fig. 10b) is about one order of magnitude higher. Despite reductions there obviously still exist identical signals in the gravity residuals of the two sensors, probably generated by the environment. An indication for a small deviation in the hydrological effect in the records of the two sensors could be detected by experiment (Kroner, 2001) in which the water contents of one specific area near the instrument was systematically enhanced. It showed a difference of some 10 nm/s2 over the time span of the experiment of 1 h. This order of magnitude could also be
Fig. 11. Product spectrum of gravity data (a) and barometric pressure (b) for predicted frequency range of the core modes; GGP stations: Boulder, Canberra, Moxa, Sutherland, and Wuhan; April 2000–May 2001. The dashes indicate tidal frequencies (potential HW95; Hartmann and Wenzel, 1995).
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confirmed by estimates of the very local hydrological effect for the two sensors (Kroner, 2001). The difference in the response originates from the slightly different distance upper and lower sensors have to the water masses. The effect increases when an area larger than that for the experiment is taken into account. Fittings of barometric pressure reductions to the two sensor datasets at Moxa also indicate a slightly different response of the sensors to barometric pressure.
8. Core modes and Slichter triplet One of the major aims of GGP is to detect signals related to the core modes and the Slichter triplet. Signals of the core modes are predicted for the period range from 6 h onwards (Crossley and Rochester, 1980; Smylie and Rochester, 1981; Friedl¨ander, 1985; Crossley et al., 1991), the Slichter triplet, if it exists, is expected to occur somewhere between 3 and 6 h (Smylie, 1992; Crossley et al., 1992; Rieutord, 2002). A lot of efforts have already been undertaken with regard to their detection, especially the Slichter modes, but the result is still controversial (Hinderer et al., 1995; Courtier et al., 2000). Another attempt is described in the following. There is general agreement that a detection will only be possible by a stack of low noise gravity data in order to enhance significantly the signal-to-noise ratio in the respective frequency ranges.
Fig. 12. Product spectrum of gravity data (a) and barometric pressure (b) for predicted frequency range of the Slichter triplet; GGP stations: Boulder, Canberra, Moxa, Sutherland, and Wuhan; April 2000–May 2001. The arrows indicate possible frequencies of the Slichter triplet according to different authors, the dashes tidal frequencies (potential HW95; Hartmann and Wenzel, 1995).
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For our study we set the following prerequisites regarding the station/data selection: no coastal stations, identical number of stations from each continent, and identical observation period as well as data treatment. The second criterion was laid down to avoid an influence of regional effects on the results. Following these criteria we came up with five stations (Boulder, Canberra, Moxa, Sutherland, and Wuhan) and an observation period of 14 months (April 2000–May 2001), accepting that the geographical distribution of the stations is not optimal for a detection. Preferable would be a more zonal station distribution. The gravity residuals used in the calculations were stripped of all known signals. The product spectrum and mean coherence spectrum were calculated from the data. Product spectrum means the geometric mean of the individual station spectra (Smylie, 1992). To obtain the mean coherence spectrum the coherence between each station combination was determined and the resulting ten coherence spectra averaged. The advantage of the coherence is that it takes (at least between two stations) the phase information into account. The same was done with the barometric pressure data of the observation period in order to be able to identify pressure-related signals in the gravity spectra. The results given in Figs. 11–14 can be summarized as follows: • peaks above the noise level can generally either be related to earth tides or barometric pressure; • there are no conspicuous peaks even slightly above the noise level in the tide-free gap between the
diurnal and semi-diurnal tides that could be related to core modes; • no significant peaks can be found at predicted frequencies of the Slichter triplet; • no other obvious triplet structures can be found; • there is one interesting peak in the product spectrum in Fig. 12 close to 0.23 cph, but whether this peak
has any meaning as one component of the Slichter triplet or is purely accidental remains to be seen.
Fig. 13. Mean coherence of gravity data (a) and barometric pressure (b) for predicted frequency range of the core modes; GGP stations: Boulder, Canberra, Moxa, Sutherland, and Wuhan; April 2000–May 2001. The dashes indicate tidal frequencies (potential HW95; Hartmann and Wenzel, 1995).
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Fig. 14. Mean coherence of gravity data (a) and barometric pressure (b) for predicted frequency range of the Slichter triplet; GGP stations: Boulder, Canberra, Moxa, Sutherland, and Wuhan; April 2000–May 2001. The arrows indicate possible frequencies of the Slichter triplet according to different authors, the dashes tidal frequencies (potential HW95; Hartmann and Wenzel, 1995).
These findings mean: • either that neither core modes nor Slichter triplet were excited during the time under investiga-
tion; • the noise level of the datasets is still too high for a detection tantamount to more stations, stations
with a different geographical distribution, longer datasets and still better environmental reductions are needed; or • neither core modes nor Slichter triplet produce a signal in the gravity field.
9. Conclusions The Geodynamic Observatory Moxa with its generally low noise level is a SG station well suited for broadband geodynamic studies. Among the SG stations worldwide Moxa is one of the quietest for frequencies of the free oscillations and the earth tides at present as shown by Rosat et al. (2002), Ducarme et al. (2002), and our own studies (Kroner et al., 2001). The long-term part of the data also looks promising. The noise levels between 3 and 6 cpd are sufficiently low to use these data together with data from other quiet SG stations to look for signals from core and Slichter modes. The recordings of the two gravimeter sensors are characterised by a high correlation with similar signal and noise contents. Both sensors show a small linear instrumental drift but with different drift rates. Due to their high quality the recordings of upper and lower sensor are both valuable for geodynamic studies.
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Besides, comparisons of the recordings help to identify local noise sources and to verify the effectiveness of the respective correction. We find a significant hydrological influence on the gravity data. A major part of these effects originates from the area above the gravimeter level. We can take care of some of these effects by using groundwater table data which reflect part of the hydrological changes occurring. Regarding this the hydrogeological situation of Moxa observatory must be better understood and longer datasets are necessary in order to develop an adequate correction. A joint analysis of gravity data from five globally distributed stations yielded no significant signals that could be attributed to core modes or the Slichter triplet. This might be explained by the number of stations used in the study as well as their geographical distribution, the length of the datasets and/or by an insufficient noise reduction. A strong indication for the latter is given by the clearly different noise levels of the gravity residuals of dual sensor instruments and the noise levels of the difference data and the sum of the residuals.
Acknowledgements The superconducting gravimeter was provided by funds of the University Development Plan (Hochschulentwicklungsplan) and by the Government of Thuringia. We thank the International Earth Rotation Service, the National Atmospheric and Oceanographic Administration, the members of the Global Soil Wetness Project and the NASA Oceanography Active Archive Center for making their data available to the scientific community. We also thank Wernfrid K¨uhnel and Matthias Meininger for their engagement to keep the gravimeter running. The support of Reinhard Falk from the Federal Agency for Cartography and Geodesy (BKG) by doing absolute gravity measurements at Moxa observatory is gratefully acknowledged. We also thank the members of GGP for making their data available to us.
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Ducarme, B., Sun, H.-P., Xu, J.-Q., 2002. New investigation of tidal gravity results from the GGP network. Bul. d’Inf. Mar´ees Terr. 136, 10761–10776. Eanes, R., 1994. Diurnal and semidiurnal tides from TOPEX/Poseidon altimetry. EOS Trans. Am. Geophys. Union 75 (16), 108. Friedl¨ander, S., 1985. Internal oscillations in the earth’s fluid core. Geophys. J. R. Astron. Soc. 80, 345–361. Hartmann, T., Wenzel, H.-G., 1995. The HW95 tidal potential catalogue. Geophys. Res. Lett. 22 (24), 3553–3556. Hinderer, J., Crossley, D., Jensen, O., 1995. A search for the Slichter triplet in superconducting gravimeter data. Phys. Earth Planet. Int. 90, 183–195. Jahr, Th., Jentzsch, G., Kroner, C., 2001. The Geodynamic Observatory Moxa/Germany: instrumentation and purposes. J. Geodyn. Soc. Jpn. 47 (1), 34–39. Kroner, C., 2001. Hydrological effects on gravity data of the Geodynamic Observatory Moxa. J. Geodyn. Soc. Jpn. 47 (1), 353–358. Kroner, C., Jahr, Th., Jentzsch, G., 2001. Comparison of datasets recorded with the dual sphere superconducting gravimeter CD-034 at the Geodynamic Observatory Moxa. J. Geodyn. Soc. Jpn. 47 (1), 398–403. Kroner, C., Jentzsch, G., 1999. Comparison of different barometric pressure reductions for gravity data and resulting consequences. Phys. Earth Planet. Int. 115, 205–218. Le Provost, C., Bennet, A.F., Cartwright, D.E., 1995. Ocean tides for and from TOPEX/Poseidon. Science 267, 639–642. Loyer, S., Hinderer, J., Boy, J.-P., 1999. Determination of the gravimetric factor at the Chandler period from earth orientation data and superconducting gravimeter observations. Geophys. J. Int. 136, 1–7. Peterson, J., 1993. Observations and modeling of seismic background noise. Open file report 93-332, U.S. Department of Interior, Geological Survey, Albuquerque, New Mexico. Rieutord, M., 2002. Slichter modes of the earth revisited. Phys. Earth Planet. Int. 131, 269–278. Rosat, S., Hinderer, J., Crossley, D., 2002. A comparison of the seismic noise levels at various GGP stations. Bull. d’Inf. Mar´ees Terr. 135, 10689–10700. Sato, T., Fukuda, Y., Aoyama, Y., McQueen, H., Shibuya, K., Tamura, Y., Asari, K., Ooe, M., 2001. On the observed annual gravity variation and the effect of sea surface height variations. Phys. Earth Planet. Int. 123, 45–63. Schwiderski, E.W., 1980a. On chartering global ocean tides. Rev. Geophys. Space Phys. 18 (1). Schwiderski, E.W., 1980b. Global ocean tides. V. The diurnal principle lunar tide (O1), Rep. NSWC, Dahlgren. Smylie, D., 1992. The inner core translational triplet and the density near earth’s center. Science 255, 1678. Smylie, D., Rochester, M., 1981. Compressibility, core dynamics and the subseismic wave equation. Phys. Earth Planet. Int. 24, 308–309. van Camp, M., 1999. Measuring seismic normal modes with the GWR C021 superconducting gravimeter. Phys. Earth Planet. Int. 116, 81–92. van Dam, T., Wahr, J., Milly, C., Samakin, A., Francis, O., 2001. Hydrological loading and gravity observations. J. Geodyn. Soc. Jpn. 47 (1), 249–254. Wahr, J.M., 1985. Deformation induced by polar motion. J. Geophys. Res. 90, 9363–9368. Warburton, R., Brinton, E., 1995. Recent developments in GWR Instruments’ superconducting gravimeters. Cahiers Centre Europ. de G´eodynamique et de S´eismologie 11, 23–56. Warburton, R., Goodkind, J., 1977. The influence of barometric pressure variations on gravity. Geophys. J. R. Astron. Soc. 48, 281–291. Wenzel, H.-G., 1996. The nanogal software: earth tide processing package ETERNA 3.30. Bull. d’Inf. Mar´ees Terr. 124, 8425– 9439. Z¨urn, W., Widmer, R., 1995. On noise reduction in vertical seismic records below 2 mHz using local barometric pressure. Geophys. Res. Lett. 22 (24), 3537–3540. Z¨urn, W., Laske, G., Widmer-Schnidrig, R., Gilbert, F., 2000. Observation of Coriolis coupled modes below 1 mHz. Geophys. J. Int. 143, 113–118.
Results from 44 months of observations with a superconducting gravimeter at Moxa/Germany C. Kroner∗ , Th. Jahr, G. Jentzsch Institut f¨ur Geowissenschaften, Friedrich-Schiller-Universit¨at Jena, Burgweg 11, D-07749 Jena, Germany Received 4 November 2003; received in revised form 2 June 2004; accepted 9 July 2004
Abstract Results for more than 42 months of observations with the superconducting gravimeter CD-034 at the Geodynamic Observatory Moxa are discussed. Moxa observatory is one of the newer stations within the ‘Global Geodynamics Project’ (GGP). A special feature of the gravimeter at Moxa is its dual sensor system; differences in the results obtained from the two sensor recordings are generally well within the standard deviations of the tidal analysis. One significant difference concerns the slightly different drift rates of 31 and 49.5 nm/s2 per year for upper and lower sensor; both sensor drifts can be fitted by a linear function. We find that the noise levels are close to the ‘New Low Noise Model’ for the seismic-modes and are also low in the tidal bands. Due to this low noise, Moxa is a station well suited to search for small geodynamic signals. The long-period variation in the gravity residuals correlates well with the polar motion. The difference signal between the two sensor recordings has a peak-to-peak amplitude of about 6 nm/s2 and shows systematic variations. Its spectrum is characterised by instrumental noise between 0.2 and 0.4 cph. The noise level of the difference and of the sum of the two residual datasets are clearly lower, respectively, higher than the noise contents of the gravity residuals themselves. This is a strong indication for the existence of broadband signals common to the two residual datasets, leading to the conjecture that the reduction of environmental effects is still not sufficient. Our results once more emphasize the necessity to correct the data for barometric pressure effects when analyzing the data for seismic modes. The reduction visibly increases the signal-to-noise ratio in the low frequencies of the mode band and helps to avoid misinterpreations of peaks. Besides the well known barometric pressure influence we can establish hydrological effects in the data which are probably caused by soil moisture and groundwater table variations as well as by batch-wise water movement within the weathering layer. As the major part of the observatory surroundings is above gravimeter level, an anticorrelation between hydrological and gravity changes is observed. In addition, it can be shown that global hydrological effects reach an order of magnitude that makes it necessary ∗
Corresponding author. Tel.: +49 3641 948611; fax: +49 3641 948662. E-mail addresses: [email protected] (C. Kroner), [email protected] (Th. Jahr), [email protected] (G. Jentzsch). 0264-3707/$ – see front matter © 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jog.2004.07.012
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to consider these effects when analyzing long-period signals like polar motion. Vice versa these effects are large enough to be detectable in the gravity data. A first joint analysis of five datasets from the GGP network shows no indications for signals related to the Slichter triplet or core modes. © 2004 Elsevier Ltd. All rights reserved.
1. Introduction Temporal changes in earth’s gravity field express deformations of the earth’s solid body and mass transfers in the geosphere. The study of gravity field variations yields information about the earth’s dynamic properties and processes as well as interactions between the atmosphere, hydrosphere and solid body. In the last 20 years, superconducting gravimeters (SG) have been increasingly used for long-term gravity observations. Besides long-term stability, this type of instrument has the advantage of a wide bandwidth of observation which covers the frequencies of the earth’s free oscillations just as well as the polar motion. The results presented in this paper concern gravity observations carried out with a SG installed at the Geodynamic Observatory Moxa in 1999. Moxa observatory, which started as a pure seismological station in 1964 is located about 30 km south of Jena (Fig. 1) at the rim of the Thuringian Slate Mountains (Jahr et al., 2001). It is partly built into a hill in order to reduce environmental noise. The surroundings consist of slate and graywacke of Lower Visean age. The observatory with the SG CD-034 is part of the ‘Global Geodynamics Project’ (Crossley et al., 1999) dedicated to the study of global geodynamic signals such as earth tides, polar motion, core and the Slichter modes, as well as hydrology-related phenomena. 2. Instrument The SG CD-034 installed at Moxa observatory is a dual sensor instrument. About 20 cm above the ‘lower’ sensor a second ‘upper’ sensor unit is built in. Originally, the dual sensor gravimeter was developed in order to detect and correct instrument-induced offsets of some nm/s2 in the gravity data; this was a problem with some of the older generation gravimeters (Warburton and Brinton, 1995). Up to now, no single-sensor offsets were found in the recordings of the instrument at Moxa. Comparisons of the upper and lower datasets give information about instrumental effects as well as the efficiency of reductions of environmental effects applied to the datasets. The gravimeter is installed on a pillar in a temperature-stabilized room that is separated from the rest of the observatory. A long-term temperature stability of ±0.5◦ C is achieved by heating panels beneath the ceiling. The gravimeter chamber directly borders to the hill into which the observatory is built, and the area above the room is covered by an about 3 m thick layer of gravel and clay for additional screening. Conditions inside and around the gravimeter/observatory such as air/He temperature, air/He pressure, wind, precipitation, and tilt compensation are continuously monitored. In a 50 m deep borehole in front of the observatory buildings, groundwater table fluctuations are observed. The water level is about 2–3 m below the well head. The gravimeter was installed at Moxa at Easter 1999. At the end of that year, the data acquisition system was replaced. Due to this and a number of maintenance events during the first months of operation a more extensive analysis of the gravity data did not start until mid-December 1999. The instrument
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Fig. 1. Location of Moxa observatory and other European SG stations.
was amplitude calibrated to ± 0.1% by three 2–3-day long parallel recordings with a FG5 absolute gravimeter of the Federal Agency for Cartography and Geodesy (BKG, Frankfurt). An accurate phase lag determination was not done yet. Therefore, we use a value of 0 s, but we are aware that the SG CD-034 has a time lag of about 5–7 s.
3. Data treatment The gravity data are recorded in 1 s samples. After filtering to 1 min samples and provisional subtraction of earth tides and barometric pressure effects data disturbances such as spikes, offsets, and earthquakes
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are removed. Processing of the minute data is sufficient as there is only a small number of disturbances in the data. Data gaps up to a maximum of 4 h are filled by linear interpolation. For the data processing the interactive graphic software PREGRED of the ETERNA software package is used (Wenzel, 1996). The gravity data then are filtered to hourly values. Barometric pressure data used for reductions are recorded at both 1 and 10 s samples. The other environmental parameters are monitored in 10 s or 1 min intervals. All these data are processed in their original sampling interval and then decimated to 1 h samples. Barometric pressure is additionally resampled to 1 min intervals.
4. Earth tides For the study of small geodynamic signals, it is necessary to remove the earth tides from the gravity data. In order to eliminate the tides in the data, tidal parameters were derived from the 44-month long dataset (1 January 2000–31 August 2003) reduced with regard to barometric pressure and hydrological effects. The local tidal parameters (amplitude factor δ, phase ∆) were determined with the tidal analysis software ETERNA 3.4 (Wenzel, 1996) using the tidal potential HW95 (Hartmann and Wenzel, 1995). The tidal analysis was carried out several times: in a first run a priori tidal parameters were estimated in order to be able to remove the tides from the data for the treatment. After the treatment, the tidal analysis was redone. Generally, short-period tides up to 0.5 cpd and the longer-period ones were separately adjusted. For the short periods all components below 0.5 cpd were eliminated by filtering. Before the parameters of the long-period tides were determined, a linear drift was removed from the datasets. The final results for the lower sensor are given in Table 1 assuming a time delay of 0 s. Besides ter-diurnal waves several diurnal and semi-diurnal wave groups derived from the third degree potential are separated. Tidal constituents with frequencies lower than wave group MSM were not adjusted because the datasets are still not long enough to give reliable results and additional long-term signals (especially annual) interfere with the long-period tides from Sta to Sa. In Fig. 2, the tidal parameters for the principle long- and short-period waves obtained for lower and upper sensors and the Wahr–Dehant–Zschau earth model (Dehant, 1987) are compared. The results for the two sensors are either identical or differ within the standard deviations of the tidal parameters which is determined by a least squares adjustment. Single exception is the amplitude factor of S2 which shows a discrepancy of 0.02%. The standard deviations explain only a discrepancy of 0.01%. A good correspondence is also observable between observed and modelled values. The differences in the short periods between model and observation are mainly due to oceanic loading. The biggest deviations between the two sensors as well as between observation and model exist for the long periods. Upper and lower sensor differ at maximum about 0.2% for the tide MF. A maximum difference between observation and model of about 3% occurs for MTM. The larger deviations for the long periods are due to the short length of the datasets for these periods and hydrological effects still present in the data (Section 6). In Table 2, ocean loading effects for the principle tides calculated with the ocean tidal models CRSN 3.0 (Eanes, 1994), FES95 (Le Provost et al., 1995), and SCW80 (Schwiderski, 1980a,b) are summarized. The loading effects were calculated with the software LOAD89 supplied by O. Francis (ECGS, Luxembourg). The best ocean loading reduction in terms of closest result of observed tidal parameters to modelled ones is obtained when using the CRSN 3.0 model.
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Table 1 Tidal parametersa for Moxa (SG, lower sensor), 1 January 2000–31 August 2003 From (cpd)
To (cpd)
Wave group
δ
0.025812 0.033407 0.060132 0.072436 0.096423 0.106137 0.130596 0.721500 0.851183 0.860896 0.892331 0.892950 0.895216 0.921941 0.934245 0.958085 0.965843 0.966299 0.968565 0.989049 0.996968 0.999853 1.001825 1.005329 1.007595 1.028550 1.036292 1.039324 1.039795 1.075174 1.099161 1.719381 1.825518 1.858777 1.859543 1.863634 1.888387 1.895363 1.895674 1.900529 1.923766 1.958233 1.968271 1.968875 1.969169 1.999706 2.003032 2.031287
0.031744 0.044653 0.070611 0.080797 0.104931 0.115411 0.249951 0.833113 0.859690 0.892184 0.892935 0.894010 0.906315 0.932893 0.940487 0.965827 0.966284 0.966756 0.974188 0.995143 0.998028 1.000147 1.003651 1.005623 1.013689 1.034467 1.039192 1.039649 1.073349 1.080944 1.216397 1.823399 1.856953 1.859381 1.862428 1.872142 1.895069 1.895673 1.898720 1.906462 1.942753 1.966593 1.968727 1.969037 1.998287 2.002885 2.013689 2.047391
MSM MM MSF MF MSTM MTM MSQM SMQ1 2Q1 SIG1 3MK1 Q1 RO1 O1 TAU1 499 M1 M1 CHI1 PI1 P1 S1 K1 PSI1 PHI1 THE1 J1 3MO1 SO1 OO1 NY1 3N2 EPS2 3MJ2 2N2 MY2 839 N2 N2 NY2 M2 LMB2 L2 L2 T2 S2 K2 ETA2
1.20815 1.15744 1.12676 1.14466 1.09440 1.13411 1.18233 1.14899 1.15075 1.15048 1.08306 1.14625 1.14726 1.14925 1.14634 1.15267 1.08438 1.15189 1.14842 1.15371 1.14974 1.19618 1.13685 1.26528 1.17742 1.15653 1.15524 1.08645 1.14922 1.15528 1.14802 1.13231 1.14764 1.07582 1.16347 1.16016 1.17474 1.05885 1.17746 1.17905 1.18637 1.18318 1.16930 1.08097 1.18954 1.18504 1.18720 1.18156
∆ (◦ ) 0.10350 0.01706 0.05270 0.00402 0.07004 0.01400 0.05180 0.00613 0.00181 0.00157 0.00887 0.00039 0.00141 0.00005 0.00391 0.00391 0.00655 0.00141 0.00365 0.00205 0.00012 0.00707 0.00004 0.00502 0.00275 0.00360 0.00101 0.00823 0.00383 0.00102 0.00525 0.00833 0.00389 0.00803 0.00174 0.00099 0.01654 0.00229 0.00024 0.00084 0.00003 0.00406 0.00159 0.00255 0.00106 0.00006 0.00022 0.00357
1.1995 0.7811 2.1155 0.1646 −0.6194 −1.4541 0.8558 −0.2640 −0.6718 −0.5902 1.9463 −0.2144 −0.2437 0.0793 −0.0617 0.1008 0.3554 0.0637 0.5705 0.2187 0.1323 3.3783 0.1748 0.2617 −0.0456 0.0778 0.1076 −0.2934 0.1937 0.0321 0.2706 1.7333 1.4830 −0.6725 2.6036 2.3112 1.8988 0.1518 2.0719 1.9845 1.4881 0.8153 1.4781 −2.1976 0.2359 0.2725 0.4493 0.0615
4.8601 0.8352 2.6672 0.2014 3.6601 0.7084 2.5163 0.3056 0.0901 0.0783 0.4691 0.0193 0.0703 0.0025 0.1955 0.1944 0.3461 0.0703 0.1819 0.1020 0.0060 0.3386 0.0020 0.2272 0.1336 0.1783 0.0501 0.4341 0.1911 0.0506 0.2620 0.4215 0.1943 0.4277 0.0854 0.0488 0.8067 0.1241 0.0114 0.0409 0.0014 0.1965 0.0780 0.1351 0.0509 0.0030 0.0105 0.1731
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Table 1 (Continued) ∆ (◦ )
From (cpd)
To (cpd)
Wave group
δ
2.067579 2.753244 2.892641 2.927107 2.965990
2.182843 2.869713 2.903886 2.940325 3.081254
2K2 MN3 M3 ML3 MK3
1.18059 1.06129 1.06989 1.07806 1.07689
a
−0.3605 0.6139 0.2768 1.7446 0.3142
0.01101 0.00542 0.00152 0.03057 0.01094
0.5342 0.2924 0.0816 1.6246 0.5819
Standard deviations from least squares adjustment by ETERNA 3.4.
Fig. 2. Tidal parameters obtained for lower sensor (∗), upper sensor (), and Wahr–Dehant–Zschau earth model (•), 1 January 2000–31 August 2003. Table 2 Ocean loading for Moxa observatory Wave group
Ocean tidal model CRSN 3.0
FES95
O1 K1 M2 S2
◦
SCW80
Amplitude (nm/s )
Phase ( )
Amplitude (nm/s )
Phase ( )
Amplitude (nm/s2 )
Phase (◦ )
1.41 2.05 12.16 4.08
147.585 78.169 55.442 28.058
1.27 2.01 11.82 3.61
151.134 59.759 53.398 25.481
1.39 1.41 13.02 4.14
159.168 64.984 49.553 21.890
2
2
◦
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5. Long-term variations One of the main reasons to develop a gravimeter with long-term stability was interest in the gravity signal of polar motion. For studies of long-term variations, tides and environmental influences need to be removed from the gravity data to obtain the gravity residuals. For the subtraction of the tidal waves, Sa and Ssa model tidal parameters (δ = 1.16545, ∆ = 0◦ ) were used. 5.1. Instrumental drift For studies of the drift behaviour the polar motion signal δgpol was additionally eliminated from the gravity residuals according to δgpol = 3.9 × 10−8 sin2 2θ[m1 cos λ − m2 sin λ]
(nm/s2 )
(1)
(Wahr, 1985; Crossley and Xu, 1998). In this m1 and m2 are the polar motion parameters in radians and θ and λ the colatitude and longitude of the observatory. Usually a linear or exponential function is assumed for the drift. At Moxa, a linear drift (as the simpler of the two drift models) was fitted. It yields a value of 49.5 nm/s2 /a for the lower sensor and 31 nm/s2 /a for the upper sensor. Absolute gravity measurements carried out at Moxa between December 2000 and May 2003 showed no significant change in the absolute gravity value (Falk, personal communication). Therefore, the drift should be instrumental. A reliable explanation of the drift behaviour of the two sensors is still missing. 5.2. Polar motion For the calculation of the polar motion signal smoothed 1-day polar motion data provided by the International Earth Rotation Service (IERS) on its webpage were used. In Fig. 3, the gravity residuals of both sensors (earth tides, environmental effects, drift subtracted) and the modelled polar motion signal are plotted. The two residual curves are identical within a few nm/s2 . All three curves show a very good agreement. A fit between the lower and upper sensor data to the polar motion signal yields an amplitude factor of 1.11 for the lower sensor and of 1.12 for the upper sensor.
Fig. 3. Gravity residuals and polar motion (model curve slightly shifted), 1 January 2000–31 August 2003. The curves of lower and upper sensor are practically not distinguishable.
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A phase shift could not be detected. The fitting of two harmonic functions having periods of 365.25 and 432 days to the data makes it possible to separately determine parameters for the annual and the Chandler wobble avoiding the necessity of 6.5 years long time series for the separation of the two polar motion components. This estimate yields annual wobble: Chandler wobble:
lower sensor, δ = 1.00, ∆ = 2.3◦ ; lower sensor, δ = 1.16, ∆ = 3.1◦ ;
upper sensor, δ = 0.98, ∆ = −0.1◦ , upper sensor, δ = 1.17, ∆ = 5.9◦ .
The results for the two sensors show a good correspondence and are in the same range as the theoretically favored amplitude factor of about δ = 1.18 (Loyer et al., 1999). The low δ-factor of the annual component can be explained by additional signals present in the data such as long-period ocean loading, hydrological influences and other seasonal effects in the gravity residuals not yet modelled.
6. Environmental influences A part of the variations a gravimeter observes is of atmospheric and hydrologic origin. As these effects significantly enhance the noise contents in the data and thus cover small geodynamic signals, they need to be removed. Barometric pressure fluctuations produce effects in the order of magnitude of 200– 300 nm/s2 . Hydrological effects generated by groundwater table and soil moisture changes can reach an order of magnitude of several 10 nm/s2 . The barometric pressure influence was removed using a complex admittance as discussed by Warburton and Goodkind (1977), Crossley et al. (1995), Kroner and Jentzsch (1999). The importance of the barometric pressure reduction even for the higher frequencies becomes clear when looking at seismic normal-mode spectra. The low-frequency section of the normal-mode spectrum of the Peru earthquake, 23 June 2001, depth 33 km, Mw 8.4, observed at Moxa observatory is given in Fig. 4. As shown before by Z¨urn and Widmer (1995), van Camp (1999) the pressure reduction significantly improves the signal-to-noise ratio, in this example by a factor of 2 for frequencies below 0.7 mHz. Additionally, some of the signals that could be interpreted as free oscillations, especially as Coriolis coupled modes (Z¨urn et al., 2000) are partly pressure-induced in this case. The pressure correction therefore is necessary to avoid misinterpretations. The second environmental influence known at Moxa observatory is hydrology-related. A large portion of the observatory surroundings in which soil moisture variations and changes in the amount of water in the weathering layer occur is above gravimeter level (Kroner, 2001). This hydrological influence is only partly compensated by soil moisture and groundwater table fluctuations below the gravimeter. Due to this we observe an anticorrelation between the gravity residuals and i.e. precipitation (Fig. 5). Additionally geology as well as signatures in the gravity data indicate the occurrence of a batch-wise water movement downhill towards the gravimeter location some time after a rain event. The hydrological changes in the observatory area are largely reflected in the groundwater table variations, thus making it possible to use these data to remove part of the hydrological influence from the gravity residuals. Depending on the time-scale the vertical distance and the dimension of the area involved in producing noticeable hydrological effects at the gravimeter site vary. Seasonal soil moisture variations e.g. affect a larger area and deeper layers than short-term soil moisture changes. Besides, groundwater table and soil moisture variations show similarities as they both originate from precipitation, but there are distinct
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Fig. 4. Section of the seismic normal-mode spectrum (lower sensor) from the Peru earthquake, 23 June 2001, without and with barometric pressure reduction.
differences and phase shifts which could be shown by first test measurements. Due to the fact that at present only the groundwater table measurements can be used for a correction these effects are taken care of by applying a slightly frequency-dependent hydrological reduction. For the long periods (e.g. annual), the coefficient is 0.06 nm/s2 /mm, for the periods of the diurnal to ter-diurnal tides and shorter the coefficient is 0.055 nm/s2 /mm. In between the value changes gradually. For the phase a constant value of 180◦ is applied. The hydrological correction used is given in Fig. 6. A more extensive regime of measurements and a more sophisticated correction are presently being developed. An additional hydrological effect occurs due to large-scale soil moisture changes and sea surface height anomalies. The significance of these effects was addressed by van Dam et al. (2001) and Sato et al. (2001). A similar estimate to that of these two groups of the composed effect of global soil moisture, snow depth and sea surface height variations for Moxa for the years 1987–1988 yields an order of magnitude of 20– 30 nm/s2 for this influence that has seasonal characteristics (Fig. 7). The data used for the computation were taken from the webpages provided by the ‘Global Soil Wetness Project’, the ‘NASA Physical Oceanography Distributed Active Archive Center’ at the Jet Propulsion Laboratory, California Institute of Technology, and the ‘National Oceanographic and Atmospheric Administration’. In the estimate changes in groundwater table and surface water were neglected. Calculations for more recent time spans are not possible yet due to the lack of availability of global hydrological data. This global hydrological influence
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Fig. 5. Gravity residuals lower sensor (a), accumulated precipitation (per hour) (b), and groundwater table variations (c), 18 April–2 May 2000.
Fig. 6. Hydrological reduction, 1 January 2000–31 August 2003.
Fig. 7. Estimated effect of global hydrological variations on gravity, January 1987–January 1989.
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Fig. 8. Typical mean power spectral density observed at Moxa and compared to the NLNM (a), and mean power spectral density of difference between the two sensors (b).
is sufficiently large that it needs to be considered when looking at long-period phenomena like polar motion. On the other hand the scale of the effect is such that it should be detectable in the gravity data.
7. Residuals Gravity data reduced for all known signals (earth tides, drift, polar motion, barometric pressure and hydrological effects) can be analyzed for residual noise levels. The noise contents between 0.1 and 50 mHz was estimated according to Banka and Crossley (1999), but instead of the five quietest days five arbitrary days (arbitrary so far as only days with earthquakes M > 5 were omitted) were used to calculate the mean power spectral density (Fig. 8a). Thus we get an idea what the typical noise level looks like one encounters in the Moxa data. For comparison, additionally the curve of the ‘New Low Noise Model’ (Peterson, 1993) is given. This model describes the mean minimum noise level observed with long-period seismometers worldwide. Though we did not select the quietest days, the curves obtained for Moxa are still quite close to the model. The noise contents of upper and lower sensor is almost identical. The peak at 27 mHz in the spectrum of the lower sensor and at 23 mHz in the one of the upper sensor are due to the parasitic mode of the superconducting sensor spheres (GWR, personal communication). Other peaks in the spectra cannot be explained yet. The descending of the observed noise level below the model curve at frequencies below 0.7 mHz is primary due to the fact that pressure effects removed before the analysis while the noise model contains these effects. Rosat et al. (2002) carried out similar calculations for Moxa and other GGP stations. They could also confirm the low noise contents of the Moxa data.
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Fig. 9. Gravity residuals (lower sensor) (a), difference signal between the sensors (b) and groundwater table variations (c), 1 January 2000–31 August 2003.
In Fig. 8b, the spectrum of the difference between upper and lower sensor is plotted. Its overall noise level is slightly below that given in Fig. 8a showing that the datasets of the two sensors still contain identical signals. This is confirmed when the cross spectrum between the two datasets is computed. The constant level between 0.5 and 15 mHz indicates that the difference data is dominated by instrumental noise in this frequency range. The gravity residuals, in Fig. 9a shown for the lower sensor, have a peak-to-peak amplitude of 60 nm/s2 over the 44 months of observation. The residual signal is partly due to remaining hydrological effects in the data (Fig. 9c). This can be shown by comparison of the gravity residuals with barometric pressure, rain events, and groundwater table variations. The difference of the recordings of upper and lower sensor (Fig. 9b) varies about 6 nm/s2 and shows some kind of systematic changes which is probably also related to the hydrological influence (Kroner, 2001; Kroner et al., 2001). The difference curve was directly computed between the hourly values, only taking into account the different drift behaviour. The residual power spectra of lower and upper sensor of Fig. 10 are nearly undistinguishable. Higher amounts of energy remain in the curves of Fig. 10a at tidal frequencies. The difference spectrum (Fig. 10b) is characterised by similar peaks at tidal frequencies. These peaks occur due to the fact that the two sensors are independent units. This means they react slightly differently to disturbances due to earthquakes, maintenance works or other instrumental/non-environmental effects resulting in slightly different length of gaps and external influences such as hydrology. This affects the signals at tidal frequencies. In general, the noise level of the difference spectrum is one to two orders of magnitude below the level in Fig. 10a.
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Fig. 10. Power spectral density lower and upper sensor (a), and difference and sum of the residuals (b), 1 January 2000–31 August 2003.
The noise level of the spectrum of the sum of the residuals (Fig. 10b) is about one order of magnitude higher. Despite reductions there obviously still exist identical signals in the gravity residuals of the two sensors, probably generated by the environment. An indication for a small deviation in the hydrological effect in the records of the two sensors could be detected by experiment (Kroner, 2001) in which the water contents of one specific area near the instrument was systematically enhanced. It showed a difference of some 10 nm/s2 over the time span of the experiment of 1 h. This order of magnitude could also be
Fig. 11. Product spectrum of gravity data (a) and barometric pressure (b) for predicted frequency range of the core modes; GGP stations: Boulder, Canberra, Moxa, Sutherland, and Wuhan; April 2000–May 2001. The dashes indicate tidal frequencies (potential HW95; Hartmann and Wenzel, 1995).
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confirmed by estimates of the very local hydrological effect for the two sensors (Kroner, 2001). The difference in the response originates from the slightly different distance upper and lower sensors have to the water masses. The effect increases when an area larger than that for the experiment is taken into account. Fittings of barometric pressure reductions to the two sensor datasets at Moxa also indicate a slightly different response of the sensors to barometric pressure.
8. Core modes and Slichter triplet One of the major aims of GGP is to detect signals related to the core modes and the Slichter triplet. Signals of the core modes are predicted for the period range from 6 h onwards (Crossley and Rochester, 1980; Smylie and Rochester, 1981; Friedl¨ander, 1985; Crossley et al., 1991), the Slichter triplet, if it exists, is expected to occur somewhere between 3 and 6 h (Smylie, 1992; Crossley et al., 1992; Rieutord, 2002). A lot of efforts have already been undertaken with regard to their detection, especially the Slichter modes, but the result is still controversial (Hinderer et al., 1995; Courtier et al., 2000). Another attempt is described in the following. There is general agreement that a detection will only be possible by a stack of low noise gravity data in order to enhance significantly the signal-to-noise ratio in the respective frequency ranges.
Fig. 12. Product spectrum of gravity data (a) and barometric pressure (b) for predicted frequency range of the Slichter triplet; GGP stations: Boulder, Canberra, Moxa, Sutherland, and Wuhan; April 2000–May 2001. The arrows indicate possible frequencies of the Slichter triplet according to different authors, the dashes tidal frequencies (potential HW95; Hartmann and Wenzel, 1995).
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For our study we set the following prerequisites regarding the station/data selection: no coastal stations, identical number of stations from each continent, and identical observation period as well as data treatment. The second criterion was laid down to avoid an influence of regional effects on the results. Following these criteria we came up with five stations (Boulder, Canberra, Moxa, Sutherland, and Wuhan) and an observation period of 14 months (April 2000–May 2001), accepting that the geographical distribution of the stations is not optimal for a detection. Preferable would be a more zonal station distribution. The gravity residuals used in the calculations were stripped of all known signals. The product spectrum and mean coherence spectrum were calculated from the data. Product spectrum means the geometric mean of the individual station spectra (Smylie, 1992). To obtain the mean coherence spectrum the coherence between each station combination was determined and the resulting ten coherence spectra averaged. The advantage of the coherence is that it takes (at least between two stations) the phase information into account. The same was done with the barometric pressure data of the observation period in order to be able to identify pressure-related signals in the gravity spectra. The results given in Figs. 11–14 can be summarized as follows: • peaks above the noise level can generally either be related to earth tides or barometric pressure; • there are no conspicuous peaks even slightly above the noise level in the tide-free gap between the
diurnal and semi-diurnal tides that could be related to core modes; • no significant peaks can be found at predicted frequencies of the Slichter triplet; • no other obvious triplet structures can be found; • there is one interesting peak in the product spectrum in Fig. 12 close to 0.23 cph, but whether this peak
has any meaning as one component of the Slichter triplet or is purely accidental remains to be seen.
Fig. 13. Mean coherence of gravity data (a) and barometric pressure (b) for predicted frequency range of the core modes; GGP stations: Boulder, Canberra, Moxa, Sutherland, and Wuhan; April 2000–May 2001. The dashes indicate tidal frequencies (potential HW95; Hartmann and Wenzel, 1995).
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Fig. 14. Mean coherence of gravity data (a) and barometric pressure (b) for predicted frequency range of the Slichter triplet; GGP stations: Boulder, Canberra, Moxa, Sutherland, and Wuhan; April 2000–May 2001. The arrows indicate possible frequencies of the Slichter triplet according to different authors, the dashes tidal frequencies (potential HW95; Hartmann and Wenzel, 1995).
These findings mean: • either that neither core modes nor Slichter triplet were excited during the time under investiga-
tion; • the noise level of the datasets is still too high for a detection tantamount to more stations, stations
with a different geographical distribution, longer datasets and still better environmental reductions are needed; or • neither core modes nor Slichter triplet produce a signal in the gravity field.
9. Conclusions The Geodynamic Observatory Moxa with its generally low noise level is a SG station well suited for broadband geodynamic studies. Among the SG stations worldwide Moxa is one of the quietest for frequencies of the free oscillations and the earth tides at present as shown by Rosat et al. (2002), Ducarme et al. (2002), and our own studies (Kroner et al., 2001). The long-term part of the data also looks promising. The noise levels between 3 and 6 cpd are sufficiently low to use these data together with data from other quiet SG stations to look for signals from core and Slichter modes. The recordings of the two gravimeter sensors are characterised by a high correlation with similar signal and noise contents. Both sensors show a small linear instrumental drift but with different drift rates. Due to their high quality the recordings of upper and lower sensor are both valuable for geodynamic studies.
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Besides, comparisons of the recordings help to identify local noise sources and to verify the effectiveness of the respective correction. We find a significant hydrological influence on the gravity data. A major part of these effects originates from the area above the gravimeter level. We can take care of some of these effects by using groundwater table data which reflect part of the hydrological changes occurring. Regarding this the hydrogeological situation of Moxa observatory must be better understood and longer datasets are necessary in order to develop an adequate correction. A joint analysis of gravity data from five globally distributed stations yielded no significant signals that could be attributed to core modes or the Slichter triplet. This might be explained by the number of stations used in the study as well as their geographical distribution, the length of the datasets and/or by an insufficient noise reduction. A strong indication for the latter is given by the clearly different noise levels of the gravity residuals of dual sensor instruments and the noise levels of the difference data and the sum of the residuals.
Acknowledgements The superconducting gravimeter was provided by funds of the University Development Plan (Hochschulentwicklungsplan) and by the Government of Thuringia. We thank the International Earth Rotation Service, the National Atmospheric and Oceanographic Administration, the members of the Global Soil Wetness Project and the NASA Oceanography Active Archive Center for making their data available to the scientific community. We also thank Wernfrid K¨uhnel and Matthias Meininger for their engagement to keep the gravimeter running. The support of Reinhard Falk from the Federal Agency for Cartography and Geodesy (BKG) by doing absolute gravity measurements at Moxa observatory is gratefully acknowledged. We also thank the members of GGP for making their data available to us.
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