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China and its application to geodynamics
Journal of Geodynamics 33 (2002) 187–198 www.elsevier.com/locate/jgeodyn
Tidal gravity observations obtained with a superconducting gravimeter at Wuhan/China and its application to geodynamics§ He-Ping Suna,*, Hou-Tze Hsua, Gerhard Jentzschb, Jian-Qiao Xua a
Open Laboratory of Dynamics Geodesy, Institute of Geodesy and Geophysics, Chinese Academy of Sciences, 54 Xu-Dong Road, 430077 Wuhan, PR China b Institute of Geosciences, University of Jena, Burgweg 11, D-07749, Jena, Germany
Abstract The long period tidal gravity observations recorded with a superconducting gravimeter at station Wuhan/ China from 1 January 1986 to 31 December 1994 (old series) and from 20 December 1997 to 30 April 2000 (new series) are studied comprehensively. The new tidal amplitude factors and phase differences are determined precisely using modern international standard data processing techniques. The tidal gravity signals due to the geophysical sources as of global ocean tides and local atmospheric pressure are comparatively studied. The dynamic influences of the Earth’s core, i.e. the resonance parameters (eigenperiod, quality factor and resonance strength) of the free core nutation, are determined and the corresponding results are compared with those obtained in the previous studies. # 2002 Elsevier Science Ltd. All rights reserved.
1. Introduction As the rapid improvement of the modern instruments [such as Goodkind-Warburton-Reineman superconducting gravimeter (SG) and FG-5 absolute gravimeter (AG)] and of the theoretical prediction (such as tidal catalogues, oceanic and atmospheric models), the study of geophysics and geodynamics using tidal gravity has become a common recognition. Compared to any spring gravimeters, the SG occupy many excellent characteristics as of the wide measuring range, low noise level, high stability and sensitivity, i.e. a resolution at the order of a nanogal (1012 g, Warburton, 1985; Goodkind, 1991). The SG observations with high sampling from global distributed stations, especially after eliminating instrumental drift and various systematic errors, can be used to study the geophysical and geodynamical problems, such as Earth tides, the interaction §
Paper presented to JSA37 Earth’s Gravity and Magnetic Fields From Space IUGG99, Birmingham, UK. * Corresponding author. Tel./fax: +86-27-86783841. E-mail addresses: [email protected] (H.-P. Sun), [email protected] (G. Jentzsch).
0264-3707/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0264-3707(01)00063-1
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of the Earth with ocean and atmosphere, resonance effect of the free core nutation (FCN), the modes of the Earth’s core, gravity change due to the tectonic motion and so on (Sun, 1992, 1995; Smylie et al., 1993; Hinderer et al., 1993; Defraigne and Dehant, 1994; Melchior and Francis, 1996; Kroner and Jentzsch, 1999, Courtier et al, 2000). The Global Geodynamics Project (GGP) started since July 1997, with participation of about 18 SG stations around the world (Crossley et al., 1999). The SG numbered as T004 was installed in November 1985 on the ground floor of the tidal gravity laboratory (30.58 N, 114.36 E, 34 m) in the main building of the Institute of Geodesy and Geophysics (IGG), Chinese Academy of Sciences (CAS) in Wuhan. It is about 1.5 km away from East Lake in the suburbs of the city. The city activities from the main road about 60 m away from instrument increase the station background noise (Hsu et al., 1989). At the end of 1997, the instrument was moved to a new site, about 25 km from the central city (30.52 N, 114.49 E, 89 m) after upgrading in accordance with GGP regulations, it is found that the site background noise is reduced significantly. The instrument room is air-conditioned, the yearly change of the room temperature is kept at the level of less than 1 C. In the period from 23 November 1985 to 24 August 1988, the analogue recordings were available. The data acquisition system developed by the German group, the first one was installed in November 1988 in order to increase the dynamic range (Kroner et al., 1995). The records with every 20 s interval are obtained from the original sampling of every 1 s and sent to a 22-bit digital voltmeter. Later, in 1997, in connection with the upgrading old SG meter, the second data acquisition system in accordance with the GGP regulations was installed. For the first stage, the pressure data are obtained from Wuhan meteorological fundamental station while since July 1994 they were recorded with 10-min sampling at the SG site. Both the hourly tidal gravity and pressure data are obtained after applying for the preprocessing procedures (Sun et al., 1998). Based on the tidal gravity measurements using two Lacost-Romberg Earth Tidal (LCR-ET) instrument numbered as 16 and 21 during the China-England international cooperation campaign (Hsu et al., 1989) at the same station, the amplitude calibration factor is determined using a weighted mean technique of the main tidal wave amplitude factors. The phase transfer function determined by the GWR manufacture is used in the data analysis.
2. Computation techniques In order to improve effectively the accuracy of the tidal gravity parameters, the data preprocessing is carried out carefully. Under the precondition of not damaging the inner quality of the observations, the non-tidal gravity signals were eliminated sufficiently. Spikes and ‘‘offsets’’ up to several mgal of unknown origin frequently occur. The abnormal signals are detected and eliminated by using a moving window function. Short term gaps, due to the power failures, earthquakes, liquid helium refilling, are filled using a spline interpolation based on a synthetic tidal gravity model. To correct numerically the background noise, it is important to avoid systematic effects prior to data reduction by filtering (Kroner et al., 1995; Banka et al., 1998). In the data processing, the modern standard international data analysis techniques as of Eterna (Wenzel, 1996) and Nsv (Venedikov, 1997) are applied. The high precision tide generating potential with 505 components (Cartwright, Tayler and Edden, CTE505, 1971) and with 1200
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components (Tamura, 1981) are employed in data reduction. The band pass filtering is used to eliminate instrumental drift and long term change in gravity for the first step. The so-called observation equations are constructed respectively for long period (LP), diurnal (D), semi-diurnal (SD) and ter-diurnal (TD) wave bands based on the continuous hourly data sets. These equations are then solved using classic least square method, the tidal parameters and the associated root mean square (RMS) errors are determined. The temporal changes of the tidal gravity residuals are obtained after subtracting the synthetic tidal gravity signals from the original observations. The fast Fourier transform (FFT) technique is used to determine the residual amplitude and standard deviations, i.e. noise level. The regression coefficients between the tidal residual and the change in atmospheric pressure at station are determined in both temporal and frequency domains, then the pressure influence on gravity is removed from the tidal measurements before the determination of the tidal parameters.
3. Results of the tidal parameters The long period tidal gravity observations from 1 January 1986 to 31 December 1994 (old series) and from 20 December 1997 to 30 April 2000 (new series) are used in this study. The tidal parameters and the associated RMS errors for 20 waves in D band, 13 waves in SD band and 2 waves in TD band are determined precisely based on the Eterna technique. The corresponding tidal parameters of 8 main waves are given in columns 2 and 3 in Table 1 and those of an other 14 small waves in columns 6 and 7 in Table 2. From the tidal analysis it is found that the accuracy of the main wave amplitude to be at 0.01 mgal level and that of the phase differences to be at 0.01 level. The stability of the amplitude factor calibration and of the high inner accuracy of the SG measurements are the main reasons for close fitting its results to theoretical computation. Comparing these results to those obtained from other stations in Europe as Brussels, Strasbourg and Potsdam (Sun et al., 1998; Neumeyer and Dittfeld, 1997), it is found that the phase differences at Wuhan are appeared to be the negative ones. Late we will show that it relates mainly to the oceanic tidal characters in Pacific and Atlantic oceans. Table 1 Tidal amplitude factors and phase differences for 8 main waves before and after ocean loading correctiona Model
Observed
Schwiderski (1)
0
Wave
’/( )
Q1 O1 P1 K1 N2 M2 S2 K2
1.1849 1.1787 1.1702 1.1514 1.1799 1.1762 1.1731 1.1673
0.28 0.58 0.82 0.73 0.66 0.63 0.58 0.56
1.1611 1.1566 1.1598 1.1382 1.1667 1.1668 1.1646 1.1551
0
CSR3.0 (2) 0
’ /( )
0.21 0.26 0.40 0.34 0.61 0.64 0.60 0.60
1.1603 1.1568 1.1585 1.1398 1.1646 1.1675 1.1639 1.1564
FES95 (3) 0
0
ORI (4) 0
0
’ /( )
’ /( )
0.04 0.22 0.27 0.13 0.48 0.48 0.47 0.44
1.1649 1.1580 1.1569 1.1381 1.1674 1.1689 1.1693 1.1589
0.35 0.26 0.26 0.15 0.15 0.01 0.16 0.17
1.1610 1.1578 1.1570 1.1379 1.1594 1.1584 1.1588 1.1533
ORI96 (5) 0
’ /( )
0
’0 /( )
0.47 0.16 0.22 0.17 0.91 0.67 0.38 0.57
1.1605 1.1579 1.1581 1.1385 1.1658 1.1646 1.1649 1.1584
0.04 0.25 0.40 0.26 0.49 0.46 0.42 0.40
a Note: (, ’) are the observed tidal gravity amplitude factor and phase, (0 , ’0 ) are those after oceanic loading correction.
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Table 2 Tidal residual amplitude and amplitude factors for some other small waves before and after ocean loading correctiona Tidal residuals
Amplitude factor
Wave
B/mgal
/( )
X/mgal
/( )
’/( )
0
’0 /( )
SIGQ RO1 NO1 PI1 PSI1 PHI1 TETA J1 OO1 2N2 MU2 NU2 L2 T2
0.010 0.030 0.054 0.038 0.028 0.018 0.011 0.057 0.026 0.043 0.042 0.040 0.009 0.055
127.46 23.79 26.77 21.78 32.87 145.93 48.02 41.67 74.81 25.89 5.35 54.34 4.57 77.33
0.029 0.009 0.009 0.025 0.026 0.022 0.007 0.037 0.026 0.015 0.008 0.027 0.005 0.052
172.26 77.25 20.16 15.56 45.71 167.96 52.52 41.42 73.30 53.01 31.36 98.39 148.47 93.05
1.1244 1.1812 1.1758 1.1976 1.3451 1.1428 1.1743 1.1764 1.1618 1.1905 1.1869 1.1742 1.1686 1.1712
2.00 0.59 0.55 0.90 2.14 0.91 0.95 0.86 1.06 0.65 0.11 0.78 0.02 1.74
0.9935 1.1563 1.1578 1.1895 1.3509 1.1240 1.1680 1.1715 1.1634 1.1702 1.1675 1.1605 1.1594 1.1612
1.26 0.53 0.08 0.52 3.56 0.49 0.73 0.65 1.22 0.49 0.14 0.76 0.10 1.99
a Note: (B, ) are the observed tidal gravity residual amplitude and phase, (X, w) are those after the oceanic loading correction; (, ’) are the observed tidal gravity amplitude factor and phase, (0 , ’0 ) are those after the loading correction.
It is an important criterion to check the standard deviations (Stdv) obtained from harmonic analysis since they can be used to judge the quality of the tidal parameters. The average Stdv are investigated systematically by using the NSV technique when taking various considerations, such as to use the CTE505 and Tamura’s tidal generating potential, to consider the weight of filtered numbers, to apply for pressure correction, to remove erroneous data and so on. It is found that the Stdv are reduced significantly from 2.33 to 0.90, from 1.85 to 0.62 and from 0.68 to 0.42 mgal in D, SD and TD wave bands respectively. While the global Stdv is given as 0.70 mgal when using Eterna technique, which shows that two data reduction techniques give similar results. When analysing the new series, the Stdv is given as 0.3 mgal, which indicates that the background noise at new site is largely reduced. In order to show the stability of the instrument and to study the temporal characteristics of the Earth’s response to tidal generating forces, the temporal variation of the monthly tidal parameters (amplitude factors and phase differences) in D and SD wave bands are investigated (Figs. 1 and 2). It is found that the perturbations at waves O1 and M2 relate to the interruption of the power supply or an instrumental adjustment, the discretion at P1S1K1 mainly relates to the meteorological influence and the regular variation at S2 corresponds to the seasonal disturbances of the continental pressure field (Fig. 1). No apparent relation of these results with local geophysical phenomena, such as an earthquake event and so on, is found. The temporal change of the M2 amplitude factor is relatively stable compared to that of the O1 wave. The scattering of the phase differences for P1S1K1 and S2K2 is up to 1.0 . It may be due to some regional sources as pressure, temperature, storms, underground water and so on, producing variations of the physical properties in the Earth’s interior. The uncertainty of the phase calibration may be also the reason to induce this disparity.
H.-P. Sun et al. / Journal of Geodynamics 33 (2002) 187–198
Fig. 1. Temporal changes of the monthly tidal amplitude factors for 4 main waves.
Fig. 2. Temporal changes of the monthly tidal phase differences for 4 main waves.
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4. Influence of the oceanic loading The oceanic tide is one of the main perturbations in the tidal gravity observations (Francis and Mazzega, 1990; Sun, 1992; Melchior, 1994; Jentzsch, 1997). It is important to remove the loading signals before the tidal parameters to be applied to the study of the geodynamics (Ducarme and van Ruymbeke, 1991; Courtier et al., 2000; Hsu et al., 2000). In 1980 Schwiderski provided us with the basic oceanic models for loading computations. As the rapid development of the Topex/ Poseidon altimeter and the finite element technique since 1992, the oceanic models are improved significantly. Therefore, to select the better models in removing the oceanic signals from tidal gravity observations is extremely important. The global oceanic models used in this study include Schwiderski’s (Scw80) and the most recent ones, such as Csr3.0 (Eanes), Fes952 (Grenoble), Ori and Ori96 (Matsumoto) models. The recent models occupy excellent characteristics, as wider coverage, higher resolution and accuracy as well as smaller residual amplitudes (PODAAC, 1999). Based on the model Earth Green’s functions (Farrell, 1972), the tidal gravity loading of above 5 models for 4 waves in D band (Q1, O1, P1 and K1) and 4 waves in SD band (N2, M2, S2 and K2) are calculated using a direct discrete convolution method (Francis and Mazzega, 1990; Sun, 1992). The effect of the ocean to gravity includes the direct attraction of the ocean tidal mass, and the loading contribution induced by the elastic deformation of the Earth. In order to check the suitability of the tidal gravity models and the oceanic models, let’s introduce observed residual amplitude and phase (B, ) and final residual amplitude and phase (X, w). The (B, ) can be obtained by subtracting synthetic tides from the tidal observations, and the (X, w) can be computed when subtracting oceanic loading from observed residuals. The tidal gravity residual amplitudes before and after oceanic loading correction are given in Fig. 3. The column 0 represents the observed residual amplitudes, and columns 1–5, the loading corrected residual amplitudes, 1, based on Schwiderski models, 2, Csr3.0 models, 3, Fes95.2 models, 4 and 5 Ori and Ori96 models respectively. The largest observed residual amplitude reaches
Fig. 3. Tidal gravity residual amplitudes before and after oceanic tidal loading correction (column 0, observed residual amplitudes; columns 1, 5 after correction based on various models).
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1.04 mgal (M2). It is found a relative more effective correction in D wave band, especially for the O1 and K1 wave, while in SD band, there have still large residuals at M2 and S2 waves, it may relate to other gravity signals. It is found that the Grenoble Fes95 models fit better tidal measurements in SD band, while no obvious advantages are found in D band. Table 1 demonstrates the tidal amplitude factors and phase differences before and after removing loading signals. Comparing to those in the theoretical tidal prediction (TTP, Dehant et al., 1998) as of the O1 (1.15376) and M2 (1.16262), the discrepancies of the observed ones and of those after loading correction are reduced significantly. For the O1 wave, it is reduced from 2.16% to 0.25% (Scw80), 0.26% (Csr3.0), 0.37% (Fes95), 0.35% (Ori and Ori96) and for the M2 wave, from 1.17% to 0.36% (Sch), 0.42% (Csr3.0), 0.54% (Fes95), 0.36% (Ori) and 0.17% (Ori96). It seems that in SD band, the discrepancy with respect to the TTP is smaller when using Ori96 models comparing to those when using other models. The oceanic models are not enough when the tidal parameters are used to study geodynamics. Especially there are no models presently for waves 1 and 1 that occupy a period close to the FCN resonance, i.e. one sidereal day. Based on the loading amplitudes and phases of 8 main waves obtained from Schwiderski models and a second order polynomial interpolation technique, the loading influence for other smaller waves, 9 waves in D band and 5 waves in SD band are calculated. Table 2 shows the tidal amplitude factors of other small waves before and after removing loading signals. It is found that the observed residual amplitude is reduced by about 8% ( 1), while it is increased by about 18% (1). The amplitude factors and phases fit better the tidal prediction after loading correction. However, the discrepancy still remains, it may relate to the station surroundings and to the calibration of the phase response, a further work will be orientated to this problem.
5. Effect of the atmospheric pressure A strong correlation between tidal residual and barometric pressure is found during the data reduction. In order to eliminate the pressure influence, the regression technique is employed. The frequency dependent regression coefficients, as of 0.3780.021 (LP), 0.3000.026 (D), 0.1990.041 (SD) and 0.1470.016 (TD) mgal/hPa, are used to correct the barometric influence on tidal gravity observations. These coefficients fit well for LP band, but they are relative low in other bands comparing to those given in theoretical prediction (0.36 mgal/hPa) under the assumption of hydrostatic atmospheric model (Sun, 1995) and to those determined at other stations as Brussels, Strasbourg and Cantly (Sun et al., 1998; Merriam, 1995). The temporal changes of monthly atmospheric gravity coefficients are given in Fig. 4. It is found the atmospheric gravity admittance are not stable and the discretion to be relative large. Analysis shows that it is due to the seasonal disturbances of the special meteorological condition in China and the mixed temperature signals in pressure records (see also Fig. 1). The harmonic analysis of the barometric pressure is given as 0.9530.015 hPa (S1), 0.0140.001 hPa (O1), 0.0750.001 hPa (K1), 0.04 0.004 hPa (M2), 0.7420.004 hPa (S2). It indicates that the pressure energy concentrates on S1 and S2 waves in tidal bands. After removing pressure signals, the amplitude factors are reduced to better fit with those obtained from the TTP, it is about 0.3% reduced for S2 wave, and the standard deviation is at 4% level reduced.
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Fig. 4. Temporal changes of the monthly atmospheric pressure gravity admittance.
6. Determination of the FCN resonance parameters The dynamic influence of the Earth’s core within a rotating, elastic and elliptical mantle will lead to a rotating eigenmode associated with the wobble of the fluid core with respect to the mantle. Owing to the oceanic loading, the mantle inelasticity, dissipating coupling torques (as electromagnetic and topographic torques) and the tidal friction (Herring et al., 1991), the FCN resonance parameters are expressed in complex. The imaginary parts relate to the damping characteristics of the Earth’s interior. Previous studies show that the FCN resonance processes the eigenperiod close to one sidereal day in the mantle reference frame and approximately 435 sidereal days in the space reference frame (Cummins and Wahr, 1993; Hinderer et al., 1993). Due to the diurnal forcing of the Moon and the Sun and the presence of the FCN, a resonance appears in the tesseral diurnal response of the Earth. The tides mostly affected by this resonance are P1, S1, K1, 1 and 1 waves, therefore, the tidal parameters of these waves can be used to investigate the resonance originating from the FCN. Furthermore some nutations associated with these tides, as of annual retrograde and prograde, semi-annual retrograde and prograde ones, are also perturbed by FCN resonance. In order to retrieve the resonance parameters, the influence of the ocean tides and atmospheric pressure are removed for the first step. Then the same procedures as Neuberg et al. (1987) and Defraigne and Dehant (1994) are applied. The techniques are based on the so called least squares fit of the tidal gravity data to a damped harmonic oscillator, the computation of the eigenperiod relates to the forcing frequency, and the quality factor Q relates to the FCN frequency and the attenuation factor. Considering a relative large disparity between the forcing frequency and the resonant one, the amplitude parameters for O1 are taken as the reference. Based on the resonant equations (Neuberg
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H.-P. Sun et al. / Journal of Geodynamics 33 (2002) 187–198 Table 3 Resonance parameters obtained at various stations
Resonance strength (104) Data used (station)
Eigen frequency (f) (degree/h)
Eigen period (T) (sidereal day)
Quality factor (Q value)
Ar ( /h)
Wuhan (old) Wuhan (new) Brussels Bad Homburg Strasbourg Metsahovi Kyoto All stations
15.078044 15.076396 15.075540 15.075745 15.076176 15.076002 15.078520 15.076134
406.8 (399.6, 425.8 (420.1, 436.3 (418.5, 433.8 (430.0, 428.4 (423.1, 430.6 (418.3, 401.6 (392.5, 429.0 (424.3,
10260 (5382, 109583) 3573 (2913, 4618) 2178 (1526, 3807) 5120 (4237, 6468) 22183 (9666, 1) 4596 (2824, 12327) 3857 (6954, 2669) 9543 (6405, 18714)
6.18 5.85 6.22 6.57 6.32 5.68 5.76 6.10
(0.000666) (0.000477) (0.001470) (0.000307) (0.000439) (0.001029) (0.000870) (0.000387)
414.2) 431.6) 455.8) 437.6) 433.9) 443.6) 411.2) 433.7)
(0.64) (0.23) (0.50) (0.16) (0.25) (0.45) (0.80) (0.20)
Ai ( /h) 0.35 (0.64) 0.50 (0.23) 0.66 (0.50) 0.16 (0.16) 0.15 (0.25) 0.17 (0.45) 0.06 (0.80) 0.01 (0.20)
et al., 1987), the differences between tidal parameters of P1, K1, c1 and f1 waves and that of O1 are considered, and the equations are solved using the least square technique. The determined resonant parameters are given in Table 3. Ar and Ai represent the real and imaginary parts of the resonant strength. The obtained FCN resonant parameters are given as (T=406.8 sidereal days, Q=10260, Ar=6.18104, Ai=0.35104) when using old series, while they are (T=425.8 sidereal days, Q=3573, Ar=5.85104, Ai=0.50104) when using new series. The numerical value of the eigenperiod is reasonable due to the low background noise at new site, while a low quality factor value is given. The same calculations are carried out for some other stations, as Brussels, Belgium (data from April 1982 to July 1995), Bad Homburg, Germany (data from May 1981 to May 1984), Strasbourg, France (data from November 1987 to December 1991), Metsahovi, Finland (data from November 1994 to October 1996) and Kyoto, Japan (data from October 1990 to November 1997). The corresponding results are also listed in Table 3 for comparison, the numerical values in parenthesis represent the error or error range.
Fig. 5. FCN resonance curves of the tidal parameters obtained at station Wuhan/China: (a) real part of the amplitude factor (cos’) and (b) imaginary part of the amplitude factor (sin’). Stars represent the results obtained from the old series and triangles those obtained for the new series.
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When stacking all the data sets above mentioned, the resonant contribution turns out to be (T=429.0 sidereal days, Q=9543, Ar=6.10104, Ai=0.01104). It signifies that our results from station Wuhan are close to the stacking one, the difference is less than 1%. Our results correspond to the previous studies inferred from stacking tidal gravity and nutation observations, or from VLBI measurements (Neuberg et al., 1987; Herring et al., 1991; Cummins and Wahr, 1993; Hinderer et al., 1993; Defraigne and Dehant, 1994; Flosch et al., 1994). It is also found that the influence of the ocean tides and the barometric pressure are the main error sources, the maximum discrepancy on eigenperiod can reach to 3% when using various oceanic models. In addition to these, the errors of the phase differences can be responsible for a biased Q. The tidal catalogue used in data reduction appears to be only of small importance. However, comparing to the eigenperiod in the case of inelastic mantle as of 462.8 sidereal days given by Wahr and Sasao (1981), the observed eigenperiods are low, the reasons should be further investigated. Fig. 5 shows the comparison of the tidal parameters between the TTP and the observed ones in the form of real and imaginary parts. It clearly shows the resonance influence of the Earth’s core in tidal parameters. The real parts fit better to those in TTP, while a relative large disparity for the imaginary parts is found.
7. Conclusions Based on the modern SG and data processing techniques, the tidal parameters at Wuhan, China, are determined precisely. The stability of the amplitude factor calibration and the high inner accuracy of the measurements are the main reasons for the good fit of the results to tidal models. It is found that the Grenoble (Fes95) ocean models fit better the tidal residuals. The small disparity of the tidal amplitude factors in SD band with respect to tidal models is found when using Ori96. The resonance parameters are determined when using Wuhan SG observations, the results obtained from new series fit better to those determined in previous studies, it is due to the low site background noise. The oceanic and barometric pressure influences can cause an error to the eigenperiod of about 3%, the phase differences can be responsible for a biased Q value. The tidal catalogue used in the tidal analysis appears to be only of small importance. A further study should be developed in checking influence of the change in room temperature and why the big difference appeared between theoretical prediction and ground measurements.
Acknowledgements This study is supported jointly by the Nature Science Foundation of China (49774223, 49925411) and the Chinese Academy of Sciences (KZ952-J1-411, KZCX2-106). The first data acquisition system at Wuhan was based on a development of Dr. G. Asch and provided by the Volkswagen Foundation (No. I/63542), the second system was developed by Dr. M. Ramatschi and made available at Wuhan by the Thyssen Foundation (No. 9.23/95) via co-author G.J. Late Professor H.-G. Wenzel and Professor A. Venedikov provided their outstanding tidal analysis packages. Dr. Defraigne gave fruitful comments for the stacking of tidal gravity observations, and Professor B. Ducarme suggested an interpolation technique of the oceanic loading influence for other small waves. All above are gratefully acknowledged.
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References Banka, D., Jentzsch, G., Crossley, D., 1998. Investigations of superconducting gravity records in the frequency range of the free oscillations of the Earth- the noise magnitude. In: Ducarme, B., Paquet, P. (Eds.), Proc. 13th Int. Symp. Earth Tides, Brussels, 20–24 July 1997, Se´rie Ge´ophysique. Royal Observatory of Belgium, Brussels, pp. 641–649. Courtier, N., Ducarme, B., Goodkind, J., Hinderer, J., Imanishi, Y., Seama, N., Sun, H.P., Merriam, J., Bengert, B., Smylie, D.E., 2000. Global superconducting gravimeter observations and the search for the translational modes of the inner core. Physics of the Earth and Planetary Interiors 117, 2–20. Crossley, D., Hinderer, J., Casula, G., Francis, O., Hsu, H.-T., Imanishi, Y., Jentzsch Ka¨a¨ria¨inen, J., Merriam, J., Meurers, B., Neumeyer, J., Richter, B., Shibuya, K., Sato, T., van Dam, T., 1999. Network of superconducting gravimeters benefits a number of disciplines. Eos, Transactions, American Geophysical Union 80 (11), 121–125–126. Cummins, P.R., Wahr, J.M., 1993. A study of the Earth’s free core nutation using international development of accelerometers gravity data. J. Geophysical Research 98 (B2), 2091–2103. Defraigne, P., Dehant, V., 1994. Stacking gravity tide measurements and nutation observations in order to determine the complex eigenfrequency of the nearly diurnal free wobble. J. Geophysical Research 99(B5), 9203–9213. Dehant, V., Defraigne, P., Wahr, J.M., 1998. Tides for an Earth in a non-hydrostatic equilibrium. In: Ducarme, B., Paquet, P. (Eds.), Proc. 13th Int. Symp. Earth Tides, Brussels, 20–24 July 1997, Se´rie Ge´ophysique. Royal Observatory of Belgium, Brussels, pp. 261–263. Ducarme, B., van Ruymbeke, M., 1991. On tidal parameters at Brussels fundamental station. In: Kakkuri, J. (Ed.), Proc. 11th Int. Symp. Earth Tides, E. Schweizerbart’sch Verlagsbuchhandlung. Nagele u. Obermiller, Stuttgart, pp. 157–166. Farrell, W.D., 1972. Deformation of the Earth by surface loads. Rev. Geophys. 10, 761–779. Florsch, N., Chambat, F., Hinderer, J., Legros, H., 1994. A simple method to retrieve the complex eigenfrequency of the Earth’s Nearly Free Wobble, application to the Strasbourg superconducting gravimeter data. Geophys. J. Int. 116, 53–63. Francis, O., Mazzega, P., 1990. Global charts of ocean tide loading effects. J. Geophys. Res. 95, 11411–11424. Goodkind, J.M., 1991. The SGs principles of operation, current performance and future prospects. In: Poitevin C. (Ed.), Proc. of the Workshop on Non-tidal Gravity Changes, Luxembourg, pp. 81–90. Herring, T.B., Buffett, P., Mathews, P., Shapiro, I., 1991. Forced nutations of the Earth: Influence of inner core dynamics, a very long baseline Interferometry data analysis. J. Geophys. Res. 96, 8243–8257. Hinderer, J., Crossley, J., Xu, H., 1993. The accuracy of tidal gravimetric factors and nearly diurnal free wobble resonance parameters in superconducting gravimetry. In: Hsu, H.T. (Ed.), Proc. 12th Int. Symp. Earth Tides, Beijing, 4–8 August 1993. Science Press, Beijing, pp. 289–297. Hsu, H.T., Becker, M., Groten, E., Tao, G.X., 1989. Comparison of gravity tidal observations by ET16 and ET21 at Wuhan station of China. Bull. d’Inf. Marees Terrestres 104, 7379–7394. Hsu, H.T., Sun, H.-P., Xu, J.Q., Tao, G.X., 2000. International tidal gravity reference values at Wuhan station. Science in China (series D) 43 (1), 77–83. Jentzsch, G., 1997. Earth tides and ocean tidal loading. In: Wilhelm, H., Zurn, W., Wenzel, HG. (Eds.), Tidal Phenomena. Lecturer Notes in Earth Sciences, vol. 66, pp. 145–171. Kroner, C., Hsu, H.T., Jahr, T., Jentzsch, G., Tao, G.X., Weise, A., 1995. Long-term stability and tidal parameters of the SCG record at Wuhan, China. In: Hsu, H.T. (Ed.), Proc. 12th Int. Symp. Earth Tides, Beijing, 4–8 August 1993. Science Press, Beijing, pp. 265–276. Kroner, C., Jentzsch, G., 1999. Comparison of different barometric pressure reductions for gravity data and resulting consequences. Phys. Earth Planet. Inter. 115, 205–218. Melchior, P., 1994. A new data bank for tidal gravity measurements (DB92). Phys. Earth Planet. Inter. 82, 125–155. Melchior, P., Francis, O., 1996. Comparison of recent ocean tidal models using ground based tidal gravity measurements. Marine Geodesy 19, 291–330. Merriam, J.B., 1995. The atmospheric pressure correction in gravity at Cantley Quebec. In: Hsu, H.T. (Ed.), Proc. 12th Inter. Symp. Earth Tides, Beijing, 3–4 August 1993. Science Press, Beijing, pp. 161–168. Neuberg, J., Hinderer, J., Zurn, W., 1987. Stacking gravity tide observations in central Europe for the retrival of the complex eigenfrequency of the nearly diurnal free wobble. Geophyd. J. Roy. Astr. Soc. 91, 853–868. Neumeyer, J., Dittfeld, H.J., 1997. Results of three years observation with superconducting gravimeter at the GeoForschungsZentrum Potsdam. Journal of Geodesy 71 (2), 59–80.
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PODAAC, 1999. A collection of global ocean tide models, NASA Physical Oceanography Distribution Active Archive Center at the Jet Propulsion Laboratory, California Institute of Technology, USA. Smylie, D.E., Hinderer, J., Richter, B., Ducarme, B., Mansinha, L., 1993. A comparative analysis of superconducting gravimeter data. Dynamics of Earth’s Deep Interior and Earth Rotation. Geophysical Monograph 72 IUGG 12, 91–96. Sun, H.-P., 1992. Comprehensive researches for the effect of the ocean loading on gravity observations in the Western Pacific area. Bull. d’Inf. Marees Terrestres 113, 8271–9292. Sun, H.-P., 1995. Static Deformation and Gravity Changes at the Earth’s Surface Due to the Atmospheric Pressure. PhD thesis in Catholic University of Louven (Belgium), Se´rie Ge´ophysique, Royal Observatory of Belgium, Brussels, 280 pp. Sun, H.-P., Ducarme, B., Hindered, J., Hsu, H.T., 1998. Intercomparison of the (non-) tidal gravity observations with superconducting gravimeters at stations Wuhan, Brussels and Strasbourg. In: Ducarme, B., Paquet, P. (Eds.), Proc. 13th Int. Symp. Earth Tides, Brussels, 20–24 July 1997, Se´rie Ge´ophysique. Royal Observatory of Belgium, Brussels, pp. 455–462. Tamura, Y., 1981. A harmonic development of the tidal generating potential. Bull. d’Inf. Marees Terrestres 64, 677– 700. Venedikov, A.P., Vienna, R., deToro, C., Arnoso, J., 1997. A new program developed in Madrid for tidal data processing. Bull. d’Inf. Marees Terrestres 126, 9669–9704. Wahr, J.M., Sasao, T., 1981. A diurnal resonance in the ocean tide and in the Earth’s load response due to the resonant free core nutation. Geophys. J. Roy. Astr. Soc. 64, 747–765. Warburton, R.J., 1985. GWR superconducting gravimeter operation manual. GWR instruments company. San Diago, USA. Wenzel, H.G., 1996. The nanogal software: data processing package Eterna 3.3. Bull. d’Inf. Marees Terrestres 124, 9425–9439.
Tidal gravity observations obtained with a superconducting gravimeter at Wuhan/China and its application to geodynamics§ He-Ping Suna,*, Hou-Tze Hsua, Gerhard Jentzschb, Jian-Qiao Xua a
Open Laboratory of Dynamics Geodesy, Institute of Geodesy and Geophysics, Chinese Academy of Sciences, 54 Xu-Dong Road, 430077 Wuhan, PR China b Institute of Geosciences, University of Jena, Burgweg 11, D-07749, Jena, Germany
Abstract The long period tidal gravity observations recorded with a superconducting gravimeter at station Wuhan/ China from 1 January 1986 to 31 December 1994 (old series) and from 20 December 1997 to 30 April 2000 (new series) are studied comprehensively. The new tidal amplitude factors and phase differences are determined precisely using modern international standard data processing techniques. The tidal gravity signals due to the geophysical sources as of global ocean tides and local atmospheric pressure are comparatively studied. The dynamic influences of the Earth’s core, i.e. the resonance parameters (eigenperiod, quality factor and resonance strength) of the free core nutation, are determined and the corresponding results are compared with those obtained in the previous studies. # 2002 Elsevier Science Ltd. All rights reserved.
1. Introduction As the rapid improvement of the modern instruments [such as Goodkind-Warburton-Reineman superconducting gravimeter (SG) and FG-5 absolute gravimeter (AG)] and of the theoretical prediction (such as tidal catalogues, oceanic and atmospheric models), the study of geophysics and geodynamics using tidal gravity has become a common recognition. Compared to any spring gravimeters, the SG occupy many excellent characteristics as of the wide measuring range, low noise level, high stability and sensitivity, i.e. a resolution at the order of a nanogal (1012 g, Warburton, 1985; Goodkind, 1991). The SG observations with high sampling from global distributed stations, especially after eliminating instrumental drift and various systematic errors, can be used to study the geophysical and geodynamical problems, such as Earth tides, the interaction §
Paper presented to JSA37 Earth’s Gravity and Magnetic Fields From Space IUGG99, Birmingham, UK. * Corresponding author. Tel./fax: +86-27-86783841. E-mail addresses: [email protected] (H.-P. Sun), [email protected] (G. Jentzsch).
0264-3707/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0264-3707(01)00063-1
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of the Earth with ocean and atmosphere, resonance effect of the free core nutation (FCN), the modes of the Earth’s core, gravity change due to the tectonic motion and so on (Sun, 1992, 1995; Smylie et al., 1993; Hinderer et al., 1993; Defraigne and Dehant, 1994; Melchior and Francis, 1996; Kroner and Jentzsch, 1999, Courtier et al, 2000). The Global Geodynamics Project (GGP) started since July 1997, with participation of about 18 SG stations around the world (Crossley et al., 1999). The SG numbered as T004 was installed in November 1985 on the ground floor of the tidal gravity laboratory (30.58 N, 114.36 E, 34 m) in the main building of the Institute of Geodesy and Geophysics (IGG), Chinese Academy of Sciences (CAS) in Wuhan. It is about 1.5 km away from East Lake in the suburbs of the city. The city activities from the main road about 60 m away from instrument increase the station background noise (Hsu et al., 1989). At the end of 1997, the instrument was moved to a new site, about 25 km from the central city (30.52 N, 114.49 E, 89 m) after upgrading in accordance with GGP regulations, it is found that the site background noise is reduced significantly. The instrument room is air-conditioned, the yearly change of the room temperature is kept at the level of less than 1 C. In the period from 23 November 1985 to 24 August 1988, the analogue recordings were available. The data acquisition system developed by the German group, the first one was installed in November 1988 in order to increase the dynamic range (Kroner et al., 1995). The records with every 20 s interval are obtained from the original sampling of every 1 s and sent to a 22-bit digital voltmeter. Later, in 1997, in connection with the upgrading old SG meter, the second data acquisition system in accordance with the GGP regulations was installed. For the first stage, the pressure data are obtained from Wuhan meteorological fundamental station while since July 1994 they were recorded with 10-min sampling at the SG site. Both the hourly tidal gravity and pressure data are obtained after applying for the preprocessing procedures (Sun et al., 1998). Based on the tidal gravity measurements using two Lacost-Romberg Earth Tidal (LCR-ET) instrument numbered as 16 and 21 during the China-England international cooperation campaign (Hsu et al., 1989) at the same station, the amplitude calibration factor is determined using a weighted mean technique of the main tidal wave amplitude factors. The phase transfer function determined by the GWR manufacture is used in the data analysis.
2. Computation techniques In order to improve effectively the accuracy of the tidal gravity parameters, the data preprocessing is carried out carefully. Under the precondition of not damaging the inner quality of the observations, the non-tidal gravity signals were eliminated sufficiently. Spikes and ‘‘offsets’’ up to several mgal of unknown origin frequently occur. The abnormal signals are detected and eliminated by using a moving window function. Short term gaps, due to the power failures, earthquakes, liquid helium refilling, are filled using a spline interpolation based on a synthetic tidal gravity model. To correct numerically the background noise, it is important to avoid systematic effects prior to data reduction by filtering (Kroner et al., 1995; Banka et al., 1998). In the data processing, the modern standard international data analysis techniques as of Eterna (Wenzel, 1996) and Nsv (Venedikov, 1997) are applied. The high precision tide generating potential with 505 components (Cartwright, Tayler and Edden, CTE505, 1971) and with 1200
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components (Tamura, 1981) are employed in data reduction. The band pass filtering is used to eliminate instrumental drift and long term change in gravity for the first step. The so-called observation equations are constructed respectively for long period (LP), diurnal (D), semi-diurnal (SD) and ter-diurnal (TD) wave bands based on the continuous hourly data sets. These equations are then solved using classic least square method, the tidal parameters and the associated root mean square (RMS) errors are determined. The temporal changes of the tidal gravity residuals are obtained after subtracting the synthetic tidal gravity signals from the original observations. The fast Fourier transform (FFT) technique is used to determine the residual amplitude and standard deviations, i.e. noise level. The regression coefficients between the tidal residual and the change in atmospheric pressure at station are determined in both temporal and frequency domains, then the pressure influence on gravity is removed from the tidal measurements before the determination of the tidal parameters.
3. Results of the tidal parameters The long period tidal gravity observations from 1 January 1986 to 31 December 1994 (old series) and from 20 December 1997 to 30 April 2000 (new series) are used in this study. The tidal parameters and the associated RMS errors for 20 waves in D band, 13 waves in SD band and 2 waves in TD band are determined precisely based on the Eterna technique. The corresponding tidal parameters of 8 main waves are given in columns 2 and 3 in Table 1 and those of an other 14 small waves in columns 6 and 7 in Table 2. From the tidal analysis it is found that the accuracy of the main wave amplitude to be at 0.01 mgal level and that of the phase differences to be at 0.01 level. The stability of the amplitude factor calibration and of the high inner accuracy of the SG measurements are the main reasons for close fitting its results to theoretical computation. Comparing these results to those obtained from other stations in Europe as Brussels, Strasbourg and Potsdam (Sun et al., 1998; Neumeyer and Dittfeld, 1997), it is found that the phase differences at Wuhan are appeared to be the negative ones. Late we will show that it relates mainly to the oceanic tidal characters in Pacific and Atlantic oceans. Table 1 Tidal amplitude factors and phase differences for 8 main waves before and after ocean loading correctiona Model
Observed
Schwiderski (1)
0
Wave
’/( )
Q1 O1 P1 K1 N2 M2 S2 K2
1.1849 1.1787 1.1702 1.1514 1.1799 1.1762 1.1731 1.1673
0.28 0.58 0.82 0.73 0.66 0.63 0.58 0.56
1.1611 1.1566 1.1598 1.1382 1.1667 1.1668 1.1646 1.1551
0
CSR3.0 (2) 0
’ /( )
0.21 0.26 0.40 0.34 0.61 0.64 0.60 0.60
1.1603 1.1568 1.1585 1.1398 1.1646 1.1675 1.1639 1.1564
FES95 (3) 0
0
ORI (4) 0
0
’ /( )
’ /( )
0.04 0.22 0.27 0.13 0.48 0.48 0.47 0.44
1.1649 1.1580 1.1569 1.1381 1.1674 1.1689 1.1693 1.1589
0.35 0.26 0.26 0.15 0.15 0.01 0.16 0.17
1.1610 1.1578 1.1570 1.1379 1.1594 1.1584 1.1588 1.1533
ORI96 (5) 0
’ /( )
0
’0 /( )
0.47 0.16 0.22 0.17 0.91 0.67 0.38 0.57
1.1605 1.1579 1.1581 1.1385 1.1658 1.1646 1.1649 1.1584
0.04 0.25 0.40 0.26 0.49 0.46 0.42 0.40
a Note: (, ’) are the observed tidal gravity amplitude factor and phase, (0 , ’0 ) are those after oceanic loading correction.
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Table 2 Tidal residual amplitude and amplitude factors for some other small waves before and after ocean loading correctiona Tidal residuals
Amplitude factor
Wave
B/mgal
/( )
X/mgal
/( )
’/( )
0
’0 /( )
SIGQ RO1 NO1 PI1 PSI1 PHI1 TETA J1 OO1 2N2 MU2 NU2 L2 T2
0.010 0.030 0.054 0.038 0.028 0.018 0.011 0.057 0.026 0.043 0.042 0.040 0.009 0.055
127.46 23.79 26.77 21.78 32.87 145.93 48.02 41.67 74.81 25.89 5.35 54.34 4.57 77.33
0.029 0.009 0.009 0.025 0.026 0.022 0.007 0.037 0.026 0.015 0.008 0.027 0.005 0.052
172.26 77.25 20.16 15.56 45.71 167.96 52.52 41.42 73.30 53.01 31.36 98.39 148.47 93.05
1.1244 1.1812 1.1758 1.1976 1.3451 1.1428 1.1743 1.1764 1.1618 1.1905 1.1869 1.1742 1.1686 1.1712
2.00 0.59 0.55 0.90 2.14 0.91 0.95 0.86 1.06 0.65 0.11 0.78 0.02 1.74
0.9935 1.1563 1.1578 1.1895 1.3509 1.1240 1.1680 1.1715 1.1634 1.1702 1.1675 1.1605 1.1594 1.1612
1.26 0.53 0.08 0.52 3.56 0.49 0.73 0.65 1.22 0.49 0.14 0.76 0.10 1.99
a Note: (B, ) are the observed tidal gravity residual amplitude and phase, (X, w) are those after the oceanic loading correction; (, ’) are the observed tidal gravity amplitude factor and phase, (0 , ’0 ) are those after the loading correction.
It is an important criterion to check the standard deviations (Stdv) obtained from harmonic analysis since they can be used to judge the quality of the tidal parameters. The average Stdv are investigated systematically by using the NSV technique when taking various considerations, such as to use the CTE505 and Tamura’s tidal generating potential, to consider the weight of filtered numbers, to apply for pressure correction, to remove erroneous data and so on. It is found that the Stdv are reduced significantly from 2.33 to 0.90, from 1.85 to 0.62 and from 0.68 to 0.42 mgal in D, SD and TD wave bands respectively. While the global Stdv is given as 0.70 mgal when using Eterna technique, which shows that two data reduction techniques give similar results. When analysing the new series, the Stdv is given as 0.3 mgal, which indicates that the background noise at new site is largely reduced. In order to show the stability of the instrument and to study the temporal characteristics of the Earth’s response to tidal generating forces, the temporal variation of the monthly tidal parameters (amplitude factors and phase differences) in D and SD wave bands are investigated (Figs. 1 and 2). It is found that the perturbations at waves O1 and M2 relate to the interruption of the power supply or an instrumental adjustment, the discretion at P1S1K1 mainly relates to the meteorological influence and the regular variation at S2 corresponds to the seasonal disturbances of the continental pressure field (Fig. 1). No apparent relation of these results with local geophysical phenomena, such as an earthquake event and so on, is found. The temporal change of the M2 amplitude factor is relatively stable compared to that of the O1 wave. The scattering of the phase differences for P1S1K1 and S2K2 is up to 1.0 . It may be due to some regional sources as pressure, temperature, storms, underground water and so on, producing variations of the physical properties in the Earth’s interior. The uncertainty of the phase calibration may be also the reason to induce this disparity.
H.-P. Sun et al. / Journal of Geodynamics 33 (2002) 187–198
Fig. 1. Temporal changes of the monthly tidal amplitude factors for 4 main waves.
Fig. 2. Temporal changes of the monthly tidal phase differences for 4 main waves.
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4. Influence of the oceanic loading The oceanic tide is one of the main perturbations in the tidal gravity observations (Francis and Mazzega, 1990; Sun, 1992; Melchior, 1994; Jentzsch, 1997). It is important to remove the loading signals before the tidal parameters to be applied to the study of the geodynamics (Ducarme and van Ruymbeke, 1991; Courtier et al., 2000; Hsu et al., 2000). In 1980 Schwiderski provided us with the basic oceanic models for loading computations. As the rapid development of the Topex/ Poseidon altimeter and the finite element technique since 1992, the oceanic models are improved significantly. Therefore, to select the better models in removing the oceanic signals from tidal gravity observations is extremely important. The global oceanic models used in this study include Schwiderski’s (Scw80) and the most recent ones, such as Csr3.0 (Eanes), Fes952 (Grenoble), Ori and Ori96 (Matsumoto) models. The recent models occupy excellent characteristics, as wider coverage, higher resolution and accuracy as well as smaller residual amplitudes (PODAAC, 1999). Based on the model Earth Green’s functions (Farrell, 1972), the tidal gravity loading of above 5 models for 4 waves in D band (Q1, O1, P1 and K1) and 4 waves in SD band (N2, M2, S2 and K2) are calculated using a direct discrete convolution method (Francis and Mazzega, 1990; Sun, 1992). The effect of the ocean to gravity includes the direct attraction of the ocean tidal mass, and the loading contribution induced by the elastic deformation of the Earth. In order to check the suitability of the tidal gravity models and the oceanic models, let’s introduce observed residual amplitude and phase (B, ) and final residual amplitude and phase (X, w). The (B, ) can be obtained by subtracting synthetic tides from the tidal observations, and the (X, w) can be computed when subtracting oceanic loading from observed residuals. The tidal gravity residual amplitudes before and after oceanic loading correction are given in Fig. 3. The column 0 represents the observed residual amplitudes, and columns 1–5, the loading corrected residual amplitudes, 1, based on Schwiderski models, 2, Csr3.0 models, 3, Fes95.2 models, 4 and 5 Ori and Ori96 models respectively. The largest observed residual amplitude reaches
Fig. 3. Tidal gravity residual amplitudes before and after oceanic tidal loading correction (column 0, observed residual amplitudes; columns 1, 5 after correction based on various models).
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1.04 mgal (M2). It is found a relative more effective correction in D wave band, especially for the O1 and K1 wave, while in SD band, there have still large residuals at M2 and S2 waves, it may relate to other gravity signals. It is found that the Grenoble Fes95 models fit better tidal measurements in SD band, while no obvious advantages are found in D band. Table 1 demonstrates the tidal amplitude factors and phase differences before and after removing loading signals. Comparing to those in the theoretical tidal prediction (TTP, Dehant et al., 1998) as of the O1 (1.15376) and M2 (1.16262), the discrepancies of the observed ones and of those after loading correction are reduced significantly. For the O1 wave, it is reduced from 2.16% to 0.25% (Scw80), 0.26% (Csr3.0), 0.37% (Fes95), 0.35% (Ori and Ori96) and for the M2 wave, from 1.17% to 0.36% (Sch), 0.42% (Csr3.0), 0.54% (Fes95), 0.36% (Ori) and 0.17% (Ori96). It seems that in SD band, the discrepancy with respect to the TTP is smaller when using Ori96 models comparing to those when using other models. The oceanic models are not enough when the tidal parameters are used to study geodynamics. Especially there are no models presently for waves 1 and 1 that occupy a period close to the FCN resonance, i.e. one sidereal day. Based on the loading amplitudes and phases of 8 main waves obtained from Schwiderski models and a second order polynomial interpolation technique, the loading influence for other smaller waves, 9 waves in D band and 5 waves in SD band are calculated. Table 2 shows the tidal amplitude factors of other small waves before and after removing loading signals. It is found that the observed residual amplitude is reduced by about 8% ( 1), while it is increased by about 18% (1). The amplitude factors and phases fit better the tidal prediction after loading correction. However, the discrepancy still remains, it may relate to the station surroundings and to the calibration of the phase response, a further work will be orientated to this problem.
5. Effect of the atmospheric pressure A strong correlation between tidal residual and barometric pressure is found during the data reduction. In order to eliminate the pressure influence, the regression technique is employed. The frequency dependent regression coefficients, as of 0.3780.021 (LP), 0.3000.026 (D), 0.1990.041 (SD) and 0.1470.016 (TD) mgal/hPa, are used to correct the barometric influence on tidal gravity observations. These coefficients fit well for LP band, but they are relative low in other bands comparing to those given in theoretical prediction (0.36 mgal/hPa) under the assumption of hydrostatic atmospheric model (Sun, 1995) and to those determined at other stations as Brussels, Strasbourg and Cantly (Sun et al., 1998; Merriam, 1995). The temporal changes of monthly atmospheric gravity coefficients are given in Fig. 4. It is found the atmospheric gravity admittance are not stable and the discretion to be relative large. Analysis shows that it is due to the seasonal disturbances of the special meteorological condition in China and the mixed temperature signals in pressure records (see also Fig. 1). The harmonic analysis of the barometric pressure is given as 0.9530.015 hPa (S1), 0.0140.001 hPa (O1), 0.0750.001 hPa (K1), 0.04 0.004 hPa (M2), 0.7420.004 hPa (S2). It indicates that the pressure energy concentrates on S1 and S2 waves in tidal bands. After removing pressure signals, the amplitude factors are reduced to better fit with those obtained from the TTP, it is about 0.3% reduced for S2 wave, and the standard deviation is at 4% level reduced.
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Fig. 4. Temporal changes of the monthly atmospheric pressure gravity admittance.
6. Determination of the FCN resonance parameters The dynamic influence of the Earth’s core within a rotating, elastic and elliptical mantle will lead to a rotating eigenmode associated with the wobble of the fluid core with respect to the mantle. Owing to the oceanic loading, the mantle inelasticity, dissipating coupling torques (as electromagnetic and topographic torques) and the tidal friction (Herring et al., 1991), the FCN resonance parameters are expressed in complex. The imaginary parts relate to the damping characteristics of the Earth’s interior. Previous studies show that the FCN resonance processes the eigenperiod close to one sidereal day in the mantle reference frame and approximately 435 sidereal days in the space reference frame (Cummins and Wahr, 1993; Hinderer et al., 1993). Due to the diurnal forcing of the Moon and the Sun and the presence of the FCN, a resonance appears in the tesseral diurnal response of the Earth. The tides mostly affected by this resonance are P1, S1, K1, 1 and 1 waves, therefore, the tidal parameters of these waves can be used to investigate the resonance originating from the FCN. Furthermore some nutations associated with these tides, as of annual retrograde and prograde, semi-annual retrograde and prograde ones, are also perturbed by FCN resonance. In order to retrieve the resonance parameters, the influence of the ocean tides and atmospheric pressure are removed for the first step. Then the same procedures as Neuberg et al. (1987) and Defraigne and Dehant (1994) are applied. The techniques are based on the so called least squares fit of the tidal gravity data to a damped harmonic oscillator, the computation of the eigenperiod relates to the forcing frequency, and the quality factor Q relates to the FCN frequency and the attenuation factor. Considering a relative large disparity between the forcing frequency and the resonant one, the amplitude parameters for O1 are taken as the reference. Based on the resonant equations (Neuberg
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H.-P. Sun et al. / Journal of Geodynamics 33 (2002) 187–198 Table 3 Resonance parameters obtained at various stations
Resonance strength (104) Data used (station)
Eigen frequency (f) (degree/h)
Eigen period (T) (sidereal day)
Quality factor (Q value)
Ar ( /h)
Wuhan (old) Wuhan (new) Brussels Bad Homburg Strasbourg Metsahovi Kyoto All stations
15.078044 15.076396 15.075540 15.075745 15.076176 15.076002 15.078520 15.076134
406.8 (399.6, 425.8 (420.1, 436.3 (418.5, 433.8 (430.0, 428.4 (423.1, 430.6 (418.3, 401.6 (392.5, 429.0 (424.3,
10260 (5382, 109583) 3573 (2913, 4618) 2178 (1526, 3807) 5120 (4237, 6468) 22183 (9666, 1) 4596 (2824, 12327) 3857 (6954, 2669) 9543 (6405, 18714)
6.18 5.85 6.22 6.57 6.32 5.68 5.76 6.10
(0.000666) (0.000477) (0.001470) (0.000307) (0.000439) (0.001029) (0.000870) (0.000387)
414.2) 431.6) 455.8) 437.6) 433.9) 443.6) 411.2) 433.7)
(0.64) (0.23) (0.50) (0.16) (0.25) (0.45) (0.80) (0.20)
Ai ( /h) 0.35 (0.64) 0.50 (0.23) 0.66 (0.50) 0.16 (0.16) 0.15 (0.25) 0.17 (0.45) 0.06 (0.80) 0.01 (0.20)
et al., 1987), the differences between tidal parameters of P1, K1, c1 and f1 waves and that of O1 are considered, and the equations are solved using the least square technique. The determined resonant parameters are given in Table 3. Ar and Ai represent the real and imaginary parts of the resonant strength. The obtained FCN resonant parameters are given as (T=406.8 sidereal days, Q=10260, Ar=6.18104, Ai=0.35104) when using old series, while they are (T=425.8 sidereal days, Q=3573, Ar=5.85104, Ai=0.50104) when using new series. The numerical value of the eigenperiod is reasonable due to the low background noise at new site, while a low quality factor value is given. The same calculations are carried out for some other stations, as Brussels, Belgium (data from April 1982 to July 1995), Bad Homburg, Germany (data from May 1981 to May 1984), Strasbourg, France (data from November 1987 to December 1991), Metsahovi, Finland (data from November 1994 to October 1996) and Kyoto, Japan (data from October 1990 to November 1997). The corresponding results are also listed in Table 3 for comparison, the numerical values in parenthesis represent the error or error range.
Fig. 5. FCN resonance curves of the tidal parameters obtained at station Wuhan/China: (a) real part of the amplitude factor (cos’) and (b) imaginary part of the amplitude factor (sin’). Stars represent the results obtained from the old series and triangles those obtained for the new series.
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When stacking all the data sets above mentioned, the resonant contribution turns out to be (T=429.0 sidereal days, Q=9543, Ar=6.10104, Ai=0.01104). It signifies that our results from station Wuhan are close to the stacking one, the difference is less than 1%. Our results correspond to the previous studies inferred from stacking tidal gravity and nutation observations, or from VLBI measurements (Neuberg et al., 1987; Herring et al., 1991; Cummins and Wahr, 1993; Hinderer et al., 1993; Defraigne and Dehant, 1994; Flosch et al., 1994). It is also found that the influence of the ocean tides and the barometric pressure are the main error sources, the maximum discrepancy on eigenperiod can reach to 3% when using various oceanic models. In addition to these, the errors of the phase differences can be responsible for a biased Q. The tidal catalogue used in data reduction appears to be only of small importance. However, comparing to the eigenperiod in the case of inelastic mantle as of 462.8 sidereal days given by Wahr and Sasao (1981), the observed eigenperiods are low, the reasons should be further investigated. Fig. 5 shows the comparison of the tidal parameters between the TTP and the observed ones in the form of real and imaginary parts. It clearly shows the resonance influence of the Earth’s core in tidal parameters. The real parts fit better to those in TTP, while a relative large disparity for the imaginary parts is found.
7. Conclusions Based on the modern SG and data processing techniques, the tidal parameters at Wuhan, China, are determined precisely. The stability of the amplitude factor calibration and the high inner accuracy of the measurements are the main reasons for the good fit of the results to tidal models. It is found that the Grenoble (Fes95) ocean models fit better the tidal residuals. The small disparity of the tidal amplitude factors in SD band with respect to tidal models is found when using Ori96. The resonance parameters are determined when using Wuhan SG observations, the results obtained from new series fit better to those determined in previous studies, it is due to the low site background noise. The oceanic and barometric pressure influences can cause an error to the eigenperiod of about 3%, the phase differences can be responsible for a biased Q value. The tidal catalogue used in the tidal analysis appears to be only of small importance. A further study should be developed in checking influence of the change in room temperature and why the big difference appeared between theoretical prediction and ground measurements.
Acknowledgements This study is supported jointly by the Nature Science Foundation of China (49774223, 49925411) and the Chinese Academy of Sciences (KZ952-J1-411, KZCX2-106). The first data acquisition system at Wuhan was based on a development of Dr. G. Asch and provided by the Volkswagen Foundation (No. I/63542), the second system was developed by Dr. M. Ramatschi and made available at Wuhan by the Thyssen Foundation (No. 9.23/95) via co-author G.J. Late Professor H.-G. Wenzel and Professor A. Venedikov provided their outstanding tidal analysis packages. Dr. Defraigne gave fruitful comments for the stacking of tidal gravity observations, and Professor B. Ducarme suggested an interpolation technique of the oceanic loading influence for other small waves. All above are gratefully acknowledged.
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