武汉和京都台站超导重力仪高精度潮汐重力观测结果

利用高精度潮汐重力场观测研究地球物理学和地球动力学问题已成为当今地学工作者的共识.由于某些信号十分微弱且具有区域和全球分布特征,相当一部分信号被混合在常规仪器的观测噪声水平上,因此获得全球分布的第一手高精度观测资料显得尤为重要.超导重力仪具有精度高,连续性和稳定性好等特征,期望能在测定区域和全球重力场的精细结构方面发挥重要作用.有18个台站参加的全球地球动力学合作项目于1997年7月份开始实施,其主要目的是解决诸如固体潮、地核近周日晃动、核模、地球自转和极移,地球和大气海洋的耦合机理以及由构造运动引起的重力场变化等热点问题.我们曾研究过中比法三国的超导重力仪潮汐观测资料,获得了欧洲和亚洲不同地区潮汐常数及分布特征.本文将利用武汉和日本京都三台超导重力仪观测资料研究亚洲地区大陆和海岛上的潮汐波振幅因子和相位滞后的时间变化特征以及各参数的误差估计等,同时将检测由大气和海潮变化产生的重力信号.文章分数据处理方法、潮汐参数测定、大气重力信号、海潮重力信号、潮汐参数的时间变化、非潮汐重力场变化特征等几方面叙述.     

Results of three year observation with a superconducting gravimeter at the GeoForschungsZentrum Potsdam

The superconducting gravimeter (SG) TT70 has been continuously recording gravity data at the GeoForschungsZentrum (GFZ) Potsdam absolute gravity site since July 1992. The recorded data are edited and preprocessed by spike and step detection and elimination and gap filling. An atmospheric pressure correction is carried out on gravity data in the time domain with a complex admittance before tidal fitting. The atmospheric pressure admittance is calculated from tide free output of SG data and local atmospheric pressure using the cross spectral method. The ground water level admittance is determined by a single coefficient. Improvements with these corrections are shown in analysis results. New tidal parameters for Potsdam site are determined and compared with recordings of an Askania spring gravimeter at a nearby site. Deviations against the Wahr-Dehant-model are shown. Polar motion data of the IERS (International Earth Rotation Service, Paris) are used to calculate variations of centrifugal acceleration caused by polar motion (pole tide). These are compared with the corrected tide free output of SG series. For drift determination the polar motion correction is applied on SG data. The nutation period equivalent to the Earth's Nearly Diurnal Free Wobble is calculated from the SG data with a value of T_FCN = (437.4 ± 1.5) sidereal days. This result is compared with those obtained from other SG stations. Received 19 December 1995; Accepted 13 September 1996     

南极中山站重力潮汐观测的海潮负荷效应

综合分析了LaCoste-Romberg(LCR)ET21高精度弹簧重力仪1998年12月26日至2000年1月9日在南极中山站的重力潮汐观测资料，采用目前普遍使用的Schwiderski、Csr3.0和Fes96.2全球海潮模型研究中山站重力潮汐观测的海潮负荷改正问题。结果表明在南极地区，目前的海潮模型存在较大的不确定性，还不足以精密确定该区域的海潮负荷改正。经海潮改正后，重力潮汐观测结果与潮汐理论值之间还存在比较大的差异，观测的周日（01）和半日（M2）潮波重力振幅因子与相应的理论值之间的平均偏差分别为3．8％和7．8％。南极地区附近海域海水的变化半导致该地区海潮负荷响应非常明显的季节性系统变化。     

A model for adjustment of differential gravity measurements with simultaneous gravimeter calibration

 A mathematical model is proposed for adjustment of differential or relative gravity measurements, involving simultaneously instrumental readings, coefficients of the calibration function, and gravity values of selected base stations. Tests were performed with LaCoste and Romberg model G gravimeter measurements for a set of base stations located along a north–south line with 1750 mGal gravity range. This line was linked to nine control stations, where absolute gravity values had been determined by the free-fall method, with an accuracy better than 10 μGal. The model shows good consistence and stability. Results show the possibility of improving the calibration functions of gravimeters, as well as a better estimation of the gravity values, due to the flexibility admitted to the values of the calibration coefficients. Received: 15 November 1999 / Accepted: 31 October 2000     

Determination of the free core nutation period from tidal gravity observations of the GGP superconducting gravimeter network

This study is based on 25 long time-series of tidal gravity observations recorded with superconducting gravimeters at 20 stations belonging to the Global Geodynamic Project (GGP). We investigate the diurnal waves around the liquid core resonance, i.e., K ₁, ψ₁ and φ₁, to determine the free core nutation (FCN) period, and compare these experimental results with models of the Earth response to the tidal forces. For this purpose, it is necessary to compute corrected amplitude factors and phase differences by subtracting the ocean tide loading (OTL) effect. To determine this loading effect for each wave, it was thus necessary to interpolate the contribution of the smaller oceanic constituents from the four well determined diurnal waves, i.e., Q ₁, O ₁, P ₁, K ₁. It was done for 11 different ocean tide models: SCW80, CSR3.0, CSR4.0, FES95.2, FES99, FES02, TPXO2, ORI96, AG95, NAO99 and GOT00. The numerical results show that no model is decisively better than the others and that a mean tidal loading vector gives the most stable solution for a study of the liquid core resonance. We compared solutions based on the mean of the 11 ocean models to subsets of six models used in a previous study and five more recent ones. The calibration errors put a limit on the accuracy of our global results at the level of ± 0.1%, although the tidal factors of O ₁ and K ₁ are determined with an internal precision of close to 0.05%. The results for O ₁ more closely fit the DDW99 non-hydrostatic anelastic model than the elastic one. However, the observed tidal factors of K ₁ and ψ₁ correspond to a shift of the observed resonance with respect to this model. The MAT01 model better fits this resonance shape. From our tidal gravity data set, we computed the FCN eigenperiod. Our best estimation is 429.7 sidereal days (SD), with a 95% confidence interval of (427.3, 432.1).     

Atmospheric, oceanic and hydrological contributions to seasonal variations in length of day

 The annual and semiannual residuals derived in the axial angular momentum budget of the solid Earth–atmosphere system reflect significant signals. They must be caused by further excitation sources. Since, in particular, the contribution for the wind term from the atmospheric layer between the 10 and 0.3 hPa levels to the seasonal variations in length of day (LOD) is still missing, it is necessary to extend the top level into the upper stratosphere up to 0.3 hPa. Under the conservation of the total angular momentum of the entire Earth, variations in the oceanic angular momentum (OAM) and the hydrological angular momentum (HAM) are further significant excitation sources at seasonal time scales. Focusing on other contributions to the Earth's axial angular momentum budget, the following data are used in this study: axial atmospheric angular momentum (AAM) data derived for the 10–0.3 hPa layer from 1991 to 1997 for computing the missing wind effects; axial OAM functions as generated by oceanic general circulation models (GCMs), namely for the ECHAM3 and the MICOM models, available from 1975 to 1994 and from 1992 to 1994, respectively, for computing the oceanic contributions to LOD changes, and, concerning the HAM variations, the seasonal estimates of the hydrological contribution as derived by Chao and O'Connor [(1988) Geophys J 94: 263–270]. Using vector representation, it is shown that the vectors achieve a close balance in the global axial angular momentum budget within the estimated uncertainties of the momentum quantities on seasonal time scales. Received: 6 April 2000 / Accepted: 13 December 2000     

Correcting superconducting gravity time-series using rainfall modelling at the Vienna and Membach stations and application to Earth tide analysis

We demonstrate the possibility to improve the signal-to-noise ratio of superconducting gravity time-series by correcting for local hydrological effects. Short-term atmospheric events associated with heavy rain induce step-like gravity signals that deteriorate the frequency spectrum estimates. Based on 4D modeling constrained by high temporal resolution rain gauge data, rainfall admittances for the Vienna and Membach superconducting gravity stations are calculated. This allows routine correction for Newtonian rain water effects, which reduces the standard deviation of residuals after tidal parameter adjustment by 10%. It also improves the correction of steps of instrumental origin when they coincide with step-like water mass signals.     

Wavelet filter analysis of local atmospheric pressure effects on gravity variations

An efficient method is proposed for the analysis of atmospheric pressure effects on gravity variations. It processes gravity and pressure signals using an orthogonal filter bank derived from high-degree Daubechies wavelets. The method introduces the atmospheric pressure admittance, which is both time- and frequency-dependent, and thus provides more information about when and how the frequency components in the pressure signal influence gravity variations. We demonstrate the efficiency of the wavelet method by applying it to observations from the Wuhan (China) superconducting gravimeter station. The analysis of gravity and pressure signals in 14 sub-bands with different bandwidths covering a frequency range from 0.176 to 720 cpd (cycles per day) reveals that local atmospheric pressure fluctuations start to induce obvious effects on gravity variations in the seismic band 0.52–1.04 mHz (periods 16 to 32 min) and highly correlate with gravity variation in the long-period seismic mode band 0.26–0.52 mHz (periods 32–64 min). The harmonics of solar-heating-induced atmospheric tides play a leading role in interfering with the variation of gravity residuals in the frequency band 0.704–11.25 cpd (periods 128 min to 1.42 day). Local atmospheric pressure effects on gravity variation are very strong in the frequency band 0.176–0.704 cpd (periods 1.42–5.69 day). Accurately filtering quarter-diurnal tides into a narrow band further demonstrates the efficiency of the wavelet method. After removing secular gravity changes and long-period atmospheric pressure variations, we show that there are obvious variations of local pressure admittance on time scales of hours to days. We also reveal seasonal variability of pressure admittances in the band 0.176–0.352 cpd (periods 2.84–5.69 day) after removing the effects of solar-heating atmospheric tides.     

基于短时间序列重力观测数据的潮汐改正方法

对于没有长期连续潮汐观测站和无精密潮汐模型的地区,研究高精度潮汐改正方法具有重要意义。给出了基于短时间序列重力观测数据的高精度潮汐改正方法,并利用全球动力学计划中TIGOConcepcion、Kamio-ka和Hsinchu三个台站的超导重力观测数据对该方法进行了试验分析。研究结果表明,利用一天或数天重力观测数据可建立高精度潮汐模型,其振幅因子和相位延迟解算精度分别优于0.01和0.5°,潮汐改正精度可以达到μGal量级,验证了该方法的正确性和有效性。本文方法为无精密潮汐模型区域的潮汐改正提供了新的途径。     

Combination of temporal gravity variations resulting from superconducting gravimeter (SG) recordings, GRACE satellite observations and global hydrology models

Gravity recovery and climate experiment (GRACE)-derived temporal gravity variations can be resolved within the μgal (10^?8 m/s ²) range, if we restrict the spatial resolution to a half-wavelength of about 1,500 km and the temporal resolution to 1 month. For independent validations, a comparison with ground gravity measurements is of fundamental interest. For this purpose, data from selected superconducting gravimeter (SG) stations forming the Global Geodynamics Project (GGP) network are used. For comparison, GRACE and SG data sets are reduced for the same known gravity effects due to Earth and ocean tides, pole tide and atmosphere. In contrast to GRACE, the SG also measures gravity changes due to load-induced height variations, whereas the satellite-derived models do not contain this effect. For a solid spherical harmonic decomposition of the gravity field, this load effect can be modelled using degree-dependent load Love numbers, and this effect is added to the satellite-derived models. After reduction of the known gravity effects from both data sets, the remaining part can mainly be assumed to represent mass changes in terrestrial water storage. Therefore, gravity variations derived from global hydrological models are applied to verify the SG and GRACE results. Conversely, the hydrology models can be checked by gravity variations determined from GRACE and SG observations. Such a comparison shows quite a good agreement between gravity variation derived from SG, GRACE and hydrology models, which lie within their estimated error limits for most of the studied SG locations. It is shown that the SG gravity variations (point measurements) are representative for a large area within the accuracy, if local gravity effects are removed. The individual discrepancies between SG, GRACE and hydrology models may give hints for further investigations of each data series.     

Geoid undulation modelling and interpretation at Ladak, NW Himalaya using GPS and levelling data

Fast and accurate relative positioning for baselines less than 20 km in length is possible using dual-frequency Global Positioning System (GPS) receivers. By measuring orthometric heights of a few GPS stations by differential levelling techniques, the geoid undulation can be modelled, which enables GPS to be used for orthometric height determination in a much faster and more economical way than terrestrial methods. The geoid undulation anomaly can be very useful for studying tectonic structure. GPS, levelling and gravity measurements were carried out along a 200-km-long highly undulating profile, at an average elevation of 4000 m, in the Ladak region of NW Himalaya, India. The geoid undulation and gravity anomaly were measured at 28 common GPS-levelling and 67 GPS-gravity stations. A regional geoid low of nearly −4 m coincident with a steep negative gravity gradient is compatible with very recent findings from other geophysical studies of a low-velocity layer 20–30 km thick to the north of the India–Tibet plate boundary, within the Tibetan plate. Topographic, gravity and geoid data possibly indicate that the actual plate boundary is situated further north of what is geologically known as the Indus Tsangpo Suture Zone, the traditionally supposed location of the plate boundary. Comparison of the measured geoid with that computed from OSU91 and EGM96 gravity models indicates that GPS alone can be used for orthometric height determination over the Higher Himalaya with 1–2 m accuracy. Received: 10 April 1997 / Accepted: 9 October 1998     

Interpretation of the tidal residuals during the 11 July 1991 total solar eclipse

Observations of gravity and atmospheric pressure variations during the total solar eclipse of 11 July 1991 in Mexico City are presented. An LCR-G402 gravimeter equipped with a feedback system and a digital data acquisition system scanned gravity and pressure every second around the totality. On the pressure record an oscillation, starting at the totality, with a peak to peak amplitude of 0.5 hPa and a periodicity of 40 to 50 min, can clearly be seen. This oscillation results from the thermal shock wave produced by the Moon shadow travelling at supersonic speed. At the 0.1 μGal (1 nm · s⁻²) level all gravity perturbations are explained by the atmospheric pressure effect. Received: 10 February 1995 / Accepted: 7 June 1996     

Determination of the main Lunar waves generated by the third degree tidal potential and validity of the corresponding body tides models

Seventeen long series of tidal gravity observations with superconducting gravimeters (SGs) belonging to the GGP network allowed to determine the main tidal waves generated by the tidal potential of third degree in the Diurnal (M1), Semi-Diurnal (3MK2, 3MO2) and Ter-Diurnal (M3) bands with a precision of 0.1%, although the amplitudes of these waves are below 10 nm s⁻² (1 μgal). Special analysis techniques have been used to separate M1, 3MK2 and 3MO2 from the neighbouring waves generated by the second degree potential. The 11 European stations form a geographically homogeneous subgroup and it is thus possible to derive some conclusions concerning the ocean tides loading and the body tides models. The results for M1, 3MK2 and 3MO2 are not in contradiction with the recent models and the results for M3 are even in agreement with them.     

超导重力数据检测到的2011年日本东北大地震(Mw 9.0)震前重力异常及同震重力变化

高精度的超导重力数据已广泛应用于地球动力学的研究,对大地震前重力异常和同震重力变化的探测有助于震源机制和地震预警的研究,同时高精度的同震观测数据可用于断层滑动模型的反演。本文利用日本、中国及欧洲7个超导台站2011年3月的秒采样数据研究日本东北大地震（M_w 9.0）产生的重力变化,经潮汐、气压、漂移等预处理改正后,得到改正后的重力变化。对比同时段日本岛附近发生的2861次M_b≥4级地震,分析滤波后的重力变化数据,排除非主震的影响,发现0.12 Hz≤f≤0.18 Hz频段显示了明显的震前重力异常扰动信息,所有台站在震前89 h均开始出现重力异常扰动,Medicina站的震前最大异常扰动振幅达到28×10^-8 m/s²。另外,利用球形位错理论及地震的CMT解计算得到的地表同震重力变化理论值与超导重力观测值非常接近,同震重力变化绝对值与震中距成反比,近场站点的观测值比远场站点更接近于理论计算值,前者可作为断层反演的约束条件。     

Precise geoid determination over Sweden using the Stokes–Helmert method and improved topographic corrections

 Four different implementations of Stokes' formula are employed for the estimation of geoid heights over Sweden: the Vincent and Marsh (1974) model with the high-degree reference gravity field but no kernel modifications; modified Wong and Gore (1969) and Molodenskii et al. (1962) models, which use a high-degree reference gravity field and modification of Stokes' kernel; and a least-squares (LS) spectral weighting proposed by Sj?berg (1991). Classical topographic correction formulae are improved to consider long-wavelength contributions. The effect of a Bouguer shell is also included in the formulae, which is neglected in classical formulae due to planar approximation. The gravimetric geoid is compared with global positioning system (GPS)-levelling-derived geoid heights at 23 Swedish Permanent GPS Network SWEPOS stations distributed over Sweden. The LS method is in best agreement, with a 10.1-cm mean and ±5.5-cm standard deviation in the differences between gravimetric and GPS geoid heights. The gravimetric geoid was also fitted to the GPS-levelling-derived geoid using a four-parameter transformation model. The results after fitting also show the best consistency for the LS method, with the standard deviation of differences reduced to ±1.1 cm. For comparison, the NKG96 geoid yields a 17-cm mean and ±8-cm standard deviation of agreement with the same SWEPOS stations. After four-parameter fitting to the GPS stations, the standard deviation reduces to ±6.1 cm for the NKG96 geoid. It is concluded that the new corrections in this study improve the accuracy of the geoid. The final geoid heights range from 17.22 to 43.62 m with a mean value of 29.01 m. The standard errors of the computed geoid heights, through a simple error propagation of standard errors of mean anomalies, are also computed. They range from ±7.02 to ±13.05 cm. The global root-mean-square error of the LS model is the other estimation of the accuracy of the final geoid, and is computed to be ±28.6 cm. Received: 15 September 1999 / Accepted: 6 November 2000     

A study of gravity variations caused by polar motion using superconducting gravimeter data from the GGP network

Long-term continuous gravity observations, recorded at five superconducting gravimeter (SG) stations in the Global Geodynamic Project (GGP) network, as well as data on orientation variations in the Earths rotation axis (i.e. polar motion), have been used to investigate the characteristics of gravity variations on the Earths surface caused by polar motion. All the SG gravity data sets were pre-processed using identical techniques to remove the luni-solar gravity tides, the long-term trends of the instrumental drift, and the effects of atmospheric pressure. The analysis indicates that the spectral peaks, related to the Chandler and annual wobbles, were identified in both the power and product spectral density estimates. The magnitude of gravity variations, as well as the gravimetric amplitude factor associated with the Chandler wobble, changed significantly at different SG stations and during different observation periods. However, when all the SG observations at these five sites were combined, the gravimetric parameters of the Chandler wobble were retrieved accurately: 1.1613 ± 0.0737 for the amplitude factor and –1°.30 ± 1°.33 for the phase difference. The value of the estimated amplitude factor is in agreement with that predicted theoretically for the zonal tides of an elastic Earth model.     

Unification of vertical datums by GPS and gravimetric geoid models with application to Fennoscandia

The second Baltic Sea Level (BSL) GPS campaign was run for one week in June 1993. Data from 35 tide gauge sites and five fiducial stations were analysed, for three fiducial stations (Onsala, Mets?hovi and Wettzell) fixed at the ITRF93 system. On a time-scale of 5 days, precision was several parts in 10⁹ for the horizontal and vertical components. Accuracies were about 1 cm in comparison with the International GPS Geodynamical Service (IGS) coordinates in three directions. To connect the Swedish and the Finnish height systems, our numerical application utilises three approaches: a rigorous approach, a bias fit and a three-parameter fit. The results between the Swedish RH70 and the Finnish N 60 systems are estimated to −19.3 ± 6.5, −17 ± 6 and −15 ± 6 cm, respectively, by the three approaches. The results of the three indirect methods are in an agreement with those of a direct approach from levelling and gravity measurements. Received: 3 April 1996 / Accepted: 4 August 1997     

Gravity recovery using COSMIC GPS data: application of orbital perturbation theory

 COSMIC is a joint Taiwan–US mission to study the atmosphere using the Global Positioning System (GPS) occultation technique. Improved formulas are developed for the radial, along-track, and cross-track perturbations, which are more accurate than the commonly used order-zero formulas. The formulas are used to simulate gravity recovery using the geodetic GPS data of COSMIC in the operational phase. Results show that the EGM96 model can be improved up to degree 26 using 1 year of COSMIC data. TOPEX/POSEIDON altimeter data are used to derive a temporal gravity variation. COSMIC cannot reproduce this gravity variation perfectly because of data noise and orbital configuration, but the recovered field clearly shows the gravity signature due to mass movement in an El Ni?o. Received: 3 March 2000 / Accepted: 10 November 2000     

A-10绝对重力仪残差谱分析

自由落体式绝对重力仪A-10的测量数据拟合残差呈现出明显的周期信号,对4个测站的残差进行FFT处理,并进行频谱分析,结果表明残差组平均的频谱更加稳定,主峰频率与测站无关,主峰幅值与测站明显相关,加周期项改正的绝对重力值偏小。     

Global mean sea surface and marine gravity anomaly from multi-satellite altimetry: applications of deflection-geoid and inverse Vening Meinesz formulae

 Global mean sea surface heights (SSHs) and gravity anomalies on a 2^′×2^′ grid were determined from Seasat, Geosat (Exact Repeat Mission and Geodetic Mission), ERS-1 (1.5-year mean of 35-day, and GM), TOPEX/POSEIDON (T/P) (5.6-year mean) and ERS-2 (2-year mean) altimeter data over the region 0^∘–360^∘ longitude and –80^∘–80^∘ latitude. To reduce ocean variabilities and data noises, SSHs from non-repeat missions were filtered by Gaussian filters of various wavelengths. A Levitus oceanic dynamic topography was subtracted from the altimeter-derived SSHs, and the resulting heights were used to compute along-track deflection of the vertical (DOV). Geoidal heights and gravity anomalies were then computed from DOV using the deflection-geoid and inverse Vening Meinesz formulae. The Levitus oceanic dynamic topography was added back to the geoidal heights to obtain a preliminary sea surface grid. The difference between the T/P mean sea surface and the preliminary sea surface was computed on a grid by a minimum curvature method and then was added to the preliminary grid. The comparison of the NCTU01 mean sea surface height (MSSH) with the T/P and the ERS-1 MSSH result in overall root-mean-square (RMS) differences of 5.0 and 3.1 cm in SSH, respectively, and 7.1 and 3.2 μrad in SSH gradient, respectively. The RMS differences between the predicted and shipborne gravity anomalies range from 3.0 to 13.4 mGal in 12 areas of the world's oceans. Received: 26 September 2001 / Accepted: 3 April 2002 Correspondence to: C. Hwang Acknowledgements. This research is partly supported by the National Science Council of ROC, under grants NSC89-2611-M-009-003-OP2 and NSC89-2211-E-009-095. This is a contribution to the IAG Special Study Group 3.186. The Geosat and ERS1/2 data are from NOAA and CERSAT/France, respectively. The T/P data were provided by AVISO. The CLS and GSFC00 MSS models were kindly provided by NASA/GSFC and CLS, respectively. Drs. Levitus, Monterey, and Boyer are thanked for providing the SST model. Dr. T. Gruber and two anonymous reviewers provided very detailed reviews that improved the quality of this paper.