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.     

大气负荷响应计算误差估计模型

用数理统计技术，建立格林函方法计算大气变化引起重力和形焦等效应的精度评定模型，并利用中国及其邻区的大气观,蛭大气误差常数和一个计算方案的精度估计，其结果与固体潮汐检测在不同气候条件下的响应情况相一致，该系统也可应用于格林函数积分形式的其它物理模型的误差估计。     

Precise tidal gravity recorded with superconducting gravimeters at stations Wuhan (China) and Kyoto (Japan)

 Three long series of tidal gravity observations, totalizing approximately 24 years and recorded with three superconducting gravimeters, T004, T008, and T009, at stations Wuhan (China) and Kyoto (Japan), are studied. The tidal amplitude factors and phase differences are determined precisely using Eterna and Nsv techniques. The precision of the main tidal amplitudes is at the same level of 0.01 μGal. The atmospheric gravity signals are corrected using the coefficients determined with a regression method between tidal gravity residual and station air pressure. The oceanic gravity signals are modeled based on five global oceanic models. It is found that the oceanic models developed by the analysis of measurements from Topex/Poseidon altimeters have the best fit to the superconducting gravimeter measurements, since the observed residuals and the discrepancies between the amplitude factors and the theoretical tidal models are reduced more significantly. The long-period gravity variations are dominated by the non-linear drift phenomena of the instruments, and the short-term variations in gravity are due to the background noise at the stations. Received: 20 January 2000 / Accepted: 15 September 2000     

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。     

Shallow-water loading tides in Japan from superconducting gravimetry

Gravity observations from superconducting gravimeters are used to observe loading effects from shallow-water tides on the Japanese east and west coasts. Non-linear third-diurnal and higher-frequency shallow-water tides are identified in the tide-gauge observations from these coastal areas. The most energetic constituents in the tide gauge observations are also seen in the gravity observations due to their loading effects on the deformation of the Earth. Even though the shallow-water tides at the Japanese east coast have an amplitude of only a few millimetres, they are still able to generate a loading signal at gravity sites located several hundred kilometres inland. In particular, the S₃, S₄ and S₅ solar tides occur in both gravity and tide gauge observations. It is indicated that in other shelf regions with large shallow water tides, the shallow water loading signals account for a significant signal, which should be taken into account.Acknowledgement The authors would like to thank the Hydrographic and Oceanographic Department (Japan Coast Guard), Japan Meteorological Agency and Hokkaido Development Agency for access to the tide-gauge data. Also, the Global Geodynamic Project Information System and Data Center (GGP-ISDC) is acknowledged for providing the gravity data.     

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.     

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。     

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     

The gravitational effect of ocean tide loading at high latitude coastal stations in Norway

Gravity measurements close to the ocean are strongly affected by ocean tide loading (OTL). The gravitational OTL effect consists of three parts, i.e. a change in gravity caused by direct attraction from the variable water-masses, by displacement of the observing point due to the load, and by redistribution of masses due to crustal deformation. We compare the OTL gravitational effect of several global models to observed time-series of gravity to identify the best model for four arctic observation sites. We also investigate if the global models are sufficient for correcting gravity observations. The NAO99b model fits the observations best at three stations. At two stations (Tromsø and Bodø) the global models explain the variability in the observations well. At the other two (Honningsvåg and Andøya), a significant periodic signal remains after the OTL correction has been applied. We separate two of the gravitational effects, the direct attraction and the change in gravity due to displacement, to study the local effects. Simple geometric models of the water load and independent measurements from local tide-gauges are used to calculate these effects. This leads to improved correspondence with the OTL signal, hence demonstrating the importance of careful modelling of local effects for correction of gravity observations in coastal stations.     

不同固体潮改正公式及国家重力网的统一

本文讨论了不同的潮汐公式,及其引起的重力测量计算成果不一致的问题,计算了当潮汐改正公式不统一时,对我国范围内绝对重力测量、相对重力测量、重力仪长基线格值因子标定、重力仪短基线周期误差标定及物探重力控制测量成果的影响,分析了我国85重力基本网所选取的绝对重力控制点之间的一致性、控制点与我国85网相对联测平差结果的一致性、以及85网与我国一等重力控制同之间的一致性问题。最后,为统一我国重力控制测量成果提出了一些建议。     

Sensitivity of superconducting gravimeters in central Europe on variations in regional river and drainage basins

As underpinned by various studies in the last years, temporal changes of the Earth’s gravity field contain a wealth of information on mass redistribution processes in the Earth’s system particularly associated with variations in continental water storage. By combining satellite and terrestrial observations with superconducting gravimeters (SG) a maximum of information can be gained due to the different temporal and spatial sampling. Esp. the cluster of superconducting gravimeters in central Europe is well suited for studies related to spatial and temporal changes in continental water storage. Due to the distribution of SG sites different sensitivities of the instruments are to be expected on changes in the various river and drainage basins which could, if sufficiently pronounced, be deployed to pinpoint areas in which main discrepancies between modelled and actual water storage changes occur and would thus allow us to fine-tune hydrological models. Based on the WaterGap Global Hydrological Model (WGHM), this sensitivity of the SG observations is investigated. One compartment of the WGHM is surface water, thus comprising rivers, flooding areas, and major reservoirs. This contribution is given for the total cell of 0.5° × 0.5° and not localized, e.g. in a riverbed, therefore the question arises to which extent localization or non-localization of this compartment affects the estimate if the respective surface waters are in the vicinity of 50 km around the SG stations. It can be shown, however, that the lateral distribution of the surface water masses plays only a negligible role for the central European stations meaning distributed surface water masses are an acceptable simplification when estimating hydrological effects. It emerges that variations in water storage in regions outside central Europe produce comparable effects on gravity at all sites and the impact of basins within central Europe is clearly distinguishable among the SG stations.     

Solution to the spectral filter problem of residual terrain modelling (RTM)

In physical geodesy, the residual terrain modelling (RTM) technique is frequently used for high-frequency gravity forward modelling. In the RTM technique, a detailed elevation model is high-pass-filtered in the topography domain, which is not equivalent to filtering in the gravity domain. This in-equivalence, denoted as spectral filter problem of the RTM technique, gives rise to two imperfections (errors). The first imperfection is unwanted low-frequency (LF) gravity signals, and the second imperfection is missing high-frequency (HF) signals in the forward-modelled RTM gravity signal. This paper presents new solutions to the RTM spectral filter problem. Our solutions are based on explicit modelling of the two imperfections via corrections. The HF correction is computed using spectral domain gravity forward modelling that delivers the HF gravity signal generated by the long-wavelength RTM reference topography. The LF correction is obtained from pre-computed global RTM gravity grids that are low-pass-filtered using surface or solid spherical harmonics. A numerical case study reveals maximum absolute signal strengths of \(\sim 44\) mGal (0.5 mGal RMS) for the HF correction and \(\sim 33\) mGal (0.6 mGal RMS) for the LF correction w.r.t. a degree-2160 reference topography within the data coverage of the SRTM topography model (\(56^{\circ }\hbox {S} \le \phi \le 60^{\circ }\hbox {N}\)). Application of the LF and HF corrections to pre-computed global gravity models (here the GGMplus gravity maps) demonstrates the efficiency of the new corrections over topographically rugged terrain. Over Switzerland, consideration of the HF and LF corrections reduced the RMS of the residuals between GGMplus and ground-truth gravity from 4.41 to 3.27 mGal, which translates into \(\sim 26\)% improvement. Over a second test area (Canada), our corrections reduced the RMS of the residuals between GGMplus and ground-truth gravity from 5.65 to 5.30 mGal (\(\sim 6\)% improvement). Particularly over Switzerland, geophysical signals (associated, e.g. with valley fillings) were found to stand out more clearly in the RTM-reduced gravity measurements when the HF and LF correction are taken into account. In summary, the new RTM filter corrections can be easily computed and applied to improve the spectral filter characteristics of the popular RTM approach. Benefits are expected, e.g. in the context of the development of future ultra-high-resolution global gravity models, smoothing of observed gravity data in mountainous terrain and geophysical interpretations of RTM-reduced gravity measurements.     

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.     

大气压力变化对武汉台站重力场观测的影响

利用全球2°×2.5°、中国及邻区域30′×30′ 气压资料和Farrell弹性地球模型负荷理论,采用数值积分方法,计算了大气压力变化对武汉台站重力场观测的影响。对1990年1月1日至12月31日的数值结果分析表明,全球大气压力变化对武汉台站重力的影响峰对峰达12微伽,大气重力导纳的年平均值为-0.260 μGal/mba(1 mba=1 hPa),这一结果同潮汐分析中由回归分析方法获得的导纳值相近。说明在利用超导重力仪观测资料应用于地球动力学研究之前,有必要作精细的全球气压变化改正。     

超导重力仪观测数据分析

超导重力仪作为目前研究时变重力场的主要仪器具有很高的灵敏度和稳定性、很低的噪音水平和漂移以及很宽的动态频率响应范围。探测时间序列中隐含的周期信号是超导重力仪观测数据分析的主要目标之一,通过快速傅里叶变换(FFT)和最小二乘谱分析方法分析超导重力数据中隐含信号的检测,并对两种方法结果进行了分析比较。并最终用小波分析的方法进行了检校。     

Two different methods of geoidal height determinations using a spherical harmonic representation of the geopotential, topographic corrections and the height anomaly–geoidal height difference

 It is suggested that a spherical harmonic representation of the geoidal heights using global Earth gravity models (EGM) might be accurate enough for many applications, although we know that some short-wavelength signals are missing in a potential coefficient model. A `direct' method of geoidal height determination from a global Earth gravity model coefficient alone and an `indirect' approach of geoidal height determination through height anomaly computed from a global gravity model are investigated. In both methods, suitable correction terms are applied. The results of computations in two test areas show that the direct and indirect approaches of geoid height determination yield good agreement with the classical gravimetric geoidal heights which are determined from Stokes' formula. Surprisingly, the results of the indirect method of geoidal height determination yield better agreement with the global positioning system (GPS)-levelling derived geoid heights, which are used to demonstrate such improvements, than the results of gravimetric geoid heights at to the same GPS stations. It has been demonstrated that the application of correction terms in both methods improves the agreement of geoidal heights at GPS-levelling stations. It is also found that the correction terms in the direct method of geoidal height determination are mostly similar to the correction terms used for the indirect determination of geoidal heights from height anomalies. Received: 26 July 2001 / Accepted: 21 February 2002     

HHT技术探测Slichter模三重谱线的研究

探测Slichter模态三重分裂可有效约束内核密度、内核半径及内外核边界密度跳跃。虽然Smylie(1992)声称探测到了Slichter模态三重分裂,但至今未被国际学术界公认。本文结合一个实验算例,阐述了Hilbert-Huang变换(HHT)分析方法的核心思想,并将该方法应用于探测Slichter模三重分裂谱线的研究。我们选取了全球分布的8个台站连续记录两年的小时间隔超导重力数据,进行了潮汐和气压改正后,将它们叠加获得重力残差;然后对重力残差作HHT分析,得到能量谱,进而选出了12种可能的谱峰组合,其中两组结果与Smylie的结果很接近,且本文得到的谱峰分裂相比于Smylie的结果具有更好的对称性。     

相对重力测量值的改正

影响相对重力测量精度的主要因素有潮汐、气压、仪器高、零点飘移和地下水变化以及仪器格值函数等。文中研究了在中国重力基本网 2 0 0 0 (CGBN2 0 0 0 )精度要求下各影响因素的计算公式和其中存在的问题 ,给出了一组便于实际测量应用的计算公式 ;同时对重力仪格值因子的误差和选取、非构造因素中地下水活动等问题进行了讨论     

iGrav-007超导重力仪格值的精密测定

iGrav超导重力仪是当前世界上最新型的便携式相对重力仪,可提供最稳定和最高精度的连续相对重力测量。利用武汉九峰台站FG5-112绝对重力仪与iGrav-007超导重力仪连续3天的同址观测结果,基于最小二乘线性回归和迭代算法,精密确定iGrav-007的格值。数据处理结果表明,iGrav-007的格值为(-91.640 2±0.085 2)×10-8 m·s-2/V,相对标定精度为0.092 9%,连续1天的FG5绝对重力观测获得的格值精度优于0.2%,连续3天的FG5绝对重力观测获得的格值精度优于0.1%。     

Improved relativistic transformations in GPS

For GPS satellite clocks, a nominal (hardware) frequency offset and a conventional periodic relativistic correction derived as a dot product of the satellite position and velocity vectors, are used to compensate the relativistic effects. The conventional hardware clock rate offset of 38,575.008 ns/day corresponds to a nominal orbit semi-major axis of about 26,561,400 m. For some of the GPS satellites, the departures from the nominal semi-major axis can cause an apparent clock rate up to 10 ns/day. GPS orbit perturbations, together with the earth gravity field oblateness, which is largely responsible for the orbit perturbations, cause the standard GPS relativistic transformations to depart from the rigorous relativity transformation by up to 0.2 ns/day. In addition, the conventional periodic relativistic correction exhibits periodic errors with amplitudes of about 0.1 and 0.2 ns, with periods of about 6 h and 14 days, respectively. Using an analytical integration of the gravity oblateness term (J₂), a simple analytical approximation was derived for the apparent clock rate and the 6-h periodic errors of the standard GPS gravity correction. For daily linear representations of GPS satellite clocks, the improved relativistic formula was found to agree with the precise numerical integration of the GPS relativistic effects within about 0.015 ns. For most of the Block IIR satellites, the 6-h periodical errors of the GPS conventional relativistic correction are already detectable in the recent IGS final clock combinations.