利用超导重力数据探测Slichter模三重分裂信号

本文基于2004苏门答腊地震后全球地球动力学计划观测网中9台超导重力仪13200h的连续重力观测数据,联合利用整体经验模态分解(EEMD)、最优序列估计(OSE)、积谱密度分析(PSA)和自回归估计(AR)方法,探测地球固态内核平动振荡模态(Slichter模)的三重分裂信号.利用EEMD提取常规预处理后的重力残差中包含目标频段的本征模态函数(IMFs)作为最终的重力残差之后,将每个台站的重力残差平均分成无重叠的3个子数据块,再应用OSE和PSA方法获取Slichter模三重分裂谱线的积谱密度,并采用AR方法估计各积谱中弱共振信号的中心频率及其误差.结果表明,结合OSE和PSA方法探测到三个清晰的谱峰,周期分别为5.8307±7.1×10-4h、5.2161±8.1×10-4 h和4.7536±5.2×10-4 h,分别对应Slichter模三重分裂谱线m=-1、m=0和m=+1,且三个谱峰的周期与Crossley(1992)、Rochester和Peng(1993)、Peng(1997)和Rogister(2003)基于PREM地球模型给出的Slichter模理论周期非常接近,也与Ding和Shen(2013)建议的"可能的观测结果"较为接近.参考现有的理论和观测结果,本文认为这三个信号可能是Slichter模三重分裂谱线.     

利用全球超导重力仪数据检测长周期核模

采用全球地球动力学计划观测网中13台超导重力仪长期连续观测资料,探讨了长周期核模检测的可能性。采用相同的方法剔除了所有13个观测序列中的重力潮汐信号、仪器漂移和大气重力信号,估计了各个序列的功率谱密度及其积谱密度,估计并分析了非潮汐不同频段背景噪声。结果表明,在两个潮汐间频段（0.047~0.075cph和0.089~0.117cph)和亚潮汐频段(0.172~0.333cph),全球超导重力仪的平均噪声水平分别为0.0649,0.0350nm/s2和0.0138nm/s2,可以检测到的全球谐信号幅度极限分别为0.0416,0.0231nm/s2和0.0098nm/s2,表明全球超导重力仪观测资料基本可以识别长周期核模信号.在全球超导重力观测中,在潮汐间频段发现周期分别16.55,15.79,11.00h和10.09h的全球谐信号谱峰,可能来自于液核长周期振荡;在亚潮汐频段没有Smylie 1992年发现的Slichter模信号,但存在8个全球谐信号的谱峰,参考现有的理论模拟结果,Slichter模是这些信号可能的来源之一.     

Least-squares self-coherency analysis of superconducting gravimeter records in search for the Slichter triplet

We develop a new approach for the spectral analysis of the superconducting gravimeter data to search for the spheroidal oscillation ₁S₁ of the Earth solid inner core. The new method, which we call least-squares (LS) self-coherency analysis, is based on the product of the least-squares spectra of segments of the time series under consideration. The statistical foundation of this method is presented in the new least-squares product spectrum theorem that establishes rigorously confidence levels for detecting significant peaks. We apply this approach along with a number of other innovative ideas to a 6-year long gravity series collected at the Canadian Superconducting Gravimeter Installation (CSGI) in Cantley, Canada, by splitting it into 72 statistically independent monthly records. Each monthly record is analysed spectrally and all monthly LS spectra are multiplied to construct the self-coherency spectrum of the 6-year gravity series. The self-coherency spectrum is then used to detect significant peaks in the band 3-7 h at various significant levels with the aim to identify a triplet of periods associated with the rotational/ellipsoidal splitting of ₁S₁ (Slichter triplet). From all the Slichter periods predicted by various researchers so far, Smylie's triplet appears to be the most supported one, albeit very weakly, both, before and after the atmospheric pressure effect is removed from the series. Using the viscous splitting law [Smylie, D.E., 1992. The inner core translational triplet and the density near Earth's center. Science 255, 1678-1682] as guide, we can also see one interesting and statistically significant triplet with periods A = {4.261 h, 4.516 h, 4.872 h}, which changes slightly to A′ = {4.269 h, 4.516 h, 4.889 h} after the atmospheric pressure correction is applied to the gravity series.     

Temporal variations in free core nutation period

Based on the nearly diurnal resonance in the tidal gravity observations,the temporal variations in period of the Earth's free core nutation (FCN) are investigated by using the tidal gravity observations of 18-year duration recorded continu-ously with a superconducting gravimeter (SG) at Brussels. The effects of the global oceanic tide loading and local barometric pressure on the SG observations have been removed by using eleven high-precision global digital models of oceanic tides and barometric pressure me...     

A search for atmospheric effects on gravity at different time and space scales

We investigate in this paper various approaches to correct gravity changes for the effect of atmospheric pressure changes. Two specific locations are considered: Strasbourg (France) as mid-latitude station, where regular pressure fronts occur and Djougou (Benin) as equatorial station with large thermally driven S₁ and S₂ waves of planetary extent. We first review the classical approaches based on a constant or frequency-dependent admittance using only local pressure and gravity data. We consider then a model of atmospheric loading and show the barometric admittance in terms of elastic, Newtonian and total load, as a function of the distance from the station. We consider both a 2D pressure model (surface loading) and a 2.5D model, where the density decreases with height (standard atmosphere). Assuming horizontal advection in the atmospheric dynamics, we convert this spatially dependent admittance into a frequency-dependent admittance. Using global pressure data from European Centre for Medium-Range Weather Forecasts (ECMWF) at about 12 km spatial resolution and 3 h sampling, we compute the model-predicted pressure admittance for Djougou and Strasbourg and we simulate the frequency dependence inferred from gravity and pressure observations below 4 cycle per day. A long gravity and pressure data set (1996–2013) from Strasbourg is used to investigate the low frequency part of the pressure admittance while a common 2.5 year data set (August 2010–February 2013) for Strasbourg and Djougou is then analyzed to investigate the high frequency part of the admittance. In both cases, our results are in close agreement with the predictions inferred from an atmospheric 2.5D loading model with a distance–time relationship due to horizontal advection. The frequency dependence of the barometric admittance is explained by the competing contributions of Newtonian attraction and elastic surface deformation according to the distance from the gravimeter. In the far field (low frequencies), the magnitude of the admittance decreases with frequency because of the combined elasticity effect and Newtonian attraction (when the atmosphere is below the horizon) while, on the contrary, in the near field (high frequencies), elasticity becomes negligible and the pressure admittance mainly decreases with increasing frequency because of the decreasing attraction effect of the atmospheric masses inside the cylindrical pressure cell centered on the sensor location of decreasing radius. In the last part, we show that there is variability in time in the pressure admittance for both stations.     

The search for weak harmonic signals in a spectrum with application to gravity data

When considering the search for discovery or amplitude estimation of a spectral line with a probabilistic approach, great attention must be paid to the meaning of each step. We give the probability law for the amplitude of a spectral peak in the presence of random noise appearing in a periodogram and discuss the effective probability of the existence of the corresponding wave. We find that the estimated amplitude of a spectral peak is biased and should be corrected when the signal-to-noise ratio is small. As a first application to gravity data, it results in a re-estimation of the gravimetric amplitude factors (delta factors) provided by least-squares tidal analysis. We also estimate the probability of observing a spectral line above a given level in the spectrum of a purely random noise. This allows us to compute for given spectrum the number of peaks expected to overcross the classical levels used in statistical analysis (like nσ, where σ is the standard deviation of the temporal noise distribution and n is an integer with typical values equal to 2 or 3). A specific application to real data is investigating the gravity spectrum derived from a 5 year record of the French superconducting gravimeter and we show that the predicted statistics are indeed in agreement with the observations. We also show the statistical consequence of using longer observing periods to obtain the spectral estimations. The problem of detecting translational motion of the Earth's solid inner core (Slichter modes) in a gravity spectrum is analyzed and the probabilities of having a triplet of random peaks thresholding specific levels in a given frequency window are computed. We show that, in the case of a typical gravity spectrum (1 year of hourly data and a frequency window of 0.03 cycle h⁻¹), the probability of having a random set of three peaks exceeding a level of 3 σ, is very high. This emphasizes the need for a very careful analysis of spectral lines before inferring the existence of a true physical signal.     

Results from 44 months of observations with a superconducting gravimeter at Moxa/Germany

Results for more than 42 months of observations with the superconducting gravimeter CD-034 at the Geodynamic Observatory Moxa are discussed. Moxa observatory is one of the newer stations within the ‘Global Geodynamics Project’ (GGP). A special feature of the gravimeter at Moxa is its dual sensor system; differences in the results obtained from the two sensor recordings are generally well within the standard deviations of the tidal analysis. One significant difference concerns the slightly different drift rates of 31 and 49.5 nm/s² per year for upper and lower sensor; both sensor drifts can be fitted by a linear function. We find that the noise levels are close to the ‘New Low Noise Model’ for the seismic-modes and are also low in the tidal bands. Due to this low noise, Moxa is a station well suited to search for small geodynamic signals. The long-period variation in the gravity residuals correlates well with the polar motion.The difference signal between the two sensor recordings has a peak-to-peak amplitude of about 6 nm/s² and shows systematic variations. Its spectrum is characterised by instrumental noise between 0.2 and 0.4 cph. The noise level of the difference and of the sum of the two residual datasets are clearly lower, respectively, higher than the noise contents of the gravity residuals themselves. This is a strong indication for the existence of broadband signals common to the two residual datasets, leading to the conjecture that the reduction of environmental effects is still not sufficient.Our results once more emphasize the necessity to correct the data for barometric pressure effects when analyzing the data for seismic modes. The reduction visibly increases the signal-to-noise ratio in the low frequencies of the mode band and helps to avoid misinterpreations of peaks. Besides the well known barometric pressure influence we can establish hydrological effects in the data which are probably caused by soil moisture and groundwater table variations as well as by batch-wise water movement within the weathering layer. As the major part of the observatory surroundings is above gravimeter level, an anticorrelation between hydrological and gravity changes is observed. In addition, it can be shown that global hydrological effects reach an order of magnitude that makes it necessary to consider these effects when analyzing long-period signals like polar motion. Vice versa these effects are large enough to be detectable in the gravity data. A first joint analysis of five datasets from the GGP network shows no indications for signals related to the Slichter triplet or core modes.     

On the ratio noise-signal of long-periodic oscillations in the general atmospheric circulation

Summary Characteristic features of long-periodic oscillations in the general atmospheric circulation may be deduced from the correlation existing between the monthly, the three-monthly, the six-monthly and the twelve-monthly figures of the barometric pressure at two distant stations and from the autocorrelation of the same figures at each station.It is shown that the monthly figures of the barometric pressure at Easter Island and those at Djakarta during the six years 1950–1955 have, when plotted as a function of time, one oscillation in common, whereas further these figures have both their own rhythms and their own noise. The period of the common oscillation is 28.6 months, while the phase difference between both stations amounts to 180°. The r.m.s. value of the noise is 0.76 times the value of the amplitude of the oscillation. The rhythms differ in wave length, amplitude and phase.It is also shown that the monthly figures of the barometric pressure at Ponta Delgada and those at Stykkisholm have, when plotted as a function of time, a whole spectrum of oscillations jointly, while all oscillations have the same phase difference (238°) between both stations. These features are deduced from observations during 40 years (1896–1915 and 1921–1940). If yearly figures are used instead of monthly ones, then the greater part of the spectrum of oscillations is smoothed away and only a few common oscillations are left. The first common oscillation has a wave length of 26.5 months and the second one has a wave length of 38.7 months.     

Performance of superconducting gravimeters from long-period seismology to tides

The first phase (1997–2003) of the Global Geodynamics Project (GGP) has now been completed. Data from superconducting gravimeters (SGs) within GGP have shown great capabilities in a wide spectrum of geophysical applications from the tidal studies to the long-period seismology. Here, we compare the noise levels of the different contributing stations over the whole spectrum. We use three different processing procedures to evaluate the combined instrument-plus-site noise in the long-period seismic band (200–600 s), in the sub-seismic band (1–6 h) and in the tidal bands (12–24 h). The analysis in the seismic band has demonstrated that SGs are particularly well suited for the studies of the long-period normal modes and thus are complementary to long-period seismometers. In the sub-seismic band, the power spectral densities, computed over a period of 15 continuous days for every GGP station, cross the New Low Noise Model of Peterson from T = 16 min to T = 4.6 h. SG data are therefore appropriate for studying long-period seismic and sub-seismic modes. In the tidal bands, the noise comparison is realised by a least-squares fit to tides, local air pressure and instrumental drift, leading to gravity residuals where we estimate a standard deviation and average noise levels in different tidal frequency bands. Tidal gravity observations using SGs have also shown to be an independent validation tool of ocean tidal models, and they are therefore complementary to tide gauge and altimetric data sets. Knowledge of the noise levels at each station is important in a number of studies that combine the data to determine global Earth parameters. We illustrate it with the stacking of the data in the search for the gravity variations associated with the sub-seismic translational motions of the inner core, the so-called Slichter triplet.     

Difference between the spectra of acoustic gravity waves in daytime and nighttime hours due to nonequilibrium effects in the atmosphere

The singularities of the wave disturbance spectra of the nonequilibrium atmosphere in the range of acoustic gravity waves (AGWs) have been analyzed. Using the dispersion ratio for AGWs in the nonequilibrium atmosphere, it has been established that the spectra in the daytime and nighttime hours are different and this difference, caused by a nonequilibrium spectrum sensitivity to atmospheric temperature, can reach several percent in certain atmospheric regions. For the spectrum of the equilibrium model of the atmosphere, the difference between the daytime and nighttime spectra makes up several fractions of percent. As a result of the spectral treatment of variations in pressure and intensity of cosmic rays (CRs), it has been found out that the daytime AGW spectrum is higher-frequency than the nighttime spectrum. A comparison of the theoretical calculations of the AGW spectrum with observations has made it possible to distinguish the effect of nonequilibrium in the AGW spectral composition.     

Wavelet approach to the determination of gravity tide parameters

A new approach is proposed for the determination of gravity tide parameters.Three pairs of compactly supported wavelet filters are introduced in the approach.They can efficiently extract the objective tides from the gravity observation series.The new approach guarantees a direct and precise analysis on the tidal gravity records of any sampling length.The new approach is applied to the harmonic analysis on Wuhan superconducting gravimeter records.The results clearly show the resonant effects of the Earth Nearly Diurnal Free Wobble (NDFW).     

Least squares self-coherence for sub-nGal signal detection in the superconducting gravimeter records

In this paper, we use superconducting gravimeter (SG) data recorded at three stations of the global geodynamics project (GGP) network, with good geographical distribution, to search for possible significant peaks in the gravity spectrum that are in the assumed period range of the Slichter triplet. Seven-year long series from Cantley (Canada), and four-year long series from both Canberra (Australia) and Moxa (Germany) stations are used. First, a solid Earth and ocean tide model is subtracted from the data, followed by a local atmospheric pressure correction based on a frequency-, and location-dependent admittance estimated by the least squares response method. Subsequently, the residual series are filtered with a Parzen-based bandpass filter with a passband (12 h–78 s). A sub-nGal detection level is confirmed by injecting an artificial sine wave of different amplitudes. The Least Squares Self-Coherency spectrum shows the existence of many apparently statistically significant peaks at the 95% confidence level in the band (3–8 h). Although a few peaks are close to the claimed Slichter periods in previous research, the large number of candidate peaks may be related to other mechanisms such as global pressure variations, or hydrology.     

气压变化及其对地壳形变和深井水位的影响

根据北京塔院地区1984和1985年的微气压计记录采用频谱分析和调和分析两种方法得出了大气潮谱的详细结构;用负荷勒甫数代替潮汐勒甫数,仿照固体潮的有关公式,导出了大气潮引起的地壳应变和地倾斜公式;使用北京塔院井的水位观测资料结合当地的气压资料,分析了气压变化对深井水位的影响.理论计算和实测资料的分析结果基本相符,特别是两种结果都得出S₂大气潮引起的体膨胀约为S₂固体潮体膨胀的20％.     

气压变化及其对地壳形变和深井水位的影响

根据北京塔院地区1984和1985年的微气压计记录采用频谱分析和调和分析两种方法得出了大气潮谱的详细结构;用负荷勒甫数代替潮汐勒甫数,仿照固体潮的有关公式,导出了大气潮引起的地壳应变和地倾斜公式;使用北京塔院井的水位观测资料结合当地的气压资料,分析了气压变化对深井水位的影响.理论计算和实测资料的分析结果基本相符,特别是两种结果都得出S_2大气潮引起的体膨胀约为S_2固体潮体膨胀的20％.     

大气变化对位移、重力和倾斜观测影响的理论计算

利用弹性地球负荷理论和流体静力学平衡假设条件下的干空气及其垂直温度梯度分布,理论计算了大气压力作用下地表位移、重力和倾斜格林函数．详细讨论了不同地球模型、台站高程、周边地形、地表大气温度和水汽含量等因素对计算结果的影响．数值结果说明大气效应弹性项影响主要来自于远离台站的区域;引力项对重力的影响主要贡献来自于台站近区,对倾斜的影响来自于远离台站的区域．各种因素对大气重力和倾斜格林函数的影响分别在01°和1°角距范围内,但其综合影响较为复杂．     

Loading effects in Metsähovi from the atmosphere and the Baltic Sea

Loading by atmosphere and by the Baltic Sea cause gravity change at Metsähovi, located 15 km from the open sea. Gravity is changed by both the Newtonian attraction of the loading mass and by the crustal deformation. We have performed loading calculations using appropriate Green's function for both gravity and deformation, for both atmospheric and Baltic loading. The loading by atmosphere has been computed using a detailed surface pressure field from high resolution limited area model (HIRLAM) for north Europe up to 10° distances. Baltic Sea level is modelled using tide gauge records. Calculations show that 1 m of uniform layer of water corresponds to 31 nm s⁻² in gravity and −11 mm in height. Modelled loading is compared with observations of the superconducting gravimeter T020 for years 1994–2002. The combination of HIRLAM and a tide gauge record decreases RMS of gravity residuals by 14% compared to single admittance in air pressure corrections without sea level data. Regression of gravity residuals on the tide gauge record at Helsinki (at 30 km distance) gives a gravity effect of 26 nm s⁻² m⁻¹ for Baltic loading.The gravity station is co-located with a permanent GPS station. We have also associated the loading effects of the atmosphere and of the Baltic Sea with temporal height variations. The range of modelled vertical motion due to air pressure was 46 mm and that due to sea level 18 mm. The total range was 38 mm. The effects of the Baltic Sea and of the atmosphere partly cancel each other, since at longer periods the inverse barometer assumption is valid. Regression of the modelled height on local air pressure gives −0.37 mm hPa⁻¹, corresponding approximately to width 6° for pressure system.We have tested the models using one year of daily GPS data. Multilinear regression on local air pressure and sea level in Helsinki gives the coefficient −0.34 mm hPa⁻¹ for pressure, and −11 mm m⁻¹ for sea level. These match model values. Loading by air pressure and Baltic Sea explains nearly 40% of the variance of daily GPS height solutions.     

中高频带地下水位对气压和固体潮的响应特征分析

我国前兆观测网络数字化改造的完成, 使得对地震地下水位观测的孕震信息提取和干扰因素排除的研究拓宽至更广的频率范围, 而对原有一些认识的重新考察也成为可能。 本文从中国地震前兆台网挑选出数据质量较好的10个台站, 分析各个台站2008年1月1日至5月11日的地下水位和气压资料及理论重力固体潮的频谱及其频域相关性特征, 并分析了地下水位对气压响应的时移。 结果表明, 中高频带地下水位对气压的响应没有低频带好, 两者相关性随周期的减小而减弱; 含水层岩性对中高频带地下水位的气压和固体潮响应特征有较大影响, 部分灰岩井在高频频段存在地下水位对气压响应异常的现象; 时移效应对水位的气压响应整体特征影响不大, 体现出两种信号自身的复杂性。     

基于小波分析的水位观测气压效应研究

为研究水位气压效应的主要特征, 采用广西南宁石埠、 九塘两个台站的水位、 气压观测资料, 利用小波分析、 交叉小波分析、 小波相干分析方法在时间-频率空间内对二者的周期特征以及二者的相关特征进行了分析。 结果表明: 水位观测数据的显著周期为7.8~14.7 h, 气压观测数据的显著周期为7.8~14.7 h和17.5~27.8 h; 水位和气压存在7.8~14.7 h尺度的共振周期; 水位和气压在较宽的周期尺度上存在着显著的相关性, 且水位和气压的相关系数随周期和时间变化, 二者的相对相位角也因周期的不同而存在差异。     

北京塔院井水位微动态资料的分析和应用

对塔院井地下水水位微动态资料和气压观测资料,采用三种方法计算了气压效率,作了谱分析和调和分析,并利用所得结果求出了该井所在含水层的水文地质参数     

Clear evidence for the sign-reversal of the pressure admittance to gravity near 3 mHz

The influence of the atmosphere on gravity measurements by Newtonian attraction and vertical displacements due to surface loading is well known and studied especially at frequencies below 1 mHz. Less work has been done at the higher seismic frequencies where inertial effects come into play. The sensor mass of a vertical accelerometer responds to several forces caused by the atmosphere, on global, regional and local scales. For the seismic frequencies the atmosphere above the observation site has the largest influence. A simple “Gedankenexperiment” demonstrates that the gravitational effect on one hand and the free air and inertial effects due to deformation on the other have opposite sign. Since the inertial effect is strongly frequency-dependent there should be a crossover-frequency where the pressure admittance to gravity changes sign. Simple analytical models clearly show this property near frequencies of a few mHz and are used here to amplify the variance reduction of the gravity residuals. The crossover-frequency depends on the properties of the models of the atmospheric phenomena and the elasticity of the Earth’s crust. Therefore in reality it must be expected to vary in time and space.We show one extremely clear example of this sign-reversal detected in the gravity data from the superconducting gravimeter GWR-C025 in Vienna among other examples which demonstrate the reality of this effect.