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.     

基于旋转微椭地球模型的内核平动振荡三重谱线理论模拟与实验探测

本文基于旋转微椭地球模型,采用简正模理论计算了地球内核平动振荡三重谱线的本征周期,理论上系统研究了地球内部介质(包括密度、地震波速等)分布异常对三重谱线本征周期的影响,计算了不同的内外核密度差和地核中的不同的P/S波速对应的内核平动振荡理论三重谱线周期;利用全球分布的9个超导台站,迭积每个台站长达54个月的高精度超导重力仪数据,在亚潮汐频段(0.162~0.285cph)检测内核平动振荡三重谱线.结果发现,三重谱线本征周期对内外核边界的密度跳跃非常敏感,随着密度差的增加,以类似于双曲线的特征减小;无论是采用地球质量不变的方法还是采用浮力频率为常数的方法,计算得到的三重谱线本征周期结果相差较小,且随着内外核密度差的增大,差距逐渐减小;内、外核P波波速分布异常对三重谱线周期的影响基本相当,内核S波波速分布异常比P波波速分布异常对三重谱线周期的影响小1个量级;探测到一组信噪比较高且满足谱峰分裂特征的三重谱线的信号(0.19281,0.21456和0.24151cph),有极大的可能是来自于内核平动振荡.基于探测结果可以推断实际的地球模型其内外核密度差应该介于PREM模型和1066A地球模型之间,更接近于1066A模型.     

探测一阶模态三重分裂的MSE技术和SHS方法的比较研究

完全剥离一阶模态_nS₁的三重分裂信号将有助于识别出其全部分裂谱线,进而更好地约束地球内部结构.理想情况下,球谐叠加法(SHS)与多台站实验技术(MSE)均可剥离一阶模态_nS₁的三重分裂信号,但部分学者持不同观点.本文基于对二者的理论分析进一步确认,在自耦合前提下,MSE方法可成功剥离_nS₁的三重分裂信号;而SHS方法在实际应用中无法成功剥离_nS₁的三重分裂信号,但可相对增强目标信号的振幅强度.此外,本文解释了MSE可剥离单线态信号的真实原因,并指出由于MSE未考虑全频段耦合影响,故仅适用于1 mHz以下的低频模态.鉴于超导重力(SG)数据在1 mHz以下比宽频地震数据具有更高的信噪比,因此,为验证本文结论并弄清MSE和SHS的实质,基于模拟数据及SG台站实测数据,本文利用MSE和SHS分别对一阶模态的合成信号及模态₃S₁进行了探测分析.实验结果表明,MSE可成功剥离一阶模态三重分裂信号,SHS则无法完全剥离,验证了我们的理论结论,表明前人部分结果需重新审视与评价.此外,本文基于三种不同方法并利用13个SG 台站数据给出的₃S₁的分裂宽度比分别为1.008, 1.000和1.001,远小于异常分裂判别临界值1.5, 因此,₃S₁应是正常分裂模态.     

基于EEMD分解的气压改正方法研究

利用超导重力仪观测数据精确测定低于1 mHz的地球自由振荡简正模式的分裂频率,是在不与任何弹性系数发生联系的情况下改善一维密度模型的有效方法.但在该频段台站局部气压变化对重力观测数据的影响成为主要干扰来源,且具有频率依赖特性,因此精细地开展气压改正成为利用超导重力数据检测低频自由振荡信号的必要手段.本文基于EEMD方法,提出了一种具有频率依赖特性的气压改正方法.该方法将重力观测和气压变化分解成处于不同频段的本征模态函数,并在相应频段上分别进行重力-气压变化的回归分析,计算得到具有频率依赖特性的气压导纳值,精细地消除气压变化对重力观测的影响,并以此对微弱低频地球自由振荡信号开展高分辨率分析.基于本文提出的气压改正方法,利用大地震后的超导重力数据检测了频率小于1.5 mHz的低频地球自由振荡及其频谱分裂现象.研究结果表明：利用该方法进行气压改正后检测得到的各简正模具有更高的信噪比,估计的本征频率误差水平明显降低,获得的基频球型振荡₀S₂和₀S₃以及一阶球型振荡₁S₂的分裂谱峰的估计精度更高,同时还检测到了部分环型振荡在重力观测中的耦合现象.对低频地球振荡的高分辨率检测结果验证了基于EEMD分解提出的气压改正方法的有效性,同时再次证明了超导重力仪观测数据在低频地球自由振荡检测中的优势.     

基于集合经验模态分解法的重力极潮提取与研究

重力极潮,即极移引起的重力变化,是地球由于惯性离心力变化导致地球形变的综合反映,其观测和研究有助于了解地球在长周期频段的响应,约束地球形变、地球内部构造和物理参数.区别于以往研究,本文采用了集合经验模态分解方法（Ensemble Empirical Mode Decomposition,EEMD）从全球5个超导重力仪台站连续重力观测资料中提取重力极潮、消除仪器漂移及极潮频段以外的大部分噪声信号,该方法所用的基函数是基于自身信号获得的;在此基础上,利用最小二乘匹配法分离极潮中的周年项和Chandler项,估算Chandler周期的极潮潮汐因子.结果表明,基于EEMD得到的极潮潮汐因子与前人基于其他消除仪器漂移方法（数学模型或小波分析）得到的结果相符合,精度相当,但由于这种方法是自适应的,因此本文结果更能反映实际物理过程.     

地球自由振荡弹性简正模研究进展与展望

在构建现代地球模型时,地球内部分层结构主要是根据地震波资料确定的;而地球内部密度及弹性参数,特别是地幔以下大尺度结构的密度分布,则主要是根据地球自由振荡的弹性简正模观测资料确定的.本文概述了地球自由振荡简正模本征值的求解理论和方法,介绍了球型和环型模态位移场表达式,讨论了地球自由振荡模态的衰减、分裂与耦合效应;总结了多线态分裂谱线探测和分裂参数估计的方法,综述了利用弹性简正模开展地震矩张量、地球三维非均匀性结构和内核超速旋转约束与反演研究的主要进展和存在的问题.最后作为展望,本文还讨论了地球自由振荡简正模的未来研究趋势.     

利用超导重力数据检测日本Mw9.0地震的低频自由振荡及谱线分裂

准确估计低频自由振荡及谱线分裂是约束地球内部结构和改进地球模型的重要手段.本文利用四个不同台站的超导重力观测数据系统研究了日本M_w9.0大地震激发的低于1.5 mHz自由振荡及谱线分裂.研究结果表明:(1)选取适当的数据长度,超导重力观测数据可以检测出低于1.5 mHz除₁S₁以外的所有自由振荡;(2)除₀S₂、₀S₃、₀S₀、₂S₁、₃S₁、₁S₂和₀T₂外,重点探测出₃S₂、₀S₄和₁S₄谱线分裂的所有谱峰;(3)与PREM模型理论频率相比,₀S₀观测频率平均向右偏移0.354×10^-3mHz,说明PREM理论模型中地幔底部参数与真实地球可能存在微小偏差;(4)₃S₂的谱线分裂率r为1.485267,比PREM理论谱线分裂宽度约宽50%,表明PREM中地球内核中部介质参数可能存在一定误差,需要进一步改善.另外,quasi-₀T₂的r为1.254206,比PREM理论谱线分裂宽度约宽25%.     

利用VP型垂直摆倾斜仪观测数据检测2011日本M_w9.0级地震激发的低频地球自由振荡

甚长周期VP型垂直摆倾斜仪对某些地球物理信号有特殊的敏感性,除了在观测小地震、慢地震等方面有优势之外,还可有效应用于低频地球自由振荡信号的探测.利用安置在武汉大学珞珈山的我国自行研制的VP型垂直摆倾斜仪在2011日本Mw9.0级大地震之后不同长度的观测数据,联合EEMD方法、自回归估计(AR)方法和bootstrap法,本文不仅检测到该地震激发的频率小于4.7 mHz的零阶球型振荡(0S2至0S38)和环型振荡(0T4至0T35)几乎所有振型以及15个谐频振型,还检测到5个其频率低于1mHz的低阶球型多线态(0S2、2S1、0S3、0S4和1S2)的部分或全部谱峰分裂现象,并给出了所有检测结果的精度评估.此外,本文分析了某些球型和环型振荡之间的耦合效应,结果表明耦合效应将显著影响地球自由振荡信号的相关参数.     

复杂追踪算法结合EEMD识别结构损伤

结构损伤会引起结构振动信号的突变,而该突变信号会淹没于环境噪声信号中。为此,文章将复杂追踪理论(CP)引入结构损伤识别领域,将损伤识别问题转化为突变特征提取问题。提出一种复杂追踪结合集合经验模态分解(EEMD)识别结构损伤的新方法,首先采用EEMD预处理结构振动信号,接着将分解得到的本征模函数(IMF)作为混合信号输入CP模型中,提取出包含损伤特征的本征模函数,进而识别出结构损伤发生的时刻及位置。最后,通过对环境激励下六自由度质量-弹簧系统和地震激励下三层框架模型的数值分析。结果表明,该方法能够准确有效地识别结构损伤异常时刻与位置。     

利用小波分析重力的长期变化

运用小波滤波方法估算Chandler和周年项的潮汐因子.本文分析了四个台站(Brussels, Boulder, Membach以及Strasbourg)的观测记录,运用合成潮方法得到重力残差后,用Daubechies小波带通滤波器滤波残差,得到256～512 d时间尺度上的序列,根据标准差最小原则确定观测极潮周年和Chandler项的周期,然后利用最小二乘法估算它们的潮汐因子,同时给出未经模型改正的周年重力.由于高阶Daubechies小波构造的滤波器具有良好的频率响应,且能压制信号中的高阶异常成分,使滤波的信号更加光滑,因此计算结果具有更小的均方差,更加可靠.     

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.     

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.     

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.     

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.     

Order statistics of functionals of strong ground motion for a class of renewal processes

In this paper, probability distribution functions are derived for the order statistics of various functionals of strong ground motion at a site. These functionals can be: Modified Mercalli Intensity (MMI), peak ground acceleration (PGA), Fourier spectral amplitudes of acceleration, response spectrum amplitudes (spectral displacement, pseudo-spectral velocity and pseudo-spectral acceleration), and amplitudes of the peaks (local maxima and local minima) in the time historyof the response of SDOF and MDOF structures at the site. Three parameters of the response of a structure are considered: displacement, shear force and bending moment at each level (storey) of the structure. The earthquake sources contributing to the risk of ground motion at the site are a number of point, area or volume sources, each with defined frequency of occurence-magnitude relationship. The magnitudes of the possible events at these sources are discretized, and the occurrence of events of different magnitudes are assumed to be statistically independent. For each magnitude, it is assumed that the eartquakes occur in a Poissonian sequence or in a renewal process which is a generalization of the Poissonian. For these assumptions, the probability distribution functions are presented for the number of earthquakes, n, during which a given level of site or structural response is exceeded during the exposure time, and for the return period of the exceedances. For example, for single-degree- of-freedom: (SDOF) or multi-degree-of-freedom structures, (MDOF) n can be the number of earthquakes during which the response of a storey will exceed a given level at least m times(m = 1, 2, 3,…) during the exposure time. These probability distribution functions can be used to extend the concept of uniform probability functionals to more than one exceedance. A more important application is to generalize the uniform probability functionals method of site response (uniform probability Fourier or response spectra) to uniform probability envelopes of displacement, shears and bending moments of a given structure. The uniform probability envelopes can be for exceedance at least once during at least one earthquake, or, in general, for exceedance at least m times per earthquake (m = 1, 2,…) during at least n earthquakes. In other words, during at least n earthquakes at least m peaks in the response can be higher than the specified level. Such uniform probability envelopes can be used (1) to define new design guidelines for building codes based on cost-benefit analysis; (2) to construct more refined probability distribution functions for the damage and total economic losses caused by earthquakes; and (3) to develop planning and decision strategies on strengthening and retrofitting existing buildings.     

Noise limitations in the core-mode band of superconducting gravimeter data

In recent years, several claims of detection of weak harmonic signals in the sub-tidal band of frequencies of high-quality gravimeter data have been made. Here, we review our attempts at confirming Smylie's claim of detection of the Slichter mode of inner-core oscillation using the same four data sets he and his colleagues used. We further examine the homogeneous 2 year data sets obtained from the superconducting gravimeters sited in Strasbourg and at Cantley, Quebec. We show that the power spectra of tidal-reduced, pressure and slew-corrected gravity residuals from these data are indistinguishable from a random walk process except in narrow bands dominated by residual earth tides and by harmonics of the diurnal thermal-atmospheric tide. Such a random ‘brown’ residual could result from mechanical instabilities and electronic noise in the instruments themselves, from site-specific tectonic noise, from local hydrological variations and pier instabilities or it could derive from unaccounted for variability in the atmospheric pressure in the vicinity of the instruments. We argue that the homogeneous 2 year data sets show no evidence whatever of Slichter harmonics even though our preprocessing methods reduce ‘apparent noise levels’ in the core-mode band by almost an order magnitude in comparison with the four data sets originally employed by Smylie et al. and, in their first attempted confirmation of his claimed discovery, by Jensen et al.     

Time Variations In Gravity And Inferences On The Earth's Structure And Dynamics

This paper reviews how the study of the surface gravity changes is able to provide useful information on the Earth's structure and global dynamics. The spectral range which is observable with superconducting gravimeters is broad and goes from the seismic frequency band to periods longer than one year. We first investigate the seismic and sub-seismic bands with a special attention paid to the gravity detection of core modes in the liquid core and to the Slichter mode of translation of the solid inner core. In the tidal bands, we show how accurate measurements allow us to infer constraints on various phenomena such as mantle (an-)elasticity, as well as ocean and atmospheric loading. The observation of the Free Core Nutation resonance in the diurnal frequency band is reviewed and indirectly suggests an increase in the ellipticity of the core-mantle boundary with respect to its hydrostatic value. A similar resonance is also theoretically predicted in the diurnal band for the rotation of the solid inner core (Free Inner Core Nutation) but we show that its detection is much more difficult because of the small amplitude and lack of a nearby tidal frequency. Oceanic and atmospheric loading mechanisms induce gravity changes over a wide spectral range and we present some recent progress in this field. Finally, because superconducting gravimeters have high calibration stability and small long-term instrumental drift, they can easily measure longperiod gravity variations due to polar motion and hydrogeology.     

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.