Analysis of seasonal signals and long-term trends in the height time series of IGS sites in China

The seasonal signal and long-term trend in the height time series of 10 IGS sites in China are investigated in this paper. The offset detection and outlier removal as well as the removal of common mode error are performed on the raw GPS time-series data developed by the Scripps Orbit and Permanent Array Center (SOPAC). The seasonal-trend decomposition procedure based on LOESS (STL) is utilized to extract precise seasonal signals, followed by an estimation of the long-term trend with the application of maximum likelihood estimation (MLE) to the seasonally adjusted time series. The Up-components of all sites are featured by obvious seasonal variations, with significant phase and amplitude modulation on some sites. After Kendall’s tau test, a significant trend (99% confidence interval) for all sites is achieved. Furthermore, the trends at sites TCMS and TNML have significant changes at epochs 2009.5384 and 2009.1493 (95% confidence interval), respectively, using the Breaks For Additive Seasonal and Trend test. Finally, the velocities and their uncertainties for all sites are estimated using MLE with the white noise plus flicker noise model. And the results are analyzed and compared with those announced by SOPAC. The results obtained in this paper have a higher precision than the SOPAC results.     

Effect of the span of Australian GPS coordinate time series in establishing an optimal noise model

The span of coordinate time series affects the determination of an optimal noise model. We analyzed position data recorded for 10 continuous Global Positioning System(GPS) sites from 1998.0 to mid-2009 on the Australian Plate to estimate the best noise model and thereafter obtain the true uncertainties of the velocity, employing the maximum likelihood estimation(MLE) method. MLE was employed to analyze the data in four ways. In the first two analyses, the noise was assumed to be a combination of flicker noise and white noise for the raw time series and spatially filtered time series. In the final two analyses, the spectral indices and amplitudes were simultaneously estimated for a power law noise plus white noise model for the raw time series and spatially filtered time series. We conclude that the noise model of GPS time series in Australia can be best described as the combination of flicker noise and white noise. Velocity uncertainties fall below ~0.2 mm/yr when the time span exceeds ~9.5 years. A comparison of noise amplitudes and maximum likelihood estimation values between the raw and spatially filtered time series suggests that traditional spatial filtering to remove common-mode errors might not be applicable to the raw time series of this region.     

香港GPS基准站坐标序列特征分析

利用香港GPS连续运行参考站网络2001年1月至2007年8月的观测资料,全面深入地分析了12个基准站坐标序列特征.本文采用主成分空间滤波算法去除公共误差,来提高坐标序列的信噪比,并采用最大似然估计准则定量估计滤波后坐标序列的噪声特性,计算了地球表面质量负荷（包括大气、非潮汐海洋、积雪和土壤水）对香港GPS基准站坐标序列的影响.研究结果表明：香港GPS基准站坐标序列具有高度的空间相关性,其公共误差具有较强的季节性变化特征;地表质量负荷变化引起的香港地壳形变可以解释公共误差序列中约为3mm的垂向周年变化,经过质量负荷改正后的公共误差序列与高阶电离层误差高度相关;滤波后坐标序列的噪声特性可以用可变白噪声加闪烁噪声模型来描述,顾及闪烁噪声所计算的速度误差要比只考虑可变白噪声计算的速度误差大2~6倍;基准站间存在达1.5 mm/yr的相对水平运动,揭示香港地区存在活动断层;部分基准站坐标具有明显的振幅为1～2 mm本地季节性变化,所有测站的残差序列也表现出强烈的季节性变化.     

Analysis on the noises from continuously monitoring GPS sites

In this paper,we analyze the time series of site coordinates of 27 continuously monitoring GPS sites covered bythe Crustal Movement Observation Network of China over the whole country.The data are obtained in the periodfrom the beginning of the observation to the November of 2005.On the basis of data processing,we analyze thepower spectrum density of coordinate component noise at each site and calculate the spectral indexes manifestingthe noise property of each component.The spectral indexes indicate that for most sites,the noise of time series ofeach coordinate component can be addressed by the model of white noise flicker noise;and for a small amountof sites,it can be described by the model of white noise flicker noise random walk noise.We also quantita-tively estimate each noise component in the model by using the criterion of maximum likelihood estimation.Theresult shows that the white noise in the time series of GPS site coordinates does not constitute the main part ofnoise.Therefore,the error estimation of site movement parameters is usually too small,or too optimistic if weconsider the white noise only.Correspondingly,if this factor is not fully considered in explaining these movementparameters,it might mislead the readers.     

连续观测站的噪声分析

分析了中国地壳运动观测网络在全国布设的27个GPS连续站开始运行以来至2005年11月的站坐标时间序列. 在对数据进行清理的基础上， 分析了各站坐标分量噪声的功率谱密度， 计算了表征各分量的噪声特性的谱指数. 谱指数显示， 大部分站的各坐标分量时间序列的噪声可以用白噪声+闪烁噪声的模型来描述， 少部分则可用白噪声+闪烁噪声+随机漫步噪声的模型来描述. 采用最大似然估计准则， 定量估计了模型中的各噪声分量. 结果表明， GPS站坐标时间序列中白噪声甚至不是噪声的主要成分. 因此， 仅顾及白噪声得到的测站运动参数的误差估计， 实际上是过高的， 或者说是过于乐观的. 相应地， 对这些运动参数作出解释时， 如果不充分考虑这一因素， 有可能会对读者产生误导.      

基于GPS和GRACE数据的三维地表形变的比较及地球物理解释

GPS技术能以高空间和高时间分辨率监测地表形变.但由于测量原理的不同,GPS监测的地表形变与GRACE存在差异.本文比较了ITRF2008-GPS残差序列与基于CSR的RL05版本的GRACE球谐系数的地表形变序列的差异.结果表明,GPS和GRACE的周年变化在高程方向上具有较好的一致性,但水平方向的差异明显.重点分析了影响GPS/GRACE地表形变差异(尤其是水平方向)的三个因素:不同GPS站时间序列间的不确定性,热弹性形变和区域形变.GPS站地表形变本身的不确定度在一定程度上导致了GPS/GRACE间的差异(特别是水平方向).结合热弹性形变理论指出,由温度变化引起的热弹性形变也是导致GPS/GRACE的南北方向差异的主要原因之一.因此利用GPS数据研究地表质量负载时,必须消除热弹性形变的影响.区域负载对GPS/GRACE水平方向差异的影响也是不可忽略的,特别是对欧洲区域.     

Characteristics of intra-, inter-annual and decadal sea-level variability and the role of meteorological forcing: the long record of Cuxhaven

This paper addresses the role of meteorological forcing on mean sea level (MSL) variability at the tide gauge of Cuxhaven over a period from 1871 to 2008. It is found that seasonal sea level differs significantly from annual means in both variability and trends. The causes for the observed differences are investigated by comparing to changes in wind stress, sea level pressure and precipitation. Stepwise regression is used to estimate the contribution of the different forcing factors to sea level variability. The model validation and sensitivity analyses showed that a robust and timely independent estimation of regression coefficients becomes possible if at least 60 to 80 years of data are available. Depending on the season, the models are able to explain between 54 % (spring, April to June) and 90 % (winter, January to March) of the observed variability. Most parts of the observed variability are attributed to changes in zonal wind stress, whereby the contribution of sea level pressure, precipitation and meridional wind stress is rather small but still significant. On decadal timescales, the explanatory power of local meteorological forcing is considerable weaker, suggesting that the remaining variability is attributed to remote forcing over the North Atlantic. Although meteorological forcing contributes to linear trends in some sub-periods of seasonal time series, the annual long-term trend is less affected. However, the uncertainties of trend estimation can be considerably reduced, when removing the meteorological influences. A standard error smaller than 0.5 mm/year requires 55 years of data when using observed MSL at Cuxhaven tide gauge. In contrast, a similar standard error in the meteorologically corrected residuals is reached after 32 years.     

南极半岛地区GPS坐标时间序列噪声分析及形变模式初探

有色噪声广泛存在于各种连续GPS站坐标时间序列,对GPS时间序列分析有重要影响.利用GAMIT/GLOBK软件解算了南极半岛地区8个GPS测站2010—2014年的实测数据,对坐标时间序列使用主分量分析法(PCA)进行了空间滤波,利用CATS软件估计了不同噪声模型下和空间滤波前后的噪声量级、站坐标时间序列参数及其不确定度,最后对南极半岛地区水平和垂向的形变模式进行了分析和讨论.结果表明,南极半岛地区GPS时间序列不仅存在白噪声,还存在较大量级的闪烁噪声,部分测站E方向在滤波前可能存在随机游走噪声;空间滤波能够有效降低这三种噪声的量级,从而有效减小线性项和周期项估计的不确定度;南极半岛地区在水平方向主要表现为板块运动,还可能存在局部性构造运动;在垂直方向上由冰川均衡调整(Glacial Isostatic Adjustment,GIA)因素引起的抬升较小,主要表现为现今冰雪质量损失引起的弹性抬升运动.     

汶川地震前后四川区域GPS时序特征演变及统计分析

为探索地震事件对GPS坐标时间序列的长周期影响,对汶川地震前后四川GPS观测网络长约10年的解算成果进行了多参数模型噪声特征分析.基于最大似然估计方法和频谱特性分析,提取了地震前后各测站坐标序列中的噪声分量,使用Λ-统计检验,得出"白噪声+闪烁噪声"模型可以作为四川GPS区域观测网络的最优噪声组合模型,同时,地震事件使得地震前后GPS噪声分量中的白噪声、闪烁噪声、随机游走噪声等发生显著改变,说明传统谱噪声分析中简单地将地震数据拼接在一起并进行统一处理的模式并不可取;使用共模误差分析方法、区域速度场变化趋势等信息对地震前后噪声模型的改变成因进行了初步的物理解析.     

连续GPS观测中的相关噪声分析

分析了中国地壳运动观测网络GPS基准站位置时间序列中相关噪声的特性.利用最大似然估计反演了幂指数噪声的谱指数;考察了多种噪声模型,发现除闪烁噪声之外,约50%台站的东分量中的相关噪声可用"随机漫步噪声+一阶高斯-马尔可夫噪声"模型来描述,与其它分析机构产出的全球解并不一致,显示出处理策略的不同能够造成相关噪声的差异.白噪声和闪烁噪声的大小存在明显的地理分异,东南沿海台站的噪声要大于西北内陆台站.考虑相关噪声时,各站的速率估计方差要增大一个数量级以上,水平分量多在1mm/a以内,而垂向分量则较大.     

MAXIMUM-LIKELIHOOD ESTIMATION OF SEISMIC IMPULSE RESPONSES*

A seismic trace is assumed to consist of a known signal pulse convolved with a reflection coefficient series plus a moving average noise process (colored noise). Multiple reflections and reverberations are assumed to be removed from the trace by conventional means. The method of maximum likelihood (ML) is used to estimate the reflection coefficients and the unknown noise parameters. If the reflection coefficients are known from well logs, the seismic pulse and the noise parameters can be estimated. The maximum likelihood estimation problem is reduced to a nonlinear least-squares problem. When the further assumption is made that the noise is white, the method of maximum likelihood is equivalent to the method of least squares (LS). In that case the sampling rate should be chosen approximately equal to the Nyquist rate of the trace. Statistical and numerical properties of the ML- and the LS-estimates are discussed briefly. Synthetic data examples demonstrate that the ML-method gives better resolution and improved numerical stability compared to the LS-method. A real data example shows the ML- and LS-method applied to stacked seismic data. The results are compared with reflection coefficients obtained from well log data.     

利用GRACE卫星重力资料解算气候驱动的地表周年垂直形变

卫星重力和GPS测量技术可以监测地表流体(大气、海洋和陆地水)质量季节性迁移引起的地表周年形变;与陆地水等地表流体模型综合模拟的地表形变相比,卫星重力的形变监测结果避免了模型的精度不确定性带来的误差.本文利用前60阶GRACE卫星时变重力资料和“去相关”、组合滤波两类滤波方法分别解算了中国及邻区的地表季节性垂直形变,并与区内42个GPS台站上观测到的季节性信号进行了比较,发现采用“去相关”滤波方法处理后的结果优于采用组合滤波处理后的结果.文中采用“去相关”滤波方法,GRACE解算的周年垂直形变的振幅、相位和GPS结果总体上一致;少数站上GRACE和GPS得到的振幅或相位相差较大,主要因素可能与GPS解算策略、GPS观测资料的连续性或局部大气、水文过程等地球物理因素有关.在中国及邻区的陆地上GRACE解算的周年垂直形变的振幅最小值出现在TASH台站东南,约1×10^-3 m;最大值出现在恒河-澜沧江流域,可达10×10^-3 m.文中的结果证实了在中国及邻区可以用GRACE卫星重力这种新手段监测大尺度的地表周年垂直形变.     

利用GPS与GRACE监测陆地水负荷导致的季节性水平形变：以喜马拉雅山地区为例

地表陆地水负荷变化是引起重力场和地壳形变呈现季节性特征的主要因素,并且能够利用地表及空间大地测量技术对其进行有效的监测.本文通过对质量负荷形变效应的理论模拟,描述了水平分量的形变指向以及垂直与水平分量的幅值比可以提高对负荷区域的辨别程度,并且联合GPS坐标时间序列及GRACE模型对喜马拉雅山地区的季节性负荷形变进行了详细对比分析,研究结果显示两者垂直分量的季节性变化具有较好的一致性,且GPS周年项幅值要大于GRACE.而由GRACE解算得到的水平分量结果表明该地区季节性形变主要受东南亚及印度东北部地区的陆地水负荷控制,位于喜马拉雅山地区多数GPS台站的垂直分量及北向分量的初相位与GRACE模型解算结果相近,而部分GPS台站的东向分量与GRACE模型存在明显不同,由此导致GPS与GRACE监测到的形变指向存在差异.通过对GRACE估算精度以及GPS垂直与水平分量幅值比的深入分析,发现GPS对局部周边地区的河流、谷地及农田灌溉等负荷变化造成的形变效应较为敏感,而GRACE由于截断阶次及平滑滤波等影响因素,不仅造成在水平分量上的分辨率远低于垂直分量,而且整体估算精度要低于GPS观测得到的形变信息.     

基于ARMA模型非因果空间预测滤波(英文)

常规频域预测滤波方法是建立在自回归(autoregressive,AR)模型基础上的,这导致滤波过程中前后假设的不一致,即首先利用源噪声的假设计算误差剖面,却又将其作为可加噪声而从原始剖面中减去来得到有效信号。本文通过建立自回归-滑动平均(autoregres sive/moving-average,ARMA)模型,首先求解非因果预测误差滤波算子,然后利用自反褶积形式投影滤波过程估计可加噪声,进而达到去除随机噪声目的。此过程有效避免了基于AR模型产生的不一致性。在此基础上,将一维ARMA模型扩展到二维空间域,实现了基于二维ARMA模型频域非因果空间预测滤波在三维地震资料随机噪声衰减中的应用。模型试验与实际资料处理表明该方法在很好保留反射信息同时,压制随机噪声更加彻底,明显优于常规频域预测去噪方法。     

IDENTIFICATION OF SEISMIC REFLECTIONS USING SINGULAR VALUE DECOMPOSITION*

Singular value decomposition (SVD) is applied to the identification of seismic reflections by using two different models: the impulse response model, where a seismic trace is assumed to consist of a known signal pulse convolved with a reflection coefficient series plus noise, and the delayed pulse model, where the seismic signal is assumed to consist of a small number of delayed pulses of known shape and with unknown amplitudes and arrival times. SVD clearly shows how least-squares estimation of the reflection coefficients may become unstable, since a division by the singular values is required. Two methods for stabilizing this procedure are investigated. The inverse of the singular values may be replaced by zeros when they are less than a given threshold. This is called the SVD cut-off method. Alternatively, we may use ridge regression which in filter design corresponds to assuming white noise. Statistical methods are used to compute an optimal SVD cut-off level and also to compute an optimal weighting parameter in ridge regression. Numerical studies indicate that the use of SVD cut-off or ridge regression stabilizes the least-squares procedure, but that the results are inferior to maximum-likelihood estimation where the noise is assumed to be filtered white noise. For the delayed pulse model, we use a linearization procedure to iteratively update the estimates of both the reflection amplitudes and the arrival times. In each step, the optimal SVD cut-off method is used. Confidence regions for the estimated reflection amplitudes and arrival times are also computed. Synthetic data examples demonstrate the effectiveness of this method. In a real data example, the maximum-likelihood method assuming an impulse response model is first used to obtain initial estimates of the number of reflections and their amplitudes and traveltimes. Then the iterative procedure is used to obtain improved estimates of the reflection amplitudes and traveltimes.     

Error analysis for European IGS stations

Each of the GPS time series that describes the changes of topocentric components consists of a deterministic and a stochastic part, whose character influences the errors of the deterministic parameters. As to the uncertainties of reliable velocities of permanent satellite station systems, surveys that estimate and take into account any dependencies that may affect subsequent operational efficiency are very important. For this analysis, we used 42 stations from the IGS (International GNSS Service) network from Europe, processed at the Military University of Technology EUREF Permanent Network Local Analysis Centre (MUT LAC). The deterministic part of the GPS time series was removed using the least squares method. The seasonal periods in topocentric components were determined assuming the existence of the residual Chandler oscillation (1.67 cpy), as well as the annual tropical (1 cpy) and draconitic (1.04 cpy) oscillations with their harmonics up to 4th. We assumed the character of the residue as a combination of white and powerlaw noise. The obtained results show, that in the case of the European sub-network of IGS stations we are dealing with the coloured noise between white and flicker noise with the amplitudes between 3 to 6 mm/year^-k/4 for horizontal components and between 6 to 15 mm/year^-κ/4 for the vertical ones, where κ is a spectral index. Finally, we showed that the amplitudes and spectral indices of noise are reduced after performing a spatio-temporal filtering. All the elicited results referred to the uncertainties of velocities by estimating them before and after filtration and the simulation of their values for different lengths of the time series.     

基于Hessian矩阵的地震随机噪声压制方法

随机噪声的压制在提高地震资料信噪比方面发挥重要作用.考虑到传统去噪方法在构造复杂地区难以取得理想的去噪结果,本文提出基于Hessian矩阵特征值对应的线性目标关系在多个尺度上对随机噪声进行压制.该方法将地震信号看作不同尺度的曲线,从而利用Hessian矩阵在曲线检测方面表现出的良好性能实现信噪分离.该方法与传统方法相比不受地层倾角的限制,因此能够处理构造较为复杂地区的地震数据.利用模型及实际资料对该方法进行了验证并与传统方法F-X反褶积的去噪结果做对比,结果表明基于Hessian矩阵的随机噪声压制方法在构造复杂地区能够保持有效信号的完整性.     

基于有色噪声模型的GPS速度场精度与时间序列长度相关性研究

利用2010—2015年陆态网络GPS连续观测站的三维站坐标时序资料, 在采用最大似然估计MLE方法计算得到云南地区GPS基准站三维站坐标分量最优噪声模型的基础上, 进一步定量对比分析了有色噪声和白噪声模型下陆态网络GPS连续站速度场稳定性与时间序列长度的关系。 结果表明: 在闪烁噪声模型下, 中国大陆大部分地区GPS连续站1 a时段的速度不确定度大。 而随着时间的逐年累积, 闪烁噪声模型下的速度不确定度与同时段白噪声模型下的差异逐步减小, 闪烁噪声模型下3～4 a时段的速度不确定度与同时段白噪声模型的差异小于0.2 mm。 研究说明在有色噪声模型下要获得高精度的速度场需要3～4 a的观测数据, 白噪声模型下GPS速度场精度可靠可信的前提是采用不少于3～4 a的数据。     

中国区域IGS基准站坐标时间序列非线性变化的成因分析

GPS坐标时间序列呈现显著的季节性变化,通常认为大气压、非潮汐海洋负载及水文负载(统称为地表质量负载)是引起测站谐波变化的主要因素.本文计算了不同地表质量负载造成的测站位移,以此修正中国区域11个IGS基准站的坐标时间序列.建立了地球物理现象与测站季节性变化及噪声特性之间的初步数值联系,认为其会造成测站的噪声特性变化,主要表现为带通及随机漫步噪声特征,且仅能减小测站U分量的周年运动,但并不是造成测站U分量半周年运动及水平方向周年运动的主要原因.深入分析了造成中国区域IGS基准站非线性变化的其他可能因素,重点探讨了周日(S1)、半周日(S2)大气潮汐对基准站周年振幅的贡献,由此提出S1、S2大气潮汐是造成中国区域IGS基准站周年运动,尤其是中南部测站垂向周年运动的主要因素之一.     

Comparative study of monthly inflow prediction methods for the Three Gorges Reservoir

Due to the complexity of influencing factors and the limitation of existing scientific knowledge, current monthly inflow prediction accuracy is unable to meet the requirements of various water users yet. A flow time series is usually considered as a combination of quasi-periodic signals contaminated by noise, so prediction accuracy can be improved by data preprocess. Singular spectrum analysis (SSA), as an efficient preprocessing method, is used to decompose the original inflow series into filtered series and noises. Current application of SSA only selects filtered series as model input without considering noises. This paper attempts to prove that noise may contain hydrological information and it cannot be ignored, a new method that considerers both filtered and noises series is proposed. Support vector machine (SVM), genetic programming (GP), and seasonal autoregressive (SAR) are chosen as the prediction models. Four criteria are selected to evaluate the prediction model performance: Nash–Sutcliffe efficiency, Water Balance efficiency, relative error of annual average maximum (RE_max) monthly flow and relative error of annual average minimum (RE_min) monthly flow. The monthly inflow data of Three Gorges Reservoir is analyzed as a case study. Main results are as following: (1) coupling with the SSA, the performance of the SVM and GP models experience a significant increase in predicting the inflow series. However, there is no significant positive change in the performance of SAR (1) models. (2) After considering noises, both modified SSA-SVM and modified SSA-GP models perform better than SSA-SVM and SSA-GP models. Results of this study indicated that the data preprocess method SSA can significantly improve prediction precision of SVM and GP models, and also proved that noises series still contains some information and has an important influence on model performance.