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.      

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.     

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.     

高频GPS坐标时序的噪声特性分析

为研究高频GPS坐标时序的噪声特性,对芦山地震前后三天,北京时间8:00—9:00,位于四川盆地8个CORS站50Hz的高频观测资料进行解算与分析。分析过程中,分别采用恒星日滤波和主成分滤波分析以及去除时空噪声,并采用功率谱分析经滤波后的坐标时序。结果表明,高频GPS坐标时序的谱指数在1.6~2.0间,符合白噪声+随机游走噪声模型特性。建议当利用高频GPS研究地表运动特性、监测大型建筑的运动结构或确定GPS动态实验平台姿态时,应考虑高频GPS坐标时序的这一噪声特性。     

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.     

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.     

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。     

环境负载对云南地区基准站时间序列的噪声模型特性研究

以云南地区27个GPS基准站坐标时间序列为研究对象,使用赤池信息量和贝叶斯信息量估计准则（AIC/BIC）对其进行噪声分析,计算并扣除时间序列中大气负载、非潮汐海洋负载和水文负载3种环境负载引起的位移量,得到各基准站分量在环境负载改正前后的最优噪声模型。结果表明,部分基准站分量经过负载改正后最优噪声模型会发生变化,改正前后的大部分基准站噪声特性均体现为闪烁+白噪声和幂律噪声。环境负载对基准站的垂向位移影响比水平向更为显著,水文负载成为影响基准站的最大因素,最大位移量达到厘米级。分析环境负载改正前后噪声特性的变化表明,环境负载改正在U分量上的影响最大,N分量次之,E分量最小,噪声模型的变化在地域上并未呈现明显规律。     

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.     

数学形态滤波法在GPS基线分析中的应用

通过GAMIT软件得到福建省连续观测GPS基准站基线时间序列,并引人数学形态滤波法,过滤基线中的白噪音和脉冲扰动.以福建省主要断裂带为研究背景,研究GPS基线时间序列、跨断层短水准观测资料与福建主要断层的相关性,分析了影响基线变化的因素,以及地壳水平运动与应力积累的关系.     

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.     

基于迭代PCA的GPS时间序列震后形变估计方法和应用

GPS时间序列的震后形变分析对于研究区域震后形变机制和岩石圈流变学特性以及维持国际动态地球参考框架具有重要意义.本文在现有参数估计方法的基础上,提出兼顾震后形变衰减特征空间相关性和整体建模的"迭代PCA参数估计方法",并利用模拟数据证实了新方法可以获取更稳健可靠的震后形变、同震形变和震间速度参数.最后,以37个新西兰GPS连续站坐标时间序列为例,利用迭代PCA方法提取了2016年11月13日Kaikoura地震共性的震后形变时间演化过程和各站点的震后形变,并定量分析了震后形变对地表速度的影响.结果表明各站的震后形变在时间域上以衰减常数τ为4天的对数模型持续松弛;空间域上南岛北东部和北岛最南部震后形变较大,其中,最大震后形变点为cmbl站,截至2017年6月10日NEU方向累计的震后形变分别达到107mm,135mm和187mm,地表速度分别达到133.58mm·a-1,112.05mm·a-1和175.58mm·a-1,仍高于稳定的震间速度.     

陆态网络GNSS基准站阶跃偏移量的精确估计

通过对发生阶跃的GNSS基准站坐标序列谱指数的求解,表明了其具有有色噪声的特性,并对三分量分别建立了最优噪声模型,以此对GNSS基准站坐标的阶跃偏移量进行了精确估计,探明了地震和仪器更换对测站产生的精细影响。同时利用求解的阶跃偏移量对坐标序列进行修正,对获取连续性变化的测站坐标序列和获取精确的测站三维运动参数具有重要意义。     

Very broadband seismic background noise analysis of permanent good vaulted seismic stations

This paper describes the results of a preliminary study conducted to analyze seismic background noise at sites of recently deployed very broadband stations of the Egyptian National Seismological Network (ENSN). The main purpose of the study is to assess the effects of permanent seismic vault construction and also to establish characteristics and origin of seismic noise at those sites. Another goal of this study is to determine the time needed for noise at those sites to stabilize. The power spectral densities of background noise at short period band (SP), very broadband (VBB), and ultra long period band (ULP) for each component of each broadband seismometer deployed in the different investigated sites are calculated. A MATLAB code has been developed that manages data processing and data analysis and compares the results with the high-noise model (NHNM) and low-noise model (NLNM) of Peterson (1993). Based on the obtained analysis, the noise stability and the efficiency of each station to record regional and teleseismic events are measured. The results of this study could be used in the future to evaluate station quality, to improve those processes that require background noise values, such as automatic association, and to improve the estimation of station and network detection and location thresholds.     

基于非线性运动分析的CGCS2000下我国CORS站运动特征

CGCS2000(中国地心坐标系统2000)下CORS(全球导航卫星系统连续运行参考站)站的非线性运动主要受到地壳非构造形变信息、框架点公共误差信息和观测误差信息的组合影响,分析我国CORS站坐标时间序列中包含的非线性运动信息是维护CGCS2000坐标框架精确性、可靠性的基础.本文研究方法首先采用国际卫星对地观测数据及相关地球物理模型,计算了由质量负荷效应造成的地壳非构造形变, 并以此修正了这些非构造形变对国家CORS站坐标时间序列的影响.其次采用主成分空间滤波算法(PCA)提取质量负荷改正后的CGCS2000坐标框架公共误差(Common Mode Errors, CME)的时空特性.最后采用最大似然法定量估计了负荷改正和滤波后的国家CORS网坐标时间序列的噪声特性,采用加权最小二乘法评定了考虑不同噪声影响的CGCS2000框架下的国家CORS网年速度估值和实际精度.     

The influence of seasonal signals on the estimation of the tectonic motion in short continuous GPS time-series

Most GPS time-series exhibit a seasonal signal that can have an amplitude of a few millimetres. This seasonal signal can be removed by fitting an extra sinusoidal signal with a period of one year to the GPS data during the estimation of the linear trend.However, Blewitt and Lavallée (2002) showed that including an annual signal in the estimation process still can give a larger linear trend error than the trend error estimated from data from which the annual signal has been removed by other means. They assumed that the GPS data only contained white noise and we extend their result to the case of power-law plus white noise which is known to exist in most GPS observations. For the GPS stations CASC, LAGO, PDEL and TETN the difference in trend error between having or not having an annual signal in the data is around ten times larger when a power-law plus white noise model is used instead of a pure white noise model. Next, our methodology can be used to estimate for any station how much the accuracy of the linear trend will improve when one tries to subtract the annual signal from the GPS time-series by using a physical model.Finally, we demonstrate that for short time-series the trend error is more influenced by the fact that the noise properties also need to be estimated from the data. This causes on average an underestimation of the trend error.     

GPS坐标时间序列中非构造噪声的剔除方法研究进展

GPS台站坐标解算中包含多种地球物理参量造成的不确定性、系统误差和随机噪声.回顾了GPS台站坐标噪声分析的研究进展,包括功率谱分析、最大似然估计、区域叠加滤波、主成分变换以及质量负荷下的地壳弹性形变模拟等,并讨论了各种方法在分析噪声的类型和强度、共模误差(common-mode errors)的物理起源等方面的作用及局限性,展望了下一阶段的研究思路.     

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.     

Fractal velocity models in refraction seismology

The introduction of noise components to a simple crustal velocity model is shown to markedly affect the appearance of synthetic seismograms calculated according to ray theory applied to refraction experiments. Here we simulate noise by a self-similar process with a power spectral density which falls off as inverse wavenumber to a simple power (0–2). The major effect is to destroy the coherency of the arrival branches normally expected from deterministic velocity models; the arrival amplitudes also show large trace-to-trace variations and considerable sensitivity to shot position. Some of these differences can be ascribed to the variety of noise model chosen (i.e., white noise, flicker noise and brown noise). It is argued that there is no clear distinction between coherent noise and geological structure.