GPS位置时间序列中的中长期误差研究
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摘要
连续GPS(global positioning system)已成为监测地壳形变的主要手段之一,遍布于全球的数千个GPS台站为研究板块运动、断层滑动、强震形变场等提供了可靠的数据。在GPS位置时间序列中还包含了时、空相关的噪声,与构造活动造成的位移混叠在一起,难以分离。如何有效地提取与剔除GPS中的非构造成分已成为国际上的前沿研究。本论文开展的研究内容对于加深GPS中噪声性质、起源的认识具有重要意义,并最终有益于GPS应用领域的进展。
本论文的研究对象是GPS位置时间序列中的中-长期(T > 1天,即日尺度至十年尺度)误差,主要表现为共模误差(common-mode error,即CME),即全球框架下区域网空间尺度上GPS台站位置中的公共运动。论文从非构造噪声的特征入手,利用时间序列分析理论来确定噪声的类型和强度、分析GPS台站周期性运动的振幅、相位特征,通过比较有色噪声的大小、周期项的振幅或相位、沉降或抬升趋势等,筛选出相对稳定的GPS台站;基于GPS台站残差位置时间序列,采用相关性分析来研究GPS台站间公共噪声的空间变化规律,研究提取不同空间尺度上CME和瞬态构造信息的空间滤波技术;研究参考框架的稳定性对CME的影响。
为了获取高质量的GPS位置时间序列,本论文采用最新版本的数据处理软件(GAMIT/GLOBK v10.3)、模型,对中国地壳运动观测网络(Crustal Motion Observation Network of China,即CMONOC)GPS基准站及100多个ITRF2005 GPS框架站自1999年以来近11年的历史数据进行了重新解算,所得GPS台站位置时间序列是本论文的主要数据来源。同时,本论文也参考了SOPAC(Scripps Orbit and Permanent Array Center)、JPL(Jet Propulsion Laboratory)和CMONOC数据中心产出的GPS位置时间序列成果,在有色噪声、周期项、CME等方面进行了对比。
全球框架下GPS位置时间序列中的CME是相关噪声(并非白噪声)。本论文以中国境内GPS基准站网络为主要研究对象,利用最大似然估计分析了CMONOC网络中GPS基准站位置时间序列中有色噪声的类型,除闪烁噪声和随机漫步噪声之外,还考虑了分数谱指数幂指数噪声、一阶高斯-马尔科夫噪声、带通滤波噪声,发现CMONOC网络中主导有色噪声类型为闪烁噪声,这与其他地区的研究成果一致。经过空间滤波后的GPS位置时间序列中噪声的大小(尤其是闪烁噪声)明显减小,表明CME主要具有闪烁噪声的性质。考虑有色噪声时,各站的速率估计方差要增大一个量级以上,但多在1 mm/a以内。
基于本论文的CMONOC数据再分析结果,获取了GPS基准站周年运动特征的新认识。在海拉尔(HLAR)、哈尔滨(HRBN)等地发现了难以解释的周年运动。而几个短基线台站对(如长春CHAN-CHUN、昆明KMIN-KUNM)的对比结果显示,局部因素能够造成周年项振幅或相位的明显差异。对于周边没有其他GPS连续站的台站来说,对其观测结果的解释要慎重。探索了GPS位置时间序列中周期项的起因。计算了大气、土壤水等地表质量负荷造成的垂向周年运动,发现大多数台站的垂向周年项可以用负荷效应较好地解释,但是在南方台站(QION、YONG、XIAM)、拉萨(LHAS、LHAZ)、和塔什库尔干(TASH)等地,仍有较大的残余周年项振幅,表明尚存在其他未知的因素或较大的模拟残差。针对拉萨站,地球物理负荷改正后尚有2~3 mm的残余振幅,其周边GPS台站的验证结果表明拉萨GPS台站垂向周年项的相位没有明显异常,振幅偏大。在青藏高原和喜马拉雅地区,GPS垂向分量周年项主要受到地表水体因子控制,存在明显的相位变化。
在CMONOC及周边IGS(International GNSS Service)台站的位置时间序列中均发现了周期约为351/n(n=1,…,6)天的“异常”周期项。此类周期项是全球框架下GPS位置中CME的组成部分,经过空间滤波后,大部分“异常”周期项消失。地表质量负荷造成的位移序列中并没有与前述“异常”周期项对应的成分,不是异常周期项的来源。
提出了一套新的空间滤波思路用于提取共模分量( common-mode component,即CMC)──即传统的CME和区域构造信号。该新方法采用两种加权因子:1)采用台站残差位置时间序列间的相关性大小作为距离加权因子;2)利用基于CMC基准站的Voronoi图形面积作为方位加权因子。与传统的区域叠加滤波方法相比,本论文提出的相关加权叠加滤波能够带来5%~15%的残差RMS(root mean square)改进。通过变换距离因子,新方法能够提取不同空间尺度上的CMC,例如发生在消减带地区的慢滑移事件。与以往的方法相比,本论文提出的相关加权叠加滤波技术不再受空间尺度的限制,也不需人工干预。
采用相关加权叠加滤波技术分析了127个全球GPS台站的公共噪声,在96个台站提取到了CMC序列。较大CMC的台站位置与闪烁噪声大小的空间分布规律对应,即CMC大的地区闪烁噪声也大,但与周年项的振幅没有明显的相关关系。CMC的主要成分的空间尺度达上千公里,其大小的空间分布规律与框架站的分布密度存在联系:即框架站密集的地区CMC小。因此,参考框架定义的不稳定性可能是CMC的主要来源。
本论文最后探索了框架站的非线性运动对GPS定位结果的影响:1)发现CMC、闪烁噪声等与框架稳定性存在相关性;2)在框架定义前进行大气压力负荷改正、消除部分垂向周年运动对框架定义的影响时,白噪声或闪烁噪声略微减小。
本论文的研究加深了对GPS中非构造信号的认识,在数据滤波和非构造信号消减方面取得了令人满意的成果。然而,针对GPS位置时间序列中误差的分析还很有限,许多GPS数据获取和处理过程中涉及的噪声尚需进一步的分析,仍需不断深入地开展研究,以加深对GPS信号和噪声剔除的理解,从而促进构造形变研究的进展。
Continuous GPS (global positioning system) has been become one of the major techniques for crustral deformation monitoring. There are thousands of GPS stations around the world which provide reliable data for studies on plate motion, fault slip, and deformation caused by earthquakes. One of problems in GPS measuerments is spatio-temporal correlated noise in GPS position time series, which contaminates tectonic signals and makes it difficult to separate signals from noises. It is now a frontal subject to extract and to remove those non-tectonic signals. This thesis is an attempt to solve this issue which is of importanance for furher understanding characteristics and origins of noises in GPS data, and would promote the research progress in GPS application fields.
This work focuses on the intermediate- and long-term (T>1 day, from 1-day to 10-year time scale) errors in GPS position time series. The most obvious part is the common-mode error (CME) which is the common motion of regional GPS stations in a global reference frame. To learn the characteristics of non-tectonic signals, the time series analysis theory is used to derive the type and magnitude of colored noise, to obtain the amplitudes and phase lags of seasonal variations of GPS stations. Then stable GPS sites are chosen with the criteria for size of colored noise, the amplitude and phase lag of seasonal tem, subsidence or uplift trend, etc. Based upon the correlation relationship of residual position time series of GPS stations, an improved spatial filtering technique is suggested to extract CME of varied spatial scales and transient tectonic activities. Finally the effect of instability of reference frame on CME is assessed.
To obtain reliable GPS position time series, this work re-analyzed nearly 11-year continuous GPS data since 1999 from CMONOC (Crustal Motion Observation Network of China) and more than 100 ITRF2005 reference frame stations in a consistent way—using the latest softare (GAMIT/GLOBK v10.3) and models. The rerun results are the major data source of this dissertation. At the same time, GPS position time series produced by SOPAC (Scripps Orbit and Permanent Array Center), JPL (Jet Propulsion Laboratory), and CMONOC data center are also used for comparision of colored noise, seasonal terms, and CME.
It is known that CME in GPS position time series under a global frame is one kind of correlated noise. The characteristics of the correlated noise in position time series for GPS fiducial stations of CMONOC is analyzed. The types of colored noises in the CMONOC network are assessed using the maximum likelihood estimator (MLE). Besides flicker noise and random walk noise, more types of noise models were considered, including pow-law noise with fractional spectral index, first-order Gaussian-Markov noise, and band-pass filtering noise. It is found that flicker noise is the primary type for CMONOC network, which is consistent with conclusions from studies in other regions. The magnitude of flicker noise in the spatially filtered GPS potition time series decreases remarkably, showing that the content of CME (common-mode error) is mainly flicker noise. When taking into account correlated noises in estimation, the rate uncertainities increase by over an order of magnitude from white noise estimates, which are usually less than 1 mm/a.
Based upon the CMONOC rerun results, this work obtains some new insights into the annual movements of GPS fiducial stations. There are unexplained annual motions at Hailaer (HLAR) and Haerbin (HRBN) stations. The results from several short-baseline GPS station pairs (e.g. at Changchun: CHAN-CHUN, at Kunming: KMIN-KUNM) suggest that local environment factors can cause obvious abnormal movement of GPS stations, either the amplitude or the phase differences of annual terms. Thus, attentions should be paid when interpretating postion results of GPS stations in the case that there are no other continuous GPS stations in the surrounding area. The above GPS-observed annual position variations can be explained at most sites with the loading displacements caused by seasaonl atmospheric pressure and soil moisture variations. However, at southern sites (QION, YONG, and XIAM), Lhasa (LHAS and LHAZ), and Tash Kurghan (TASH), there are still large residual annual amplitudes, suggesting that there are still unknown factors or large mis-modeling errors. At the Lhasa stations, the remaining amplitudes after geophysical mass loading corrections are about 2~3 mm. Results from other nearby continuous GPS stations show that there are negliable phase lag differences between these sites, and the amplitudes at Lhasa seem a bit larger. In the Tibetan plateau and the Himalaya mountain belt, the vertical annual motions are mainly controlled by hygrological factors, showing large phase lag changes.
It is found that there are sinusoidal motions with periods around 351/n (n=1,…, 6) days in position time series for CMONOC and IGS (International GNSS Service) sites around China. These periodicities reveal the existence of CME. After spatial filtering of CME was performed, a large sum of corresponding peaks in the power spectrum disappeared. This kind of seasonal terms cannot be explained by surface mass redistributions.
A spatial filtering scheme is developed to extract common-mode components (CMC) in continuous GPS positions, corresponding to either the so-called CME or regional tectonic signal. The technique utilizes two weighting factors: 1) correlations between GPS position residuals as distance weights, and 2) areas of Voronoi cells constructed from fiducial GPS sites as azimuthal weights. Comparing to the conventional regional stacking method, this scheme has achieved 5%~15% more reduction of residual RMS (root mean square). And by varying the distance window, it can extract CMC of various spatial scales, such as signals of slow slip events occurring periodically at certain subduction zones. Different from existing spatial filtering algorithms, the correlation-based stacking method presented in this thesis overcomes the spatial scale limit when doing filtering, and does nor need manual interferences.
The correlation-based spatial filtering technique is then used to extract CMC for 127 global GPS stations and results are obtained at 96 sites. The magnitude of CMC is found to be correlated with size of flicker noise, i.e., those with larger scatters in CMC are the stations with larger flicker noise. But this relationship does not exist between scatter measurements of CMC and amplitude of annual term. The spatial scale of the major part of CMC is usually larger than 1000 km. It is interesting that the size of CMC is correlated with the density of frame stations, i.e., the CMC are usually smaller in areas with relatively denser GPS stations used in the frame stabilization procedure. This implies that the instability of reference frame definition may account for major part of CMC.
In the last section of this thesis, the effect of non-linear reference frame on GPS positioning results is assessed tentatively. It is found that the magnitudes of CMC and flicker noise are correlated with the stability of reference frame definition. It is also shown that applying ATML corrections at the observation level could produce small improvements in reducing the magnitudes of white noises and flicker noises, by reducing the effect of vertical annual motions on frame stabilization.
This work has improved the understanding of non-tectonic signals in GPS position time series, and satisfying results in data filtering and non-tectonic noise reduction have been obtained. Nevertheless, only limited analyses on GPS time series errors have been performed, and many kinds of noises in GPS data aquisation and processing remain to be further explored. More work need to be done in this field for deeper understanding of GPS signals and noise removal, so that to promote research of tectonic deformation.
本论文的研究对象是GPS位置时间序列中的中-长期(T > 1天,即日尺度至十年尺度)误差,主要表现为共模误差(common-mode error,即CME),即全球框架下区域网空间尺度上GPS台站位置中的公共运动。论文从非构造噪声的特征入手,利用时间序列分析理论来确定噪声的类型和强度、分析GPS台站周期性运动的振幅、相位特征,通过比较有色噪声的大小、周期项的振幅或相位、沉降或抬升趋势等,筛选出相对稳定的GPS台站;基于GPS台站残差位置时间序列,采用相关性分析来研究GPS台站间公共噪声的空间变化规律,研究提取不同空间尺度上CME和瞬态构造信息的空间滤波技术;研究参考框架的稳定性对CME的影响。
为了获取高质量的GPS位置时间序列,本论文采用最新版本的数据处理软件(GAMIT/GLOBK v10.3)、模型,对中国地壳运动观测网络(Crustal Motion Observation Network of China,即CMONOC)GPS基准站及100多个ITRF2005 GPS框架站自1999年以来近11年的历史数据进行了重新解算,所得GPS台站位置时间序列是本论文的主要数据来源。同时,本论文也参考了SOPAC(Scripps Orbit and Permanent Array Center)、JPL(Jet Propulsion Laboratory)和CMONOC数据中心产出的GPS位置时间序列成果,在有色噪声、周期项、CME等方面进行了对比。
全球框架下GPS位置时间序列中的CME是相关噪声(并非白噪声)。本论文以中国境内GPS基准站网络为主要研究对象,利用最大似然估计分析了CMONOC网络中GPS基准站位置时间序列中有色噪声的类型,除闪烁噪声和随机漫步噪声之外,还考虑了分数谱指数幂指数噪声、一阶高斯-马尔科夫噪声、带通滤波噪声,发现CMONOC网络中主导有色噪声类型为闪烁噪声,这与其他地区的研究成果一致。经过空间滤波后的GPS位置时间序列中噪声的大小(尤其是闪烁噪声)明显减小,表明CME主要具有闪烁噪声的性质。考虑有色噪声时,各站的速率估计方差要增大一个量级以上,但多在1 mm/a以内。
基于本论文的CMONOC数据再分析结果,获取了GPS基准站周年运动特征的新认识。在海拉尔(HLAR)、哈尔滨(HRBN)等地发现了难以解释的周年运动。而几个短基线台站对(如长春CHAN-CHUN、昆明KMIN-KUNM)的对比结果显示,局部因素能够造成周年项振幅或相位的明显差异。对于周边没有其他GPS连续站的台站来说,对其观测结果的解释要慎重。探索了GPS位置时间序列中周期项的起因。计算了大气、土壤水等地表质量负荷造成的垂向周年运动,发现大多数台站的垂向周年项可以用负荷效应较好地解释,但是在南方台站(QION、YONG、XIAM)、拉萨(LHAS、LHAZ)、和塔什库尔干(TASH)等地,仍有较大的残余周年项振幅,表明尚存在其他未知的因素或较大的模拟残差。针对拉萨站,地球物理负荷改正后尚有2~3 mm的残余振幅,其周边GPS台站的验证结果表明拉萨GPS台站垂向周年项的相位没有明显异常,振幅偏大。在青藏高原和喜马拉雅地区,GPS垂向分量周年项主要受到地表水体因子控制,存在明显的相位变化。
在CMONOC及周边IGS(International GNSS Service)台站的位置时间序列中均发现了周期约为351/n(n=1,…,6)天的“异常”周期项。此类周期项是全球框架下GPS位置中CME的组成部分,经过空间滤波后,大部分“异常”周期项消失。地表质量负荷造成的位移序列中并没有与前述“异常”周期项对应的成分,不是异常周期项的来源。
提出了一套新的空间滤波思路用于提取共模分量( common-mode component,即CMC)──即传统的CME和区域构造信号。该新方法采用两种加权因子:1)采用台站残差位置时间序列间的相关性大小作为距离加权因子;2)利用基于CMC基准站的Voronoi图形面积作为方位加权因子。与传统的区域叠加滤波方法相比,本论文提出的相关加权叠加滤波能够带来5%~15%的残差RMS(root mean square)改进。通过变换距离因子,新方法能够提取不同空间尺度上的CMC,例如发生在消减带地区的慢滑移事件。与以往的方法相比,本论文提出的相关加权叠加滤波技术不再受空间尺度的限制,也不需人工干预。
采用相关加权叠加滤波技术分析了127个全球GPS台站的公共噪声,在96个台站提取到了CMC序列。较大CMC的台站位置与闪烁噪声大小的空间分布规律对应,即CMC大的地区闪烁噪声也大,但与周年项的振幅没有明显的相关关系。CMC的主要成分的空间尺度达上千公里,其大小的空间分布规律与框架站的分布密度存在联系:即框架站密集的地区CMC小。因此,参考框架定义的不稳定性可能是CMC的主要来源。
本论文最后探索了框架站的非线性运动对GPS定位结果的影响:1)发现CMC、闪烁噪声等与框架稳定性存在相关性;2)在框架定义前进行大气压力负荷改正、消除部分垂向周年运动对框架定义的影响时,白噪声或闪烁噪声略微减小。
本论文的研究加深了对GPS中非构造信号的认识,在数据滤波和非构造信号消减方面取得了令人满意的成果。然而,针对GPS位置时间序列中误差的分析还很有限,许多GPS数据获取和处理过程中涉及的噪声尚需进一步的分析,仍需不断深入地开展研究,以加深对GPS信号和噪声剔除的理解,从而促进构造形变研究的进展。
Continuous GPS (global positioning system) has been become one of the major techniques for crustral deformation monitoring. There are thousands of GPS stations around the world which provide reliable data for studies on plate motion, fault slip, and deformation caused by earthquakes. One of problems in GPS measuerments is spatio-temporal correlated noise in GPS position time series, which contaminates tectonic signals and makes it difficult to separate signals from noises. It is now a frontal subject to extract and to remove those non-tectonic signals. This thesis is an attempt to solve this issue which is of importanance for furher understanding characteristics and origins of noises in GPS data, and would promote the research progress in GPS application fields.
This work focuses on the intermediate- and long-term (T>1 day, from 1-day to 10-year time scale) errors in GPS position time series. The most obvious part is the common-mode error (CME) which is the common motion of regional GPS stations in a global reference frame. To learn the characteristics of non-tectonic signals, the time series analysis theory is used to derive the type and magnitude of colored noise, to obtain the amplitudes and phase lags of seasonal variations of GPS stations. Then stable GPS sites are chosen with the criteria for size of colored noise, the amplitude and phase lag of seasonal tem, subsidence or uplift trend, etc. Based upon the correlation relationship of residual position time series of GPS stations, an improved spatial filtering technique is suggested to extract CME of varied spatial scales and transient tectonic activities. Finally the effect of instability of reference frame on CME is assessed.
To obtain reliable GPS position time series, this work re-analyzed nearly 11-year continuous GPS data since 1999 from CMONOC (Crustal Motion Observation Network of China) and more than 100 ITRF2005 reference frame stations in a consistent way—using the latest softare (GAMIT/GLOBK v10.3) and models. The rerun results are the major data source of this dissertation. At the same time, GPS position time series produced by SOPAC (Scripps Orbit and Permanent Array Center), JPL (Jet Propulsion Laboratory), and CMONOC data center are also used for comparision of colored noise, seasonal terms, and CME.
It is known that CME in GPS position time series under a global frame is one kind of correlated noise. The characteristics of the correlated noise in position time series for GPS fiducial stations of CMONOC is analyzed. The types of colored noises in the CMONOC network are assessed using the maximum likelihood estimator (MLE). Besides flicker noise and random walk noise, more types of noise models were considered, including pow-law noise with fractional spectral index, first-order Gaussian-Markov noise, and band-pass filtering noise. It is found that flicker noise is the primary type for CMONOC network, which is consistent with conclusions from studies in other regions. The magnitude of flicker noise in the spatially filtered GPS potition time series decreases remarkably, showing that the content of CME (common-mode error) is mainly flicker noise. When taking into account correlated noises in estimation, the rate uncertainities increase by over an order of magnitude from white noise estimates, which are usually less than 1 mm/a.
Based upon the CMONOC rerun results, this work obtains some new insights into the annual movements of GPS fiducial stations. There are unexplained annual motions at Hailaer (HLAR) and Haerbin (HRBN) stations. The results from several short-baseline GPS station pairs (e.g. at Changchun: CHAN-CHUN, at Kunming: KMIN-KUNM) suggest that local environment factors can cause obvious abnormal movement of GPS stations, either the amplitude or the phase differences of annual terms. Thus, attentions should be paid when interpretating postion results of GPS stations in the case that there are no other continuous GPS stations in the surrounding area. The above GPS-observed annual position variations can be explained at most sites with the loading displacements caused by seasaonl atmospheric pressure and soil moisture variations. However, at southern sites (QION, YONG, and XIAM), Lhasa (LHAS and LHAZ), and Tash Kurghan (TASH), there are still large residual annual amplitudes, suggesting that there are still unknown factors or large mis-modeling errors. At the Lhasa stations, the remaining amplitudes after geophysical mass loading corrections are about 2~3 mm. Results from other nearby continuous GPS stations show that there are negliable phase lag differences between these sites, and the amplitudes at Lhasa seem a bit larger. In the Tibetan plateau and the Himalaya mountain belt, the vertical annual motions are mainly controlled by hygrological factors, showing large phase lag changes.
It is found that there are sinusoidal motions with periods around 351/n (n=1,…, 6) days in position time series for CMONOC and IGS (International GNSS Service) sites around China. These periodicities reveal the existence of CME. After spatial filtering of CME was performed, a large sum of corresponding peaks in the power spectrum disappeared. This kind of seasonal terms cannot be explained by surface mass redistributions.
A spatial filtering scheme is developed to extract common-mode components (CMC) in continuous GPS positions, corresponding to either the so-called CME or regional tectonic signal. The technique utilizes two weighting factors: 1) correlations between GPS position residuals as distance weights, and 2) areas of Voronoi cells constructed from fiducial GPS sites as azimuthal weights. Comparing to the conventional regional stacking method, this scheme has achieved 5%~15% more reduction of residual RMS (root mean square). And by varying the distance window, it can extract CMC of various spatial scales, such as signals of slow slip events occurring periodically at certain subduction zones. Different from existing spatial filtering algorithms, the correlation-based stacking method presented in this thesis overcomes the spatial scale limit when doing filtering, and does nor need manual interferences.
The correlation-based spatial filtering technique is then used to extract CMC for 127 global GPS stations and results are obtained at 96 sites. The magnitude of CMC is found to be correlated with size of flicker noise, i.e., those with larger scatters in CMC are the stations with larger flicker noise. But this relationship does not exist between scatter measurements of CMC and amplitude of annual term. The spatial scale of the major part of CMC is usually larger than 1000 km. It is interesting that the size of CMC is correlated with the density of frame stations, i.e., the CMC are usually smaller in areas with relatively denser GPS stations used in the frame stabilization procedure. This implies that the instability of reference frame definition may account for major part of CMC.
In the last section of this thesis, the effect of non-linear reference frame on GPS positioning results is assessed tentatively. It is found that the magnitudes of CMC and flicker noise are correlated with the stability of reference frame definition. It is also shown that applying ATML corrections at the observation level could produce small improvements in reducing the magnitudes of white noises and flicker noises, by reducing the effect of vertical annual motions on frame stabilization.
This work has improved the understanding of non-tectonic signals in GPS position time series, and satisfying results in data filtering and non-tectonic noise reduction have been obtained. Nevertheless, only limited analyses on GPS time series errors have been performed, and many kinds of noises in GPS data aquisation and processing remain to be further explored. More work need to be done in this field for deeper understanding of GPS signals and noise removal, so that to promote research of tectonic deformation.
引文
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