高采样率GPS数据非差精密处理方法及其在地震学中的应用研究
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摘要
2008年5月12日,我国四川汶川发生了Ms8.0级地震,造成了巨大的人员伤亡和财产损失,因此地震学研究是科技工作者面临的艰巨使命。GNSS技术作为现代大地测量的主要观测手段之一,能获取地震时期高精度的地壳形变信息,特别是利用高采样率GNSS数据能获得地震时期瞬时同震地壳形变,从而得到地震波信号,为进一步研究地震震源破裂过程、地震波特性、地震震中反演等地震学问题提供一种新的数据源。利用高采样率GNSS技术研究地震已成为GNSS应用领域最热门的研究课题之一。
高采样率GNSS技术研究地震有许多地震仪无法比拟的优势,例如：1)GNSS技术可直接获得瞬时动态形变位移,而地震仪需要积分后才能获得位移形变结果,积分的过程会造成信号扭曲和噪声放大现象；2)GNSS技术不存在饱和问题,而速度型地震仪在近场强震的情况容易出现饱和现象,即观测的数据由于超过仪器记录的最大值而被削减；3)GNSS技术能获得地面倾斜位移量,而地震仪是依靠重力的原理工作,地面倾斜会造成地震仪产生加速度系统偏差,无法准确的恢复地面倾斜位移量。
随着我国重大科学工程“中国大陆构造环境监测网络(CMONOC)"的建成,覆盖我国大陆构造板块体和主要地震带的GNSS跟踪站的数据采样率最高可达50Hz。另外,我国许多省市陆续建成的CORS网也能接收高采样率的GNSS数据。它们将为地震研究提供大范围、高采样率的GNSS观测数据。
然而,高采样率GNSS技术研究地震还存在许多问题。首先是高精度GNSS数据处理方法及软件还不能完全满足cm级甚至mm级的动态形变分析的要求。目前动态定位处理主要采用两种模式,即网解模式和精密单点定位(PPP)模式。网解模式的动态定位需要选择一个或者多个静止的测站作为参考站,然而当强震发生时,地震波波及范围达到几百甚至上千公里,在震中附近通常很难找到静止的测站作为参考站,若从远处选取不受地震影响的参考站,会导致解算基线过长而使网解动态定位精度严重降低。PPP模式采用单站进行作业,定位方式灵活,不受基线长度影响,但是,PPP模式无法采用双差的方法消除系统误差,使PPP的动态定位精度通常低于短基线双差定位精度。如何进一步提高高采样率GNSS动态定位精度,以满足高精度的动态形变分析需求,是一个难点问题。其次,由于GNSS技术与地震仪工作原理完全不同,导致GNSS技术获得的地震瞬时动态形变有其自己的特点,如何充分利用和挖掘GNSS技术获取的瞬时动态形变信息和地震波信号,反演地震学中的有关问题,也是目前研究的难点。
本文上述两个问题展开研究,提出了一套采用高采样率GPS数据获取高精度的瞬时地壳形变的动态数据处理方法。该方法基于非差处理模式,固定PPP网解模糊度,并结合恒星日滤波及S-变换方法后处理去噪,可获得高精度的动态形变结果。以此为基础,处理了地震时期实测GPS数据,并利用获得的结果反演震中位置和发震时刻等地震学问题。其主要研究内容和成果包括：
1)归纳分析了高采样率GPS技术在地震学研究中的优势,从高采样率GPS观测网的布设情况、高采样率GPS数据处理方法和软件的发展现状以及高采样率GPS技术在地震学中的应用三个方面总结了高采样率GPS技术在国内外的研究现状。从高采样率GPS技术对高精度GPS数据处理方法和软件的需求出发,阐明了如何进一步提高GPS动态定位精度是目前亟待解决的问题。
2)介绍了目前两种主要的非差精密定位方法,PPP方法和非差网解方法。并比较了PPP方法和非差网解方法的动态定位精度。
3)深入研究了PPP中的动态定位模糊度固定问题,实现了PPP的动态定位模糊度固定。实例分析表明,模糊度固定可以提高测站E方向定位精度,但是,当浮点解精度RMS优于1cm时,模糊度固定的效果不太明显。对于N方向,模糊度固定后定位精度的提高并不明显。
4)深入分析了恒星日滤波方法消除与测站环境和卫星几何结构有关的GPS连续观测数据处理系统误差(多路径误差、卫星轨道误差)的关键问题所在,通过恒星日滤波周期的选择改进恒星日滤波法。实验分析表明,与直接采用恒星日周期进行恒星日滤波相比,采用实际计算的平均卫星轨道重复周期进行恒星日滤波能提高约10%的定位精度。
5)深入研究并实现了S-变换去噪方法,并将该方法运用于GPS地震波的去噪处理,从而使地震波到达时间的确定更加准确。针对GPS地震波信号存在长周期误差项的特点,提出了S-变换加趋势项改正的去除长周期的GPS定位噪声的方法,从而有利于GPS地震波信号应用于进一步的地震学分析。
6)为了验证高采样率GPS技术的定位精度,利用设计的GPS地震仪模拟平台进行了实验分析,实验结果表明,采用GPS获得的震动结果与采用地震仪获得的震动结果具有很好的一致性。
7)提出了基于高采样率GPS数据动态处理结果的地震震中反演方法,并推导了由GPS数据反演震中和发震时刻的数学模型。基于该方法,利用汶川地震时期GPS数据反演得到的震中位置和发震时刻与中国地震局公布的结果比较,反演震中误差为12.5km,发震时刻误差为7s。利用Chile地震GPS数据反演的震中和发震时刻与美国地质调查局(USGS)结果比较,反演震中误差为27.4km,发震时刻误差为5s。
The 12 May 2008 Ms 8.0 Wenchuan earthquake caused a large amount of casualties and property losses. Global Navigation Satellite Systems (GNSS), as a primary technique of modern geodetic observation, can obtain the accurate crustal deformation. Futhermore, with the high-rate GNSS data, we can obtain the transient crustal deformation and seismic wave. The high-rate GNSS provides a new tool to study the earthquake rupture process, seismic wave characteristics, the position of earthquake epicenter inversion etc. Therefore GNSS seismology has become the forefront topic in the present research field of GNSS applications.
Compared with traditional seismic measurements, High-rate GNSS have a lot of advantages.1) when recovery of displacements is desired, GNSS directly estimates them, but seismic data must be integrated once or twice in order to recover displacement. Integration is an often error-prone process and has the potential to amplify noise and distort the true signal.2) Seismic instruments can saturate or clip with sufficiently large ground motions so that the instrument does not record the full amplitude of local velocity or acceleration. GNSS observations will not saturate in amplitude because, unlike seismometers, no instrument response limits the observation capability of the receiver.3) Seismometers operate based on the theory of gravity, and tilt of the instrument can produce artificial horizontal acceleration, but GNSS instruments are not affected in this way.
The Crustal Movement Observation Network of China (CMONOC) is a network of large scale and high precision that covers over the whole China mainland, the sampling rate of GNSS can be up to 50Hz. In addition, many provinces in China have built the Continuously Operating Reference Station (CORS) network, which can also provide high-rate GNSS data. All of them will provide a large scale and high-rate GNSS data for researching GNSS seismology.
However, there are many shortcomings while using the high-rate GNSS technology for GNSS seismology. Firstly, the approaches and software of high-rate GNSS data processing are not fully meet the high precision application requirements of the dynamic deformation analysis. To date, there are two approaches in estimating station positions with high-rate GPS data: network solution and Precise Point Positioning (PPP) technique. In the former approach, at least one station must be fixed or tightly constrained to its known values, although it is normally also displaced by the seismic motions. Therefore, the displacements estimated for the other stations are biased by the displacement of the fixed station. In order to obtain displacement with respect to a reference frame, stations which are not affected by the earthquake should be included as reference stations into the data processing. As the position accuracy in the relative positioning degrades usually along with the baseline length, the inter-station distance is limited to several tens to hundreds kilometers. In the PPP approach where satellite clocks and orbits are fixed to pre-estimated precise values, and the coordinates can be estimated station by station in the reference frame defined by the orbits and clocks. However, PPP approach induces systematic errors such as multipath error, unmodeled antenna phase center varitions, and errors of the satellite orbit, so the position are significantly influenced by these errors. Secondly, the seismic waves obtained by high-rate GNSS positioning are different from that obtained by seismograph, how to make full use of GNSS seismic wave for seismology research is a critical topic.
The paper aims at the improvement of high-rate GPS non-difference dynamic positioning acurracy and application to seismology, and focuses on the following research: A method to obtain the high precision transient crustal deformation by non-difference positioning with high-rate GPS data is proposed. It is based on network solutions PPP ambiguity fixing, sidereal filtering, and S-transform denosing. After getting the GPS seismic wave, some inversions are researched in seismology. Main constents and results in this paper include the follow parts:
1) The paper first summarized the development trends of high-rate GPS technology, the construction of GPS observation network in global area, and the GPS data processing software. According to the application requirements of high-rate GPS positioning approach and software, it clarified that the method to obtain the high precision transient crustal deformation by non-difference positioning with high-rate GPS data need to be developed urgently.
2) Two major non-difference GPS positioning methods are introduced, PPP and non-difference network solution. And two critical issues of GPS dynamic positioning are investigated. Finally, the positioning accuracy of the PPP and non-difference network solution method are compared.
3) The problem of ambiguity fixing in dynamic positioning with PPP is further studied and realized. Analysis with examples illustrates that ambiguity fixing is able to enhance positioning precision in East direction, but the effects will not be so obvious when the precision of float solution higer than lcm. With regard to North direction, there is no significant improvement in positioning precision even after ambiguity fixing.
4) Sidereal filtering technique is used to eliminate systematic errors (such as multipath error) related to station environment and geometric structure of satellites. Meanwhile, effects of different period on sidereal filtering are analyzed. Results show that compared with directly using sidereal period, actually-calculated mean satellite orbit repetition period can improve about 10% in positioning precision,
5) S-transform denoising method is studied, realized and applied to denoising processing of GPS seismic wave, which leads to more accurate seismic wave arrival time. Considering the existence of longer-period error terms in GPS seismic signals, S-transform plus trend correction approach is proposed, which helps GPS seismic signals contribute in seismic analysis.
6) To verify the positioning precision of high sampling rate GPS technology, experimental analysis is conducted with auto-designed GPS-Seismometer simulation platform. It is illustrated that sound consistence exists between vibrations recovered from GPS and that from seismometer.
7) Epicenter inversion method based on dynamic processing result of high sampling rate GPS observables, and mathematic model for inversion of epicenter and original time with GPS data is deduced. Based on this method, GPS data during Wenchuan earthquake is used to inverse the epicenter and earthquake time. Compared with the results issued by China Seismological Bureau, inversed epicenter and earthquake time have errors of 12.5km and 7s, respectively. GPS data during Chile earthquake is used to inverse the epicenter and earthquake time, the inversion errors are 27.4km and 5s compared with the results provided by United States Geological Survey (USGS).
高采样率GNSS技术研究地震有许多地震仪无法比拟的优势,例如：1)GNSS技术可直接获得瞬时动态形变位移,而地震仪需要积分后才能获得位移形变结果,积分的过程会造成信号扭曲和噪声放大现象；2)GNSS技术不存在饱和问题,而速度型地震仪在近场强震的情况容易出现饱和现象,即观测的数据由于超过仪器记录的最大值而被削减；3)GNSS技术能获得地面倾斜位移量,而地震仪是依靠重力的原理工作,地面倾斜会造成地震仪产生加速度系统偏差,无法准确的恢复地面倾斜位移量。
随着我国重大科学工程“中国大陆构造环境监测网络(CMONOC)"的建成,覆盖我国大陆构造板块体和主要地震带的GNSS跟踪站的数据采样率最高可达50Hz。另外,我国许多省市陆续建成的CORS网也能接收高采样率的GNSS数据。它们将为地震研究提供大范围、高采样率的GNSS观测数据。
然而,高采样率GNSS技术研究地震还存在许多问题。首先是高精度GNSS数据处理方法及软件还不能完全满足cm级甚至mm级的动态形变分析的要求。目前动态定位处理主要采用两种模式,即网解模式和精密单点定位(PPP)模式。网解模式的动态定位需要选择一个或者多个静止的测站作为参考站,然而当强震发生时,地震波波及范围达到几百甚至上千公里,在震中附近通常很难找到静止的测站作为参考站,若从远处选取不受地震影响的参考站,会导致解算基线过长而使网解动态定位精度严重降低。PPP模式采用单站进行作业,定位方式灵活,不受基线长度影响,但是,PPP模式无法采用双差的方法消除系统误差,使PPP的动态定位精度通常低于短基线双差定位精度。如何进一步提高高采样率GNSS动态定位精度,以满足高精度的动态形变分析需求,是一个难点问题。其次,由于GNSS技术与地震仪工作原理完全不同,导致GNSS技术获得的地震瞬时动态形变有其自己的特点,如何充分利用和挖掘GNSS技术获取的瞬时动态形变信息和地震波信号,反演地震学中的有关问题,也是目前研究的难点。
本文上述两个问题展开研究,提出了一套采用高采样率GPS数据获取高精度的瞬时地壳形变的动态数据处理方法。该方法基于非差处理模式,固定PPP网解模糊度,并结合恒星日滤波及S-变换方法后处理去噪,可获得高精度的动态形变结果。以此为基础,处理了地震时期实测GPS数据,并利用获得的结果反演震中位置和发震时刻等地震学问题。其主要研究内容和成果包括：
1)归纳分析了高采样率GPS技术在地震学研究中的优势,从高采样率GPS观测网的布设情况、高采样率GPS数据处理方法和软件的发展现状以及高采样率GPS技术在地震学中的应用三个方面总结了高采样率GPS技术在国内外的研究现状。从高采样率GPS技术对高精度GPS数据处理方法和软件的需求出发,阐明了如何进一步提高GPS动态定位精度是目前亟待解决的问题。
2)介绍了目前两种主要的非差精密定位方法,PPP方法和非差网解方法。并比较了PPP方法和非差网解方法的动态定位精度。
3)深入研究了PPP中的动态定位模糊度固定问题,实现了PPP的动态定位模糊度固定。实例分析表明,模糊度固定可以提高测站E方向定位精度,但是,当浮点解精度RMS优于1cm时,模糊度固定的效果不太明显。对于N方向,模糊度固定后定位精度的提高并不明显。
4)深入分析了恒星日滤波方法消除与测站环境和卫星几何结构有关的GPS连续观测数据处理系统误差(多路径误差、卫星轨道误差)的关键问题所在,通过恒星日滤波周期的选择改进恒星日滤波法。实验分析表明,与直接采用恒星日周期进行恒星日滤波相比,采用实际计算的平均卫星轨道重复周期进行恒星日滤波能提高约10%的定位精度。
5)深入研究并实现了S-变换去噪方法,并将该方法运用于GPS地震波的去噪处理,从而使地震波到达时间的确定更加准确。针对GPS地震波信号存在长周期误差项的特点,提出了S-变换加趋势项改正的去除长周期的GPS定位噪声的方法,从而有利于GPS地震波信号应用于进一步的地震学分析。
6)为了验证高采样率GPS技术的定位精度,利用设计的GPS地震仪模拟平台进行了实验分析,实验结果表明,采用GPS获得的震动结果与采用地震仪获得的震动结果具有很好的一致性。
7)提出了基于高采样率GPS数据动态处理结果的地震震中反演方法,并推导了由GPS数据反演震中和发震时刻的数学模型。基于该方法,利用汶川地震时期GPS数据反演得到的震中位置和发震时刻与中国地震局公布的结果比较,反演震中误差为12.5km,发震时刻误差为7s。利用Chile地震GPS数据反演的震中和发震时刻与美国地质调查局(USGS)结果比较,反演震中误差为27.4km,发震时刻误差为5s。
The 12 May 2008 Ms 8.0 Wenchuan earthquake caused a large amount of casualties and property losses. Global Navigation Satellite Systems (GNSS), as a primary technique of modern geodetic observation, can obtain the accurate crustal deformation. Futhermore, with the high-rate GNSS data, we can obtain the transient crustal deformation and seismic wave. The high-rate GNSS provides a new tool to study the earthquake rupture process, seismic wave characteristics, the position of earthquake epicenter inversion etc. Therefore GNSS seismology has become the forefront topic in the present research field of GNSS applications.
Compared with traditional seismic measurements, High-rate GNSS have a lot of advantages.1) when recovery of displacements is desired, GNSS directly estimates them, but seismic data must be integrated once or twice in order to recover displacement. Integration is an often error-prone process and has the potential to amplify noise and distort the true signal.2) Seismic instruments can saturate or clip with sufficiently large ground motions so that the instrument does not record the full amplitude of local velocity or acceleration. GNSS observations will not saturate in amplitude because, unlike seismometers, no instrument response limits the observation capability of the receiver.3) Seismometers operate based on the theory of gravity, and tilt of the instrument can produce artificial horizontal acceleration, but GNSS instruments are not affected in this way.
The Crustal Movement Observation Network of China (CMONOC) is a network of large scale and high precision that covers over the whole China mainland, the sampling rate of GNSS can be up to 50Hz. In addition, many provinces in China have built the Continuously Operating Reference Station (CORS) network, which can also provide high-rate GNSS data. All of them will provide a large scale and high-rate GNSS data for researching GNSS seismology.
However, there are many shortcomings while using the high-rate GNSS technology for GNSS seismology. Firstly, the approaches and software of high-rate GNSS data processing are not fully meet the high precision application requirements of the dynamic deformation analysis. To date, there are two approaches in estimating station positions with high-rate GPS data: network solution and Precise Point Positioning (PPP) technique. In the former approach, at least one station must be fixed or tightly constrained to its known values, although it is normally also displaced by the seismic motions. Therefore, the displacements estimated for the other stations are biased by the displacement of the fixed station. In order to obtain displacement with respect to a reference frame, stations which are not affected by the earthquake should be included as reference stations into the data processing. As the position accuracy in the relative positioning degrades usually along with the baseline length, the inter-station distance is limited to several tens to hundreds kilometers. In the PPP approach where satellite clocks and orbits are fixed to pre-estimated precise values, and the coordinates can be estimated station by station in the reference frame defined by the orbits and clocks. However, PPP approach induces systematic errors such as multipath error, unmodeled antenna phase center varitions, and errors of the satellite orbit, so the position are significantly influenced by these errors. Secondly, the seismic waves obtained by high-rate GNSS positioning are different from that obtained by seismograph, how to make full use of GNSS seismic wave for seismology research is a critical topic.
The paper aims at the improvement of high-rate GPS non-difference dynamic positioning acurracy and application to seismology, and focuses on the following research: A method to obtain the high precision transient crustal deformation by non-difference positioning with high-rate GPS data is proposed. It is based on network solutions PPP ambiguity fixing, sidereal filtering, and S-transform denosing. After getting the GPS seismic wave, some inversions are researched in seismology. Main constents and results in this paper include the follow parts:
1) The paper first summarized the development trends of high-rate GPS technology, the construction of GPS observation network in global area, and the GPS data processing software. According to the application requirements of high-rate GPS positioning approach and software, it clarified that the method to obtain the high precision transient crustal deformation by non-difference positioning with high-rate GPS data need to be developed urgently.
2) Two major non-difference GPS positioning methods are introduced, PPP and non-difference network solution. And two critical issues of GPS dynamic positioning are investigated. Finally, the positioning accuracy of the PPP and non-difference network solution method are compared.
3) The problem of ambiguity fixing in dynamic positioning with PPP is further studied and realized. Analysis with examples illustrates that ambiguity fixing is able to enhance positioning precision in East direction, but the effects will not be so obvious when the precision of float solution higer than lcm. With regard to North direction, there is no significant improvement in positioning precision even after ambiguity fixing.
4) Sidereal filtering technique is used to eliminate systematic errors (such as multipath error) related to station environment and geometric structure of satellites. Meanwhile, effects of different period on sidereal filtering are analyzed. Results show that compared with directly using sidereal period, actually-calculated mean satellite orbit repetition period can improve about 10% in positioning precision,
5) S-transform denoising method is studied, realized and applied to denoising processing of GPS seismic wave, which leads to more accurate seismic wave arrival time. Considering the existence of longer-period error terms in GPS seismic signals, S-transform plus trend correction approach is proposed, which helps GPS seismic signals contribute in seismic analysis.
6) To verify the positioning precision of high sampling rate GPS technology, experimental analysis is conducted with auto-designed GPS-Seismometer simulation platform. It is illustrated that sound consistence exists between vibrations recovered from GPS and that from seismometer.
7) Epicenter inversion method based on dynamic processing result of high sampling rate GPS observables, and mathematic model for inversion of epicenter and original time with GPS data is deduced. Based on this method, GPS data during Wenchuan earthquake is used to inverse the epicenter and earthquake time. Compared with the results issued by China Seismological Bureau, inversed epicenter and earthquake time have errors of 12.5km and 7s, respectively. GPS data during Chile earthquake is used to inverse the epicenter and earthquake time, the inversion errors are 27.4km and 5s compared with the results provided by United States Geological Survey (USGS).
引文
[1]Agnew, D. C., and K. M. Larson (2007), Finding the repeat times of the GPS constellation, GPS Solutions,11(1),71-76.
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