GPS地面台网和掩星观测结合的时变三维电离层层析
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摘要
电离层是日一地系统的重要组成，不仅保护了地球上的生物免受太阳紫外辐射和宇宙高能粒子的直接作用，而且对穿电离层传播的无线电波产生反射、散射、吸收和折射等效应。电离层与日一地系统的其它区域，包括太阳、行星际介质、磁层、热层和中层之间存在着强烈地耦合相互作用。由于太阳活动引起的地球空间环境扰动和各种等离子体不稳定性过程，电离层中存在不同尺度的不规则结构并常处于扰动状态之下，对短波通讯、卫星通讯和全球定位系统GPS的导航定位精度等产生严重影响。积极监测与研究电离层中的各种现象，从而揭示现象背后的物理机制，探索电离层对人类生存环境的影响，是空间天气研究的重要内容之一，对社会经济的发展十分重要。
电离层层析成像技术是计算机层析成像技术在电离层探测中的应用，适合于监测电离层电子密度的大尺度空间分布及其扰动。结合GPS地面台网观测和GPS掩星技术的时变三维电离层层析是近年来发展起来的一种新技术，在电离层形态与扰动的监测研究方面有很大的科学意义和应用价值。尽管近年来针对结合地基GPS与掩星观测的时变三维电离层层析已经开展了模拟和实测数据的反演成像研究，但由于时变三维电离层层析问题的复杂性，还有许多问题尚待进行深入地研究。比如，结合地基GPS与掩星观测的时变三维电离层层析成像数学上的重建公式尚未建立，由GPS地面台网观测和低轨卫星获得的掩星观测数据实现时变三维电离层层析的反演算法和计算机程序有待发展等等。
本论文研究工作的科学目标是，协同利用GPS地面台网和低轨卫星GPS掩星期间获得的GPS双频信标数据，重建待探测区域电离层电子密度的时变三维分布。文中着重在理论上探讨了时变三维电离层层析的数学基础，进而建立了结合地基GPS与掩星观测的时变三维电离层层析成像重建公式，然后提出了利用相对TEC数据实现时变三维电离层层析成像的方法。使用本文提出的方法，对实测数据进行了处理和反演成像，获得了一些有重要科学意义的结果。本文主要的研究工作在国内尚属首次，在国际上也是近几年才开展起来的。本文的研究表明，利用GPS地面台网和掩星观测结合的时变三维电离层层析成像技术可以对电离层大尺度结构的时空演变进行较为有效的监测。论文的主要研究工作和结果归纳如下：
1．从傅立叶变换理论出发，推导得到了地基平行束投影定理和掩星平行束投影定理，结合地
基平行束投影定理和掩星平行束投影定理，建立了结合地基GPS与掩星观测的时变三维
电离层层析成像重建公式。这一创新性研究成果为进一步研究时变三维电离层层析成像技
术提供了坚实的理论依据。
》根据观测几何构形和傅立叶变换公式，首先推导得到了地基平行束投影定理，它建立
了投影(电子密度的路径积分，即TEc)的时空三维Fourier谱与电子密度的时空四维
Fourier谱之间的联系，是CIT重建的基础。利用地基平行束投影定理和傅立叶逆变
换公式，推导得到了由地基投影数据重建电子密度分布的时变三维电离层层析成像重
建公式。
》根据地基平行束投影定理，不能由仰角为O或兀的地基GPS观测数据确定电子密度谱
在Fourie:空间中相应超平面上的值。在实际应用中，考虑到地球曲率、电离层对低
仰角射线的强折射效应后，满足反演条件的地基GPS射线大多在垂直或接近垂直方
向上，有限扫描视角的问题非常严重。地基射线仰角范围的限制导致单独使用地基
GPS观测数据重建电离层电子密度分布时电子密度谱信息丢失，其后果是反演得到
的电子密度分布图像垂直方向上的分辨率很低。掩星平行束投影定理的建立表明，利
用GPS掩星观测数据可以补充由于地基数据仰角范围限制而丢失的电子密度谱信
息，从而改善电子密度分布图像的重建质量。
》结合地基平行束投影定理和掩星平行束投影定理，推导得到了结合地基GPS与掩星
观测的时变三维电离层层析成像重建公式，这为进一步研究时变三维电离层层析成像
的具体实现算法提供了理论依据。
2.从结合地基GPS与掩星观测的时变三维电离层层析成像重建公式出发，推导得到了时空
四维脉冲源函数的重建公式。在理想条件和非理想条件下，根据本文推导的重建公式对脉
冲源进行了重建。
》在理想条件下(地基接收机和星载接收机连续分布，接收机在任何时刻都有观测数
据)，若地基GPS射线无仰角范围限制，由地基数据可以无畸变地重建时空四维脉冲
源函数;若地基射线仰角受限，结合地基GPS数据和掩星数据亦可无畸变地重建时
空四维脉冲源函数。
》在接收机数量稀少、视角有限以及观测数据时间采样有限等非理想条件下，对脉冲源
函数的重建必须根据重建公式利用数值方法进行。根据本文推导得到的重建公式分别
对空间三维脉冲源和时空四维脉冲源进行了重建，其结果均能很好地重现源函数。通
过与单独使用地基数据得到的重建结果比较后可以看到，添加掩星数据后，重建结果
特别是其垂直结构的重建质量得到了明显改善，表明协同使用地基GPS与掩星观测
数据
The Earth's ionosphere is one of the main regions in the solar-terrestrial system. The ionosphere not only protects creatures on the Earth from direct actions of solar UV (EUV) radiation and cosmic energetic particles, but also influences radio propagation through it by reflection, scattering, absorption and refraction. The ionosphere is strongly coupled with the other regions in the solar-terrestrial system, including the sun, the interplanetary medium, the magnetosphere, the thermosphere, and the mesosphere. Because of various disturbances of the Earth's space environment induced by solar activities and plasma instability processes, various irregular structures with widely different spatial scales exist in the ionosphere and the ionosphere is often in disturbed conditions, which influences seriously shortwave communication, satellite communication, navigation and positioning precision of GPS and so on. It's one of the main topics in space weather research to monitor and investigate ionospheric phenomena, r
eveal physical mechanism of ionospheric phenomena, and analyze the influences of the ionosphere on living environment, which is very important for the development of economy.
Computerized Ionospheric Tomography (CIT) is the application of computerized tomography to ionospheric sounding and is suitable for monitoring large-scale spatial structures and disturbances of ionospheric electron density. Time-dependent 3-D CIT with ground-based GPS network observations and GPS occupation measurements is a new technique just at beginning research in recent years, which is of high value to monitor and investigate ionospheric morphology and perturbations. Simulations and inversions based on observations for time-dependent 3-D CIT with ground-based GPS network and occultation observations have been performed in recent years. However, due to the complicated nature of time-dependent 3-D CIT, there still remains lots of questions needed to be studied further, such as the reconstruction formula of time-dependent 3-D CIT with ground-based GPS network and occultation observations should be established, inversion algorithm and computer program of time-dependent 3-D CIT with ground-based GPS network
and occultation observations should be developed and so on.
The research work discussed in this dissertation aims to image time-dependent 3-D distribution of ionospheric electron density, Ne, in the region to be recovered from the combination of ground-based GPS network measurements and GPS beacon observations obtained by a receiver on board of Low Earth Orbit (LEO) satellite when the GPS satellite is occulted by the surface of the Earth as seen by the receiver. After discussing theoretically the mathematical foundation of
time-dependent 3-D CIT and deducing its reconstruction formula with ground-based GPS network and occultation observations, a new reconstruction method is proposed to perform time-dependent 3-D CIT with relative Total Electron Content (TEC) data. Observations have been processed with the above reconstruction method and some results with important geophysical implications have been obtained. The main research work in this dissertation is the first attempt in China, and also a topic just at beginning research all over the world in recent years. The studies in this dissertation demonstrate that time-dependent 3-D CIT with ground-based GPS network and occultation observations is rather effective to monitor the spatio-temporal evolution of large-scale ionospheric structures. The main results of this dissertation are summarized as follows.
1. According to the Fourier transform theory, the projection theorem of ground-based parallel-beam rays and the projection theorem of occultation parallel-beam rays are deduced respectively. Based on the two projection theorems, the reconstruction formula of time-dependent 3-D CIT with ground-based GPS network and occultation observations is established. This research result is innovative and provides the theoretical basis to investigate time-dependent 3-D CIT further.
? On the b
电离层层析成像技术是计算机层析成像技术在电离层探测中的应用，适合于监测电离层电子密度的大尺度空间分布及其扰动。结合GPS地面台网观测和GPS掩星技术的时变三维电离层层析是近年来发展起来的一种新技术，在电离层形态与扰动的监测研究方面有很大的科学意义和应用价值。尽管近年来针对结合地基GPS与掩星观测的时变三维电离层层析已经开展了模拟和实测数据的反演成像研究，但由于时变三维电离层层析问题的复杂性，还有许多问题尚待进行深入地研究。比如，结合地基GPS与掩星观测的时变三维电离层层析成像数学上的重建公式尚未建立，由GPS地面台网观测和低轨卫星获得的掩星观测数据实现时变三维电离层层析的反演算法和计算机程序有待发展等等。
本论文研究工作的科学目标是，协同利用GPS地面台网和低轨卫星GPS掩星期间获得的GPS双频信标数据，重建待探测区域电离层电子密度的时变三维分布。文中着重在理论上探讨了时变三维电离层层析的数学基础，进而建立了结合地基GPS与掩星观测的时变三维电离层层析成像重建公式，然后提出了利用相对TEC数据实现时变三维电离层层析成像的方法。使用本文提出的方法，对实测数据进行了处理和反演成像，获得了一些有重要科学意义的结果。本文主要的研究工作在国内尚属首次，在国际上也是近几年才开展起来的。本文的研究表明，利用GPS地面台网和掩星观测结合的时变三维电离层层析成像技术可以对电离层大尺度结构的时空演变进行较为有效的监测。论文的主要研究工作和结果归纳如下：
1．从傅立叶变换理论出发，推导得到了地基平行束投影定理和掩星平行束投影定理，结合地
基平行束投影定理和掩星平行束投影定理，建立了结合地基GPS与掩星观测的时变三维
电离层层析成像重建公式。这一创新性研究成果为进一步研究时变三维电离层层析成像技
术提供了坚实的理论依据。
》根据观测几何构形和傅立叶变换公式，首先推导得到了地基平行束投影定理，它建立
了投影(电子密度的路径积分，即TEc)的时空三维Fourier谱与电子密度的时空四维
Fourier谱之间的联系，是CIT重建的基础。利用地基平行束投影定理和傅立叶逆变
换公式，推导得到了由地基投影数据重建电子密度分布的时变三维电离层层析成像重
建公式。
》根据地基平行束投影定理，不能由仰角为O或兀的地基GPS观测数据确定电子密度谱
在Fourie:空间中相应超平面上的值。在实际应用中，考虑到地球曲率、电离层对低
仰角射线的强折射效应后，满足反演条件的地基GPS射线大多在垂直或接近垂直方
向上，有限扫描视角的问题非常严重。地基射线仰角范围的限制导致单独使用地基
GPS观测数据重建电离层电子密度分布时电子密度谱信息丢失，其后果是反演得到
的电子密度分布图像垂直方向上的分辨率很低。掩星平行束投影定理的建立表明，利
用GPS掩星观测数据可以补充由于地基数据仰角范围限制而丢失的电子密度谱信
息，从而改善电子密度分布图像的重建质量。
》结合地基平行束投影定理和掩星平行束投影定理，推导得到了结合地基GPS与掩星
观测的时变三维电离层层析成像重建公式，这为进一步研究时变三维电离层层析成像
的具体实现算法提供了理论依据。
2.从结合地基GPS与掩星观测的时变三维电离层层析成像重建公式出发，推导得到了时空
四维脉冲源函数的重建公式。在理想条件和非理想条件下，根据本文推导的重建公式对脉
冲源进行了重建。
》在理想条件下(地基接收机和星载接收机连续分布，接收机在任何时刻都有观测数
据)，若地基GPS射线无仰角范围限制，由地基数据可以无畸变地重建时空四维脉冲
源函数;若地基射线仰角受限，结合地基GPS数据和掩星数据亦可无畸变地重建时
空四维脉冲源函数。
》在接收机数量稀少、视角有限以及观测数据时间采样有限等非理想条件下，对脉冲源
函数的重建必须根据重建公式利用数值方法进行。根据本文推导得到的重建公式分别
对空间三维脉冲源和时空四维脉冲源进行了重建，其结果均能很好地重现源函数。通
过与单独使用地基数据得到的重建结果比较后可以看到，添加掩星数据后，重建结果
特别是其垂直结构的重建质量得到了明显改善，表明协同使用地基GPS与掩星观测
数据
The Earth's ionosphere is one of the main regions in the solar-terrestrial system. The ionosphere not only protects creatures on the Earth from direct actions of solar UV (EUV) radiation and cosmic energetic particles, but also influences radio propagation through it by reflection, scattering, absorption and refraction. The ionosphere is strongly coupled with the other regions in the solar-terrestrial system, including the sun, the interplanetary medium, the magnetosphere, the thermosphere, and the mesosphere. Because of various disturbances of the Earth's space environment induced by solar activities and plasma instability processes, various irregular structures with widely different spatial scales exist in the ionosphere and the ionosphere is often in disturbed conditions, which influences seriously shortwave communication, satellite communication, navigation and positioning precision of GPS and so on. It's one of the main topics in space weather research to monitor and investigate ionospheric phenomena, r
eveal physical mechanism of ionospheric phenomena, and analyze the influences of the ionosphere on living environment, which is very important for the development of economy.
Computerized Ionospheric Tomography (CIT) is the application of computerized tomography to ionospheric sounding and is suitable for monitoring large-scale spatial structures and disturbances of ionospheric electron density. Time-dependent 3-D CIT with ground-based GPS network observations and GPS occupation measurements is a new technique just at beginning research in recent years, which is of high value to monitor and investigate ionospheric morphology and perturbations. Simulations and inversions based on observations for time-dependent 3-D CIT with ground-based GPS network and occultation observations have been performed in recent years. However, due to the complicated nature of time-dependent 3-D CIT, there still remains lots of questions needed to be studied further, such as the reconstruction formula of time-dependent 3-D CIT with ground-based GPS network and occultation observations should be established, inversion algorithm and computer program of time-dependent 3-D CIT with ground-based GPS network
and occultation observations should be developed and so on.
The research work discussed in this dissertation aims to image time-dependent 3-D distribution of ionospheric electron density, Ne, in the region to be recovered from the combination of ground-based GPS network measurements and GPS beacon observations obtained by a receiver on board of Low Earth Orbit (LEO) satellite when the GPS satellite is occulted by the surface of the Earth as seen by the receiver. After discussing theoretically the mathematical foundation of
time-dependent 3-D CIT and deducing its reconstruction formula with ground-based GPS network and occultation observations, a new reconstruction method is proposed to perform time-dependent 3-D CIT with relative Total Electron Content (TEC) data. Observations have been processed with the above reconstruction method and some results with important geophysical implications have been obtained. The main research work in this dissertation is the first attempt in China, and also a topic just at beginning research all over the world in recent years. The studies in this dissertation demonstrate that time-dependent 3-D CIT with ground-based GPS network and occultation observations is rather effective to monitor the spatio-temporal evolution of large-scale ionospheric structures. The main results of this dissertation are summarized as follows.
1. According to the Fourier transform theory, the projection theorem of ground-based parallel-beam rays and the projection theorem of occultation parallel-beam rays are deduced respectively. Based on the two projection theorems, the reconstruction formula of time-dependent 3-D CIT with ground-based GPS network and occultation observations is established. This research result is innovative and provides the theoretical basis to investigate time-dependent 3-D CIT further.
? On the b
引文
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