【作者】 蔡林；

【导师】 周泽兵；

【作者基本信息】 华中科技大学 ， 地球物理， 2013， 博士

【摘要】 卫星重力测量技术被公认为是探测和研究全球重力场最有效且极具发展潜力的方法之一。自进入21世纪以来，基于卫星跟踪卫星技术的CHAMP和GRACE以及基于卫星重力梯度技术的GOCE重力卫星计划相继成功实施，使得人们得以获取高精度和高分辨率的全球重力场信息，进一步提高了对全球物质分布、物质转移交换和地球内部精细结构等科学问题的认识水平。为了研究卫星重力测量计划中指标参数与科学目标之间的关系和评估各种噪声对恢复重力场精度的影响，传统研究方法一般是将重力观测值作为位置或者时间的函数，在此基础上利用最小二乘法进行相关的误差分析。最小二乘误差分析方法从数值的角度间接地进行评估参数的影响，难以直接评估某些单一参数的影响，而且随着解算模型的分辨率越来越高和阶数越来越大，计算量急剧增长并带来严重的数值不稳定性问题。为了快速评估和确定卫星重力测量计划有关参数，以及评估不同类型载荷噪声的影响，根据仪器功率谱密度和重力位系数阶方差的定义，建立了卫星重力梯度测量噪声与恢复重力场模型精度的直接对应关系。利用二维傅立叶变换性质、二维采样定理和相应的调制理论，进一步推导出了卫星重力测量结果中所含二维空间信号与观测值的一维时间频率的联系，从而可以解析地评估卫星重力测量中色噪声的影响。利用此关系，首先讨论分析了白噪声模型下卫星重力测量技术中测量噪声、卫星轨道高度及运行时间等参数对重力场恢复精度的影响。接着分析了色噪声对恢复重力场模型精度的影响，结果表明低频的噪声在整个频带上都对恢复重力场位系数有影响。考虑到实际测量噪声为色噪声的情况下，如果不采取滤波措施，低频处的1/f噪声将较大地影响恢复重力场的空间分辨率和精度。但是，在使用滤波器后低频噪声得到抑制的同时，重力场信号每一阶所含有的低频信息也被抑制，可能使得单独使用梯度观测值恢复重力场模型系数时产生失真。此外，根据高低卫—卫跟踪测量原理并结合线性扰动理论和控制理论，我们建立起了高低卫—卫跟踪测量噪声功率谱与重力场恢复精度之间的解析表达式，并在此基础上分析讨论了高低卫—卫跟踪中GPS定位误差和静电悬浮加速度计测量噪声对所恢复重力场精度的影响。结果表明目前高低卫—卫跟踪得到的地球重力场精度主要受限于GPS的测量精度。为了获取高精度的月球引力场模型，开展了月球卫星引力梯度测量方案的研究。月球引力梯度测量不仅有利于恢复月球引力场的中短波分量信息，而且还有利于消除探月卫星受到的非保守力的影响，可望利用运行在轨道高度为20km的极圆轨道上、梯度测量水平为30mE/Hz1/2的重力梯度卫星，在半波长为7km的空间分辨率上，确定月球水准面的精度约为20.5cm的月球引力场模型。相对于传统的研究卫星重力测量误差分析和恢复能力论证的方法，我们提出的方法具有简单和直接等优点，且不需要消耗大量计算资源，特别适合项目建议初期对部分观测量或者载荷指标进行快速评估和确定，也可以对卫星重力测量系统数值模拟仿真中参数选择和优化设计提供指导。更多还原

【Abstract】 Satellite gravimetry is recognized as one of the most effective and potential techniquefor exploring and researching the Earth‘s gravity field with a global coverage. In thebeginning of the21st century, dedicated gravity field missions like CHAMP, GRACE andGOCE were successfully launched. Based on the high spatial resolution and accuracygravity field information retrieved from the missions, we can have a further understandingof the mass transport, mass anomalies, mass distribution in the Earth system, the finestructure of the Earth, and so on. Currently, the corresponding methods of error analysis,which determine science requirements and mission parameters, are mainly based onleast-squares (LS) theory, and basically divided into two types: the time-wise approachand the space-wise approach. The solution to the equations based on LS has the optimumstatistical properties, but both the time-wise and space-wise approaches address the effectof measurement errors and estimate the resolution of gravity field models mainly from anumerical point of view. It is difficult to directly estimate the effect of the parameters, andthe latest and incoming gravitational models with increasing accuracy and resolutionmakes the computation more difficult since the computation become huge and seriousnumerical instabilities arise when degree/order of models gets higher.For the reasons mentioned above, it is important to develop a direct and efficientprocedure of error analysis for satellite gravity field determination. Direct relationshipbetween the power spectrum density of satellite gravimetry observations and thecoefficients of the Earth‘s gravity potential is established based on definitions of theinstrument‘s power spectrum density and the Earth‘s gravity field potential, and then theeffect of measurement accuracy, the altitude of the satellite, and the operation duration onrecovering of the Earth‘s gravity field is analyzed by using this method which is based on the assumption that the measurement errors are white. Furthermore, the relationshipbetween the spatial frequencies and the temporal frequencies is concluded based on2-DFourier methods,2-D sample theorem and modulation theory. Thus, it is possible toquantify the effect of color noise in missions. From the results in this study, it is indicatedthat the low frequency noise degrades the gravity field recovery in all degrees and thesignals of gravity information at low frequencies are also filtered out when filters areemployed, so the colored noise must be processed carefully.The analytical relationship between the measurement error PSD of SST-hl and thecoefficient of the Earth gravity potential is established by using a method based on theprinciples of SST-hl, the linear perturbations theory and control theory. Then we analysisthe effects of GPS and accelerometer measurement errors on the accuracy of the Earthgravity field recovery, which is limited by the accuracy of GPS.In addition, the lunar satellite gravity gradiometry is also proposed and discussed forimproving the Moon‘s gravity field model. This mode not only is effective in recoveringthe medium and short wavelength gravity field information, but also can reduce the effectof non-gravitational forces in order to improve the recovery accuracy. The missionscenario with a high accuracy of14mGal and the geoid with an accuracy of20.5cm at aspatial resolution of7km is recommended, which is under the conditions of orbit heightof20km and gradiometer accuracy level of30mE/Hz1/2.The method established in this study is effective and direct compared with the othersbased on the least square approach, and is very useful to design and verify the parametersfor the Earth gravity recovery missions.更多还原