基于海平面方程约束的GRACE时变重力场反演

During GRACE temporal gravity field recovery, derived monthly solutions represented in terms of spherical harmonics coefficients. Unfortunately, unconstrained harmonic solutions from GRACE have typically suffered from poor observability of east-west gradients, resulting in the so-called "stripes" that are conventionally removed via empirical smoothing and "destriping" algorithms before any geophysical exploitation. In addition, leakage errors are inherent in the spherical harmonic GRACE solutions due to the modest spatial resolution of the derived solutions coupled with the necessity to smooth the solutions to damp high-degree errors. In order to solve above problems, constrained time variable spherical harmonic solutions are calculated via the regularization algorithms by applying combination of constraint parameter to reduce the stripe errors and leakage effects, however, because the spherical harmonic basis functions do not have any spatial local characteristics, it’s difficult to design regularization matrix used for signal leakage correction. Using mascon basis functions arguably provides a more convenient architecture in which the regularization matrix can be derived, since mascon basis functions are local, rather than global, however, land-ocean mass exchange along coastline are ignored by purely mathematical and empirical method during leakage correction. This lead to leakage corrections has no real geophysical meaning. In our research, we will use radial basis functions constrained by sea level equation to represent time variable mass information, and modified local basis functions force the total load mass to be conserved and to allow the land-ocean mass exchange along coastline. Besides, improved radial basis function has spatial local characteristics, which is convenient for us to design regularization matrix. This study focus on separating the land/ocean signal along coastline during the time variable mass parameterization and our research is expected to suffer from less leakage effects in land/ocean coastline during the time variable gravity field inversion, the solution is expected to have a better application in regions where suffer from more signal leakage effects.

在GRACE时变重力场反演中，由于GRACE的轨道特性以及仪器观测误差、力模型误差等因素影响，无约束GRACE时变重力场解表现出南北条带误差特性，在应用中需采取后处理技术去除相关噪声，其有限的空间分辨率及后处理技术会造成信号泄漏问题。尽管在时变重力场模型解算中进行正则化处理能过对相关误差进行压制，但球谐函数不具有空间局部特性，难以针对海陆边界的信号泄漏问题进行约束。Mascon方法的基函数具有空间局部特性，但在针对信号海陆边界信号泄漏改正时忽略了海陆质量块间的相互影响。本研究基于海平面方程改进径向基函数，所构建的局部基函数遵循质量守恒和地表质量负荷理论，具有更为真实的物理内涵，且改进的径向基函数具有空间局部特性，利于设计约束矩阵。本研究通过在基函数构建中考虑海陆边界的物质交换削弱GRACE时变重力场反演中海陆边界信号泄漏问题，解算结果将在海陆边界信号泄漏影响较大的地区获得更好的应用。

本项目针对GRACE时变重力场有限的空间分辨率及后处理技术会造成信号泄漏问题，针对海陆边界的信号泄漏问题进行基于海平面方程改进径向基函数开展时变重力场反演研究，研究中以高精度KBRR观测残差作为输入数据，开展了径向基函数的特征、海平面方程约束径向基函数并基于改进基函数提取时变信号等相关研究。其中，高精度KBRR观测残差获取是时变重力场获取的重要输入数据，而KBRR观测残差计算依赖于参考轨道的计算、背景模型的选取、加速度计数据校正策略等因素。本项目分析了KBRR计算中的相关因素，并基于KBRR残差数据计算了GRACE时变重力场，时变重力场解算结果与GRACE RL05精度相当，相关结果已被ICGEM官方网站收录，并在GRACE FO发射后开展了GRACE FO时变重力场加速计校正策略研究和时变重力场反演工作；项目研究中进一步分析GRACE时变重力场反演中的最大误差源-混频误差，模拟反演以及评估了时变重力场反演精度，评估了传统球谐函数解算结果精度制约因素，分析表明时变重力场解算精度的提高依赖于非潮汐的大气、海洋模型质量变化的精度以及函数模型精度；在基于海平面方程约束的时变重力场解算中，系统研究了RBF与海平面方程约束的基函数特征，以Icosahedron格网做为RBF算法的几何架构开展了基于Shannon类型90阶球谐展开形式的RBF改造。相比传统的RBF，海平面方程约束的RBF算法的精度与节点数目具有相关性，且在同等精度水平下，基于普通的RBF基函数比海平面方程约束的RBF需要更多的节点数目（大约多出10%），分析2009-2010年间海平面方程约束的时变重力场解算结果表明，该方法获取的结果在海陆边界处信号泄露问题能够获得大幅改善，对南极、格陵兰等冰川时变信号的提取能够比传统球谐函数方法获取的趋势项和周年振幅局有约25%的提升。尽管该方法对于信号泄露效果显著，但对于海洋上信号的提取如突发地震信号提取，或位于海陆边界的信号提取等具有一定的限制，推测其原因是解算中的过度约束，相关问题仍需要进一步解决。