Spherical gravitational curvature boundary-value problem
Spherical gravitational curvature boundary-value problem
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DOI：
10.1007/s00190-016-0905-x
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发表时间：
2016-05
影响因子：
4.4
通讯作者：
M. Šprlák;P. Novák
中科院分区：
文献类型：
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作者：
M. Šprlák;P. Novák
地球引力场的标量、矢量和二阶张量参数值已被大地测量学和地球物理学中的各种传感器收集。这些可观测量已广泛应用于引力场建模的不同参数化方法中。此外，这些量的理论方面已被广泛研究和充分理解。另一方面，用于观测引力曲率（即三阶引力张量的组成部分）的新传感器目前正在开发中。由于引力曲率代表了新型可观测值，因此利用它们对地球引力场进行建模是本研究的一个主题。首先，将引力曲率张量分解为六部分，并用三阶张量球谐函数展开。其次，在谱域和空间域中对四种引力曲率组合定义的引力曲率边值问题进行了公式化和求解。第三，研究了相应的子积分核的性质。所提出的数学公式揭示了引力曲率的一些重要性质，并扩展了所谓的迈斯尔方案，即与地球引力场的各种参数相关的重要理论框架。
Values of scalar, vector and second-order tensor parameters of the Earth’s gravitational field have been collected by various sensors in geodesy and geophysics. Such observables have been widely exploited in different parametrization methods for the gravitational field modelling. Moreover, theoretical aspects of these quantities have extensively been studied and well understood. On the other hand, new sensors for observing gravitational curvatures, i.e., components of the third-order gravitational tensor, are currently under development. As the gravitational curvatures represent new types of observables, their exploitation for modelling of the Earth’s gravitational field is a subject of this study. Firstly, the gravitational curvature tensor is decomposed into six parts which are expanded in terms of third-order tensor spherical harmonics. Secondly, gravitational curvature boundary-value problems defined for four combinations of the gravitational curvatures are formulated and solved in spectral and spatial domains. Thirdly, properties of the corresponding sub-integral kernels are investigated. The presented mathematical formulations reveal some important properties of the gravitational curvatures and extend the so-called Meissl scheme, i.e., an important theoretical framework that relates various parameters of the Earth’s gravitational field.