Temporal variations in the Earth's gravity field can be used for monitoring of lithospheric deformations The network of continuously-operating gravity stations is required for this purpose but a global coverage by such network is currently extremely sparse Temporal variations in long-wavelength part of the Earth's gravity field have been, however, observed by two satellite missions, namely the Gravity Recovery And Climate Experiment (GRACE) and the GRACE Follow-On (GRACE-FO) These satellite gravity observations can be used to study long-wavelength deformations of the lithosphere Consequently, considering the lithosphere as a spherical elastic shell and solving the partial differential equation of elasticity for it, the stress, strain and displacement inside the lithosphere can be estimated The lower boundary of this shell is assumed to be stressed by mantle convection, which has a direct relation to the Earth's gravity field according to Runcorn's theory Changes in gravity field lead to changes in the sub-lithospheric stress and the stress propagated throughout the lithosphere In this study, we develop mathematical models in spherical coordinates for describing the stress propagation from the sub-lithosphere through the lithosphere We then organise a system of observation equations for finding a special solution to the boundary-value problem of elasticity in the way that provides a stable solution In contrast, models presented in previously published studies are ill-posed Furthermore, we use constants of the solution determined from the boundary stresses to determine the strain and displacements leading to these stresses, while in previous studies only the stress has been considered according to rheological properties of the lithosphere We demonstrate a practical applicability of this theoretical model to estimate the stress-strain redistribution caused by the Sar-e-Pol Zahab 2018 earthquake in Iran by using the GRACE-FO monthly solutions

中文翻译：

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GRACE-FO 时变重力引起的岩石圈应力、应变和位移变化：2018 年 Sar-e-Pol Zahab 地震的案例研究

地球重力场的时间变化可用于监测岩石圈变形 为此目的需要连续运行的重力站网络，但此类网络的全球覆盖目前极为稀疏 地球重力长波长部分的时间变化然而，两个卫星任务已观测到该领域，即重力恢复和气候实验 (GRACE) 和 GRACE 后续 (GRACE-FO) 这些卫星重力观测可用于研究岩石圈的长波长变形 因此, 将岩石圈视为球形弹性壳并求解其弹性偏微分方程, 应力,可以估计岩石圈内的应变和位移 假设该壳层的下边界受到地幔对流的压力，根据朗科恩的理论，这与地球重力场有直接关系 重力场的变化导致亚岩石圈的变化应力和整个岩石圈传播的应力 在这项研究中，我们开发了球坐标中的数学模型，用于描述从亚岩石圈到岩石圈的应力传播 然后我们组织了一个观测方程系统，以找到边界值的特殊解以提供稳定解决方案的方式弹性问题相比之下，先前发表的研究中提出的模型是不适定的 此外，我们使用由边界应力确定的解的常数来确定导致这些应力的应变和位移，而在以前的研究中，根据岩石圈的流变特性只考虑了应力 我们证明了该理论模型的实际适用性来估计使用 GRACE-FO 月度解法分析由 2018 年伊朗 Sar-e-Pol Zahab 地震引起的应力应变重新分布