球坐标系中图形单元应变与旋转张量及其误差解算

利用泰勒级数展开和弹性力学的几何方程，推导了球坐标系中由GPS位移数据解算图形单元应变和旋转张量的解析公式. 通过线性化处理，并利用误差传播定律，详细推导了图形单元应变和旋转张量的误差公式. 利用川滇地区最新的GPS测站位移速率数据，采用图形单元法解算了该区的面应变率及最大剪切应变率分布，并对其进行了初步的分析. 同时阐述了图形单元应变数学模型的局限性，讨论了图形单元法计算应变的意义以及图形单元的选择问题，进一步分析了应变计算的定权方法，还讨论了GPS观测网图形单元的地心半径差异与应变的关系问题. 

Computation of strain and rotation tensor and their uncertainty for small arrays in spherical coordinate system

Based on Taylor series expansion and strain component expressions in elastic mechanics, we derive the formula of strain and rotation tensor for small arrays in spherical coordinate system. By linearization process of the formula, we also derive the expressions of strain components and Euler vector uncertainty, respectively for subnets using the law of uncertainty propagation. Taking GPS velocity field in Sichuan--Yunnan region as an example, we compute the area strain rate and maximum shear rate using the above procedure, and their characteristics are preliminarily explored. Limits of mathematical strain model for small arrays are also discussed. We make detailed explanations on the small array method and the choice of small arrays. How to set the weight of GPS observations are further discussed. Moreover, the relationship between strain and radius of GPS subnets is also analyzed.