四维整体大地测量的有限单元法

FINITE ELEMENT METHOD OF FOURDIMENSIONAL INTEGRATED GEODESY

本文以有限单元法为基础，将四维整体大地测量模型与固体力学方程求解构造应力场结合起来，在四维整体大地测量方程中加入了由地壳构造运动产生的地面点重力变化的观测方程，其中包含测点的位移参数，边界结点上待求参数利用有限单元法在四维整体大地测量平差过程中推估，采用统一的插值函数。将边界结点位移的推估值和实测值一并作为边界约束，由此强化了约束，降低了刚度矩阵的阶数，同时可改善其数学结构，是一种用大地测量资料反演构造应力场的新尝试。最后。

A new method for calculating the tectonic stress field with Finite Element Method of Fourdimensional Integrated Geodesy (FEMFIG) is proposed, and its mathematical models are developed in this paper. The observational equation of temporal gravity changes induced by crustal tectonic movement is derived and it is included in the model of fourdimensional integrated geodesy, besides the GPS, levelling, GPS+levelling and gravity observation equations. FEMFIG combines fundamental equations of solid mechanics with the model of fourdimensional integrated geodesy, which could effectively process the geodetic data and geophysical data. It strengthens the boundary constraints from geodetic data for tectosome by fourdimensional integrated geodesy model, then it can reduce the degrees of stiffness matrix and ameliorate its structure, consequently, it will improve the stability and reliability of solutions for the tectonic stress field.