构造应力场边界载荷反演的有限元逆逼近法

构造应力场问题的边界条件、加载方式是地应力场分析的难题，由于构造运动未知和地质构造复杂，无法直接求解。边界力反演是进行构造应力场研究的重要手段。从弹性力学基本方程出发，针对油气储层地应力场反问题，结合对区域构造应力场认识，利用阻尼最小二乘法建立了应力场反演的约束模型，提出了一种用于反演构造应力场边界力的反分析方法，该方法根据部分实测点的应力值进行边界力反演，并与有限元方法和有限差分法相结合，以边界力为参量逼近目标函数。根据研究区少量地应力实测资料采用该方法进行最优化计算，使得计算应力场与实测应力达到最优拟合，以弥补目前的回归反演方法和边界载荷调整法的不足来提高计算精度。算例表明了该方法的有效性，可用于解决构造应力场边界力的反演问题。

Finite element inverse analysis of boundary load for tectonic stress field

Tectonic stress analysis is particular important in the course of petroleum exploration and development. The geological structure complexity, its boundary problem, the loading paths, etc. are difficult problems in the numerical simulation of tectonic stress field; and the field stress data is very limited. Because of the unknown tectonic movement and complicated geological structure, tectonic stress field cannot be calculated immediately. The boundary load inversion is a particular important means for tectonic stress field analysis. Starting from the fundamental equations of elastic mechanics, the inverse problem of tectonic stress field of oil-gas reservoirs is proposed. Based on the least square method, a method is presented to identify and calculate inversely the boundary load on the geological model by the stresses in the geological model. The finite element method and the finite difference method are combined to apply the method that chooses the boundary loads as fitting parameters in the objective function. The calculated results are in good agreement with the in-situ measured data. This method has excellent practical value and can provide references to the back analysis of tectonic stress field. This method and model can get over the shortage of common back analysis method such as adjusting boundary loads and regression method; so it can calculate exactly the tectonic stress field by back analysis. The results show that the method is simple, credible and has high precision and rapid calculation velocity. Therefore, it may find its uses in the boundary load inversion of tectonic stress field. This method can provide references to petroleum exploration and production.