基于广义逆的层析成像反演方法研究

为了解决常规反演算法收敛速度慢、无法处理不完全投影和先验信息等问题.提出基于广义逆的层析成像反演方法,将广义逆和求解一般方程组的理论统一起来.阻尼系数的确定是此类反演算法的关键,在分析解估计评价指标与阻尼系数关系的基础上,提出阻尼系数的最优化技术,在多目标优化的框架下,采用理想点法求解,分别对核心异常模型和复合模型进行了数值仿真计算,结果表明该阻尼系数优选方法对初始值不敏感,所得阻尼系数合理,反演结果与原设定模型具有较高的相关性,比常规反演算法有更高的求解效率和精度.

Study on inversion methods for travel time tomography based on generalized inverse theory

Conventional inversion methods of computer tomography (IMCT) have low convergence rates, and cannot deal with prior information and incomplete projection problems. To improve their robustness, firstly, a new IMCT based on generalized inverse theory was proposed for solving the inversion equation system. Then, a multi-objective optimization problem was constructed and resolved using the ideal point method to avoid another bottleneck in the conventional IMCT, i.e., finding an optimum damping coefficient. Two numerical examples were modeled to validate the above-devised two measures. It was shown that the optimal methodology is insensitive to the initial values of damping coefficient, and that the proposed IMCT is more effective and accurate than the conventional ones.