一维大地电磁信赖域反演法研究  

A study of one-dimensional magnetotelluric sounding inversion using the trust region algorithm

作　　者：曾奇[1] 师学明[1] 武永胜[1] 王家映[1] 

机构地区：[1]中国地质大(武汉)地球物理与空间信息学院,武汉430074

出　　处：《地球物理学进展》2011年第3期885-893,共9页Progress in Geophysics

基　　金：国家自然科学基金(40204007)项目资助

摘　　要：信赖域算法是一种线性化的最优化算法,该算法在每次迭代时强制性地要求新的步长不超过某一控制量,这等价于在以当前迭代点为中心的一个邻域内对一个近似于原问题的近似模型求极值,从而提高了算法的稳定性.将信赖域算法引入到层状介质大地电磁数据的反演,得到了一维层状介质的信赖域反演法.数值试验结果发现该算法收敛性强,收敛速度快.抗噪音试验的结果表明,该方法具有较强的抗噪能力.通过典型测试函数和层状介质大地电磁模型数值试验,结果表明,信赖域算法迭代次数少,收敛速度快.但是和其它很多线性化最优化方法一样,信赖域方法对初始模有依赖性,而且容易陷入局部极小值,必须通过取多个初始模型,来排除陷入局部极小值的情况.因此建议与其它线性、非线性的反演方法相结合,发展混合优化算法.The trust region algorithm is a linear optimization algorithm. In this method the size of a new step does not exceed a certain control variable at each iteration. This is equivalent to searching for the minimum point of a similar model around the current point. Therefore, the stability of the algorithm is enhanced. In this paper, in order to find a new and a more effective algorithm for magnetotellurie data inversion, we introduced the trust region algorithm into magnetotellurie data inversion for layered media. Numerical experiment results show strong convergence of the algorithm. Anti-noise test results show that the method has strong anti-noise ability. It also has good result in numerical experiments of test function and theoretical magnetotelluric models. However, like many other linear optimization methods, the trust region method is dependent on the initial model, and is easy to fall into local minimum. It is necessary to take many different initial models to avoid local minimum. Therefore, it is a good choice to combine the trust region method with other linear or non-linear inversion method to create a more effective methods.

关 键 词：大地电磁 信赖域算法 反演 最优化 

分 类 号：P318[天文地球—固体地球物理学]