跨孔地震CT中的逐次线性化方法

SUCCESSIVE LINEARIZATION METHOD IN CROSS-HOLE TOMOGRAPHY

非线性问题的逐次线性化方法的每个线性化过程可通过最小二乘ＱＲ分解算法求解．为了精确地描述和控制逐次线性化迭代过程，引入迭代阻尼系数．首先根据模型拟合表最小的准则确定满足最佳一次线性化效果的最佳初始迭代阻尼系数；然后随遂次线性化迭代而减小迭代阻尼系数，并加入松弛因子对每次迭代输出的波速修正量进行控制；最后根据混沌理论，采用Ｌｙａｐｕｎｏｖ指数和模型拟合差的变化，描述第ｋ次迭代所处的状态，在解估计的方差急增之前及时停止迭代，获得可信度和分辨率最佳的解估计．模型计算与实例证明方法有效．

This paper discusses the realizing technique of the successive linearization method.Each linearizing process of the successive linearization method of the nonlinear problem can be solved by least square QR algorithm.In order to describe and control the successive linearization process accuratly,the iterative damping factor is introduced.First,determining the oPtimal initial iterative damping factor to satisfy optimal once linearization result according to the criterion of the minimization of model fitting error;then the iterative damping factor reduced with iterative numbers,meanwhile,the relaxation factor is introduced to control the increment of each iterative output.Based on chaos theory,the state of k'th iteration can be described by Lyapunov exponent and model derivation,if iteration stopped before the variance sharp incresment,the estimated solution of optimal reliability and resolution an be obtained.The efficiency of the method have been proved by modeling andexamples.