弹性动力学反问题的非线性及其迭代反演

分析了弹性动力学反问题的非线性及在迭代反演过程中表现出的复杂非线性现象。迭代反演的结果依赖于反演系统参数和迭代初值，而系统参数对应的Mandelbrot集和迭代初值对应的Julia集都是复杂的分形集。随反演系统状态参数的变化，完全确定性的反演系统却可能产生一系列无规则的，不可预测的迭代输出序列。反演迭代过程中出现的分形和混沌现象反映了表面简单的反演迭代后隐藏的复杂性，正是这种复杂性给迭代系统参数的合理选择带来困难，进而使反演迭代不总能给出满意的结果。

NONLINEAR CHARACTERISTICS OF ELASTODYNAMICS INVERSE PROBLEM AND ITERATIVE APPROACH

Nonlinear characteristics of elastodynamics inverse problem and the nonlinear phenomena shown in iterative approach are analyzed. The results of iterative inversion depend strongly upon the initial value and system parameters and the Mandelbrot sets of system parameter and Julia sets of initial value are both fractal sets. It is possible that iterative results of a deterministic system may become irregular, random and unpredicable when the system parameter takes some special values. The phenomena imply that iterative sequences have become out-of-order or chaos. The nonlinear phenomena of fractal nature and chaos appearing in the iterative inverse process reflect the hidden complexity although the iterative algorithm is superficially simple. It is just the complexity that makes the right selection of system parameters difficult and the results from the iterative inverse method unsatisfied sometime.