地震道的非线性混沌反演——Ⅰ.理论和数值试验

NONLINEAR CHAOTIC INVERSION OF SEISMIC TRACES:(I)THEORY AND NUMERICAL EXPERIMENTS

全文以地震道反演的数值实验为例,根据混沌理论讨论了非线性地震反演的以下特性:1.对于带误差的地震数据和极其平滑的初始模型,逐次线性化的迭代过程产生的输出序列最终走向无序,这是非线性反演系统本身的特性决定的;2.迭代(非线性反演)系统是由Poin-care映的或系统方程描述的;3.可以根据地震反问题的特点,用多种不同的方法定义相应的Lyapunov指数,它们的数值和组合是非线性反演系统状态的有效指示;4.取决于系统参数的选取,发现在二维相空间有奇异吸引子的对应物.总之,从混沌理论的角度来研究纯数学的非线性地震反问题,可以揭示某些过去鲜为人知的内在规律性.本文为全文的上篇,主要讨论前两个问题,即理论和地震道反演数值试验结果.

Based on the deterministic chaos theory and demonstrated by carefully selected numerical experiments, following characteristics of nonlinear seismic inversions are revealed: 1. for smooth initial models and erroneous seismic data, the output sequences produced by the successive linearization iteration will finally become disorder; the nonlinearity of the iteration system is responsible for this behavior. 2. The nonlinear iteration is controlled by the Poincare map or the system equation. 3. Corresponding Lyapunov exponents can be defined by more than one ways suitable for seismic inverse problems, they are effective indicators of iteration system states. 4. If the damping parameter varies during the iteration then attractors, looking like strange attractors, can be found in the phase space.The study of nonlinear inversion from the angle of chaos gives us valuable insights into the nonlinear inverse problems. This is the first part of the complete paper and deals with the first two aspects, i.e., the theory and the numerical experiments.