| 非线性地震道的混沌反演——Ⅱ.关于Lyapunov指数和吸引子 |
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| 引用本文： | 杨文采.非线性地震道的混沌反演——Ⅱ.关于Lyapunov指数和吸引子[J].地球物理学报,1993(3). |
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| 作者姓名： | 杨文采 |
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| 作者单位： | 地质矿产部地球物理地球化学勘查研究所 河北省廊坊 |
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| 摘 要： | 在本文上篇《非线性地震道的混沌反演——1.理论和数值试验》中讨论了非线性反问题逐次线性化方法及迭代过程的系统特性、递推法和广义线性反演法输出波阻抗序列的特征。本篇参照混沌理论中关于Lyapunov指数、相空间和吸引子的概念,深入研究逐次线性化迭代的状态变化的阶段性及其定量描述.当引用相空间描述系统的演化时,对于随迭代变化的阻尼因子可以发现几种吸引子.最后,总结了非线性地震混沌反演的要点,指出非线性反演迭代的复杂阶段性要川混沌理论来描述,而Lyapunov指数等才是控制迭代过程的实质性参数.
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| 关 键 词： | 非线性反问题 混沌 地震反演 Lyapunov指数 吸引子 |
NONLINEAR CHAOTIC INVERSION OF SEISMIC TRACES: II. LYAPUNOV EXPONENTS AND ATTRACTORS |
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| YANG WEN-CAI.NONLINEAR CHAOTIC INVERSION OF SEISMIC TRACES: II. LYAPUNOV EXPONENTS AND ATTRACTORS[J].Chinese Journal of Geophysics,1993(3). |
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| Authors: | YANG WEN-CAI |
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| Abstract: | In part one of this paper, I has discussed the successive linearization methods- system characteristics of the inversion iteration, the recursive method and the generalized linear inversion of seismic traces together with the features of output sequences of acoustic impedance, this part of the paper continues to discuss the Lyapunov exponents and the attractors in the phase space in nordinear chaotic inversions. Based on chaos concepts, I define the lyaounov exponents for nonlinear Iteration of seismic inversion which are indeed excellent indicators of the system state and the iteration stages. When the phase space is reconstructed, I find that "phase changes" can occur during the iteration if the damping factor varies. Abnormal attractors are revealed in the numerical experiments. Finally some conclusions and suggestions for the chaotic inversion of seismic traces are proposed, such as the iteration is characterized by complicated stages which should be described by the chaos theory; Lyapuniv exponents are the essential control parameters for the iteration, etc. |
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| Keywords: | Nonlinear inverse problem Chaos Seismic inversion Lyapunov exponents Auractors |
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