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《Chinese Journal of Geophysics》 1993-02
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NONLINEAR CHAOTIC INVERSION OF SEISMIC TRACES:(I)THEORY AND NUMERICAL EXPERIMENTS

YANG WEN-CAI(Institute of Geophysical & Geochemlcal Exploration Ministry of Geology and Mineral Resources, Langjang 102849)  
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.
【Fund】: 国家自然科学基金委员会、中国科学院、中国石油天然气总公司和大庆石油管理局联合资助
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