基于非线性动力学的地震反演方法
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摘要
混沌是非线性动力系统的普遍现象。针对地震反演动力系统中出现的混沌现象 ,提出一种用Lyapunov指数自适应调整控制参数 ,使系统快速向不动点稳定演化的混沌控制反演方法。从最简单的Logistic方程入手 ,探讨非线性动力系统混沌演化过程中控制参数、Lyapunov指数与系统演化的关系 ;建立了用Lyapunov指数进行混沌控制的地震信号反演系统方程。数值模拟结果表明该方法能够有效地控制反演系统中的混沌现象 ,加入噪声后 ,仍然能得到可靠的反演结果。
Chaos is a kind of prevalent phenomenon in a nonlinear dynamic system. Aiming at the chaotic feature of seismic inversion dynamic system, a novel inversion algorithm is proposed. It can make an adaptive control of parameters using Lyapunov exponent and lead the system to evolve to a fixed point rapidly. Beginning at the simplest Logistic Equation, we have discussed the relations among controlling parameter, Lyapunov exponent and evolution process of a nonlinear dynamic system, and a nonlinear inversion equation is developed for seismic signals based on the chaotic control. A numerical simulation shows that this method can effectively control chaotic phenomenon in a nonlinear inversion system. It can provide reliable inversion results even adding noise in.
Chaos is a kind of prevalent phenomenon in a nonlinear dynamic system. Aiming at the chaotic feature of seismic inversion dynamic system, a novel inversion algorithm is proposed. It can make an adaptive control of parameters using Lyapunov exponent and lead the system to evolve to a fixed point rapidly. Beginning at the simplest Logistic Equation, we have discussed the relations among controlling parameter, Lyapunov exponent and evolution process of a nonlinear dynamic system, and a nonlinear inversion equation is developed for seismic signals based on the chaotic control. A numerical simulation shows that this method can effectively control chaotic phenomenon in a nonlinear inversion system. It can provide reliable inversion results even adding noise in.
引文
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2 杨文采.地震道的非线性混沌反演(一).地球物理学报,1993,36(2):223～231
3 杨文采.地震道的非线性混沌反演(二).地球物理学报,1993,36(3):376～387
4 杨磊,张向君,李幼铭.地震道非线性反演的参数反馈控制及效果.地球物理学报,1999,42(5):677～684
5 LiTianyan,YorkeJA .Periodthreeimplieschaos.MathMonthly,America,1975,82:985～992
6DanielKaplan,LeonGlass.Understandingnonlineardynamics.WorldBooksPublishingCompany,1997
7 郝柏林.从抛物线谈起———混沌动力学引论.上海:上海科技教育出版社,1993
8 OttE ,GrebogiC ,YorkeJA .Controllingchaos.PhysicalReview,1990,64:1196～1199
9 RamakrishnaRamaswamy,SudeshnaSinha,NeelimaGupte.Targetingchaosthroughadaptivecontrol.PhysicalReview,1998,57(3)
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