大震过程中地壳形变的混沌和多重分形特征及其预报意义
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摘要
以地壳形变中地倾斜观测为例，用常熟观测台石英摆地倾斜仪记录到的1995年7月1日至1997年6月30日SN测向的观测数据作为研究的原始资料，采用时间延迟相空间重构法计算并研究了1996年11月9日南黄海Ms6．1级地震前后地倾斜系统混沌吸引子的关联维数D2、二阶熵K2和最大Lyanunov指数λ1，并用推广GP法和数盒子法研究了地震前后系统多重分形的广义维数谱Dq和奇异性谱f（α）．研究结果表明：地倾斜系统为混沌系统，系统的自由度在2～14之间；地震过程中系统有降维减熵现象；震前广义维数谱Dq左半边曲线变陡，奇异性谱f（α）曲线中α的取值范围增大，曲线右端下降．研究结果对认识大震过程中地壳形变的非线性动力学特征和利用这些特征进行地震预报具有重要的参考价值．
With the observational ground tilt data in the NE direction which is recorded from 1 July 1995 to 30 June 1997 by the horizontal pendulum tiltmeter at Changsu Station, the correlation dimension D2 and ordepe-2 Renyi entropy K2 as well as the largest Lyapunov exponent λ1 of the strange attractors of the ground tilt system before and after South Yellow Sea earthquake (Ms 6.1) in 9 November 1996 are calculated and studied with the time-delay phase space reconstruction algorithm, besides, the generalized fractal dimension spectrum Dq and singularity spectrum f(α) before and after the earthquake are also calculated and studied with the generalized Grassberger-Procaccia algorithm and the box-counting algorithm. It is indicated that the ground hit system is a chaotic system, the freedom degree of which is within the range of 2～14, and the dimension and entropy of the system declines before the earthquake. It is also indicaTed that the left half of the generalized fractal dimension spectrum Dq curve appears steep, the a value variation range of the singularity spectrum f(α) curve increases, and the right end of the curve declines before the earthquake. The conclusion on this research can be of great reference value to recognizing the nonlinear dynamic features of the crustal deformation and its application in earthquake prediction.
With the observational ground tilt data in the NE direction which is recorded from 1 July 1995 to 30 June 1997 by the horizontal pendulum tiltmeter at Changsu Station, the correlation dimension D2 and ordepe-2 Renyi entropy K2 as well as the largest Lyapunov exponent λ1 of the strange attractors of the ground tilt system before and after South Yellow Sea earthquake (Ms 6.1) in 9 November 1996 are calculated and studied with the time-delay phase space reconstruction algorithm, besides, the generalized fractal dimension spectrum Dq and singularity spectrum f(α) before and after the earthquake are also calculated and studied with the generalized Grassberger-Procaccia algorithm and the box-counting algorithm. It is indicated that the ground hit system is a chaotic system, the freedom degree of which is within the range of 2～14, and the dimension and entropy of the system declines before the earthquake. It is also indicaTed that the left half of the generalized fractal dimension spectrum Dq curve appears steep, the a value variation range of the singularity spectrum f(α) curve increases, and the right end of the curve declines before the earthquake. The conclusion on this research can be of great reference value to recognizing the nonlinear dynamic features of the crustal deformation and its application in earthquake prediction.
引文
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[14]朱令人,周仕勇,杨马陵等.对强震前地震分形谱异常的研究,地震学报,1997,19(3):331～333.
[2]陈 等.分形与浑沌在地球科学中的应用.北京:学术期刊出版社,1989,85～111.
[3]王赤,陈金波,王水.地球变化磁场的分形和混沌特征.地球物理学报,1995,38(1):16～24.
[4]王卫国,谢应齐,邱金桓等.北半球不同纬度吴氧层系统混沌吸引子的特征研究.地球物理学报,1997,40(3):317～323.
[5]朱传镇,王琳瑛,前震活动特征及其识别的研究(Ⅰ).地球物理学报,1996,39(1):80～88.
[6]陈 .分形几何与地球科学.华南地震, 1996, 16(1): 71～77.
[7]Takens,F,Dgnamical Systems and Turbulence.Berlin: Spnnger-Veriag, 1981, 366～391.
[8]Grassberger,P,Procaccia.J, Dimensions and Entropies of Strange Attractors from A Fluctuating Dynamics Approach.Physica D, 1984. 13: 34 ～54.[9] Wolf A, Swift.J.B.. Swinney. H.L..et al. Determining Lyapunov Exponents from A Time Series. Physica D, 1985,16:285～317.
[10]杨展如.分形物理学.上海:上海科技教育出版社,1996,162～203.
[11]Grassbetger,P.Generalized Dimensions of Strange Attractors .Phys.Lett, 1983, 97A: 227～320.
[12]Halsey,T.C,Jenson,M.H, Fractal Messures and Their Singularities: The Characterization of Strange Sets.Phys.Rev.A,1986.33: 1141 ～1151.
[13]郑兆芯,张军.小震空间分布奇异性谱f(α)研究.中国地震,1994,10(4):371～377.
[14]朱令人,周仕勇,杨马陵等.对强震前地震分形谱异常的研究,地震学报,1997,19(3):331～333.
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