汶川大地震余震等待时间序列——基于混沌理论的研究
|
摘要
根据混沌理论,对汶川大地震余震等待时间通过相空间重构,应用互信息法、Cao方法确定出重构参数,并分别计算了该序列的关联维、最大Lyapunov指数以及Kolmogorov熵等特征量。结果表明汶川大地震余震等待时间序列中存在明显的混沌特性,是非线性混沌动力系统演化的结果;并对余震等待时间序列的混沌性态及其产生的根源进行了简单的探索。研究结果可进一步研究汶川大地震余震等待时间序列的复杂性、演化规律及预测参考。
According to chaos theory,through the waiting time series of aftershocks of Wenchuan earthquake,and the phase space reconstruction,the reconstruction parameters were determined by the application of mutual information and Cao method,and the characteristic quantities as correlation dimension,maximal Lyapunov index and the Kolmogorov entropy were calculated.All the results indicate that there is an obvious chaotic characteristic in the waiting time series of aftershocks of Wenchuan earthquake which is resulted from evolution of the non-linear chaotic dynamic system.Finally,the chaotic behavior of waiting time series of aftershocks and its source were discussed.The research gives a reference to further study on the complexity and evolutionary law of the waiting time series of aftershocks of Wenchuan earthquake.
According to chaos theory,through the waiting time series of aftershocks of Wenchuan earthquake,and the phase space reconstruction,the reconstruction parameters were determined by the application of mutual information and Cao method,and the characteristic quantities as correlation dimension,maximal Lyapunov index and the Kolmogorov entropy were calculated.All the results indicate that there is an obvious chaotic characteristic in the waiting time series of aftershocks of Wenchuan earthquake which is resulted from evolution of the non-linear chaotic dynamic system.Finally,the chaotic behavior of waiting time series of aftershocks and its source were discussed.The research gives a reference to further study on the complexity and evolutionary law of the waiting time series of aftershocks of Wenchuan earthquake.
引文
[1]张培震,徐锡伟,闻学泽,等.2008年汶川8.0级地震发震断裂的滑动速率、复发周期和构造成因[J].地球物理学报,2008,51(4):1066-1073.
[2]徐锡伟,闻学泽,于慎鄂.汶川M8.0地震地表破裂及其发震构造讨论[J].地震地质,2008,30(3):597-629.
[3]谷继成,谢小碧,赵莉.强余震的时间分布特征及其理论解释[J].地球物理学报,1979,22(1):32-46.
[4]秦乃岗.广东及邻区地震频度衰减系数和余震等待时间[J].华南地震,1990,10(4):42-49.
[5]王勤彩,陈章立,郑斯华.汶川大地震余震序列震源机制的空间分段特征[J].科学通报,2009,54(16):2348-2354.
[6]Abe S,Suzuki N.Aging and scaling of earthquake aftershocks[J].Physica A,2004,332:533-538.
[7]Caccamo D,Barbieri F M,LaganàC,et al.The temporal series of the New Guinea 29 April 1996 aftershock sequence[J].Physics of the Earthand Planetary Interiors,2005,153(4):175-180.
[8]Telesca L,Cuomo V,Lapenna V,et al.Analysis of the temporal properties of Greek aftershock sequences[J].Tectonophysics,2001,341(1-4):163-178.
[9]D'Amico S,Cacciola M,Parrillo F,et al.Heuristic advances in identifying aftershocks in seismic sequences[J].Computers&Geosciences,2009,35(2):245-254.
[10]吕金虎,陆君安,陈士华,等.混沌时间序列分析及其应用[M].武汉:武汉大学出版社,2002.106-108.
[11]Takens F.Detecting strange attractors in turbulence[J].Lecture Notes in Math.,1981,898:366-381.
[12]汪慰军,吴昭同,陈进,等.基于伪相图的大机组非线性故障诊断技术[J].上海交通大学学报,2000,34(9):1261-1264.
[13]Packard N H,Crutchfield J P,Farmer J D,et al.Geometry From aTime Series[J].Physical Review Letters,1980,45(9):712-716.
[14]修春波,刘向东,张宇河.相空间重构延迟时间与嵌入维数的选择[J].北京理工大学报,2003,23(2):219-224.
[15]马红光,李夕海,王国华等.相空间重构中嵌入维和时间延迟的选择[J].西安交通大学学报,2004,38(4):335-338.
[16]胡晓棠,胡茑庆,陈敏.一种新的选择相空间重构参数的方法[J].振动工程学报,2001,14(2):242-244.
[17]Fraser A M,Swinney H L.Independent coordinates for strange attractors from mutual in formation[J].Physical Review A,1986,33(2):1134-1140.
[18]吕小青,曹彪,曾敏,等.确定延迟时间互信息法的一种算法[J].计算物理,2006,23(2):184-188.
[19]Kennel M B,Brown R,Abarbanel H D I.Determinating embedding dimension for phase-space reconstruction using a geometrical construction[J].Physical Review A,1992,45(6):3403-3411.
[20]Cao L.Practical method for determining the minimum embedding dimension of a scalar time series[J].Physica D,1997,110(1-2):43-50.
[21]李国良,付强,冯艳,等.基于混沌的三江平原月降水时间序列分析[J].数学的实践与认识,2007,37(6):76-81.
[22]黄润生,黄浩.混沌及其应用[M].武汉:武汉大学出版社,2000.198-202.
[23]Panas E,Ninni V.Are oil markets chaoticA non-lineardynamic analysis[J].Energy Economics,2000,22(5):549-568.
[24]Grassberger P,Procaccia I.Measuring the strangeness of strange attractor[J].Physica D,1983,9(1-2):189-208.
[25]Eckman J P,kamphorst S O,Ruelle D,et al.Lyapunov exponents from a time serises[J].Physical Review A,1986,34(4):4971-4980.
[26]Wolf A,Swift J B,Swinny H L,et al.Determining Lyapunov exponents from a time serises[J].Physica D,1985,16(3):285-317.
[27]Rosenstein M T,Collins J J,De Luca C J.A practical method for calculating largest Lyapunov exponents from small data sets[J].Physical D,1993,65(1-2):117-134.
[28]Galganil B G,Strelcyn J M.Kolmogorov entropy and numerical experiments[J].Physical Review A,1976,14(3):2338-2345.
[29]Cohen Av,Procaccia I.Computing the Kolmogorov entropy from a time signals of dissipative and conservative dynamical systems[J].PhysicalReview A,1985,31(3):1872-1880.
[30]Gassberger P,Procaccia L.Estimical of the Kolmogorov entropy from a chaotic signals[J].Physical Review A,1983,28(4):2591-2593.
[31]Mandelbrot B B.Fractals:form,chance and dimension[M].San Frareiso:Freeman W H,1977.56-85.
[32]马建华,管华.系统科学及其在地理学中的应用[M].北京:科学出版社,2003.134.
[33]张济忠.分形[M].北京:清华大学出版社,1995.142.
[2]徐锡伟,闻学泽,于慎鄂.汶川M8.0地震地表破裂及其发震构造讨论[J].地震地质,2008,30(3):597-629.
[3]谷继成,谢小碧,赵莉.强余震的时间分布特征及其理论解释[J].地球物理学报,1979,22(1):32-46.
[4]秦乃岗.广东及邻区地震频度衰减系数和余震等待时间[J].华南地震,1990,10(4):42-49.
[5]王勤彩,陈章立,郑斯华.汶川大地震余震序列震源机制的空间分段特征[J].科学通报,2009,54(16):2348-2354.
[6]Abe S,Suzuki N.Aging and scaling of earthquake aftershocks[J].Physica A,2004,332:533-538.
[7]Caccamo D,Barbieri F M,LaganàC,et al.The temporal series of the New Guinea 29 April 1996 aftershock sequence[J].Physics of the Earthand Planetary Interiors,2005,153(4):175-180.
[8]Telesca L,Cuomo V,Lapenna V,et al.Analysis of the temporal properties of Greek aftershock sequences[J].Tectonophysics,2001,341(1-4):163-178.
[9]D'Amico S,Cacciola M,Parrillo F,et al.Heuristic advances in identifying aftershocks in seismic sequences[J].Computers&Geosciences,2009,35(2):245-254.
[10]吕金虎,陆君安,陈士华,等.混沌时间序列分析及其应用[M].武汉:武汉大学出版社,2002.106-108.
[11]Takens F.Detecting strange attractors in turbulence[J].Lecture Notes in Math.,1981,898:366-381.
[12]汪慰军,吴昭同,陈进,等.基于伪相图的大机组非线性故障诊断技术[J].上海交通大学学报,2000,34(9):1261-1264.
[13]Packard N H,Crutchfield J P,Farmer J D,et al.Geometry From aTime Series[J].Physical Review Letters,1980,45(9):712-716.
[14]修春波,刘向东,张宇河.相空间重构延迟时间与嵌入维数的选择[J].北京理工大学报,2003,23(2):219-224.
[15]马红光,李夕海,王国华等.相空间重构中嵌入维和时间延迟的选择[J].西安交通大学学报,2004,38(4):335-338.
[16]胡晓棠,胡茑庆,陈敏.一种新的选择相空间重构参数的方法[J].振动工程学报,2001,14(2):242-244.
[17]Fraser A M,Swinney H L.Independent coordinates for strange attractors from mutual in formation[J].Physical Review A,1986,33(2):1134-1140.
[18]吕小青,曹彪,曾敏,等.确定延迟时间互信息法的一种算法[J].计算物理,2006,23(2):184-188.
[19]Kennel M B,Brown R,Abarbanel H D I.Determinating embedding dimension for phase-space reconstruction using a geometrical construction[J].Physical Review A,1992,45(6):3403-3411.
[20]Cao L.Practical method for determining the minimum embedding dimension of a scalar time series[J].Physica D,1997,110(1-2):43-50.
[21]李国良,付强,冯艳,等.基于混沌的三江平原月降水时间序列分析[J].数学的实践与认识,2007,37(6):76-81.
[22]黄润生,黄浩.混沌及其应用[M].武汉:武汉大学出版社,2000.198-202.
[23]Panas E,Ninni V.Are oil markets chaoticA non-lineardynamic analysis[J].Energy Economics,2000,22(5):549-568.
[24]Grassberger P,Procaccia I.Measuring the strangeness of strange attractor[J].Physica D,1983,9(1-2):189-208.
[25]Eckman J P,kamphorst S O,Ruelle D,et al.Lyapunov exponents from a time serises[J].Physical Review A,1986,34(4):4971-4980.
[26]Wolf A,Swift J B,Swinny H L,et al.Determining Lyapunov exponents from a time serises[J].Physica D,1985,16(3):285-317.
[27]Rosenstein M T,Collins J J,De Luca C J.A practical method for calculating largest Lyapunov exponents from small data sets[J].Physical D,1993,65(1-2):117-134.
[28]Galganil B G,Strelcyn J M.Kolmogorov entropy and numerical experiments[J].Physical Review A,1976,14(3):2338-2345.
[29]Cohen Av,Procaccia I.Computing the Kolmogorov entropy from a time signals of dissipative and conservative dynamical systems[J].PhysicalReview A,1985,31(3):1872-1880.
[30]Gassberger P,Procaccia L.Estimical of the Kolmogorov entropy from a chaotic signals[J].Physical Review A,1983,28(4):2591-2593.
[31]Mandelbrot B B.Fractals:form,chance and dimension[M].San Frareiso:Freeman W H,1977.56-85.
[32]马建华,管华.系统科学及其在地理学中的应用[M].北京:科学出版社,2003.134.
[33]张济忠.分形[M].北京:清华大学出版社,1995.142.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心