地震活动“密集—平静”现象的混沌特性探讨
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摘要
把概率论方法与Logistic方程结合起来,采用随机变量(X)分布的统计参量:即变异系数Cv、偏态系数γ1、峰态系数2γ、信息熵H(X)和h*量值以及分数维维数D0*和D1*等参量,探讨了定量描述"密集—平静"不均匀分布现象和判断系统处于平衡状态和非平衡状态的方法。研究认为:地震活动性异常的实质是X的概率分布由单峰型(平衡状态)转为双峰型或多峰型(非平衡状态)分布,可以由上述参量尤其是γ2和h*量值的综合分析来区分。对于"密集—平静"的前震序列和强余震发生前的序列,这种转变可以由"时间分支行为"来解释;并且提出了根据有震(X≥1)和无震(X=0)两种定态的时段之比,来判断前震序列的一种简易方法。中国大陆M≥7.0地震年频度分布存在双峰型分布特征,可能说明中国大陆M≥7.0地震活动处于远离力学平衡状态。一个大地震在其发生演化过程中,地震活动及前兆现象经历了从弹性应变积累阶段的无序状态(表现为单峰型的泊松过程)到非弹性应变中期阶段的有序状态(有序的自组织结构,表现为双峰或多峰型),再到短临阶段的无序状态。这时出现各种异常现象的同步变化被显著破坏为特征的混沌状态,系统不可逆转地被推向失稳状态;触发因素在这时起重要作用,将引发大地震发生,使系统进入应变能大释放和长期衰减的新状态,而后开始新一轮孕育过程。对于地震及其前兆所具有的这种现象,似乎不可能在纯力学的基础上探索研究,而应该视为在远离平衡条件下非线性动力学体系一般性问题的组成部分。这种认识本身的深化可能就是地震预报研究领域一个重要的突破点。
Combining the probability theory method with the Logistic equation,we explored methods trying to describe the swarm-equanimity phenomenon quantitatively and judge the system in equilibrium state or not by some statistical parameters of variant(X) distribution,i.e.the variation coefficient Cv,skewness coefficient γ1,kurtosis coefficient γ2,the information entropy H(X) and h* quantity value and fractal dimension D*0,D*1.It is believed that the substance of the earthquake activity anomaly is actually the statistical distribution of X transforming from single-peak distribution(equanimity state) to two-or more-peak distribution(non-equanimity state) which can be distinguished by integratedly analyzing the above described statistical parameters,especially the γ2 and h*.The transformation for fore earthquake sequence and ex-sequence of strong aftershock can be explained by "time branch behavior".We propose a simple method to estimate fore earthquake sequence type by the ratio of time period with earthquake(X≥1) to that without earthquake(X=0).The two-peak distribution characteristics of yearly frequency for M≥7.0 earthquake in Mainland China may show that M≥7.0 earthquakes activity in the area is far from equanimity state.In the period of a strong earthquake evolvement,the seismic activity and precursor phenomenon undergo from disordered state at elastic strain accumulation step(shows single-peak Poison procedure) to ordered state at mid-term of non-elastic strain accumulation step(self-organize structure order,shows two or more peak distribution),and then to disordered state at imminent step.At this step,the chaos appears which is characterized by that synchronal anomalies are being disrupted obviously,and the system is inevitable falling into unstable state.Trigger factor is very important at this time and would cause strong earthquake occurrence,which makes the system release strain energy largely and long term attenuation.After that,it begins a new run for seismogenic period.The phenomenon of earthquake activity and its precursor seems impossible to study based on pure mechanics theory,it should be thought as a compositional part of non-linear geodynamics system that is far away from equilibrium state.The effort to deepen this cognition maybe is a breakthrough in earthquake prediction realm.
Combining the probability theory method with the Logistic equation,we explored methods trying to describe the swarm-equanimity phenomenon quantitatively and judge the system in equilibrium state or not by some statistical parameters of variant(X) distribution,i.e.the variation coefficient Cv,skewness coefficient γ1,kurtosis coefficient γ2,the information entropy H(X) and h* quantity value and fractal dimension D*0,D*1.It is believed that the substance of the earthquake activity anomaly is actually the statistical distribution of X transforming from single-peak distribution(equanimity state) to two-or more-peak distribution(non-equanimity state) which can be distinguished by integratedly analyzing the above described statistical parameters,especially the γ2 and h*.The transformation for fore earthquake sequence and ex-sequence of strong aftershock can be explained by "time branch behavior".We propose a simple method to estimate fore earthquake sequence type by the ratio of time period with earthquake(X≥1) to that without earthquake(X=0).The two-peak distribution characteristics of yearly frequency for M≥7.0 earthquake in Mainland China may show that M≥7.0 earthquakes activity in the area is far from equanimity state.In the period of a strong earthquake evolvement,the seismic activity and precursor phenomenon undergo from disordered state at elastic strain accumulation step(shows single-peak Poison procedure) to ordered state at mid-term of non-elastic strain accumulation step(self-organize structure order,shows two or more peak distribution),and then to disordered state at imminent step.At this step,the chaos appears which is characterized by that synchronal anomalies are being disrupted obviously,and the system is inevitable falling into unstable state.Trigger factor is very important at this time and would cause strong earthquake occurrence,which makes the system release strain energy largely and long term attenuation.After that,it begins a new run for seismogenic period.The phenomenon of earthquake activity and its precursor seems impossible to study based on pure mechanics theory,it should be thought as a compositional part of non-linear geodynamics system that is far away from equilibrium state.The effort to deepen this cognition maybe is a breakthrough in earthquake prediction realm.
引文
[1]河北省地震局.1966年邢台地震[M].北京:地震出版社,1986.12-20.
[2]四川省地震局.一九七六年松潘地震[M].北京:地震出版社,1979.
[3]Kagan Y Y,Jackson D D.Long term earthquake clustering[J].Geophys J Int,1991,104(1):117-133.
[4]闻学泽,罗灼礼,陈农,等.中国大陆的特征地震活动及其中-长期预测研究[J].中国地震,1994,10(2):101-111.1994,10(3):206-216.
[5]李志雄,高旭.地震非均匀度的研究及在强震中期预报中的应用[J].地震,1994,14(6):11-18.
[6]罗灼礼,王伟君,陈凌.海城、岫岩地震序列非非线性结构特征及判定前震序列时间结构诊断法[J].地震,2000,20(增刊):18-27.
[7]杨欣,龙海英.时间结构变异分析法在伽师-巴楚震群序列中的应用研究[J].中国地震.2007,23(4):30-40.
[8]彼得.柯文尼,罗杰.海菲尔德,时间之箭[M].长沙:湖南科技出版社,1995.224.
[9]李文琦.概率论与数理统计[M].北京:北京师范大学出版社,1989.
[10]Pxigogine I,Stengers I.从混沌到有序[M].上海:译文出版社,1987.252.
[11]特科特D L.分形与混沌[M].北京:地震出版社,1993.2-3.
[12]尼科里斯,普利高津.探索复杂性[M].成都:四川教育出版社,1986.141,166.
[13]仪垂祥.非线性科学及其在地学中的应用[M].北京:气象出版社,1995.180.
[14]高安秀树.分数维[M].北京:地震出版社,1989.116-117.
[15]张国民.本世纪90年代我国大陆强震活动趋势研究[A].中国地震大形势预测研究[C].北京:地震出版社,1990.25-33.
[16]罗灼礼,王伟君.震级变异系数与地震序列类型、性质的物理统计特征和早期判定方法的研究[J].地震,2005,25(4):1-14.
[17]罗灼礼,孟国杰,王伟君,等.地震活动涨落、自组织结构和大震临界状态的统计特征[J].地震,2004,24(4):1-15.
[18]哈肯H.信息与自组织[M].成都:四川教育出版社,1988.121-122.
[19]四川省地震局.1989四川巴塘强震群[M].地震出版社,1994.
[2]四川省地震局.一九七六年松潘地震[M].北京:地震出版社,1979.
[3]Kagan Y Y,Jackson D D.Long term earthquake clustering[J].Geophys J Int,1991,104(1):117-133.
[4]闻学泽,罗灼礼,陈农,等.中国大陆的特征地震活动及其中-长期预测研究[J].中国地震,1994,10(2):101-111.1994,10(3):206-216.
[5]李志雄,高旭.地震非均匀度的研究及在强震中期预报中的应用[J].地震,1994,14(6):11-18.
[6]罗灼礼,王伟君,陈凌.海城、岫岩地震序列非非线性结构特征及判定前震序列时间结构诊断法[J].地震,2000,20(增刊):18-27.
[7]杨欣,龙海英.时间结构变异分析法在伽师-巴楚震群序列中的应用研究[J].中国地震.2007,23(4):30-40.
[8]彼得.柯文尼,罗杰.海菲尔德,时间之箭[M].长沙:湖南科技出版社,1995.224.
[9]李文琦.概率论与数理统计[M].北京:北京师范大学出版社,1989.
[10]Pxigogine I,Stengers I.从混沌到有序[M].上海:译文出版社,1987.252.
[11]特科特D L.分形与混沌[M].北京:地震出版社,1993.2-3.
[12]尼科里斯,普利高津.探索复杂性[M].成都:四川教育出版社,1986.141,166.
[13]仪垂祥.非线性科学及其在地学中的应用[M].北京:气象出版社,1995.180.
[14]高安秀树.分数维[M].北京:地震出版社,1989.116-117.
[15]张国民.本世纪90年代我国大陆强震活动趋势研究[A].中国地震大形势预测研究[C].北京:地震出版社,1990.25-33.
[16]罗灼礼,王伟君.震级变异系数与地震序列类型、性质的物理统计特征和早期判定方法的研究[J].地震,2005,25(4):1-14.
[17]罗灼礼,孟国杰,王伟君,等.地震活动涨落、自组织结构和大震临界状态的统计特征[J].地震,2004,24(4):1-15.
[18]哈肯H.信息与自组织[M].成都:四川教育出版社,1988.121-122.
[19]四川省地震局.1989四川巴塘强震群[M].地震出版社,1994.
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