Hurst指数分析地震震级趋势
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摘要
应用Hurst指数及分形维D、相关系数C和V统计量图形以及散点图和拟合趋势线方法,分析全球7.0级以上地震震级序列,发现该序列是分形布朗运动,均值回复过程(粉红噪声,反持续性,逆状态持续性),且具频繁的逆转突变性或易变性,长期情况下其震级呈现极微弱的下降趋势。可供地震研究和安全研究工作参考。
The sequence of global earthquake magnitude of 7.0 and more than 7.0 is analyzed by the methods of Hurst exponent,fractal dimension D,correlation coefficient C and V-statistics and the scatter diagram and fitting trend line.The results show that this sequence is a fractional Brownian motion,mean reversion process(pink noise,anti-persistence and persistence against the state),and with a frequent reversal mutation or volatility.In the long case,the magnitude shows a very slight downward trend.Conclusion of the study can provide reference for seismic studies and safety studies.
The sequence of global earthquake magnitude of 7.0 and more than 7.0 is analyzed by the methods of Hurst exponent,fractal dimension D,correlation coefficient C and V-statistics and the scatter diagram and fitting trend line.The results show that this sequence is a fractional Brownian motion,mean reversion process(pink noise,anti-persistence and persistence against the state),and with a frequent reversal mutation or volatility.In the long case,the magnitude shows a very slight downward trend.Conclusion of the study can provide reference for seismic studies and safety studies.
引文
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[10]徐绪松,马莉莉,陈彦斌.R/S分析的理论基础:分数布朗运动[J].武汉大学学报:理学版,2004,50(5):547-550.XU Xusong,MA Lili,CHEN Yanbin.Theoretical basis of R/S analysis:fractional Brownian motion[J].Journal of Wuhan University:Natural Science Edition,2004,50(5):547-550.
[11]Hurst H E.Long-term storage capacity of reservoirs:an experimental study[M].[S.l.]:American Society of Civil Engineers,1950.
[12]Mandelbrot B B,Van Ness J W.Fractional Brownian motion,fractional noises and applications[J].SIAM Review,1968,10(4):422-437.
[13]Mandelbrot B B,Wallis J R.Robustness of the rescaled range R/S in the measurement of noncyclic long run statistical dependence[J].Water Resources Research,1969,5(5):967-988.
[14]Peters E E.Applying chaos analysis to investment and economics[M].New York:Wiley,1994.
[15]Mandelbrot B B,Wallis J R.Some long-run properties of geographysical records[J].Water Resource Research,1969,5(2):321-340.
[16]Mandelbrot B B.Statistical methodology for nonperiodic cycles:from the covariance to R/S analysis[J].Annals of Economic and Social Measurement,1972,1(12):257-288.
[2]李娟,陈颙.地震活动性参数的变尺度(R/S)分析[J].地震学报,2001,23(2):143-150.LI Juan,CHEN Yu.Rescaled range(R/S)analysis on seismic activity parameters[J].Acta Seismologica Sinica,2001,23(2):143-150.
[3]郭德科.地震频次的Hurst指数在地震预报中的应用[J].华北地震科学,2002,20(3):44-49.GUO Deke.Application of Hurst index of earthquake frequency in the prediction of earthquake[J].North China Earthquake Sciences,2002,20(3):44-49.
[4]Jiménez A.Comparison of the Hurst and DEA exponents between the catalogue and its clusters:the California case[J].Physica A:Statistical Mechanics and its Applications,2011,390(11):2146-2154.
[5]陈椿庭.中国六级以上强震史料的分档整理和统计[J].水利学报,2003(12):1-11.CHEN Chunting.Analysis on historical data of strong earthquake in China[J].Journal of Hydraulic Engineering,2003(12):1-11.
[6]Jiménez M J,Garcia-Fernandez M,Romero J.1989-1995earthquake sequences in the Galeras volcano region,SW Colombia,and possible volcano-earthquake interactions[J].Tectonophysics,2009,463(1/2/3/4):47-59.
[7]云南省昭通市防震减灾局地震信息系统.全球7.0级以上地震信息[EB/OL].[2011-01-05].http:∥www.eqzt.com/eqzt/seis/view_world.php?dzml=world7.
[8]马利华,韩延本,尹志强.全球强震的分布及其与地球自转速率变化的关系[J].天文研究与技术,2007,4(4):406-411.MA Lihua,HAN Yanben,YIN Zhiqiang.Distribution characteristics of global significant earthquakes and possible connection between earthquakes and earth’s variable rotation rate[J].Astronomical Research&Technology,2007,4(4):406-411.
[9]埃德加.E.彼得斯.分形市场分析:将混沌理论应用到投资与经济理论上[M].储海林,殷勤,译.北京:经济科学出版社,2002.
[10]徐绪松,马莉莉,陈彦斌.R/S分析的理论基础:分数布朗运动[J].武汉大学学报:理学版,2004,50(5):547-550.XU Xusong,MA Lili,CHEN Yanbin.Theoretical basis of R/S analysis:fractional Brownian motion[J].Journal of Wuhan University:Natural Science Edition,2004,50(5):547-550.
[11]Hurst H E.Long-term storage capacity of reservoirs:an experimental study[M].[S.l.]:American Society of Civil Engineers,1950.
[12]Mandelbrot B B,Van Ness J W.Fractional Brownian motion,fractional noises and applications[J].SIAM Review,1968,10(4):422-437.
[13]Mandelbrot B B,Wallis J R.Robustness of the rescaled range R/S in the measurement of noncyclic long run statistical dependence[J].Water Resources Research,1969,5(5):967-988.
[14]Peters E E.Applying chaos analysis to investment and economics[M].New York:Wiley,1994.
[15]Mandelbrot B B,Wallis J R.Some long-run properties of geographysical records[J].Water Resource Research,1969,5(2):321-340.
[16]Mandelbrot B B.Statistical methodology for nonperiodic cycles:from the covariance to R/S analysis[J].Annals of Economic and Social Measurement,1972,1(12):257-288.
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