小波多尺度熵在新疆跨断层形变资料中的应用
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摘要
跨断层形变资料的信息提取与分析是地震研究的重要内容之一。文中以小波分析和信息熵理论为基础,提出了能够反映局部数据信息有序度大小的小波多尺度熵信息提取方法。研究了新疆天山地区跨断层定点形变观测资料强震前小波多尺度熵的变化特征,并应用多元线性回归方法分析了减熵异常与地震三要素之间的关系。结果表明:跨断层形变速率的相对高频成分携带的信息量大于中低频成分,大多数强震前小波多尺度熵有低值异常出现,累计减熵量的对数与震级、异常起始至发震的时间具有显著的线性关系,表现为震级越大,异常起始至发震的时间越长,累计减熵量越大,多个测点整体熵值的减少与大范围的地壳运动及地震活跃期存在一定程度的关联性。
Information extraction and analysis about cross-fault deformation is one of the important contents in earthquake research. Based on the theory of wavelet analysis and information entropy,the wavelet multi-scale entropy that describes the ordering degree in local data has been proposed in this paper. We studied the wavelet multi-scale entropy variation characteristics before strong earthquakes and the relationship between decreasing entropy anomaly and the three elements of earthquake by using the cross-fault fixed deformation data from Tianshan area in Xinjiang. The results indicate that:the amount of information of high frequency component is more than that of low frequency in cross-fault deformation rate,and a decreasing entropy anomaly appears before most of strong earthquakes. Furthermore,the logarithm of cumulative decreasing entropy is obviously linear with magnitude and the time from the beginning of anomaly to the occurrence of earthquake. If the magnitude is larger,the time from the beginning of anomaly to earthquake will be longer,and the cumulative decreasing entropy will be larger. Finally,the association is obvious between the integral decreasing entropy of multiple stations and large range crustal movement and the seismic active period.
Information extraction and analysis about cross-fault deformation is one of the important contents in earthquake research. Based on the theory of wavelet analysis and information entropy,the wavelet multi-scale entropy that describes the ordering degree in local data has been proposed in this paper. We studied the wavelet multi-scale entropy variation characteristics before strong earthquakes and the relationship between decreasing entropy anomaly and the three elements of earthquake by using the cross-fault fixed deformation data from Tianshan area in Xinjiang. The results indicate that:the amount of information of high frequency component is more than that of low frequency in cross-fault deformation rate,and a decreasing entropy anomaly appears before most of strong earthquakes. Furthermore,the logarithm of cumulative decreasing entropy is obviously linear with magnitude and the time from the beginning of anomaly to the occurrence of earthquake. If the magnitude is larger,the time from the beginning of anomaly to earthquake will be longer,and the cumulative decreasing entropy will be larger. Finally,the association is obvious between the integral decreasing entropy of multiple stations and large range crustal movement and the seismic active period.
引文
白超英,朱令人,王海涛,等.1992.地震活动信息熵及时空分维在地震预报中的意义[J].地震,4:7—11.BAI Chao-ying,ZHU Ling-ren,WANG Hai-tao,et al.1992.Significance of seismicity entropy of information and fractaldimension in earthquake prediction[J].Earthquake,4:7—11(in Chinese).
程万正,康晋山.1990.川西中部地震活动趋势的熵估计[J].地震,3:48—55.CHENG Wan-zheng,KANG Jin-shan.1990.Entropy estimation of seismic activity trend in central part of west SichuanProvince[J].Earthquake,3:48—55(in Chinese).
刁博,王家林,程顺有.2007.重力异常小波多分辨分析分解阶次的确定[J].地球科学:中国地质大学学报,32(4):564.DIAO Bo,WANG Jia-lin,CHENG Shun-you.2007.The confirmation of decomposition level in wavelet multi-resolutionanalysis for gravity anomalies[J].Earth Science:Journal of China University of Geosciences,32(4):564(inChinese).
樊计昌,刘明军,王夫运,等.2008.浅析小波最大分解层[J].科技导报,26(10):40—42.FAN Ji-chang,LIUMing-jun,WANG Fu-yun,et al.2008.Analysis on maximum wavelet decomposition level from theoryand application[J].Review Science&Technology,26(10):40—42(in Chinese).
顾国华,张晶.2002.中国地壳运动观测网络基准站GPS观测的位移时间序列结果[J].大地测量与地球动力学,22(2):61—67.GUGuo-hua,ZHANG Jing.2002.Time series of displacements from GPS observation at fiducial station in the CrustalMovement Observation Network of China[J].Journal of Geodesy and Geodynamics,22(2):61—67(in Chi-nese).
顾国华,张晶,王武星.2005.中国地壳运动观测网络GPS观测得到的地壳运动结果[J].测绘通报,7:1—7.GU Guo-hua,ZHANG Jing,WANG Wu-xing.2005.Crustal movement result from GPS observations of China CrustalMovement Observation Network[J].Bulletin of Surveying and Mapping,7:1—7(in Chinese).
宦飞,王志中,郑崇勋.2001.睡眠EEG的多尺度信息熵分析[J].北京生物医学工程报,20(1):6—8.HUAN Fei,WANG Zhi-zhong,ZHENG Chong-xun.2001.Analysis of sleep EEG by using multi-scale entropy[J].Bei-jing Biomedical Engineering,20(1):6—8(in Chinese).
蒋靖祥.2003.天山地区断层垂直形变与现今活动特征研究[J].大地测量与地球动力学,23(1):47—52.JIANG Jing-xiang.2003.Study on vertical deformation and activity characteristics of faults in Tianshan area[J].Jour-nal of Geodesy and Geodynamics,23(1):47—52(in Chinese).
刘冠中,蒋靖祥,王建军,等.2007.跨断层定点形变观测资料“速率累加分析”及其异常初步提取方法[J].内陆地震,21(3):230—237.LIU Guan-zhong,JIANG Jing-xiang,WANG Jian-jun,et al.2007.“Rate Cumulative Analysis”on across-fault fixed de-formation data and preliminary anomaly extraction method[J].Inland Earthquake,21(3):230—237(in Chi-nese).
刘希强,林怀存,黄耘,等.2004.全球、中国大陆和华北地区地震活动韵律性时变特征及趋势分析[J].中国地震,20(3):247—256.LIUXi-qiang,LINHuai-cun,HUANG Yun,et al.2004.The rhythm of earthquake activity and earthquake tendency ana-lyses on globality,Chinese mainland and north China[J].Earthquake Research in China,20(3):247—256(inChinese).
邵辉成,傅征祥,王晓青,等.2004.中国大陆西部及邻近地区地震活动的小波分析[J].中国地震,20(3):257—262.SHAO Hui-cheng,FUZheng-xiang,WANG Xiao-qing,et al.2004.Wavelet analysis of earthquake activity in the west ofthe Chinese mainland and its adjacent area[J].Earthquake Research in China,20(3):257—262(in Chinese).
李圣强,杜建国,康春丽.2001.信息熵在地下流体资料处理中的应用[J].华北地震科学,19(2):1—7.LI Sheng-qiang,DUJian-guo,KANG Chun-li.2001.The application of information entropy in subsurface fluid data pro-cessing[J].North China Earthquake Sciences,19(2):1—7(in Chinese).
王海,孙建平,郑莉媛.2006.尺度熵及其在水电机组监测诊断系统中的应用[J].水电能源科学,24(2):17—18.WANG Hai,SUN Jian-ping,ZHENG Li-yuan.2006.Scale entropy and its application in monitoring&diagnosis systemfor hydropower sets[J].Water Resources and Power,24(2):17—18(in Chinese).
王海涛,朱令人,杨马陵,等.1991.地震前兆观测数据的信息熵分析:以乌鲁木齐10号井地下水氡为例[J].地震,5:13—17.WANG Hai-tao,ZHULing-ren,YANG Ma-ling,et al.1991.Analysis of information entropy of seismically precursory ob-servation data:Taking the groundwater radon in Urumqi no.10well for an example[J].Earthquake,5:13—17(in Chinese).
王建军.2004.跨断层形变自动化观测技术的研究与应用[J].岩石力学与工程学报,23(2):261—266.WANG Jian-jun.2004.Technique study of across-fault deformation measurement and its application[J].Chinese Jour-nal of Rock Mechanics and Engineering,23(2):261—266(in Chinese).
王在华,孔德锋,宋光甫.2005.断层形变测量资料与辅助温度观测资料相关分析[J].内陆地震,19(2):188—191.WANG Zai-hua,KONG De-feng,SONG Guang-fu.2005.Relative analysis between fault deformation observational da-tum and auxiliary temperature observational datum[J].Inland Earthquake,19(2):188—191(in Chinese).
邬焜.1996.与熵相关的几个概念的科学含义的辨析[J].自然辩证法通讯,18(5):67—74.WU Kun.1996.Scientific meaning discrimination on several concepts about entropy[J].Journal of Dialectics of Na-ture,18(5):67—74(in Chinese).
夏浩明.1989.关于地震信息熵的讨论:兼与朱令人商榷[J].地震地质,11(4):50—52.XIA Hao-ming.1989.Seismic information entropy:Also as discussion with Mr.Zhu Ling-Ren[J].Seismology and Ge-ology,11(4):50—52(in Chinese).
张凤君.2007.东北地震区地震趋势的小波分析[J].地震研究,30(2):137—141.ZHANG Feng-jun.2007.Wavelet analysis on earthquake trend of northeast China seismic region,China[J].Journal ofSeismological Research,30(2):137—141(in Chinese).
朱令人.1988.大地震前地震信息熵的异常:以乌恰地震为例[J].地震地质,10(2):29—38.ZHU Ling-ren.1988.Anomaly of information entropy before great earthquake:The case study of Wuqia earthquakes[J].Seismology and Geology,10(2):29—38(in Chinese).
朱令人,龚宇清,周仕勇,等.1990.玛纳斯地震前后地震活动信息熵及分维的动态变化[J].内陆地震,4(3):193—200.ZHU Ling-ren,GONG Yu-qing,ZHOUShi-yong,et al.1990.Dynamic variation on seismicity entropy of information andfractal dimension before and after Manasi earthquake[J].Inland Earthquake,4(3):193—200(in Chinese).
周仕勇,朱令人.1995.地震活动信息熵在地震危险区判定中的研究[J].中国地震,11(3):283—291.ZHOU Shi-yong,ZHU Ling-ren.1995.Seismic risk region determined by information entropy[J].Earthquake Researchin China,11(3):283—291(in Chinese).
Goltz C,Bose M.2002.Configurational entropy of critical earthquake populations[J].Geophysical Research Letter,29(20):51—59.
Harte D,Vere-Jones D.2005.The entropy score and its uses in earthquake forecasting[J].Pure Appl Geophys,162:1229—1253.
Nicholson T,Sambridge M,Gudmundsson O.2000.On entropy and clustering in earthquake hypocenter distributions[J].Geophys J Int,142:37—51.
Shannon C E A.1948.Mathematical theory of communication[J].Bell System Technical Journal,27:379—423.
Varotsos P A,Sarlis N V,Skordas E S,et al.2006.Entropy of seismic electric signals:Analysis in natural time undertime reversal[J].Physical Review,E73:031114.
程万正,康晋山.1990.川西中部地震活动趋势的熵估计[J].地震,3:48—55.CHENG Wan-zheng,KANG Jin-shan.1990.Entropy estimation of seismic activity trend in central part of west SichuanProvince[J].Earthquake,3:48—55(in Chinese).
刁博,王家林,程顺有.2007.重力异常小波多分辨分析分解阶次的确定[J].地球科学:中国地质大学学报,32(4):564.DIAO Bo,WANG Jia-lin,CHENG Shun-you.2007.The confirmation of decomposition level in wavelet multi-resolutionanalysis for gravity anomalies[J].Earth Science:Journal of China University of Geosciences,32(4):564(inChinese).
樊计昌,刘明军,王夫运,等.2008.浅析小波最大分解层[J].科技导报,26(10):40—42.FAN Ji-chang,LIUMing-jun,WANG Fu-yun,et al.2008.Analysis on maximum wavelet decomposition level from theoryand application[J].Review Science&Technology,26(10):40—42(in Chinese).
顾国华,张晶.2002.中国地壳运动观测网络基准站GPS观测的位移时间序列结果[J].大地测量与地球动力学,22(2):61—67.GUGuo-hua,ZHANG Jing.2002.Time series of displacements from GPS observation at fiducial station in the CrustalMovement Observation Network of China[J].Journal of Geodesy and Geodynamics,22(2):61—67(in Chi-nese).
顾国华,张晶,王武星.2005.中国地壳运动观测网络GPS观测得到的地壳运动结果[J].测绘通报,7:1—7.GU Guo-hua,ZHANG Jing,WANG Wu-xing.2005.Crustal movement result from GPS observations of China CrustalMovement Observation Network[J].Bulletin of Surveying and Mapping,7:1—7(in Chinese).
宦飞,王志中,郑崇勋.2001.睡眠EEG的多尺度信息熵分析[J].北京生物医学工程报,20(1):6—8.HUAN Fei,WANG Zhi-zhong,ZHENG Chong-xun.2001.Analysis of sleep EEG by using multi-scale entropy[J].Bei-jing Biomedical Engineering,20(1):6—8(in Chinese).
蒋靖祥.2003.天山地区断层垂直形变与现今活动特征研究[J].大地测量与地球动力学,23(1):47—52.JIANG Jing-xiang.2003.Study on vertical deformation and activity characteristics of faults in Tianshan area[J].Jour-nal of Geodesy and Geodynamics,23(1):47—52(in Chinese).
刘冠中,蒋靖祥,王建军,等.2007.跨断层定点形变观测资料“速率累加分析”及其异常初步提取方法[J].内陆地震,21(3):230—237.LIU Guan-zhong,JIANG Jing-xiang,WANG Jian-jun,et al.2007.“Rate Cumulative Analysis”on across-fault fixed de-formation data and preliminary anomaly extraction method[J].Inland Earthquake,21(3):230—237(in Chi-nese).
刘希强,林怀存,黄耘,等.2004.全球、中国大陆和华北地区地震活动韵律性时变特征及趋势分析[J].中国地震,20(3):247—256.LIUXi-qiang,LINHuai-cun,HUANG Yun,et al.2004.The rhythm of earthquake activity and earthquake tendency ana-lyses on globality,Chinese mainland and north China[J].Earthquake Research in China,20(3):247—256(inChinese).
邵辉成,傅征祥,王晓青,等.2004.中国大陆西部及邻近地区地震活动的小波分析[J].中国地震,20(3):257—262.SHAO Hui-cheng,FUZheng-xiang,WANG Xiao-qing,et al.2004.Wavelet analysis of earthquake activity in the west ofthe Chinese mainland and its adjacent area[J].Earthquake Research in China,20(3):257—262(in Chinese).
李圣强,杜建国,康春丽.2001.信息熵在地下流体资料处理中的应用[J].华北地震科学,19(2):1—7.LI Sheng-qiang,DUJian-guo,KANG Chun-li.2001.The application of information entropy in subsurface fluid data pro-cessing[J].North China Earthquake Sciences,19(2):1—7(in Chinese).
王海,孙建平,郑莉媛.2006.尺度熵及其在水电机组监测诊断系统中的应用[J].水电能源科学,24(2):17—18.WANG Hai,SUN Jian-ping,ZHENG Li-yuan.2006.Scale entropy and its application in monitoring&diagnosis systemfor hydropower sets[J].Water Resources and Power,24(2):17—18(in Chinese).
王海涛,朱令人,杨马陵,等.1991.地震前兆观测数据的信息熵分析:以乌鲁木齐10号井地下水氡为例[J].地震,5:13—17.WANG Hai-tao,ZHULing-ren,YANG Ma-ling,et al.1991.Analysis of information entropy of seismically precursory ob-servation data:Taking the groundwater radon in Urumqi no.10well for an example[J].Earthquake,5:13—17(in Chinese).
王建军.2004.跨断层形变自动化观测技术的研究与应用[J].岩石力学与工程学报,23(2):261—266.WANG Jian-jun.2004.Technique study of across-fault deformation measurement and its application[J].Chinese Jour-nal of Rock Mechanics and Engineering,23(2):261—266(in Chinese).
王在华,孔德锋,宋光甫.2005.断层形变测量资料与辅助温度观测资料相关分析[J].内陆地震,19(2):188—191.WANG Zai-hua,KONG De-feng,SONG Guang-fu.2005.Relative analysis between fault deformation observational da-tum and auxiliary temperature observational datum[J].Inland Earthquake,19(2):188—191(in Chinese).
邬焜.1996.与熵相关的几个概念的科学含义的辨析[J].自然辩证法通讯,18(5):67—74.WU Kun.1996.Scientific meaning discrimination on several concepts about entropy[J].Journal of Dialectics of Na-ture,18(5):67—74(in Chinese).
夏浩明.1989.关于地震信息熵的讨论:兼与朱令人商榷[J].地震地质,11(4):50—52.XIA Hao-ming.1989.Seismic information entropy:Also as discussion with Mr.Zhu Ling-Ren[J].Seismology and Ge-ology,11(4):50—52(in Chinese).
张凤君.2007.东北地震区地震趋势的小波分析[J].地震研究,30(2):137—141.ZHANG Feng-jun.2007.Wavelet analysis on earthquake trend of northeast China seismic region,China[J].Journal ofSeismological Research,30(2):137—141(in Chinese).
朱令人.1988.大地震前地震信息熵的异常:以乌恰地震为例[J].地震地质,10(2):29—38.ZHU Ling-ren.1988.Anomaly of information entropy before great earthquake:The case study of Wuqia earthquakes[J].Seismology and Geology,10(2):29—38(in Chinese).
朱令人,龚宇清,周仕勇,等.1990.玛纳斯地震前后地震活动信息熵及分维的动态变化[J].内陆地震,4(3):193—200.ZHU Ling-ren,GONG Yu-qing,ZHOUShi-yong,et al.1990.Dynamic variation on seismicity entropy of information andfractal dimension before and after Manasi earthquake[J].Inland Earthquake,4(3):193—200(in Chinese).
周仕勇,朱令人.1995.地震活动信息熵在地震危险区判定中的研究[J].中国地震,11(3):283—291.ZHOU Shi-yong,ZHU Ling-ren.1995.Seismic risk region determined by information entropy[J].Earthquake Researchin China,11(3):283—291(in Chinese).
Goltz C,Bose M.2002.Configurational entropy of critical earthquake populations[J].Geophysical Research Letter,29(20):51—59.
Harte D,Vere-Jones D.2005.The entropy score and its uses in earthquake forecasting[J].Pure Appl Geophys,162:1229—1253.
Nicholson T,Sambridge M,Gudmundsson O.2000.On entropy and clustering in earthquake hypocenter distributions[J].Geophys J Int,142:37—51.
Shannon C E A.1948.Mathematical theory of communication[J].Bell System Technical Journal,27:379—423.
Varotsos P A,Sarlis N V,Skordas E S,et al.2006.Entropy of seismic electric signals:Analysis in natural time undertime reversal[J].Physical Review,E73:031114.
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