基于逻辑回归分析的强震地表破裂预测方法
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摘要
强震引起的地表破裂通常会对工程结构造成严重的危害,工程建设中要对建设场地是否存在发震断裂以及能否产生地表破裂做出评价。由于地震的发生具有随机性,因此,强震引起的地表破裂也存在着不确定性,对其给予概率的表达符合当前人们对这一问题的认识水平和工程建设的风险选择要求。本文在总结强震地表破裂及震害的基础上,将逻辑回归这一研究多变量参与、预测某一事件发生概率的数学模型引入到强震地表破裂的预测研究中,介绍了逻辑回归方法的基本原理;论证了这一方法用于强震地表破裂概率预测的可行性和适宜性;提出了评价因子以及分级方法;给出了具体的数据计算方法并进行了显著性检验;以汶川特地震为例对模型的适宜性进行了检验和具体应用。本文的研究工作对从事这一领域研究的科技人员有重要的参考价值。
Surface rupture in strong earthquakes usually causes serious damage to engineering structures. In engineering construction, it is necessary to evaluate the existence of seismogenic faults and the occurrence of surface ruptures inconstruction sites. The occurrence of earthquakes is random, so the surface rupture caused by strong earthquakes is also uncertain. Therefore, given its probability expression, it meets the current people's understanding level of this problem and the requirement of risk selection in engineering construction. On the basis of summarizing the surface rupture and damage caused by strong earthquakes, this paper introduces the mathematical model of logistic regression, which is used to study multi-variable participation and predict the probability of occurrence of an event, into the prediction of surface rupture caused by strong earthquakes, meanwhile, the basic principle of logistic regression method is also introduced; the feasibility and suitability of this method for predicting the probability of surface rupture of strong earthquakes have been demonstrated; evaluation factors and classification methods were proposed; the specific data calculation method is given and the significance test is carried out; taking Wenchuan Earthquake as an example, the suitability of the model is tested and applied concretely. The work of this paper has important reference value for scientific researchers in this field.
Surface rupture in strong earthquakes usually causes serious damage to engineering structures. In engineering construction, it is necessary to evaluate the existence of seismogenic faults and the occurrence of surface ruptures inconstruction sites. The occurrence of earthquakes is random, so the surface rupture caused by strong earthquakes is also uncertain. Therefore, given its probability expression, it meets the current people's understanding level of this problem and the requirement of risk selection in engineering construction. On the basis of summarizing the surface rupture and damage caused by strong earthquakes, this paper introduces the mathematical model of logistic regression, which is used to study multi-variable participation and predict the probability of occurrence of an event, into the prediction of surface rupture caused by strong earthquakes, meanwhile, the basic principle of logistic regression method is also introduced; the feasibility and suitability of this method for predicting the probability of surface rupture of strong earthquakes have been demonstrated; evaluation factors and classification methods were proposed; the specific data calculation method is given and the significance test is carried out; taking Wenchuan Earthquake as an example, the suitability of the model is tested and applied concretely. The work of this paper has important reference value for scientific researchers in this field.
引文
[1] 陈达生.地震引起的地表破裂长度与震级之间的经验关系[J].华北地震科学,1984(2):26-32.CHEN Dasheng.The empirical relationship between the length of surface rupture caused by earthquake and the magnitude[J].North China Earthquake Sciences,1984(2):26-32.( in Chinese )
[2] 邓起东,于贵华,叶文华.地震地表破裂参数与震级关系的研究[M].国家地震局地质研究所编.活动断裂研究(2).北京:地震出版社,1987:247-264.DENG Qidong,YU Guihua,YE Wenhua.Study on relationship between seismic surface rupture parameters and magnitude[M].Institute of Geology,China Earthquake Administration.Beijing:Earthquake Press,1987:247-264.(in Chinese)
[3] 郭安宁.强震地表破裂宽度与震级的统计关系研究[J].西北地震学报,2000(3):94-98.GUO Anning.Statistical research on relation between surface fault width of strong earthquake and magnitude.[J].Northwestern Seismological Journal,2000(3):94-98.(in Chinese)
[4] 郭恩栋,邵广彪,薄景山,等.覆盖土层场地地震断裂反应分析方法[J].地震工程与工程振动,2002,22(5):122-126.GUO Endong,SHAO Guangbiao,BO Jingshan,et al.A method for earthquake rupture analysis of overlying soil site[J].Earthquake Engineering and Engineering Dynamics,2002,22(5):122-126.(in Chinese)
[5] 黄静宜,关会梅,宋洋.汶川地震北川县城地表断层破裂特征[J].防灾科技学院学报,2009,11(1):62-65.HUANG Jingyi,Guan Huimei,SONG Yang.Characteristics of ground ruptures in Beichuan County caused by Wenchuan earthquak[J].Journal of Institute of Disaster-Prevention Science and Technology,2009,11(1):62-65.(in Chinese)
[6] Bonilla M G,Mark R K,Lienkaemper J J.Statistical relations among earthquake magnitude,surface rupture length and surface fault displacement[J].Bulletin of the Seismological Society of America,1984,74(6):2379-2411.
[7] Anastasopoulos I,Gazetas G,Bransby M F,et al.Fault rupture propagation through sand:Finite element analysis and validation through centrifuge experiments[J].Journal of Geotechnical and Geoenvironmental Engineering,2007,133(8):943-958.
[8] 赵雷,李小军,霍达.数值模拟软夹层对基岩上覆土层破裂的影响[J].北京工业大学学报,2007(3):289-292.ZHAO Lei,LI Xiaojun,HUO Da.Numerically simulate the response complexion of the overlaying soil with soft interlayer due to fault bedrock dislocation [J].Journal of Beijing University of Technology,2007(3):289-292.(in Chinese)
[9] 黄静宜,薄景山,沈超,等.强震地表破裂工程评估研究的若干进展[J].自然灾害学报,2016,25(6):94-104.HUANG Jingyi,BO Jingshan,SHEN Chao,et al.Progress in research on engineering evaluation of surface ruptures in strong earthquakes[J].Journal of Natural Disasters,2016,25(6):94-104.(in Chinese)
[10] Hart E W,Bryant W.Fault-rupture hazard zones in california:alquist-priolo earthquake fault zoning act with index to earthquake fault zones maps[M].California:Division of Mines and Geology,1999:7-34.
[11] 中田高,隈元崇.活断層位置情报報からみた土地利用の問題点と「活断層法」について[J].《活断層研究》,2003:13-18.Takashi Nakana,TaKashi Kumamoto.Land use issues against potential danger of active fault,and active fault zones act[J].Active FaultResearch,2003,13:13-18 (in Japanese)
[12] European Committee for Standardization.Eurocode 8:Design of Structures for Earthquake Resistance Part 5:Foundations Retaining Structures and Geotechnical Aspects[S].Brusells:EVN:1998:14-20.
[13] Perrin N D,Wood P R.Defining the Wellington Fault within the Urban Area of Wellington City[R].Wellington:Institute of Geological & Nuclear science Client Report,2003:6-49.
[14] GB50011-2010建筑抗震设计规范[S].北京:中国建筑工业出版社,2010:12-18.GB50011-2010 Code for Seismic Design of Buildings [S].Beijing:China Architecture & Building Press,2010:12-18.(in Chinese)
[15] Albee A L,Smith J L.Earthquake characteristics and fault activity in southern California,in Engineering Geology in Southern California[J].Association of Engineering Geologists,Los Angeles Section,1966:9-34.
[16] Wegener,A.Die Entstehung der Kontinente und Ozeane[M].Braunschweig:FriedrichVieweg & Sohn Akt.Ges,1929:1-5.
[17] McKenzie D & Parker R L.The North Pacific:an example of tectonics on a sphere [J].Nature,1967,216:1276-1280.
[18] 张建毅,薄景山,李平,等.玉树地震地表破裂对建筑影响分析[J].地震工程与工程振动,2010,30(6):24-31.ZHANG jianyi,BO jingshan,LI ping,et al.Influence of surface ruptures on buildings during Ms7.1 Yushu earthquake[J].Earthquake Engineering and Engineering Dynamics,2010,30(6):24-31.(in Chinese)
[19] Wells D L,Coppersmith K J.New empirical relationships among magnitude,rupture length,rupture width,rupture area,and surface displacement (incomplete)[J].Bulletin of the Seismological Society of America,1994,84(4):974-1002.
[20] Chinnery M A.Earthquake magnitude and source parameters[J].Bulletin of the Seismological Society of America,1969,59:1969-1982.
[21] Bo Li,Jingyu Su,Donghui Ma,et al.The study on forecasting the surface rupture width under strong earthquake based on information diffusion methodology[J].Nat Hazards,2015,75:1871-1882.
[22] Emmons R C.Strike-slip rupture patterns in sand models[J].Tectonophysics,1969,7(1):71-87.
[23] Lade P V,Cole D A.Multiple failure surface over dip-slip faults[J].Journal of Geotechnical Engineering Division,1984,110(5):616-627.
[24] Taniyama,Watanabe.Deformation of sandy deposits by fault movement[C]// Proc.12th WCEE.(No.2209),2000.
[25] Roth W H,Scott R F,Austin I.Centrifuge modeling of fault propagation through alluvial soils[J].Geophysics Research Letters,1981,8(6):561-564.
[26] 董津城,刘守华.发震断裂上覆土层厚度对工程影响研究报告[R].北京:北京市勘察设计研究院,1996.DONG Jincheng,LIU Shouhua.Study on the influence of the thickness of the overlying soil layer on the engineering effect[R].Beijing:BGI Engineering Consultarcts LTD,1996.( in Chinese )
[27] 郭恩栋,冯启民,薄景山,等.覆盖土层场地地震断裂实验[J].地震工程与工程振动,2001,21(3):145-149.GUO Endong,FENG Qimin,BO Jingshan,et al.Seismic test of soil site ruptue under fault displcements[J].Earthquake Engineering and Engineering Dynamics,2001,21(3):145-149.(in Chinese)
[28] 刘守华,董津城,徐光明,等.地下断裂对不同土质上覆土层的工程影响[J].岩石力学与工程学报,2005(11):1868-1874.LIU Shouhua,DONG Jincheng,XU Guangming,et al.Influence on different overburden soils due to bedrock fracture[J].Chinese Journal of Rock Mechanics and Engineering,2005(11):1868-1874.(in Chinese)
[29] Bray J D,Raymond B S,et al.Analysis of earthquake fault rupture propagation through cohesive soil[J].Journal of Geotechnical Engineering,ASCE,1994,120(3):562-580.
[30] 李小军,赵雷,李亚琦.断层错动引发基岩上覆土层破裂过程模拟[J].岩石力学与工程学报,2009,28(增刊1):2703-2707.LI Xiaojun,ZHAO Lei,LI Yaqi.Simulation of fault movement induced rupture process of overlaying soil of bedrock[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(S1):2703-2707.(in Chinese)
[31] 张建毅,薄景山,袁一凡,等.活动断层及其避让距离研究综述[J].自然灾害学报,2012,21(2):9-18.ZHANG Jianyi,BO Jingshan,YUAN Yifan,et al.Review of research on active fault and its setback.Journal of Natural Disasters [J].2012,21(2):9-18.(in Chinese)
[32] 何晓群,刘文卿.应用回归分析[M].北京:中国人民大学出版社,2015:247-268.HE Xiaoqun,LIU Wenqing.Applied regression analysis[M].Beijing:China Renmin University Press,2015:247-268.(in Chinese )
[33] 黄静宜.强震地表破裂评估方法研究[D].哈尔滨:中国地震局工程力学研究所,2016.HUANG Jingyi.Research on The method for evaluating the earthquake surface rupture[D].Harbin:Institute of Engineering Mechanics,China Earthquake Administration,2016.(in Chinese)
[34] 汪冬华.多元统计分析与SPSS应用[M].上海:华东理工大学出版社,2010:269-277.WANG Donghua.Multivariate statistical analysis and SPSS application[M].Shanghai:East China University of Science and Technology Press,2010:269-277.(in Chinese)
[2] 邓起东,于贵华,叶文华.地震地表破裂参数与震级关系的研究[M].国家地震局地质研究所编.活动断裂研究(2).北京:地震出版社,1987:247-264.DENG Qidong,YU Guihua,YE Wenhua.Study on relationship between seismic surface rupture parameters and magnitude[M].Institute of Geology,China Earthquake Administration.Beijing:Earthquake Press,1987:247-264.(in Chinese)
[3] 郭安宁.强震地表破裂宽度与震级的统计关系研究[J].西北地震学报,2000(3):94-98.GUO Anning.Statistical research on relation between surface fault width of strong earthquake and magnitude.[J].Northwestern Seismological Journal,2000(3):94-98.(in Chinese)
[4] 郭恩栋,邵广彪,薄景山,等.覆盖土层场地地震断裂反应分析方法[J].地震工程与工程振动,2002,22(5):122-126.GUO Endong,SHAO Guangbiao,BO Jingshan,et al.A method for earthquake rupture analysis of overlying soil site[J].Earthquake Engineering and Engineering Dynamics,2002,22(5):122-126.(in Chinese)
[5] 黄静宜,关会梅,宋洋.汶川地震北川县城地表断层破裂特征[J].防灾科技学院学报,2009,11(1):62-65.HUANG Jingyi,Guan Huimei,SONG Yang.Characteristics of ground ruptures in Beichuan County caused by Wenchuan earthquak[J].Journal of Institute of Disaster-Prevention Science and Technology,2009,11(1):62-65.(in Chinese)
[6] Bonilla M G,Mark R K,Lienkaemper J J.Statistical relations among earthquake magnitude,surface rupture length and surface fault displacement[J].Bulletin of the Seismological Society of America,1984,74(6):2379-2411.
[7] Anastasopoulos I,Gazetas G,Bransby M F,et al.Fault rupture propagation through sand:Finite element analysis and validation through centrifuge experiments[J].Journal of Geotechnical and Geoenvironmental Engineering,2007,133(8):943-958.
[8] 赵雷,李小军,霍达.数值模拟软夹层对基岩上覆土层破裂的影响[J].北京工业大学学报,2007(3):289-292.ZHAO Lei,LI Xiaojun,HUO Da.Numerically simulate the response complexion of the overlaying soil with soft interlayer due to fault bedrock dislocation [J].Journal of Beijing University of Technology,2007(3):289-292.(in Chinese)
[9] 黄静宜,薄景山,沈超,等.强震地表破裂工程评估研究的若干进展[J].自然灾害学报,2016,25(6):94-104.HUANG Jingyi,BO Jingshan,SHEN Chao,et al.Progress in research on engineering evaluation of surface ruptures in strong earthquakes[J].Journal of Natural Disasters,2016,25(6):94-104.(in Chinese)
[10] Hart E W,Bryant W.Fault-rupture hazard zones in california:alquist-priolo earthquake fault zoning act with index to earthquake fault zones maps[M].California:Division of Mines and Geology,1999:7-34.
[11] 中田高,隈元崇.活断層位置情报報からみた土地利用の問題点と「活断層法」について[J].《活断層研究》,2003:13-18.Takashi Nakana,TaKashi Kumamoto.Land use issues against potential danger of active fault,and active fault zones act[J].Active FaultResearch,2003,13:13-18 (in Japanese)
[12] European Committee for Standardization.Eurocode 8:Design of Structures for Earthquake Resistance Part 5:Foundations Retaining Structures and Geotechnical Aspects[S].Brusells:EVN:1998:14-20.
[13] Perrin N D,Wood P R.Defining the Wellington Fault within the Urban Area of Wellington City[R].Wellington:Institute of Geological & Nuclear science Client Report,2003:6-49.
[14] GB50011-2010建筑抗震设计规范[S].北京:中国建筑工业出版社,2010:12-18.GB50011-2010 Code for Seismic Design of Buildings [S].Beijing:China Architecture & Building Press,2010:12-18.(in Chinese)
[15] Albee A L,Smith J L.Earthquake characteristics and fault activity in southern California,in Engineering Geology in Southern California[J].Association of Engineering Geologists,Los Angeles Section,1966:9-34.
[16] Wegener,A.Die Entstehung der Kontinente und Ozeane[M].Braunschweig:FriedrichVieweg & Sohn Akt.Ges,1929:1-5.
[17] McKenzie D & Parker R L.The North Pacific:an example of tectonics on a sphere [J].Nature,1967,216:1276-1280.
[18] 张建毅,薄景山,李平,等.玉树地震地表破裂对建筑影响分析[J].地震工程与工程振动,2010,30(6):24-31.ZHANG jianyi,BO jingshan,LI ping,et al.Influence of surface ruptures on buildings during Ms7.1 Yushu earthquake[J].Earthquake Engineering and Engineering Dynamics,2010,30(6):24-31.(in Chinese)
[19] Wells D L,Coppersmith K J.New empirical relationships among magnitude,rupture length,rupture width,rupture area,and surface displacement (incomplete)[J].Bulletin of the Seismological Society of America,1994,84(4):974-1002.
[20] Chinnery M A.Earthquake magnitude and source parameters[J].Bulletin of the Seismological Society of America,1969,59:1969-1982.
[21] Bo Li,Jingyu Su,Donghui Ma,et al.The study on forecasting the surface rupture width under strong earthquake based on information diffusion methodology[J].Nat Hazards,2015,75:1871-1882.
[22] Emmons R C.Strike-slip rupture patterns in sand models[J].Tectonophysics,1969,7(1):71-87.
[23] Lade P V,Cole D A.Multiple failure surface over dip-slip faults[J].Journal of Geotechnical Engineering Division,1984,110(5):616-627.
[24] Taniyama,Watanabe.Deformation of sandy deposits by fault movement[C]// Proc.12th WCEE.(No.2209),2000.
[25] Roth W H,Scott R F,Austin I.Centrifuge modeling of fault propagation through alluvial soils[J].Geophysics Research Letters,1981,8(6):561-564.
[26] 董津城,刘守华.发震断裂上覆土层厚度对工程影响研究报告[R].北京:北京市勘察设计研究院,1996.DONG Jincheng,LIU Shouhua.Study on the influence of the thickness of the overlying soil layer on the engineering effect[R].Beijing:BGI Engineering Consultarcts LTD,1996.( in Chinese )
[27] 郭恩栋,冯启民,薄景山,等.覆盖土层场地地震断裂实验[J].地震工程与工程振动,2001,21(3):145-149.GUO Endong,FENG Qimin,BO Jingshan,et al.Seismic test of soil site ruptue under fault displcements[J].Earthquake Engineering and Engineering Dynamics,2001,21(3):145-149.(in Chinese)
[28] 刘守华,董津城,徐光明,等.地下断裂对不同土质上覆土层的工程影响[J].岩石力学与工程学报,2005(11):1868-1874.LIU Shouhua,DONG Jincheng,XU Guangming,et al.Influence on different overburden soils due to bedrock fracture[J].Chinese Journal of Rock Mechanics and Engineering,2005(11):1868-1874.(in Chinese)
[29] Bray J D,Raymond B S,et al.Analysis of earthquake fault rupture propagation through cohesive soil[J].Journal of Geotechnical Engineering,ASCE,1994,120(3):562-580.
[30] 李小军,赵雷,李亚琦.断层错动引发基岩上覆土层破裂过程模拟[J].岩石力学与工程学报,2009,28(增刊1):2703-2707.LI Xiaojun,ZHAO Lei,LI Yaqi.Simulation of fault movement induced rupture process of overlaying soil of bedrock[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(S1):2703-2707.(in Chinese)
[31] 张建毅,薄景山,袁一凡,等.活动断层及其避让距离研究综述[J].自然灾害学报,2012,21(2):9-18.ZHANG Jianyi,BO Jingshan,YUAN Yifan,et al.Review of research on active fault and its setback.Journal of Natural Disasters [J].2012,21(2):9-18.(in Chinese)
[32] 何晓群,刘文卿.应用回归分析[M].北京:中国人民大学出版社,2015:247-268.HE Xiaoqun,LIU Wenqing.Applied regression analysis[M].Beijing:China Renmin University Press,2015:247-268.(in Chinese )
[33] 黄静宜.强震地表破裂评估方法研究[D].哈尔滨:中国地震局工程力学研究所,2016.HUANG Jingyi.Research on The method for evaluating the earthquake surface rupture[D].Harbin:Institute of Engineering Mechanics,China Earthquake Administration,2016.(in Chinese)
[34] 汪冬华.多元统计分析与SPSS应用[M].上海:华东理工大学出版社,2010:269-277.WANG Donghua.Multivariate statistical analysis and SPSS application[M].Shanghai:East China University of Science and Technology Press,2010:269-277.(in Chinese)
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