不同应力状态和摩擦系数对综合P波辐射花样影响的模拟研究
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摘要
为研究不同应力状态(包括主应力相对大小)和摩擦系数对大量地震P波初动辐射化样(综合P波辐射花样)的影响,首先给出了不同应力状态下的剪应力、摩擦应力和库仑破裂应力在断层面法向上的三维分布.表明即使在不考虑摩擦的情况下,剪应力在不同取向断层面上的分布也有很大差别,摩擦应力也在不同取向断层面上造成一定影响.其次,根据库仑破裂应力与单个地震产生的P波辐射花样大小成比例的原则,假定地震断层面均匀取样整个方向空间,将各种取向断层面产生的P波辐射花样叠加,给出了不同应力状态和摩擦系数情况下产生的大量地震综合P波辐射花样的空间分布.发现主应力的相对大小和摩擦系数同时影响综合P波辐射花样的空间形态,在一定程度上,辐射花样从一种形态改变为另一种形态可通过改变任一参数进行,表明同时反演此两种参数是困难的.但通过其他手段确定摩擦系数后,可以采用P波初动信息得到较为合理的应力相对大小.该研究为考虑摩擦系数、采用大量P波初动资料精确确定应力场提供了新的思路.
In order to study the impact of stress ratio and friction coefficient on P-wave radiation patterns from a large number of earthquakes,we present how the shear stress,friction stress and Coulomb failure stress of the fault varies as a function of its orientation with respect to different stress ratios.The results show that the shear stress on the fault plane with various orientations indicates larger differences comparing to friction stress variations for different fault orientations. Assuming the spatial distribution of Coulomb failure stress is relevant to the P wave radiation pattern,and fault plane orientations are randomly distributed over the whole space,we superpose P wave radiation patterns from all fault orientations,and illustrate the characteristics of composite P wave radiation pattern in terms of different stress ratio and friction coefficient.We find that the stress ratio and friction coefficient both affect the composite P wave radiation pattern.To some extent,the shape of the composite P wave radiation can be changed by varying any of the two parameters,indicating the difficult to solve both of the parameters indepdently. However,if the friction coefficient can be determined by other methods,we can obtain a reasonable stress ratio by using P wave first motions.This work provides new idea to accurately determine stress field considering friction coefficient by large number of P first motion polarity data.
In order to study the impact of stress ratio and friction coefficient on P-wave radiation patterns from a large number of earthquakes,we present how the shear stress,friction stress and Coulomb failure stress of the fault varies as a function of its orientation with respect to different stress ratios.The results show that the shear stress on the fault plane with various orientations indicates larger differences comparing to friction stress variations for different fault orientations. Assuming the spatial distribution of Coulomb failure stress is relevant to the P wave radiation pattern,and fault plane orientations are randomly distributed over the whole space,we superpose P wave radiation patterns from all fault orientations,and illustrate the characteristics of composite P wave radiation pattern in terms of different stress ratio and friction coefficient.We find that the stress ratio and friction coefficient both affect the composite P wave radiation pattern.To some extent,the shape of the composite P wave radiation can be changed by varying any of the two parameters,indicating the difficult to solve both of the parameters indepdently. However,if the friction coefficient can be determined by other methods,we can obtain a reasonable stress ratio by using P wave first motions.This work provides new idea to accurately determine stress field considering friction coefficient by large number of P first motion polarity data.
引文
[1]Gephart J W,Forsyth D W.An improved method for determining the regional stress tensor using earthquake focal mechanism data:application to the San Fernando earthquake sequence.J.Geophys.Res.,1984,89:9305-9320
[2]Michael A J.Determination of stress from slip data:faults and folds.J.Geophys.Res.,1984,89:11517-11526
[3]李钦祖,王泽皋,贾云年等.由单台小地震资料所得两个区域的应力场.地球物理学报,1973,16:49-61 Li Q Z,Wang Z G,Jia Y N,et al.Stress field obtained for two regions from weak earthquake data recorded at a single station.Chinese J.Geophys.(in Chinese),1973,16:49- 61
[4]许忠淮,刘玉芬,张郢珍.京津唐张地区地震应力场的方向特征.地震学报,1979,1(2):121-132 Xu Z H,Liu Y F,Zhang Y Z.On the characteristic of direction of the earthquake stress field around the Beijing area.Acta Seismologica Sinica(In Chinese),1979,1(2): 121-132
[5]许忠淮,阎明,赵仲和.由多个小地震推断的华北地区构造应力场的方向.地震学报,1983,5(3):268-279 Xu Z H,Yan M,Zhao Z H.Evaluation of the direction of tectonic stress in North China from recorded data of a large number of small earthquakes.Acta Seismologica Sinica(in Chinese),1983,5(3):268-279
[6]Xu Z H,Wang S Y,Huang Y R,et al.Tectonic stress field of China inferred from a large number of small earthquakes. J.Geophys.Res.,1992,97:11867-11877
[7]Robinson R.McGinty P J.The enigma of the Arthur's Pass, New Zealand,earthquake 2.The aftershock distribution and its relation to regional and induced stress fields.J.Geophy. Res.,2000,105(B7):16139-16150
[8]Reasenberg P A,Oppenheimer D.FPFIT,FPPLOT,and FPPAGE:Fortran computer programs for calculating and displaying earthquake fault-plane solutions.U.S.Geol. Surv.Open-FileRept,1985,85-739
[9]Kisslinger C,Bowman J R,Koch K.Procedures for computing focal mechanisms from local(SV/ P) z data. Bull.Seis.Soc.Amer.,1981,87(6):1719-1730
[10]Snoke J A,Munsey J W,Teague A G,et al.A program for focal mechanism determination by combined use of polarity and SV-P amplitude ratio data.Earthquake Notes,1984,55 (3):15
[11]梁尚鸿,李幼铭,束沛镒等.利用区域地震台网P、S振幅比资料测定小震震源参数.地球物理学报,1984,27(3):249- 256 Liang S H,Li Y M,Shu P Y,et al.On the determination of source parameters of small earthquakes by using amplitude ratios of P and S from regional network observations.Chinese J.Geophys.(in Chinese),1984,27(3):249-256
[12]吴大铭,王培德,陈运泰.用SH波和P波振幅比确定震源机制解.地震学报,1989,11(3):275-278 Wu F T,Wang P D,Chen Y T.Determination of focal mechanism using SH to P amplitude ratio.Acta Seismologica Sinica(in Chinese),1989,11(3):275-278
[13]Hardebeck J L,Shearer P M.Using S/P amplitude ratios to constrain the focal mechanisms of small earthquakes.Bull. Seism.Soc.Amer.,2003,93:2434-2444
[14]Udias A.Source parameters of earthquakes from spectra of Rayleigh waves.Geophys.J.R.Astr.Soc.,1971,51(3): 401 -435
[15]倪江川,陈运泰,王鸣等.云南禄劝地震部分余震的矩张量反演,地震学报,1991,13(4):412-419 Ni J C,Chen Y T,Wang M,et al.Moment tensor inversion of some aftershocks of the April 18,1985,Luquan,Yunnan, ??China,earthquake.Acta Seismologica Sinica(in Chinese), 1991,13(4):412-419
[16]吴忠良,臧绍先.用体波合成地震图方法确定渤海、永善两大地震的震源参数,地震学报,1991,13(1):1-7 Wu Z L,Zang S X.Source parameters of Bohai earthquake of July 18,1969 and Yongshan earthquake of May 11,1974 from synthetic seismologram of body waves.Acta Seismologica Sinica(in Chinese),1991,13(1):1-7
[17]马淑田,姚振兴,纪晨.用长周期面波波形拟合及P波初动方向估计中等地震的震源机制,地球物理学报,1999,42(6): 785-799 Ma S T,Yao Z X,Ji C.To estimate focal mechanisms of moderate earthquakes using a long period surface waveform fitting method as well as first motion signs of P waves. ChineseJ.Geophys.(in Chinese),1999,42(6):785-799
[18]万永革,吴忠良,周公威等.中国地震震源机制测定结果的比较,地震地磁观测与研究,2001,22(5):1-15 Wan Y G,Wu Z L,Zhou G W,et al.China seismic mechanisms comparison for different determination.Seismological and Geomagnetic Observation and Research(in Chinese), 2001,22(5):1-15
[19]许忠淮.用滑动方向拟合法反演唐山余震区的平均应力场.地震学报,1985,7(4):349-362 Xu Z H.1985.Mean stress field in Tangshan aftershock area obtained from focal mechanism data by fitting slip direction. Acta Seismologica Sinica(in Chinese),1985,7(4):349- 362
[20]杜兴信,邵辉成.由震源机制解反演中国大陆现代构造应力场.地震学报,1999,21(4):354-360 Du X X,Shao H C.Modern tectonic stress field in the Chinese mainland inverted from focal mechanism solutions. Acta Seismologica Sinica,1999,12(4):390-397
[21]Wan Y,Wu Z,Zhou G.Focal mechanism dependence of static stress triggering of earthquakes.Tectnophysics,2004, 390:235-243
[22]Mizoguchi K,Takahashi M,Tanikawa W,et al.Frictional strength of fault gouge in Taiwan Chelungpu fault obtained from TCDP Hole B.Tectonophysics,2008,460:198--205
[23]Mizoguchi K,Hirose T,Shimamoto T.High-velocity frictional behavior and microstructure evolution of fault gouge obtained from Nojima fault,southwest Japan.Tectonophysics, 2009,471:285-296
[24]Cattin R,Chamot-Rooke N,Pubellier M,et al.Stress change and effective friction coefficient along the Sumatra Andaman-Sagaing fault system after the 26 December 2004 (M_w=9.2) and the 28 March 2005(M_w=8.7) earthquakes, Geochem.Geophys.Geosyst.,2009,10,Q03011,doi:10. 1029/2008GC002167.
[25]Morris A,Ferrill D A,Henderson D B.Slip-tendency analysis and fault reactivation.Geology,1996,24:275-278
[26]Collettini C,Trippetta F.A slip tendency analysis to test mechanical and structural control on aftershock rupture planes.Earth and Planetary Science Letters,2007,255: 402-413
[27]Lisle R J,Srivastava D C.Test of the frictional reactivation theory for faults and validity of fault slip analysis.Geology, 2004,32:569-572
[28]Aki K,Richards P G.Quantitative Seismology:Theory and Methods.Vol 1 &2,W H Freeman,San Francisco,1980. 932
[29]万永革,沈正康,刁桂苓等.利用小震分布和区域应力场确定大震断层面参数方法研究及其在唐山地震序列中的应用.地球物理学报,2008,51(3):793-804 Wan Y G,Shen Z K,Diao G L,et al.An algorithm of fault parameter determination using distribution of small earthquakes and parameters of regional stress field and its application to Tangshan earthquake sequence.Chinese J.Geophys,(in Chinese),2008,51(3):793-801
[30]万永革.“地震静态应力触发”问题的研究[博士论文].北京:中国地震局地球物理研究所,2001 Wan Y G.Research on“seismic static stress triggering”problem.[Ph.D.thesis](in Chinese).Beijing:Institute of Geophysics,China Seismological Bureau,2001
[31]Jaeger J G,Cook G W.Fundamentals of Rock Mechanism (Third ed).London:Chapman and Hall,1979
[32]俞春泉,陶开,崔效锋等.用格点尝试法求解P波初动震源??机制解及解的质量评价.地球物理学报,2009,52(5):1402- 1411 Yu C Q,Tao K,Cui X F,et al.P wave first motion focal mechanism solutions and their quality evaluation.Chinese J. Geophys.(in Chinese),2009,52(5):1402-1411
[33]万永革.地震辐射花样的立体表示.防灾技术高等专科学校学报,2001,3(4):35-40 Wan Y G.3- D representation of seismic source radiation pattern.Journal of College of Disaster-Prevention Technique(in Chinese),2001,3(4):35-40
[34]King G C P,Stein R S,Lin J.Static stress changes and the triggering of earthquakes.Bull.Seism.Soc.Amer.,1994, 84:935-953
[35]Hauksson E.Crustal structure and seismicity distribution adjacent to the Pacific and North America plate boundary in Southern California.J.Geophys.Res.,2000,105:13875- 13903
[36]胡幸平,俞春泉,陶开等.利用P波初动资料求解汶川地震及其强余震震源机制解.地球物理学报,2008,51(6):1711- 1718 Hu X P,Yu C Q,Tao K,et al.Focal mechanism solutions of Wenchuan earthquake and its strong aftershocks obtained from initial P wave polarity analysis.Chinese J.Geophys.(in Chinese),2008,51(6):1711-1718
[2]Michael A J.Determination of stress from slip data:faults and folds.J.Geophys.Res.,1984,89:11517-11526
[3]李钦祖,王泽皋,贾云年等.由单台小地震资料所得两个区域的应力场.地球物理学报,1973,16:49-61 Li Q Z,Wang Z G,Jia Y N,et al.Stress field obtained for two regions from weak earthquake data recorded at a single station.Chinese J.Geophys.(in Chinese),1973,16:49- 61
[4]许忠淮,刘玉芬,张郢珍.京津唐张地区地震应力场的方向特征.地震学报,1979,1(2):121-132 Xu Z H,Liu Y F,Zhang Y Z.On the characteristic of direction of the earthquake stress field around the Beijing area.Acta Seismologica Sinica(In Chinese),1979,1(2): 121-132
[5]许忠淮,阎明,赵仲和.由多个小地震推断的华北地区构造应力场的方向.地震学报,1983,5(3):268-279 Xu Z H,Yan M,Zhao Z H.Evaluation of the direction of tectonic stress in North China from recorded data of a large number of small earthquakes.Acta Seismologica Sinica(in Chinese),1983,5(3):268-279
[6]Xu Z H,Wang S Y,Huang Y R,et al.Tectonic stress field of China inferred from a large number of small earthquakes. J.Geophys.Res.,1992,97:11867-11877
[7]Robinson R.McGinty P J.The enigma of the Arthur's Pass, New Zealand,earthquake 2.The aftershock distribution and its relation to regional and induced stress fields.J.Geophy. Res.,2000,105(B7):16139-16150
[8]Reasenberg P A,Oppenheimer D.FPFIT,FPPLOT,and FPPAGE:Fortran computer programs for calculating and displaying earthquake fault-plane solutions.U.S.Geol. Surv.Open-FileRept,1985,85-739
[9]Kisslinger C,Bowman J R,Koch K.Procedures for computing focal mechanisms from local(SV/ P) z data. Bull.Seis.Soc.Amer.,1981,87(6):1719-1730
[10]Snoke J A,Munsey J W,Teague A G,et al.A program for focal mechanism determination by combined use of polarity and SV-P amplitude ratio data.Earthquake Notes,1984,55 (3):15
[11]梁尚鸿,李幼铭,束沛镒等.利用区域地震台网P、S振幅比资料测定小震震源参数.地球物理学报,1984,27(3):249- 256 Liang S H,Li Y M,Shu P Y,et al.On the determination of source parameters of small earthquakes by using amplitude ratios of P and S from regional network observations.Chinese J.Geophys.(in Chinese),1984,27(3):249-256
[12]吴大铭,王培德,陈运泰.用SH波和P波振幅比确定震源机制解.地震学报,1989,11(3):275-278 Wu F T,Wang P D,Chen Y T.Determination of focal mechanism using SH to P amplitude ratio.Acta Seismologica Sinica(in Chinese),1989,11(3):275-278
[13]Hardebeck J L,Shearer P M.Using S/P amplitude ratios to constrain the focal mechanisms of small earthquakes.Bull. Seism.Soc.Amer.,2003,93:2434-2444
[14]Udias A.Source parameters of earthquakes from spectra of Rayleigh waves.Geophys.J.R.Astr.Soc.,1971,51(3): 401 -435
[15]倪江川,陈运泰,王鸣等.云南禄劝地震部分余震的矩张量反演,地震学报,1991,13(4):412-419 Ni J C,Chen Y T,Wang M,et al.Moment tensor inversion of some aftershocks of the April 18,1985,Luquan,Yunnan, ??China,earthquake.Acta Seismologica Sinica(in Chinese), 1991,13(4):412-419
[16]吴忠良,臧绍先.用体波合成地震图方法确定渤海、永善两大地震的震源参数,地震学报,1991,13(1):1-7 Wu Z L,Zang S X.Source parameters of Bohai earthquake of July 18,1969 and Yongshan earthquake of May 11,1974 from synthetic seismologram of body waves.Acta Seismologica Sinica(in Chinese),1991,13(1):1-7
[17]马淑田,姚振兴,纪晨.用长周期面波波形拟合及P波初动方向估计中等地震的震源机制,地球物理学报,1999,42(6): 785-799 Ma S T,Yao Z X,Ji C.To estimate focal mechanisms of moderate earthquakes using a long period surface waveform fitting method as well as first motion signs of P waves. ChineseJ.Geophys.(in Chinese),1999,42(6):785-799
[18]万永革,吴忠良,周公威等.中国地震震源机制测定结果的比较,地震地磁观测与研究,2001,22(5):1-15 Wan Y G,Wu Z L,Zhou G W,et al.China seismic mechanisms comparison for different determination.Seismological and Geomagnetic Observation and Research(in Chinese), 2001,22(5):1-15
[19]许忠淮.用滑动方向拟合法反演唐山余震区的平均应力场.地震学报,1985,7(4):349-362 Xu Z H.1985.Mean stress field in Tangshan aftershock area obtained from focal mechanism data by fitting slip direction. Acta Seismologica Sinica(in Chinese),1985,7(4):349- 362
[20]杜兴信,邵辉成.由震源机制解反演中国大陆现代构造应力场.地震学报,1999,21(4):354-360 Du X X,Shao H C.Modern tectonic stress field in the Chinese mainland inverted from focal mechanism solutions. Acta Seismologica Sinica,1999,12(4):390-397
[21]Wan Y,Wu Z,Zhou G.Focal mechanism dependence of static stress triggering of earthquakes.Tectnophysics,2004, 390:235-243
[22]Mizoguchi K,Takahashi M,Tanikawa W,et al.Frictional strength of fault gouge in Taiwan Chelungpu fault obtained from TCDP Hole B.Tectonophysics,2008,460:198--205
[23]Mizoguchi K,Hirose T,Shimamoto T.High-velocity frictional behavior and microstructure evolution of fault gouge obtained from Nojima fault,southwest Japan.Tectonophysics, 2009,471:285-296
[24]Cattin R,Chamot-Rooke N,Pubellier M,et al.Stress change and effective friction coefficient along the Sumatra Andaman-Sagaing fault system after the 26 December 2004 (M_w=9.2) and the 28 March 2005(M_w=8.7) earthquakes, Geochem.Geophys.Geosyst.,2009,10,Q03011,doi:10. 1029/2008GC002167.
[25]Morris A,Ferrill D A,Henderson D B.Slip-tendency analysis and fault reactivation.Geology,1996,24:275-278
[26]Collettini C,Trippetta F.A slip tendency analysis to test mechanical and structural control on aftershock rupture planes.Earth and Planetary Science Letters,2007,255: 402-413
[27]Lisle R J,Srivastava D C.Test of the frictional reactivation theory for faults and validity of fault slip analysis.Geology, 2004,32:569-572
[28]Aki K,Richards P G.Quantitative Seismology:Theory and Methods.Vol 1 &2,W H Freeman,San Francisco,1980. 932
[29]万永革,沈正康,刁桂苓等.利用小震分布和区域应力场确定大震断层面参数方法研究及其在唐山地震序列中的应用.地球物理学报,2008,51(3):793-804 Wan Y G,Shen Z K,Diao G L,et al.An algorithm of fault parameter determination using distribution of small earthquakes and parameters of regional stress field and its application to Tangshan earthquake sequence.Chinese J.Geophys,(in Chinese),2008,51(3):793-801
[30]万永革.“地震静态应力触发”问题的研究[博士论文].北京:中国地震局地球物理研究所,2001 Wan Y G.Research on“seismic static stress triggering”problem.[Ph.D.thesis](in Chinese).Beijing:Institute of Geophysics,China Seismological Bureau,2001
[31]Jaeger J G,Cook G W.Fundamentals of Rock Mechanism (Third ed).London:Chapman and Hall,1979
[32]俞春泉,陶开,崔效锋等.用格点尝试法求解P波初动震源??机制解及解的质量评价.地球物理学报,2009,52(5):1402- 1411 Yu C Q,Tao K,Cui X F,et al.P wave first motion focal mechanism solutions and their quality evaluation.Chinese J. Geophys.(in Chinese),2009,52(5):1402-1411
[33]万永革.地震辐射花样的立体表示.防灾技术高等专科学校学报,2001,3(4):35-40 Wan Y G.3- D representation of seismic source radiation pattern.Journal of College of Disaster-Prevention Technique(in Chinese),2001,3(4):35-40
[34]King G C P,Stein R S,Lin J.Static stress changes and the triggering of earthquakes.Bull.Seism.Soc.Amer.,1994, 84:935-953
[35]Hauksson E.Crustal structure and seismicity distribution adjacent to the Pacific and North America plate boundary in Southern California.J.Geophys.Res.,2000,105:13875- 13903
[36]胡幸平,俞春泉,陶开等.利用P波初动资料求解汶川地震及其强余震震源机制解.地球物理学报,2008,51(6):1711- 1718 Hu X P,Yu C Q,Tao K,et al.Focal mechanism solutions of Wenchuan earthquake and its strong aftershocks obtained from initial P wave polarity analysis.Chinese J.Geophys.(in Chinese),2008,51(6):1711-1718
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