双层黏弹介质模型条件下地震应力扰动的时空特征
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摘要
基于简化双层黏弹介质模型及其变形过程的时间属性,考虑震后地壳上层(黏滞性相对较弱)短时间的弹性扰动及后续较长时间内下层(黏滞性相对较强)黏性变形对上层应力扰动的联合作用,研究地震应力扰动的时空变化.结果显示,地震应力扰动在震后一段时间内逐渐增大,之后缓慢衰减.并且模型参数越接近真实地体,应力扰动增大及衰减过程就越缓慢,持续时间越长,即地震活动具有较长时期的时间"记忆"特性.因而,在地震活动及库仑应力变化研究中,长时期的应力扰动影响不宜忽略.地震应力扰动有一定的空间作用范围,在此范围内应力扰动随距离衰减明显,距离震源较近处衰减较快、距离震源较远处衰减相对较慢,此范围之外应力扰动可忽略不计.在本文所取与实际地壳相对较为接近的模型参数条件下,应力扰动的空间作用范围大体是震源线性破裂尺度的2.5倍.地震应力扰动随震级增大而逐渐增大,在本文模型参数条件下,震级大于6级之后,应力扰动随震级快速增加.地震破裂尺度测量误差所导致的应力扰动计算误差的相对大小,与时间无关,与破裂尺度(震级)及震源距有关,随震源距的增大而增大,但对应力扰动的总体变化趋势及变化范围影响甚微.当距离足够远时,应力扰动计算误差的相对大小趋于常数,就6、7、8级地震而言,最大应力扰动计算误差分别小于应力扰动值本身的22%、30%及38%.
Based on the simplified two-layer viscoelastic medium model and its temporal characteristics of the deformation process,considering the joint action of the instantaneous elastic stress perturbation in the upper layer(more elastic) and the delayed and long-term load on upper layer due to the viscous relaxation deformation in lower layer(more viscous),the spatio-temporal variation of the earthquake stress perturbation has been studied.The results show that the stress perturbation increases quickly during a short time since the earthquake and then decays slowly for a long time.And when model parameters approach to real data more and more,the increasing and decay process of the stress perturbation is slower,and the duration becomes gradually longer.In another word,the earthquake activity has a long-term 'memory' feature.Therefore,the long-term influence of stress perturbation could not be ignored in the study of earthquake activity or Coulomb stress changes.The stress perturbation has a limited acting range in space.It decreases obviously with distance inside the range,the decay is quick nearby the epicenter and is slow far away from the epicenter.The stress perturbation could be ignored outside the range.For the model parameters used in this paper,which approach to the real status for some extent,the effective acting range of the stress perturbation is about 2.5 times of the linear fracture size of the earthquake.The stress perturbation increases gradually with the mainshock magnitude,for the assumed model parameters in this paper,it increases more quickly when magnitude is larger than M6.The relative error of stress perturbation,resulting from the measurement errors of the fracture size,is relational to the fracture size(magnitude) and epicenter distance,and there is no relationship with the time.The relative error increases with the epicenter distance,but its total influence on changing tendency and numerical range of the stress perturbation are very small,it tends to constant when distance is large enough.For earthquake with magnitude M 6,M 7 and M 8,the maximum relative errors of stress perturbation are smaller than 22%,30% and 38%.
Based on the simplified two-layer viscoelastic medium model and its temporal characteristics of the deformation process,considering the joint action of the instantaneous elastic stress perturbation in the upper layer(more elastic) and the delayed and long-term load on upper layer due to the viscous relaxation deformation in lower layer(more viscous),the spatio-temporal variation of the earthquake stress perturbation has been studied.The results show that the stress perturbation increases quickly during a short time since the earthquake and then decays slowly for a long time.And when model parameters approach to real data more and more,the increasing and decay process of the stress perturbation is slower,and the duration becomes gradually longer.In another word,the earthquake activity has a long-term 'memory' feature.Therefore,the long-term influence of stress perturbation could not be ignored in the study of earthquake activity or Coulomb stress changes.The stress perturbation has a limited acting range in space.It decreases obviously with distance inside the range,the decay is quick nearby the epicenter and is slow far away from the epicenter.The stress perturbation could be ignored outside the range.For the model parameters used in this paper,which approach to the real status for some extent,the effective acting range of the stress perturbation is about 2.5 times of the linear fracture size of the earthquake.The stress perturbation increases gradually with the mainshock magnitude,for the assumed model parameters in this paper,it increases more quickly when magnitude is larger than M6.The relative error of stress perturbation,resulting from the measurement errors of the fracture size,is relational to the fracture size(magnitude) and epicenter distance,and there is no relationship with the time.The relative error increases with the epicenter distance,but its total influence on changing tendency and numerical range of the stress perturbation are very small,it tends to constant when distance is large enough.For earthquake with magnitude M 6,M 7 and M 8,the maximum relative errors of stress perturbation are smaller than 22%,30% and 38%.
引文
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[2]Toda S,Stein R S,Reasenberg P A,et al.Stress transferredby the 1995 Mw=6.9 Kobe,Japan,Shock:effect onaftershocks and future earthquake probabilities.J.Geophys.Res.,1998,103(B10):24543-24565.
[3]King G C P,Stein R S,Lin J.Static stress changes and thetriggering of earthquakes.Bull.Seism.Soc.Am.,1994,84(3):935-953.
[4]Reasenberg P A,Simpson R W.Response of regionalseismicity to the static stress change produced by the LomaPrieta earthquake.Science,1992,255(5052):1687-1690.
[5]Hardebeck J L,Nazareth J J,Hauksson E.The Static stresschange triggering model:constraints from two southernCalifornia aftershock sequences.J.Geophys.Res.,1998,103(B10):24427-24438.
[6]Chinnery M A.The stress changes that accompany strike-slipfaulting.Bull.Seism.Soc.Am.,1963,53(5):921-932.
[7]Smith S W,Van de Lindt W.Strain adjustments associatedwith earthquakes in southern California.Bull.Seism.Soc.Am.,1969,59(4):1569-1589.
[8]Rybichi K.Analysis of aftershocks on the basis of dislocationtheory.Phys.Earth Planet Inter.,1973,7(4):409-422.
[9]陈运泰,林邦慧,林中洋等.根据地面形变的观测研究1966年邢台地震的震源过程.地球物理学报,1975,18(3):164-182.Chen Y T,Lin B H,Lin Z Y,et al.The focal mechanism ofthe 1966 Hsingtai earthquake as inferred from the grounddeformation observations.Chinese J.Geophys.(in Chinese),1975,18(3):164-182.
[10]Yamashina K.Induced earthquakes in the Izu Peninsula bythe Izu-Hanto-Oki earthquake of 1974,Japan.Tectonophysics,1978,51(3-4):139-154.
[11]黄福明,王廷韫.倾斜断层错动产生的应力场.地震学报,1980,2(1):1-20.Huang F M,Wang T Y.The stress field of a dislocatinginclined fault.Acta Seismologica Sinica(in Chinese),1980,2(1):1-20.
[12]王仁,何国琦,殷有泉等.华北地区地震迁移规律的数学模拟.地震学报,1980,2(1):32-42.Wang R,He G Q,Yin Y Q,et al.A mathematicalsimulation for the pattern of seismic transference in northChina.Acta Seismologica Sinica(in Chinese),1980,2(1):32-42.
[13]郭增建,秦保燕.大震重复性与减震作用.//国家地震局科技司.近期强震危险性研究.北京:地震出版社,1989:455-456.Guo Z J,Qin B Y.Repeatability and weakening action of thelarge earthquakes.//Department of Science&Technology,National Seismological Bureau.Study on the Recent SeismicRisk of Large Earthquakes(in Chinese).Beijing:SeismologicalPress,1989:455-456.
[14]Das S,Scholz C H.Off-fault aftershock clusters caused byshear stress increase?Bull.Seism.Soc.Am.,1981,71(1):1669-1675.
[15]Byerlee J D.Friction of rocks.PAGEOPH,1978,116(4-5):615-626.
[16]Bak P,Tang C.Earthquakes as a self-organized criticalphenomena.J.Geophys.Res.,1989,94(B11):15635-15638.
[17]万永革,吴忠良,周公威等.几次复杂地震中不同破裂事件之间的“应力触发”问题.地震学报,2000,22(6):568-576.Wan Y G,Wu Z L,Zhou G W,et al.“Stress triggering”between different rupture events in several earthquakes.ActaSeismologica Sinica(in Chinese),2000,22(6):568-576.
[18]Sornette D,Pisarenko V F.Fractal plate tectonics.Geophys.Res.Lett.,2003,30:1105,doi:10.1029/2002_GL_015043.
[19]Ouillon G,Sornette D.Search for direct empirical spatialcorrelation signatures of the critical triggering earthquakemodel.Geophys.J.Int.,2004,157(3):1233-1246.
[20]高祥林,罗焕炎,诺依格鲍尔H J.大陆碰撞动力学的三维数值模拟.地震地质,1987,9(2):65-73.Gao X L,Luo H Y,Neugebauer H J.Three dimensionalnumerical modeling for the dynamics of the continentalcollision.Seismology and Geology(in Chinese),1987,9(2):65-73.
[21]张东宁,许忠淮.青藏高原现代构造应力状态及构造运动的三维弹粘性数值模拟.中国地震,1994,10(2):136-143.Zhang D N,Xu Z H.Three dimensional elasto-visconumerical simulation of Qinghai-Xizang Plateau′s recenttectonic stress field and its motion.Earthquake Research inChina(in Chinese),1994,10(2):136-143.
[22]王绳祖,张四昌,田勤俭.大陆动力学:网状塑性流动与多级构造变形.北京:地震出版社,2001:15-20.Wang S Z,Zhang S C,Tian Q J.Continental Dynamics:Netlike Plastic-Flow and Hierarchical Tectonic Deformation(in Chinese).Beijing:Seismological Press,2001:15-20.
[23]臧绍先,宁杰远,景志成.俯冲带流变性质的研究.中国科学(D辑),2001,31(9):705-711.Zang S X,Ning J Y,Jing Z C.Study on plastic-flowcharacteristics in subduction belt.Science in China(SeriesD)(in Chinese),2001,31(9):705-711.
[24]于泳,洪汉净,刘培洵等.粘弹性有限元与弹簧滑块耦合模型——断层与地块相互作用的数值模拟.中国科学(D辑),2003,33(增刊):82-90.Yu Y,Hong H J,Liu P X,et al.The viscoelastic finite-element and the coupling model of the spring-sliding black——numerical simulation on the interaction between faultswith the plate.Science in China(Series D)(in Chinese),2003,33(Suppl.):82-90.
[25]沈正康,万永革,甘卫军等.东昆仑活动断裂带大地震之间的黏弹性应力触发研究.地球物理学报,2003,46(6):786-795.Shen Z K,Wan Y G,Gan W J,et al.Viscoelastic triggeringamong large earthquakes along the east Kunlun fault system.Chinese J.Geophys.(in Chinese),2003,46(6):786-795.
[26]沈正康,万永革,甘卫军等.华北地区700年来地壳应力场演化与地震的关系研究.中国地震,2004,20(3):211-228.Shen Z K,Wan Y G,Gan W J,et al.Crustal stressevolution of the last 700years in North China and earthquakeoccurrence.Earthquake Research in China(in Chinese),2004,20(3):211-228.
[27]万永革,沈正康,曾跃华等.唐山地震序列应力触发的粘弹性力学模型研究.地震学报,2008,30(6):581-593.Wan Y G,Shen Z K,Zeng Y H,et al.Study on visco-elasticstress triggering model of the 1976 Tangshan earthquakesequence.Acta Seismologica Sinica(in Chinese),2008,30(6):581-593.
[28]邵志刚,周龙泉,蒋长胜等.2008年汶川Ms8.0地震对周边断层地震活动的影响.地球物理学报,2010,53(8):1784-1795.Shao Z G,Zhou L Q,Jiang C S,et al.The impact ofWenchuan Ms8.0 earthquake on the seismic activity ofsurrounding faults.Chinese J.Geophys.(in Chinese),2010,53(8):1784-1795.
[29]蒋海昆,郑建常,吴琼等.中国大陆中强以上地震余震分布尺度的统计特征.地震学报,2007,29(2):151-164.Jiang H K,Zheng J C,Wu Q,et al.Statistical features ofaftershock distribution size for moderate and large earthquakes inChinese mainland.Acta Seismologica Sinica(in Chinese),2007,29(2):151-164.
[30]Aki K.Earthquake mechanism.Tectonophysics,1972,13(1-4):423-446.
[31]Hanks T C,Bakun W H.A bilinear source-scaling model forM-logA observations of continental earthquakes.Bull.Seism.Soc.Am.,2002,92(5):1841-1846.
[32]Venkataraman A,Kanamori H.Observational constraints onthe fracture energy of subduction zone earthquakes.J.Geophys.Res.,2004,109:B05302,doi 10.1029/2003JB002549.
[33]Hardebeck J L,Aron A.Earthquake stress drops andinferred fault strength on the Hayward fault,east SanFrancisco Bay,California.Bull.Seism.Soc.Am.,2009,99(3):1801-1814.
[34]McGarr A,Fletcher J B.Mapping apparent stress and energyradiation over fault zones of major earthquakes.Bull.Seism.Soc.Am.,2002,92(5):1633-1646.
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