汶川地震地表破裂面形貌特征
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摘要
准确描述破裂面形貌对于我们理解地震断层作用是非常重要的,破裂面的形貌特征包含许多关于地震和断层机制的有用信息。在Mw7.9 2008汶川地震中断层活动产生了两个新鲜的破裂面,八角庙破裂面和沙坝破裂面。我们使用3D便携式激光扫描仪(Tri mble GX)对两个破裂表面进行测量,在野外微观尺度上研究了破裂面形貌特征。通过能谱密度和均方值两个方法分析破裂面形貌,新鲜的破裂面表现为自相仿性,能谱密度和均方值均与剖面长度存在幂律关系。在能谱密度与空间频率的对数图中,能谱密度曲线存在明显的拐点,该拐点所对应的波长称为"特征波长",表明单一分形不能准确描述破裂面形貌。八角庙破裂面在平行滑动方向上的特征波长为7 mm,在垂直方向上特征波长略大一些(区域Ⅰ为10 mm,区域Ⅱ为9 mm);沙坝破裂面在平行滑动方向上的特征波长为8 mm,但垂直方向上特征波长略小(6 mm)。均方值曲线的最小二乘拟合直线的斜率为Hurst指数,该指数依赖于剖面线方向并描述破裂面形貌的各向异性,H指数的最小值和最大值分别与平行擦痕和垂直擦痕方向对应,这与野外断层面擦痕测量结果一致。沙坝破裂面的H指数极坐标图中存在次级H指数峰值(对应剖面线方向为85°和160°),这揭示破裂面上存在一组隐匿擦痕。该组隐匿擦痕为汶川地震之前断层活动中形成的,但这还不足以推测上一次断层活动的时间和规模。另外,通过比较新鲜节理面和破裂面表明H指数是否大于0.8反映了断层类型。在整个空间频率域上,能谱密度曲线斜率(-α)和均方值曲线斜率(H)的线性拟合关系为α=1.22+1.72H,并不严格满足两者之间理论关系式,α=1+2H。这个差异是由于测量信号噪音、破裂面的多分形性和分析方法的差异造成的。
It is very important to describe accurately the topography of rupture surfaces for our understanding of seismic faulting because the topographic characteristics of the rupture include much information about the earthquake and fault mechanics.Two fresh rupture surfaces of the Mw 7.9 2008 Wenchuan earthquake,referred to as the Bajiaomiao surface and the Shaba surface,have been measured by scanning with a 3D portable laser scanner(Trimble GX).The acquired sets of DEM data were analyzed using power spectral density and root-mean-square(RMS) roughness.The fresh rupture surfaces exhibit self-affine behavior,and the power spectral density and RMS roughness both have power law relationship with the length of profiles.In log-log plot of power spectral density versus spatial frequency,there is an obvious inflexion which divides the spatial frequency into lower frequency domain and higher frequency domain.The wavelength corresponding to the inflexion is called "characteristic wavelength",and it shows that a single fractal can not describe the roughness scale for the rupture surface.The characteristic wavelength is 7 mm in the direction parallel to the slip for the Bajiaomiao surface(both in Patch Ⅰ and Ⅱ),smaller than that in the direction perpendicular to the slip(10 mm in Patch Ⅰ and 9 mm in PatchⅡ),and 8 mm in the direction parallel to the slip for the Shaba surface,but larger than that in the direction perpendicular to the slip(6 mm).The slope of least squares fitting line to the RMS roughness curve in log-log plot is the H exponent,and the H exponent depends on the direction of profile and describes the morphological anisotropy of fault surface.The maximum value and minimum value of H are in the direction perpendicular to the slip and in the direction parallel to the slip,respectively.It is accordant to the slip directions measured in field.A secondary set of H-value peaks(85° and 160°) in Shaba rupture surface revealed a set of concealed striations produced by an earthquake prior to the Wenchuan earthquake.But it is not sufficient to determine the time and magnitude of this inferred faulting event.Moreover,through the comparison of the H value between fresh joint surface and fault surface,it shows that whether the H value is larger than 0.8 probably depends on the type of fault.By linear fitting between the slopes of power spectral density(-α) and the slope of RMS roughness(H) in whole length of profile,a relationship can be obtained: α=1.22+1.72H;it does not obey the theoretical relationship α=1+2H strictly.This difference is probably caused by the noise in the data,the multi-fractal of the rupture surface and the analysis methods of roughness.
It is very important to describe accurately the topography of rupture surfaces for our understanding of seismic faulting because the topographic characteristics of the rupture include much information about the earthquake and fault mechanics.Two fresh rupture surfaces of the Mw 7.9 2008 Wenchuan earthquake,referred to as the Bajiaomiao surface and the Shaba surface,have been measured by scanning with a 3D portable laser scanner(Trimble GX).The acquired sets of DEM data were analyzed using power spectral density and root-mean-square(RMS) roughness.The fresh rupture surfaces exhibit self-affine behavior,and the power spectral density and RMS roughness both have power law relationship with the length of profiles.In log-log plot of power spectral density versus spatial frequency,there is an obvious inflexion which divides the spatial frequency into lower frequency domain and higher frequency domain.The wavelength corresponding to the inflexion is called "characteristic wavelength",and it shows that a single fractal can not describe the roughness scale for the rupture surface.The characteristic wavelength is 7 mm in the direction parallel to the slip for the Bajiaomiao surface(both in Patch Ⅰ and Ⅱ),smaller than that in the direction perpendicular to the slip(10 mm in Patch Ⅰ and 9 mm in PatchⅡ),and 8 mm in the direction parallel to the slip for the Shaba surface,but larger than that in the direction perpendicular to the slip(6 mm).The slope of least squares fitting line to the RMS roughness curve in log-log plot is the H exponent,and the H exponent depends on the direction of profile and describes the morphological anisotropy of fault surface.The maximum value and minimum value of H are in the direction perpendicular to the slip and in the direction parallel to the slip,respectively.It is accordant to the slip directions measured in field.A secondary set of H-value peaks(85° and 160°) in Shaba rupture surface revealed a set of concealed striations produced by an earthquake prior to the Wenchuan earthquake.But it is not sufficient to determine the time and magnitude of this inferred faulting event.Moreover,through the comparison of the H value between fresh joint surface and fault surface,it shows that whether the H value is larger than 0.8 probably depends on the type of fault.By linear fitting between the slopes of power spectral density(-α) and the slope of RMS roughness(H) in whole length of profile,a relationship can be obtained: α=1.22+1.72H;it does not obey the theoretical relationship α=1+2H strictly.This difference is probably caused by the noise in the data,the multi-fractal of the rupture surface and the analysis methods of roughness.
引文
[1]Power W L,Tullis T E,Weeks J D.Roughness and wearduring brittle faulting[J].Journal of Geophysical Research,1988,93(B12):15268-15278.
[2]Sagy A,Brodsky E E,Axen G J.Evolution of fault-surfaceroughness with slip[J].Geology,2007,35:283-286.
[3]Lay T,Kanamori H,Ruff L.The asperity model andthe na-ture of large subduction zone earthquakes[J].EarthquakePrediction Research,1982,1:3-71.
[4]Scholz C H.The Mechanics of Earthquakes and Faulting[M].Cambridge:Cambridge University Press,2002:496.
[5]Campillo M,Favreau P,Ionescu I R,et al.On the effectivefrictionlaw of an heterogeneous fault[J].Journal of Geo-physical Research,2001,106:307-322.
[6]Brodsky E E,Kanamori H.Elastohydrodynamic lubricationof faults[J].Journal of Geophysical Research,2001,106(16):357-374,doi:10.1029/2001JB000430.
[7]Power W L,Tullis T E,Brown S R,et al.Roughness ofnatural fault surfaces[J].Geophysical Research Letters,1987,14(1):29-32.
[8]Renard F,Voisin C,Marsan D,et al.High resolution 3Dla-ser scanner measurements of a strike-slip fault quantify itsmorphological anisotropy at all scales[J].Geophysical ResearchLetters,2006,33:L04305,doi:10.1029/2005GL025038.
[9]Schaff D P,Bokel mann G HR,Beroza G C,et al.High-res-olutioni mage of Calaveras Fault seismicity[J].Journal of Ge-ophysical Research,2002,107(B9):2186-2198,doi:10.1029/2001JB000633.
[10]Xie H P,Pariseau W G.Fractal esti mate of rock fractureroughness(JRC)[J].Science in China:Series D,1994,24(5):524-532(in Chinese).
[11]Xie H P,Zhou H W.Research on mechanical behaviors ofrockjoints based on fractal theory[J].Science Fund of Chi-na,1998,12(4):247-252(in Chinese).
[12]Xie H,Wang J A.Direct fractal measurement of fracturesurfaces[J].International Journal of Solids and Structures,1999,36:3073.
[13]Zhou H W,Xie HP,Kwasniewski M A.Progress of the re-searchin morphologic analysis of rock joint surface[J].Pro-gress in Natural Science,2001,11(7):682-688(in Chinese).
[14]Walsh J B,Groshenbaugh M A.A new model for analyzingthe effect of fractures on compressibility[J].Journal of Geo-physical Research,1979,84:3532-3536.
[15]Power WL,Tullis T E.Euclidean andfractal models for thedescription of rock surface-roughness[J].Journal of Geo-physical Research,1991,96:415-424.
[16]Lee J J,Bruhn R L.Structural anisotropy of normal faultsurfaces[J].Journal of Structural Geology,1996,18:1043-1059,doi:10.1016/0191-8141(96)00022-3.
[17]Brown S R,Scholz C H.Broad bandwidth study of the to-pography of natural rock surfaces[J].Journal of GeophysicalResearch,1985,90:2575-2582.
[18]Schmittbuhl J,Gentier S,Roux S.Field measurements ofthe roughness of fault surfaces[J].Geophysical ResearchLetters,1993,20(8):639-641.
[19]Candela T,Renard F,Bouchon M,et al.Characterization offault roughness at various scales:I mplications of three-di-mensional high resolution topography measurements[J].Pure and Applied Geophysics,2009,166:1817-1851.
[20]Brown S R.Si mple mathematical model of a rough fracture[J].Journal of Geophysical Research,1995,100:5941-5952,doi:10.1029/94JB03262.
[21]Berry MV,Lewis Z V.Onthe Weierstrass-Mandelbrot frac-tal function[J].Proc R Soc London:Series A,1980,370:459-484.
[22]China Seismic Information Net.2008 Seismological Parame-ters for theMs8.0 Wenchuan Earthquake,Sichuan[R].ht-tp:∥www.csi.ac.cn/sichuan/sichuan 080512_cs1.ht m(inChinese).
[23]Xu X W,Wen X Z,Ye J Q,et al.TheMs8.0 Wenchuanearthquake surface ruptures andits seismogenic structure[J].Seismology and Geology,2008,30(3):597-629(in Chi-nese).
[24]Li C Y,Wei Z Y.Deformation styles of the northernmostsurface rupture zone of theMs8.0 Wenchuan earthquake[J].Seismology and Geology,2009,31(1):1-8(in Chinese).
[25]Xu X W,Wen X Z,Yu G H,et al.Coseismic reverse-andoblique-slip surface faulting generated by the 2008Mw7.9Wenchuan earthquake,China[J].Geology,2008,37:515-518.
[26]Ran Y K,Shi X,Wang H,et al.The maxi mum coseismicvertical surface displacement and surface deformation patternaccompanying theMs8.0 Wenchuan earthquake[J].ChineseScience Bulletin,2009,55(3):841-850.doi:10.1007/s11434-009-0453-3.
[27]Ran Y K,Shi X,Wang H,et al.The maxi mum coseismicvertical surface displacement and surface deformation patternaccompanying theMs8.0 Wenchuan earthquake[J].ChineseScience Bulletin,2010,55(2):154-162(in Chinese).
[28]Deng Q D,Ran Y K,Yang X P,et al.Map of Active Tec-tonics in China[M].Beijing:Seismological Press,2007(inChinese).
[29]He H L,Sun Z M,Wei Z Y,et al.Rupture of theMs8.0Wenchuan earthquake along Baishahe River[J].Seismologyand Geology,2008,30(3):658-673(in Chinese).
[30]Haneberg WC.Directional roughness profiles fromthree di-mensional photogrammetric or laser scanner point clouds[C]∥Proceedings of the 1st Canada-US Rock Mechanics Sympo-sium.Vancouver,27-31 May,2007:101-106.
[31]Haneberg W C.Using close range terrestrial digital photo-grammetry for 3-D rock slope modeling and discontinuitymappingin the United States[J].Bulletin of Engineering Ge-ology and the Environment,2008,67:457-469.
[32]Power WL,Durham WB.Topography of natural and artifi-cial fractures in granitic rocks:I mplications for studies ofrock friction and fluid migration[J].International Journal ofRock Mechanics and Mining Sciences,1997,34(6):979-989.
[33]Chen G,Spetzler H A.Topographic characteristics of labora-tory-induced shear fractures[J].Pure and Applied Geophys-ics,1993,140:123-135.
[34]Scholz C H,Avites C A.The fractal geometry of faults andfaulting[M]∥Das S,Boatwritht J,Scholz C.EarthquakesSource Mechanics.Washington DC:American GeophysicalUnion Monograph,1986,37:147-156.
[10]谢和平,Pariseau W G.岩石节理粗糙系数(JRC)的分形估计[J].中国科学:D辑,1994,24(5):524-532.
[11]谢和平,周宏伟.基于分形理论的岩石节理力学行为研究[J].中国科学基金,1998,12(4):247-252.
[13]周宏伟,谢和平,Kwasniewski M A.岩体节理表面形态描述的研究进展[J].自然科学进展,2001,11(7):682-688.
[22]中国地震信息网.2008四川汶川县Ms8.0地震参数[R].http:∥www.csi.ac.cn/sichuan/sichuan 080512_cs1.ht m.
[23]俆锡伟,闻学泽,叶建青,等.汶川Ms8.0地震地表破裂带及其发震构造[J].地震地质,2008,30(3):597-629.
[24]李传友,魏占玉.汶川Ms8.0地震地表破裂带北端位置的修订[J].地震地质,2009,31(1):1-8.
[27]冉勇康,史翔,王虎,等.汶川Ms8地震最大地表同震垂直位移量及地表变形样式[J].科学通报,2010,55(2):154-162.
[28]邓起东,冉勇康,杨晓平,等.中国活动构造图[M].北京:地震出版社,2007.
[29]何宏林,孙昭民,魏占玉,等.汶川Ms8.0地震地表破裂带白沙河段破裂及其位移特征[J].地震地质,2008,30(3):658-673.
[2]Sagy A,Brodsky E E,Axen G J.Evolution of fault-surfaceroughness with slip[J].Geology,2007,35:283-286.
[3]Lay T,Kanamori H,Ruff L.The asperity model andthe na-ture of large subduction zone earthquakes[J].EarthquakePrediction Research,1982,1:3-71.
[4]Scholz C H.The Mechanics of Earthquakes and Faulting[M].Cambridge:Cambridge University Press,2002:496.
[5]Campillo M,Favreau P,Ionescu I R,et al.On the effectivefrictionlaw of an heterogeneous fault[J].Journal of Geo-physical Research,2001,106:307-322.
[6]Brodsky E E,Kanamori H.Elastohydrodynamic lubricationof faults[J].Journal of Geophysical Research,2001,106(16):357-374,doi:10.1029/2001JB000430.
[7]Power W L,Tullis T E,Brown S R,et al.Roughness ofnatural fault surfaces[J].Geophysical Research Letters,1987,14(1):29-32.
[8]Renard F,Voisin C,Marsan D,et al.High resolution 3Dla-ser scanner measurements of a strike-slip fault quantify itsmorphological anisotropy at all scales[J].Geophysical ResearchLetters,2006,33:L04305,doi:10.1029/2005GL025038.
[9]Schaff D P,Bokel mann G HR,Beroza G C,et al.High-res-olutioni mage of Calaveras Fault seismicity[J].Journal of Ge-ophysical Research,2002,107(B9):2186-2198,doi:10.1029/2001JB000633.
[10]Xie H P,Pariseau W G.Fractal esti mate of rock fractureroughness(JRC)[J].Science in China:Series D,1994,24(5):524-532(in Chinese).
[11]Xie H P,Zhou H W.Research on mechanical behaviors ofrockjoints based on fractal theory[J].Science Fund of Chi-na,1998,12(4):247-252(in Chinese).
[12]Xie H,Wang J A.Direct fractal measurement of fracturesurfaces[J].International Journal of Solids and Structures,1999,36:3073.
[13]Zhou H W,Xie HP,Kwasniewski M A.Progress of the re-searchin morphologic analysis of rock joint surface[J].Pro-gress in Natural Science,2001,11(7):682-688(in Chinese).
[14]Walsh J B,Groshenbaugh M A.A new model for analyzingthe effect of fractures on compressibility[J].Journal of Geo-physical Research,1979,84:3532-3536.
[15]Power WL,Tullis T E.Euclidean andfractal models for thedescription of rock surface-roughness[J].Journal of Geo-physical Research,1991,96:415-424.
[16]Lee J J,Bruhn R L.Structural anisotropy of normal faultsurfaces[J].Journal of Structural Geology,1996,18:1043-1059,doi:10.1016/0191-8141(96)00022-3.
[17]Brown S R,Scholz C H.Broad bandwidth study of the to-pography of natural rock surfaces[J].Journal of GeophysicalResearch,1985,90:2575-2582.
[18]Schmittbuhl J,Gentier S,Roux S.Field measurements ofthe roughness of fault surfaces[J].Geophysical ResearchLetters,1993,20(8):639-641.
[19]Candela T,Renard F,Bouchon M,et al.Characterization offault roughness at various scales:I mplications of three-di-mensional high resolution topography measurements[J].Pure and Applied Geophysics,2009,166:1817-1851.
[20]Brown S R.Si mple mathematical model of a rough fracture[J].Journal of Geophysical Research,1995,100:5941-5952,doi:10.1029/94JB03262.
[21]Berry MV,Lewis Z V.Onthe Weierstrass-Mandelbrot frac-tal function[J].Proc R Soc London:Series A,1980,370:459-484.
[22]China Seismic Information Net.2008 Seismological Parame-ters for theMs8.0 Wenchuan Earthquake,Sichuan[R].ht-tp:∥www.csi.ac.cn/sichuan/sichuan 080512_cs1.ht m(inChinese).
[23]Xu X W,Wen X Z,Ye J Q,et al.TheMs8.0 Wenchuanearthquake surface ruptures andits seismogenic structure[J].Seismology and Geology,2008,30(3):597-629(in Chi-nese).
[24]Li C Y,Wei Z Y.Deformation styles of the northernmostsurface rupture zone of theMs8.0 Wenchuan earthquake[J].Seismology and Geology,2009,31(1):1-8(in Chinese).
[25]Xu X W,Wen X Z,Yu G H,et al.Coseismic reverse-andoblique-slip surface faulting generated by the 2008Mw7.9Wenchuan earthquake,China[J].Geology,2008,37:515-518.
[26]Ran Y K,Shi X,Wang H,et al.The maxi mum coseismicvertical surface displacement and surface deformation patternaccompanying theMs8.0 Wenchuan earthquake[J].ChineseScience Bulletin,2009,55(3):841-850.doi:10.1007/s11434-009-0453-3.
[27]Ran Y K,Shi X,Wang H,et al.The maxi mum coseismicvertical surface displacement and surface deformation patternaccompanying theMs8.0 Wenchuan earthquake[J].ChineseScience Bulletin,2010,55(2):154-162(in Chinese).
[28]Deng Q D,Ran Y K,Yang X P,et al.Map of Active Tec-tonics in China[M].Beijing:Seismological Press,2007(inChinese).
[29]He H L,Sun Z M,Wei Z Y,et al.Rupture of theMs8.0Wenchuan earthquake along Baishahe River[J].Seismologyand Geology,2008,30(3):658-673(in Chinese).
[30]Haneberg WC.Directional roughness profiles fromthree di-mensional photogrammetric or laser scanner point clouds[C]∥Proceedings of the 1st Canada-US Rock Mechanics Sympo-sium.Vancouver,27-31 May,2007:101-106.
[31]Haneberg W C.Using close range terrestrial digital photo-grammetry for 3-D rock slope modeling and discontinuitymappingin the United States[J].Bulletin of Engineering Ge-ology and the Environment,2008,67:457-469.
[32]Power WL,Durham WB.Topography of natural and artifi-cial fractures in granitic rocks:I mplications for studies ofrock friction and fluid migration[J].International Journal ofRock Mechanics and Mining Sciences,1997,34(6):979-989.
[33]Chen G,Spetzler H A.Topographic characteristics of labora-tory-induced shear fractures[J].Pure and Applied Geophys-ics,1993,140:123-135.
[34]Scholz C H,Avites C A.The fractal geometry of faults andfaulting[M]∥Das S,Boatwritht J,Scholz C.EarthquakesSource Mechanics.Washington DC:American GeophysicalUnion Monograph,1986,37:147-156.
[10]谢和平,Pariseau W G.岩石节理粗糙系数(JRC)的分形估计[J].中国科学:D辑,1994,24(5):524-532.
[11]谢和平,周宏伟.基于分形理论的岩石节理力学行为研究[J].中国科学基金,1998,12(4):247-252.
[13]周宏伟,谢和平,Kwasniewski M A.岩体节理表面形态描述的研究进展[J].自然科学进展,2001,11(7):682-688.
[22]中国地震信息网.2008四川汶川县Ms8.0地震参数[R].http:∥www.csi.ac.cn/sichuan/sichuan 080512_cs1.ht m.
[23]俆锡伟,闻学泽,叶建青,等.汶川Ms8.0地震地表破裂带及其发震构造[J].地震地质,2008,30(3):597-629.
[24]李传友,魏占玉.汶川Ms8.0地震地表破裂带北端位置的修订[J].地震地质,2009,31(1):1-8.
[27]冉勇康,史翔,王虎,等.汶川Ms8地震最大地表同震垂直位移量及地表变形样式[J].科学通报,2010,55(2):154-162.
[28]邓起东,冉勇康,杨晓平,等.中国活动构造图[M].北京:地震出版社,2007.
[29]何宏林,孙昭民,魏占玉,等.汶川Ms8.0地震地表破裂带白沙河段破裂及其位移特征[J].地震地质,2008,30(3):658-673.
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