各向异性ATI介质剪切位错源地震矩张量
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摘要
考虑震源区为各向异性ATI介质情形下,给出了剪切位错源地震矩张量解析表达式并模拟了震源区各向异性对双力偶分量(DC)、补偿线性偶极子分量(CLVD)和各向同性分量(ISO)的影响.结果表明,即使剪切位错源仍能产生非双力偶各向同性分量,其导致沿着ATI介质对称轴方向体积变化;当断层面位于ATI介质对称平面或者震源区为各向同性介质时,剪切位错源在辐射意义上才可等效为双力偶机制.
Assuming the fault zone as anisotropic ATI media,the analytical expressions of seismic moment tensor in ATI media have been derived,furthermore,we have modeled the effect of anisotropic parameters on DC,CLVD,and ISO.Some results have shown that shear faulting can also generate isotropic component which will lead to volume change along ATI symmetry axis, however,when fault surface is located in the symmetry plane of ATI or fault zone is isotropic structure,shear faulting can be regarded as double couple mechanism in terms of radiation pattern.
Assuming the fault zone as anisotropic ATI media,the analytical expressions of seismic moment tensor in ATI media have been derived,furthermore,we have modeled the effect of anisotropic parameters on DC,CLVD,and ISO.Some results have shown that shear faulting can also generate isotropic component which will lead to volume change along ATI symmetry axis, however,when fault surface is located in the symmetry plane of ATI or fault zone is isotropic structure,shear faulting can be regarded as double couple mechanism in terms of radiation pattern.
引文
[1] Gilbert F, Dziewonski A M. An application of normal mode theory to the retrieval of structural parameters and source mechanisms from seismic spectra. Philos. Trans. R. Soc. ,Ser. A, 1975, 278(1280) : 187-269
[2] Fitch T J, McCowan D W, Shield M W. Estimation of the seismic moment tensor from teleseismic body wave data with applications to intraplate and mantle earthquakes. J.Geophys. Res. , 1980, 85(B7) . 3817-3828
[3] Dziewonski A M, Chou T A, Woodhouse J H. Determination of earthquake source parameters from waveform data for studies of global and region seismicity. J. Geophys. Res. , 1981, 86(B4) : 2825-2852
[4] Dziewonski A M. Woodhouse J H. An experiment in the systematic study of global seismicity: centroid-moment tensor solution for 201 moderate and large earthquakes in 1981． J.Geophys. Res. , 1983, 88: 3247-3271
[5] Dreger D S, Helmberger D V. Determination of source parameters at regional distances with three-component sparse network data. J. Geophys. Res., 1993, 98 ( B5) . 8107-8125
[6] Sipkin S A. Estimation of earthquake source parameters by the inversion of waveform data: synthetic waveforms.Physics of the Earth and Planetary Interiors, 1982, 30(2-(?)
[7] Minson S, Dreger D S. Stable inversions for complete moment tensors. Geophys. J. Int. , 2008,174:585-592
[8] Chen Y T, Xu L S, Li X, et al. Source process of the 1990 Gonghe, China, earthquake and tectonic stress field in the northeastern Qinghai-Xizang (Tibetan) plateau. Pure Appl.Geophys. , 1996, 146(3-4) : 697-715
[9] Kawakatsu H. Insignificant isotropic component in the moment tensor of deep earthquakes. Nature, 1991, 351 (6321) : 50-53
[10] Crampin S. A review of wave motion in anisotro ic and cracked elastic-media. Wave Motion , 1981, 3(4) : 343～391
[11] Booth D C, Crampin S. The anisotropic reflectivity technique: theory. Geophys. J. R. Astron, Soc. , 1983, 72 (3) : 755-766
[12] Crampin S. Effects of point singularities on shear-wave propagation in sedimentary basins. Geophys. J. R. Astron.Soc: , 1991, 107(3) : 531-543
[13] Crampin S, Peacock S. A review of the current understanding of seismic shear-wave splitting in the Earth' s crust and common fallacies in interpretation. Wave Motion , 2008, 45(6) : 675-722
[14] Crampin S. The dispersion of surface wave in multilayered anisotropic media. Geophys. J. R. Astron. Soc. , 1970, 21(3) : 387-402
[15] Gao Y, Wu J. Compressive stress field in the crust deduced from shear-wave anisotropy: an example in capital area of China. Chinese Sci. Bull. , 2008, 53(18) : 2840-2848
[16] Wu J, Gao Y, Chen Y T. Shear-wave splitting in the crust beneath the southeast Capital area of North China. J.Seism. , 2009, 13(2) : 277-286
[17] Gao Y, Wu J, Cai J A, et al. Shear-wave splitting in the southeast of Cathaysia block, South China. J. Seisin. ,2009, 13(2) : 267-275
[18] Gao Y, Wu J, Yi G X, et al. Crust-mantle coupling in North China: Preliminary analysis from seismic anisotropy. Chinese Sci. Bull., 2010, 55(31) : 3599-3605, doi: 10． 1007/ s11434-010-4135-y
[19] Chen Y, Badal J, Zhang Z J. Radial anisotropy in the crust and upper mantle beneath the Qinghai-Tibet Plateau and surrounding regions. Journal of Asian Earth Sciences,2009, 36(4-5) : 289-302
[20] Liu K, Zhang Z J, Hu J F, et al. Frequency band-dependence of S-wave splitting in China mainland and its implications. Science in China (Series D), 2001, 44(7) : 659-665
[21] Zhang Z J, Li Y K, Lu D Y, et al. Velocity and anisotropy structure of the crust in the Dabieshan orogenic belt from wide-angle seismic data. Physics of the Earth and Planetary Interiors, 2000, 122(1-2) : 115-131
[22] Zhang Z J, Teng J W, Badal J, et al. Construction of regional and local seismic anisotropic structures from wide-angle seismic data: crustal deformation in the southeast of China. J. Seism. , 2009, 13(2) : 241-252
[23] Crampin S. Effective anisotropic elastic-constants for wave propagation through cracked solids. Geophys. J. R. Astron.Soc. , 1984, 76(1) : 135-145
[24] Crampin S, Taylor D B. The propagation of surface waves in anisotropic media. Geophys. J. R. Astron. Soc. , 1971, 25(1-3) : 71-87
[25] Crampin S. A review of the effects of anisotropic layering on the propagation of seismic waves. Geophys. J. R. Astron.Soc. , 1977, 49(1) : 9-27
[26] Yao C, Xiong Y. Far-fields radiation pattern from an anisotropic dislocation point source. Can. J. Expl.Geophys. , 1993, 29, 315-323
[27] Li Y G, Aki K, Adams D, et al. Seismic guided waves trapped in the fault zone of the Landers, California,earthquake of 1992． J. Geophys. Res., 1994, 99 ( B6 ) :11705-11722
[28] Aki K, Richards P G. Quantitative Seismology: Theory and Methods. San Francisco; Freeman, 1980
[29] Aki K, Richards P G. Quantitative Seismology. California:University Science Books, 2002
[30] Ben-Menahem A, Sena A G. The elastodynamic Green' s tensor in an anisotropic half-space. Geophys. J. Int. , 1990,102(2) : 421-444
[31] Ben-Menahem A, Sena A G. Green's tensor and radiation pattern of point sources in general anisotropic inhomogeneous elastic media. Geophys. J. Int. , 1991, 107(2) : 297-308
[32] Gajewski D. Radiation from point sources in general anisotropic media. Geophys.]. Int., 1993, 113(2) : 299-317
[33] Vavrycuk V. Inversion for anisotropy from non-double-couple components of moment tensors. J. Geophys. Res. ,2004, 109(B7) : B07306, doi: 10． 1029/2003JB002926
[34] Vavrycuk V. Focal mechanisms in anisotropic media. Geophys. J. Int., 2005, 161: 334-346, doi: 10． 1111/j.1365-246X. 2005． 02585
[35] Vavrycuk V. Focal mechanisms produced by shear faulting in weakly transversely isotropic crustal rocks. Geophysics,2006, 71(5) : D145-D151, doi: 10． 1190/1． 2236378
[36] Vavrycuk V, Bohnhoff M, Jechumtalova Z, et al. Non-double-couple mechanisms of microearthquakes induced during the 2000 injection experiment at the KTB site, Germany: A result of tensile faulting or anisotropy of a rock?Tectonophysics, 2008, 456(1-2) : 74-93
[37] 姚 陈,蔡明刚.任意空间取向T1弹性张量解析表述.地球物理学报,2009,52(9) :2345～2348Yao C, Cai M G. Analytical expression of TI elastic tensor with arbitrary orientation. Chinese J. Geophys. ( in Chinese) ,2009, 52(9) : 2345-2348
[38] 郝重涛,姚 陈.任意空间取向TI介质中体波速度特征.地球物理学报,2007,50(2) :546～555Hao C T, Yao C. Analysis of body_wave velocity characteristic for TI medium with arbitrary spatial orientation.Chinese J. Geophys. (in Chinese), 2007, 50(2) : 546-555
[39] 郝重涛,姚陈.任意空间取向TI介质中P波四次时差系数特征.地球物理学报,2008,51(4) :1172～1179Hao C T, Yao C. The characteristic of quartic moveout coefficient of P-wave in the TI homogeneous media with an arbitrary orientation symmetric-axis. Chinese J. Geophys.(in Chinese), 2008,51(4) : 1172-1179
[40] 郝重涛,姚 陈.ATI介质中四次时差系数解析近似.地球物理学报,2009,52(8) :2074～2083Hao C T, Yao C. Analytic approximation of quartic moveout coefficient in the TI media with an arbitrary spatial orientation. Chinese J. Geophys. (in Chinese) , 2009 ,52(8) :2074-2083
[41] Spies M. Elastic waves in homogeneous and layered transversely isotropic media: Plane wave and Gaussian wave packets. A general approach. J. Acoust. Soc. Am. , 1994,95(4) : 1748-1760
[42] Olson A H, Apsel R J. Finite faults and inverse theory with application to the 1979 Imperial Valley earthquake. Bull,Seismol. Soc. Am. , 1982, 72(6A): 1969-2001
[43] 姚振兴,郑天愉.计算综合地震图的广义反射、透射系数矩阵和离散波数方法(二)--对不同深度点源的算法.地球物理学报,1984,27(4) :338～348Yao Z X, Zheng T Y. A generalized reflection-transmission coefficient matrix and discrete wavenumber method for synthetic seismograms (Ⅱ)-for multiple sources at different depths. Chinese J. Geophys. (Acta Geophysica Sinica) (in Chinese), 1984, 27(4) : 338-348
[44] 盖增喜,陈晓非.利用点源叠加合成有限尺度运动源的理论地震图.北京大学学报(自然科学版),2008,44(3) :407～412Ge Z X, Chen X F. Point source stacking method to compute synthetic seismogram of finite moving planar source. Acta Scientianrum Naturalium Universitatis Pekinensis (in Chinese) ,2008, 44(3) : 407-412
[45] Kanamori H, Given J W. Use of long-period surface waves for rapid determination of earthquake-source parameters.Physics of the Earth and Planetary Interiors , 1981, 27(1) :8-31
[46] 陈运泰,吴忠良,王培德等.数字地震学.北京:地震出版社,2000Chen Y T, Wu Z L, Wang P D, et al. Digital Seismology (in Chinese). Beijing: Seismological Press, 2000
[47] Thomsen L. Weak elastic anisotropy. Geophysics, 1986, 51 (10) : 1954-1966
[48] Julian B R, Miller A D, Foulger G R. Non-double-couple earthquakes 1． Theory. Reviews of Geophysics, 1998, 36 (4) : 525-549
[49] Knopoff L, Randall M J. The compensated linear vector dipole: A possible mechanism for deep earthquakes. J.Geophys. Res. , 1970, 75(26) : 4957-4963
[50] Sipkin S A. Rapid determination of global moment-tensor solution. Geophys. Res. Lett. , 1994, 21(16) : 1667-1670
[51] 陈运泰,许力生,张 勇等.2008年5月12日汶川特大地震震源特性分析报告(http://www.csi.ac.cn/sichuan).2008
[52] 石玉涛,高原,赵翠萍等.汶川地震余震序列的地震各向异性.地球物理学报,2009,52(2) :398～407Shi Y T, Gao Y, Zhao C P, et al. A study of seismic anisotropy of Wenchuan earthquake sequence. Chinese J.Geophys. (in Chinese), 2009, 52(2) : 398-407
[53] 王卫民,赵连锋,李娟等.四川汶川8． 0级地震震源过程.地球物理学报,2008,51(5) :1403～1410Wang W M, Zhao L F, Li J, et al. Rupture process of the M_s8． 0 Wenchuan earthquake of Sichuan, China. Chinese J.Geophys. (in Chinese), 2008, 51(5) : 1403-1410
[54] 蔡晓刚.各向异性ATI介质地震矩张量理论研究[博士论文].北京:北京大学地球物理系,2009Cai X G. The theoretical studies on seismic moment tensor in anisotropic ATI media [Ph. D. thesis](in Chinese). Beijing:the Department of Geophysics, Peking University, 2009
[2] Fitch T J, McCowan D W, Shield M W. Estimation of the seismic moment tensor from teleseismic body wave data with applications to intraplate and mantle earthquakes. J.Geophys. Res. , 1980, 85(B7) . 3817-3828
[3] Dziewonski A M, Chou T A, Woodhouse J H. Determination of earthquake source parameters from waveform data for studies of global and region seismicity. J. Geophys. Res. , 1981, 86(B4) : 2825-2852
[4] Dziewonski A M. Woodhouse J H. An experiment in the systematic study of global seismicity: centroid-moment tensor solution for 201 moderate and large earthquakes in 1981． J.Geophys. Res. , 1983, 88: 3247-3271
[5] Dreger D S, Helmberger D V. Determination of source parameters at regional distances with three-component sparse network data. J. Geophys. Res., 1993, 98 ( B5) . 8107-8125
[6] Sipkin S A. Estimation of earthquake source parameters by the inversion of waveform data: synthetic waveforms.Physics of the Earth and Planetary Interiors, 1982, 30(2-(?)
[7] Minson S, Dreger D S. Stable inversions for complete moment tensors. Geophys. J. Int. , 2008,174:585-592
[8] Chen Y T, Xu L S, Li X, et al. Source process of the 1990 Gonghe, China, earthquake and tectonic stress field in the northeastern Qinghai-Xizang (Tibetan) plateau. Pure Appl.Geophys. , 1996, 146(3-4) : 697-715
[9] Kawakatsu H. Insignificant isotropic component in the moment tensor of deep earthquakes. Nature, 1991, 351 (6321) : 50-53
[10] Crampin S. A review of wave motion in anisotro ic and cracked elastic-media. Wave Motion , 1981, 3(4) : 343～391
[11] Booth D C, Crampin S. The anisotropic reflectivity technique: theory. Geophys. J. R. Astron, Soc. , 1983, 72 (3) : 755-766
[12] Crampin S. Effects of point singularities on shear-wave propagation in sedimentary basins. Geophys. J. R. Astron.Soc: , 1991, 107(3) : 531-543
[13] Crampin S, Peacock S. A review of the current understanding of seismic shear-wave splitting in the Earth' s crust and common fallacies in interpretation. Wave Motion , 2008, 45(6) : 675-722
[14] Crampin S. The dispersion of surface wave in multilayered anisotropic media. Geophys. J. R. Astron. Soc. , 1970, 21(3) : 387-402
[15] Gao Y, Wu J. Compressive stress field in the crust deduced from shear-wave anisotropy: an example in capital area of China. Chinese Sci. Bull. , 2008, 53(18) : 2840-2848
[16] Wu J, Gao Y, Chen Y T. Shear-wave splitting in the crust beneath the southeast Capital area of North China. J.Seism. , 2009, 13(2) : 277-286
[17] Gao Y, Wu J, Cai J A, et al. Shear-wave splitting in the southeast of Cathaysia block, South China. J. Seisin. ,2009, 13(2) : 267-275
[18] Gao Y, Wu J, Yi G X, et al. Crust-mantle coupling in North China: Preliminary analysis from seismic anisotropy. Chinese Sci. Bull., 2010, 55(31) : 3599-3605, doi: 10． 1007/ s11434-010-4135-y
[19] Chen Y, Badal J, Zhang Z J. Radial anisotropy in the crust and upper mantle beneath the Qinghai-Tibet Plateau and surrounding regions. Journal of Asian Earth Sciences,2009, 36(4-5) : 289-302
[20] Liu K, Zhang Z J, Hu J F, et al. Frequency band-dependence of S-wave splitting in China mainland and its implications. Science in China (Series D), 2001, 44(7) : 659-665
[21] Zhang Z J, Li Y K, Lu D Y, et al. Velocity and anisotropy structure of the crust in the Dabieshan orogenic belt from wide-angle seismic data. Physics of the Earth and Planetary Interiors, 2000, 122(1-2) : 115-131
[22] Zhang Z J, Teng J W, Badal J, et al. Construction of regional and local seismic anisotropic structures from wide-angle seismic data: crustal deformation in the southeast of China. J. Seism. , 2009, 13(2) : 241-252
[23] Crampin S. Effective anisotropic elastic-constants for wave propagation through cracked solids. Geophys. J. R. Astron.Soc. , 1984, 76(1) : 135-145
[24] Crampin S, Taylor D B. The propagation of surface waves in anisotropic media. Geophys. J. R. Astron. Soc. , 1971, 25(1-3) : 71-87
[25] Crampin S. A review of the effects of anisotropic layering on the propagation of seismic waves. Geophys. J. R. Astron.Soc. , 1977, 49(1) : 9-27
[26] Yao C, Xiong Y. Far-fields radiation pattern from an anisotropic dislocation point source. Can. J. Expl.Geophys. , 1993, 29, 315-323
[27] Li Y G, Aki K, Adams D, et al. Seismic guided waves trapped in the fault zone of the Landers, California,earthquake of 1992． J. Geophys. Res., 1994, 99 ( B6 ) :11705-11722
[28] Aki K, Richards P G. Quantitative Seismology: Theory and Methods. San Francisco; Freeman, 1980
[29] Aki K, Richards P G. Quantitative Seismology. California:University Science Books, 2002
[30] Ben-Menahem A, Sena A G. The elastodynamic Green' s tensor in an anisotropic half-space. Geophys. J. Int. , 1990,102(2) : 421-444
[31] Ben-Menahem A, Sena A G. Green's tensor and radiation pattern of point sources in general anisotropic inhomogeneous elastic media. Geophys. J. Int. , 1991, 107(2) : 297-308
[32] Gajewski D. Radiation from point sources in general anisotropic media. Geophys.]. Int., 1993, 113(2) : 299-317
[33] Vavrycuk V. Inversion for anisotropy from non-double-couple components of moment tensors. J. Geophys. Res. ,2004, 109(B7) : B07306, doi: 10． 1029/2003JB002926
[34] Vavrycuk V. Focal mechanisms in anisotropic media. Geophys. J. Int., 2005, 161: 334-346, doi: 10． 1111/j.1365-246X. 2005． 02585
[35] Vavrycuk V. Focal mechanisms produced by shear faulting in weakly transversely isotropic crustal rocks. Geophysics,2006, 71(5) : D145-D151, doi: 10． 1190/1． 2236378
[36] Vavrycuk V, Bohnhoff M, Jechumtalova Z, et al. Non-double-couple mechanisms of microearthquakes induced during the 2000 injection experiment at the KTB site, Germany: A result of tensile faulting or anisotropy of a rock?Tectonophysics, 2008, 456(1-2) : 74-93
[37] 姚 陈,蔡明刚.任意空间取向T1弹性张量解析表述.地球物理学报,2009,52(9) :2345～2348Yao C, Cai M G. Analytical expression of TI elastic tensor with arbitrary orientation. Chinese J. Geophys. ( in Chinese) ,2009, 52(9) : 2345-2348
[38] 郝重涛,姚 陈.任意空间取向TI介质中体波速度特征.地球物理学报,2007,50(2) :546～555Hao C T, Yao C. Analysis of body_wave velocity characteristic for TI medium with arbitrary spatial orientation.Chinese J. Geophys. (in Chinese), 2007, 50(2) : 546-555
[39] 郝重涛,姚陈.任意空间取向TI介质中P波四次时差系数特征.地球物理学报,2008,51(4) :1172～1179Hao C T, Yao C. The characteristic of quartic moveout coefficient of P-wave in the TI homogeneous media with an arbitrary orientation symmetric-axis. Chinese J. Geophys.(in Chinese), 2008,51(4) : 1172-1179
[40] 郝重涛,姚 陈.ATI介质中四次时差系数解析近似.地球物理学报,2009,52(8) :2074～2083Hao C T, Yao C. Analytic approximation of quartic moveout coefficient in the TI media with an arbitrary spatial orientation. Chinese J. Geophys. (in Chinese) , 2009 ,52(8) :2074-2083
[41] Spies M. Elastic waves in homogeneous and layered transversely isotropic media: Plane wave and Gaussian wave packets. A general approach. J. Acoust. Soc. Am. , 1994,95(4) : 1748-1760
[42] Olson A H, Apsel R J. Finite faults and inverse theory with application to the 1979 Imperial Valley earthquake. Bull,Seismol. Soc. Am. , 1982, 72(6A): 1969-2001
[43] 姚振兴,郑天愉.计算综合地震图的广义反射、透射系数矩阵和离散波数方法(二)--对不同深度点源的算法.地球物理学报,1984,27(4) :338～348Yao Z X, Zheng T Y. A generalized reflection-transmission coefficient matrix and discrete wavenumber method for synthetic seismograms (Ⅱ)-for multiple sources at different depths. Chinese J. Geophys. (Acta Geophysica Sinica) (in Chinese), 1984, 27(4) : 338-348
[44] 盖增喜,陈晓非.利用点源叠加合成有限尺度运动源的理论地震图.北京大学学报(自然科学版),2008,44(3) :407～412Ge Z X, Chen X F. Point source stacking method to compute synthetic seismogram of finite moving planar source. Acta Scientianrum Naturalium Universitatis Pekinensis (in Chinese) ,2008, 44(3) : 407-412
[45] Kanamori H, Given J W. Use of long-period surface waves for rapid determination of earthquake-source parameters.Physics of the Earth and Planetary Interiors , 1981, 27(1) :8-31
[46] 陈运泰,吴忠良,王培德等.数字地震学.北京:地震出版社,2000Chen Y T, Wu Z L, Wang P D, et al. Digital Seismology (in Chinese). Beijing: Seismological Press, 2000
[47] Thomsen L. Weak elastic anisotropy. Geophysics, 1986, 51 (10) : 1954-1966
[48] Julian B R, Miller A D, Foulger G R. Non-double-couple earthquakes 1． Theory. Reviews of Geophysics, 1998, 36 (4) : 525-549
[49] Knopoff L, Randall M J. The compensated linear vector dipole: A possible mechanism for deep earthquakes. J.Geophys. Res. , 1970, 75(26) : 4957-4963
[50] Sipkin S A. Rapid determination of global moment-tensor solution. Geophys. Res. Lett. , 1994, 21(16) : 1667-1670
[51] 陈运泰,许力生,张 勇等.2008年5月12日汶川特大地震震源特性分析报告(http://www.csi.ac.cn/sichuan).2008
[52] 石玉涛,高原,赵翠萍等.汶川地震余震序列的地震各向异性.地球物理学报,2009,52(2) :398～407Shi Y T, Gao Y, Zhao C P, et al. A study of seismic anisotropy of Wenchuan earthquake sequence. Chinese J.Geophys. (in Chinese), 2009, 52(2) : 398-407
[53] 王卫民,赵连锋,李娟等.四川汶川8． 0级地震震源过程.地球物理学报,2008,51(5) :1403～1410Wang W M, Zhao L F, Li J, et al. Rupture process of the M_s8． 0 Wenchuan earthquake of Sichuan, China. Chinese J.Geophys. (in Chinese), 2008, 51(5) : 1403-1410
[54] 蔡晓刚.各向异性ATI介质地震矩张量理论研究[博士论文].北京:北京大学地球物理系,2009Cai X G. The theoretical studies on seismic moment tensor in anisotropic ATI media [Ph. D. thesis](in Chinese). Beijing:the Department of Geophysics, Peking University, 2009
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