用初动P波波形反演中小地震震源机制解及其在首都圈地震震源反演中的初步应用研究
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摘要
随着我国区域地震台网内台站的加密,使确定区域内频繁发生的中小地震震源机制解成为可能。这将为区域构造活动和应力场作用提供重要约束信息,也正逐渐成为地震台网拓展功能的主要发展方向之一。发展自动或半自动化的地震震源机制解反演方法,提供较可靠的分析结果,是有效利用地震台网记录、拓展信息服务功能的重要途径。
本文的研究目的,是为综合利用初动P波波形搜索中小地震震源机制的自动处理提供理论及实例的支持。随着数字台网的越来越广泛的建立,为利用波形反演地震震源机制解提供了有利的条件。利用数字台网记录的波形资料反演地震震源机制解成为国际上的一种趋势。本研究所采用的格点搜索方法,借鉴了CAP(Cut and Paste)方法的思想,综合利用初动P波波形信息,分步搜索确定震源机制解:首先使用大步长三维格点搜索震源机制解,计算理论地震图并与记录的初动P波波形进行互相关运算,分析多个台站的结果获得震源机制解的精细搜索范围;然后在精细搜索范围内以小步长搜索计算理论地震图,与大步长搜索同样步骤,最终得到震源机制解。
本文首先介绍了理论地震图计算的频率-波数积分方法(F-K)和格林函数库方法。为了本文研究以及后续处理首都圈中小地震震源机制解的方便,吸收了格林函数库思想。建立首都圈一维P波速度模型,使用F-K程序计算了首都圈区域格林函数库并编写了相关搜索过程的脚本。然后为了检验本文方法所编写的搜索分析方法,计算了4个模拟地震的震源机制解,从数值模拟角度验证了基于初动P波波形反演地震震源机制解的可行性。进一步探讨了使用较少台站获得震源机制解的可能性,发现在台站数达到4个以上、台站方位角覆盖达到180°左右并且台站方位角分布比较均匀的情况下,可以获得与多个台站数据反演比较一致的结果。
本文最后以首都圈2006年7月4日文安地震为实例进行研究。首先利用首都圈33个台站的初动P波波形资料,通过大步长与小步长搜索,获得文安地震震源机制解的一个节面为:走向20°、倾角82°、滑动角158°。然后用该震源机制解计算所有33个台站的理论波形并与实际记录的初动P波波形进行比较,结果显示二者具有很好的一致性。中小地震辐射能量较小,能被记录的台站数量往往较少且方位角覆盖可能较差,所以最后研究尝试使用较少台站反演文安地震震源机制解的可能性。发现对于文安地震,使用本文方法,在台站数达到5个以上、台站方位角覆盖达到180°左右并且台站方位角分布比较均匀的情况下,可以获得与33个台站比较一致的结果,印证了数值模拟结果。
通过数值模拟以及文安地震震源机制解的反演应用,验证了本文方法的可行性,同时也表明本文方法在利用少数台站波形资料进行中小地震震源机制解反演具有潜在的优势。本研究为综合利用初动P波波形搜索中小地震震源机制的自动处理提供了理论和实践的基础。
As the density of seismic stations in regional seismic networks gradually increasing, focal mechanism determination can be possible for small and moderate regional earthquakes that occur frequently. This will provide more important constraints on regional tectonic activities and stress field status, and also has led to an expansion of seismic network functions. Developing automatic or semi-automatic focal mechanism inversion methods to provide more reliable results is a very important way to improve seismic network data utility ratio and extend information service.
The aims of this paper is to introduce an automatic focal mechanism inversion method that uses small and moderate earthquakes’initial P waveforms, with both theoretical basis and application examples presented. As the digital seismic networks being established more and more widely, solving for focal mechanisms by digital seismic waveform inversion is becoming more convenient and tends to be an international trend. The grid search method was used in this study. Based on the idea of CAP(Cut and Paste) method, this method searches and finds focal mechanisms with a two-step strategy by fully utilizing the initial P-waveform information: in the first step, we search for focal mechanism with large grid size in 3-dimensional parameter space by cross-correlating initial P waveforms between synthetic seismograms and recorded waveforms, and limit the parameter range for the search in the next step by comparing multi-stations’results. In the second step, the final earthquake focal mechanism will be found by repeating the search procedure with smaller grid size in the limited parameter range.
This paper will first introduced a method of calculating synthetic seismogram—the frequency-wavenumber integral (F-K) method, and Green's function database method. The Green's function database adopted here is for the efficiency of the this method and future data processing which will determine a large number of earthquake focal mechanisms of small and moderate earthquake in Beijing metropolitan area. To build the database, one-dimensional P-wave velocity model of Beijing metropolitan area was established, and Green’s functions in Beijing metropolitan region were calculated using the F-K program. A search and match script was also made at this time. To test and verify this inversion method, the second part of this paper did some numerical tests. Four scenario earthquakes were used to simulate focal mechanism inversion, and the results showed that this method is capable of retrieving focal mechanisms of small and moderate earthquakes using initial P waveforms, which in turn validates the feasibility of this method from the numerical simulation perspective. Furthermore, the capability to invert focal mechanism with only a fewer stations was tested. The test showed that results similar to those using many stations can be achieved by this method if more than 4 stations with uniform azimuth distribution were available and their azimuthal coverage was around 180°.
The last part of this paper is focused on inversion method’s application on Wen’an earthquake which occurred on July 4th, 2006 in Beijing metropolitan area. Using initial P waveforms of 33 stations in the Beijing metropolitan area, based on two-step search procedure, one section of the Wen’an earthquake focal mechanism was inverted as: strike= 20°, dip =82°, slip= 158°. The initial P waveform comparisons between synthetic seismograms calculated with inverted focal mechanism and the recorded waveforms of 33 stations showed good consistency. As small earthquake radiates energy so weak that the number of recorded stations would be limited and the azimuthal coverage of recorded stations would be poor, which can restrict focal mechanism inversion. So earthquake focal mechanism inversions using fewer stations were tried. These testes showed that focal mechanism can be recovered as good as 33 stations’result by this method on the Wen’an earthquake data when over 5 stations were available with about 180°station azimuth coverage and an even station azimuth distribution. These results also confirmed the previous numerical cases.
Through the numerical test and Wen’an Earthquake’s real data inversion, the method of this study were proved to be feasible in utilizing initial P waveforms to invert for focal mechanisms of small and moderate earthquakes, it also showed that this method has potential advantages for small earthquake focal mechanism inversion when only fewer stations are available. The research in this paper has provided theoretical basis and application examples for automatic focal mechanism inversion of small and moderate earthquakes using initial P waveforms.
本文的研究目的,是为综合利用初动P波波形搜索中小地震震源机制的自动处理提供理论及实例的支持。随着数字台网的越来越广泛的建立,为利用波形反演地震震源机制解提供了有利的条件。利用数字台网记录的波形资料反演地震震源机制解成为国际上的一种趋势。本研究所采用的格点搜索方法,借鉴了CAP(Cut and Paste)方法的思想,综合利用初动P波波形信息,分步搜索确定震源机制解:首先使用大步长三维格点搜索震源机制解,计算理论地震图并与记录的初动P波波形进行互相关运算,分析多个台站的结果获得震源机制解的精细搜索范围;然后在精细搜索范围内以小步长搜索计算理论地震图,与大步长搜索同样步骤,最终得到震源机制解。
本文首先介绍了理论地震图计算的频率-波数积分方法(F-K)和格林函数库方法。为了本文研究以及后续处理首都圈中小地震震源机制解的方便,吸收了格林函数库思想。建立首都圈一维P波速度模型,使用F-K程序计算了首都圈区域格林函数库并编写了相关搜索过程的脚本。然后为了检验本文方法所编写的搜索分析方法,计算了4个模拟地震的震源机制解,从数值模拟角度验证了基于初动P波波形反演地震震源机制解的可行性。进一步探讨了使用较少台站获得震源机制解的可能性,发现在台站数达到4个以上、台站方位角覆盖达到180°左右并且台站方位角分布比较均匀的情况下,可以获得与多个台站数据反演比较一致的结果。
本文最后以首都圈2006年7月4日文安地震为实例进行研究。首先利用首都圈33个台站的初动P波波形资料,通过大步长与小步长搜索,获得文安地震震源机制解的一个节面为:走向20°、倾角82°、滑动角158°。然后用该震源机制解计算所有33个台站的理论波形并与实际记录的初动P波波形进行比较,结果显示二者具有很好的一致性。中小地震辐射能量较小,能被记录的台站数量往往较少且方位角覆盖可能较差,所以最后研究尝试使用较少台站反演文安地震震源机制解的可能性。发现对于文安地震,使用本文方法,在台站数达到5个以上、台站方位角覆盖达到180°左右并且台站方位角分布比较均匀的情况下,可以获得与33个台站比较一致的结果,印证了数值模拟结果。
通过数值模拟以及文安地震震源机制解的反演应用,验证了本文方法的可行性,同时也表明本文方法在利用少数台站波形资料进行中小地震震源机制解反演具有潜在的优势。本研究为综合利用初动P波波形搜索中小地震震源机制的自动处理提供了理论和实践的基础。
As the density of seismic stations in regional seismic networks gradually increasing, focal mechanism determination can be possible for small and moderate regional earthquakes that occur frequently. This will provide more important constraints on regional tectonic activities and stress field status, and also has led to an expansion of seismic network functions. Developing automatic or semi-automatic focal mechanism inversion methods to provide more reliable results is a very important way to improve seismic network data utility ratio and extend information service.
The aims of this paper is to introduce an automatic focal mechanism inversion method that uses small and moderate earthquakes’initial P waveforms, with both theoretical basis and application examples presented. As the digital seismic networks being established more and more widely, solving for focal mechanisms by digital seismic waveform inversion is becoming more convenient and tends to be an international trend. The grid search method was used in this study. Based on the idea of CAP(Cut and Paste) method, this method searches and finds focal mechanisms with a two-step strategy by fully utilizing the initial P-waveform information: in the first step, we search for focal mechanism with large grid size in 3-dimensional parameter space by cross-correlating initial P waveforms between synthetic seismograms and recorded waveforms, and limit the parameter range for the search in the next step by comparing multi-stations’results. In the second step, the final earthquake focal mechanism will be found by repeating the search procedure with smaller grid size in the limited parameter range.
This paper will first introduced a method of calculating synthetic seismogram—the frequency-wavenumber integral (F-K) method, and Green's function database method. The Green's function database adopted here is for the efficiency of the this method and future data processing which will determine a large number of earthquake focal mechanisms of small and moderate earthquake in Beijing metropolitan area. To build the database, one-dimensional P-wave velocity model of Beijing metropolitan area was established, and Green’s functions in Beijing metropolitan region were calculated using the F-K program. A search and match script was also made at this time. To test and verify this inversion method, the second part of this paper did some numerical tests. Four scenario earthquakes were used to simulate focal mechanism inversion, and the results showed that this method is capable of retrieving focal mechanisms of small and moderate earthquakes using initial P waveforms, which in turn validates the feasibility of this method from the numerical simulation perspective. Furthermore, the capability to invert focal mechanism with only a fewer stations was tested. The test showed that results similar to those using many stations can be achieved by this method if more than 4 stations with uniform azimuth distribution were available and their azimuthal coverage was around 180°.
The last part of this paper is focused on inversion method’s application on Wen’an earthquake which occurred on July 4th, 2006 in Beijing metropolitan area. Using initial P waveforms of 33 stations in the Beijing metropolitan area, based on two-step search procedure, one section of the Wen’an earthquake focal mechanism was inverted as: strike= 20°, dip =82°, slip= 158°. The initial P waveform comparisons between synthetic seismograms calculated with inverted focal mechanism and the recorded waveforms of 33 stations showed good consistency. As small earthquake radiates energy so weak that the number of recorded stations would be limited and the azimuthal coverage of recorded stations would be poor, which can restrict focal mechanism inversion. So earthquake focal mechanism inversions using fewer stations were tried. These testes showed that focal mechanism can be recovered as good as 33 stations’result by this method on the Wen’an earthquake data when over 5 stations were available with about 180°station azimuth coverage and an even station azimuth distribution. These results also confirmed the previous numerical cases.
Through the numerical test and Wen’an Earthquake’s real data inversion, the method of this study were proved to be feasible in utilizing initial P waveforms to invert for focal mechanisms of small and moderate earthquakes, it also showed that this method has potential advantages for small earthquake focal mechanism inversion when only fewer stations are available. The research in this paper has provided theoretical basis and application examples for automatic focal mechanism inversion of small and moderate earthquakes using initial P waveforms.
引文
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Ji C., Wald,D.J. and Helmberger D.V. 2002. Source Description of the 1999 Hector Mine,California, Earthquake,Part I: Wavelet Domain Inversion Theory and Resolution Analysis. Bull.Seism.Soc.Am., 92(4): 1192~1207.
Ji C.,Wald,D.J. and Helmberger D.V. 2002. Source Description of the 1999 Hector Mine, California,Earthquake, Part II:Complexity of Slip History [J]. Bull.Seism.Soc.Am., 92(4): 1208~1226.
Kagan Y.Y. and Houston H.. 2005. Relation between mainshock rupture process and Omori’s law for aftershock moment release rate. Geophys.J.Int. 163: 1039–1048.
Kao,H., and S.Shan. 2004. The Source-Scanning Algorithm:mapping the distribution of seismic sources in time and space. Geophys.J.Int., 157: 589-594.
Kikuchi M. and Kanamori H. 1982. Inversion of complex body waves. Bull.Seism.Soc.Am., 72: 491~506.
Kikuchi, M. and Kanamori H. 1991. Inversion of complex body waves–III, Bull. Seismol. Soc. Am., 81: 2335-2350
Kilb D. 2001. Fault parameter constraints using relocated earthquakes:implications for stress change calculations, EOS, 82: F811.
Kisslinger C. 1980. Evaluation of S to P amplitude ration for determine focal mechanism fromregional network observations. Bull.Seism.Soc.Am., 70: 999-1014.
Kisslinger C., Brown J.R. and Koch K. 1981. Computing for focal mechanism from local SV/P data. Bull.Seism.Soc.Am., 71: 1719-1729.
Kimura T. and Kakehi Y. 2005. Rupture process of the 2001 Hyogo-ken Hokubu,Japan, earthquake(mw 5.2)and comparison between the aftershock activity and the static stress changes. Bull.Seism.Soc.Am., 95(1): 145~158.
Li L.,Chen Q., Cheng X. and Niu F. 2007. Spatial clustering and repeating of seismic events observed along the 1976 Tangshan fault,north China. Geophys.Res.Lett., 34(23): L23309.
Liu P.and Archuleta R.J. 2004. A new nonlinear finite fault inversion with three-dimensional Green’s functions:Application to the 1989 Loma Prieta,California,earthquake. J.Geophys. Res., 109: B02318.
Magistrale, H., S. Day, Clayton R. W., and Graves R., 2000. The SCEC southern California reference 3D seismic velocity model Version 2, Bull. Seismol. Soc. Am. 90, no. 6B, S65-S76.
Maruyama,T. 1963. On the force equivalents of dynamical elastic dislocations with reference to the earthquake mechanism. Tokyo: Bull.Earthquake Res.Inst., Tokyo Univ., 41: 467-685.
McGuire J. 2004. Estimating finite source properties of small earthquake ruptures. Bull. Seism. Soc. Am., 94: 377-393.
Mendoza C.M. and Hartzell S.H. 1988. Inversion for slip distribution using teleseismic P waveforms:North Palm Springs,Borah Peak,and Michoacan Earthquakes, Bull. Seism. Soc. Am., 78(3): 1092~1111.
Mori J. 1996. Rupture directivity and slip distribution of the M 4.3 foreshock to the 1992 Joshua Tree Earthquake, Southern California. Bull. Seism. Soc. Am., 86(3): 805-810.
Mori J. and Hartzell S. 1990. Souce inversion of the 1988 Upland, California,Earthquake: determination of a fault plane for a small event. Bull. Seism. Soc. Am., 80(3): 507-518.
Mueller C. 1985. Source pulse enhancement by deconvolution of an empirical Green’s Functions. Geophys. Res. Lett., 12: 33~36.
Nakayama W. and Takeo M. 1997. Slip history of the 1994 Sanriku-Haruka-Oki,Japan, earthquake deduced from strong motion data. Bull. Seism. Soc. Am., 87: 918~931.
Okada T., Umino N., Ito Y. et al. 2001. Source processes of 15 September 1998 M 5.0 Sendai, Northeastern Japan, earthquake and its M 3.8 foreshock by waveform inversion. Bull. Seism. Soc. Am., 91(6): 1607-1618.
Olson A.H. and Anderson J. 1988. Implications of frequency-domain inversion of earthquake ground motions for resolving the space-time dependence of slip on an extended fault. Geophys.J.R.astr.Soc., 94: 443~455.
Olson A.H. and Apsel R.J. 1982. Finite faults and inverse theory with applications to the 1979 Imperial Valley earthquake. Bull. Seism. Soc. Am., 72: 1969~2001.
Pasyanos M., Dreger D. and Romanowicz B. 1996. Toward real-time estimation of regional moment tensors. Bull. Seism. Soc. Am., 86(5): 1255~1269.
Perry Byerly. 1934. The first preliminary waves of the Nevada earthquake of December 20, 1932. Bull. Seism. Soc. Am., 25(1): 62-80
Randall C.J. 1989. Absorbing boundary condition for the elastic wave equation: velocity-stress formulation. Geophysics, 54: 1141~1152.
Reid, H. F. 1910. The Mechanics of the Earthquake. Report of the State Investigation Commission, in The California Earthquake of April 18, 1906. Carnegie Institution of Washington: Vol. 2
Sekiguchi H. and Iwata T. 2002. Rupture process of the 1999 Kocaeli, Turkey, earthquake estimated from strong-motion waveform. Bull. Seism. Soc. Am., 92: 300~311.
Sekiguchi H., Irikura, K. and Iwata, T.. 2000. Fault geometry at the rupture termination of the 1995 Hyogo-ken Nanbu earthquake. Bull. Seism. Soc. Am., 90, 117~133.
Snoke J.A., Munsey J., Teague A., et al. 1984. A program for focal mechanism determination by combined use of polarity and SV-P amplitude ratio data. Earthquake Notes, 55(3): 15.
Stump B.W. and Johnson L.R. 1977. The determination of source properties by the linear inversion of seismograms. Bull. Seism. Soc. Am., 67(6): 1487~1502.
Takeuchi, H. & Saito, M., 1972. Seismic surface waves, in Methods in ComputationalPhysics, Vol. 11, pp. 217–295, ed. Bolt, B. A., Academic Press, New York.
Wald D.J., Helmberger D.V. and Heaton T.H. 1991. Rupture model of the 1989 Loma Prieta earthquake from the inversion of strong-motion and broadband teleseismic data. Bull. Seism. Soc. Am., 81(5): 1540~1572.
Wald, D. J., and T. H. Heaton, , 1994. Spatial and temporal distribution of slip for the 1992 Landers, California earthquake. Bull. Seismol. Soc. Am. 84: 668-691.
Zeng Y.H. and Anderson J.G. 1996. A composite sourcemodeling of the 1994 Northridge earthquake using genetic algorithm. Bull. Seism. Soc. Am., 86: 871~883.
Zhao L., Chen P. and Jordan T.H. 2006. Strain Green’s tensors, reciprocity and their applications to seismic source and structure studies. Bull. Seism. Soc. Am., 96(5): 1753~1763.
Zhao L., Jordan T.H. and Chapman C.H. 2000. Three-dimensional Fréchet differential kernels for seismic delay times. Geophys. J. Int., 141: 558–576.
Zhao L., Jordan T.H., Olsen K.B. and Chen P. 2005. Fréchet kernels for imaging regional earth structure based on three-dimensional reference models. Bull.Seism.Soc.Am., 95: 2066~2080.
Zhao L.S. and Helmgerger D.V. 1994. Source estimation from broadband regional seismograms, Bull. Seism. Soc. Am., 84(1): 91~104.
Zhu L.P. and Helmgerger D.V. 1996. Advancement in source estimation techniques using broadband regional seismograms [J]. Bull.Seism.Soc.Am., 86(5), 1634~1641.
Zhu L.P. and Rivera L.A. 2002. A note on the dynamic and static displacements from a point source in multilayered media [J]. Geophys.J.Int., 148, 619~627.
Zhou S.Y. and Chen X.F. 2003. Inversion of near-field waveform data for earthquake source rupture process(I): Method and numerical test [J]. Sci.China(D), 46: 1089~1102.
Zhou S.Y. and Chen X.F. 2006. Inversion of near-field waveform data for earthquake source rupture process(Ⅱ): Inversion of Chi-Chi earthquake source, 20 September, 1999, Taiwan [J]. Sci.China(D), 49(3): 272~282.
Zhou S.Y., Irikura K. and Chen X.F. 2004. Analysis of the reliability and resolution of the earthquake source history inferred from waveforms, taking the Chi-Chi earthquake as an example [J]. Geophys.J.Int., 157: 1217~1232.
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