震源破裂过程反演方法研究
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摘要
基于震源理论、利用地震波形资料、通过反演技术研究地震震源的破裂过程是定量认识震源运动学特性的最有效的途径,因此,地震破裂过程的数字波形反演和成像成为近年来地震学研究的前沿和热点问题。震源运动学研究的发展对于震源动力学研究、地震预测以及震后抢险救灾都有着重要的理论和现实意义,所以,能够从地震记录中获得越来越多的震源运动学信息以便更全面地描述震源破裂的复杂性成为此类研究的努力方向。然而,随着未知量的增加,分析结果的不确定性也在增加。因此,如何在确保结果的确定性或稳定性前提下,最大限度地从地震资料中获取震源运动学信息便成为当前利用数字波形资料分析震源复杂性的研究中的一大难题。例如:现有的许多关于震源破裂过程的反演分析中,为了达到使反演稳定的目的,人为地设置了关于破裂速度、子断层震源时间函数形状和发震断层机制固定不变等前提条件。众所周知,不恰当的前提条件往往会扭曲反演结果。因此,本研究的任务是基于震源基本理论,发展、改进和优化利用地震波形资料研究震源运动学问题的方法,其目标是在保证反演稳定可靠的基础上,尽量减少人为设置的前提,尽量获取多的震源信息。
本文首先从位移表示定理出发,推导了用于地震震源破裂过程反演分析的基本方程,构建了视震源时间函数反演方法和直接波形反演方法的一般形式,并首次从理论上分析讨论了不同的资料组合对反演结果的分辨能力的影响(尤其是空间分辨能力);然后,在前人工作的基础上,优化、改进和发展了多种用于震源破裂过程反演分析的方法,并通过数值试验和实际震例检验了这些方法的优越性。
为了获取稳定可靠的视震源时间函数,本文引入了PLD(映射Landweber反褶积: Projected Landweber Deconvolution)方法,并专门针对视震源时间函数的提取构造了遗传算法。数值试验和对实际资料的应用结果表明,相对于传统的水平线方法,这两种方法都有着相当的优越性。利用这两种方法,本文提取了2005年克什米尔M_W7.6地震各个震相的视震源时间函数和2001年昆仑山口西M_W7.8地震的瑞雷波视震源时间函数。与其它研究结果的比较表明,本研究得到的结果是十分可信的。
为了在震源机制固定的情况下利用视震源时间函数或直接利用波形资料获取稳定可靠且符合实际的反演结果,本文放开对子断层时间函数的形状的前提假设,引入拉普拉斯方程实现了破裂在时间上和空间上的光滑约束,以及标量地震矩最小约束,实现了约束条件的合理且高效化,构建了新的反演方程。对2005年克什米尔M_W7.6地震、2001年昆仑山口西M_W7.8地震和2007年宁洱M_S6.4地震的应用表明,本文提出的方法效果甚佳。
为了获取滑动方向在地震断层面上的变化信息,同时保证反演结果的稳定性,在保持线性反演的前提下,本文找到了约束子断层在走向和倾向上具有相同时间过程的技术途径。利用这种方法,本文分析了2004年苏门答腊—安达曼M_W9.3地震的时空破裂过程。分析结果和其它研究结果的比较表明,这种方法的应用是非常成功的。
为了获取震源机制在地震过程中的变化信息,实现对震源区不同空间位置子事件不同震源机制的再现,本文首次提出通过线性反演过程对地震破裂过程成像的方法和技术途径。利用这种方法,不但可以得到震源机制随空间的变化,而且可以通过逐步搜索法估计地震的最佳破裂速度。这种方法和技术途径的优越性在对2001年昆仑山口西M_W7.8地震的应用中得到了充分的体现。
最后,针对2008年发生在四川的汶川M_W7.9地震,除震后的快速响应外;我们还采用本文中介绍的多种方法进行综合细致的分析,得到了此次地震较为详细的破裂过程解。
Study on the earthquake rupture process based on the theory of seismic source, seismic waveform data and inversion technology is the most efficient way to quantitatively understanding the kinematical characteristics of earthquake sources. Thus, inversion or imaging of the earthquake rupture process using digital waveforms has been frontier and highlight issue of seismological study in recent years. Development of the study on kinematics of earthquake source is very important theoretically and realistically to the study on dynamics of earthquake source, earthquake prediction and earthquake hazard reduction. Therefore, to obtain more and more information about the details of earthquake kinematics from observed seismic data for describing source rupture complexity becomes a direction of this kind study. However, uncertainty of solution will be getting higher with the number of unknown parameters increasing. Therefore, it becomes a difficult problem how to obtain the information as much as possible about kinematical information of earthquake source from digital seismic waveform data analyzing the complexity of rupture process under a precondition that certainty or stability of solutions is guaranteed. For example, in most of the current research works, value of rupture velocity, shape of the sub-fault source time function and focal mechanism are kept fixed artificially as preconditions in performing inversion process in order to stabilize solution. As we know, improper precondition usually results in distorted solutions. So the task of this study is to develop, improve and optimize the methods for investigating the source kinematical issues using seismic waveform data on a basis of seismic source theory. The goal is to reduce artificial preconditions and obtain more information about earthquake source under condition of insuring inversion stable.
In this paper, at first, we derived the basic equations for rupture process inversion from the law of displacement representation, got the general forms for the methods of the apparent-source-time-function (ASTF) inversion and the direct-waveform inversion, and theoretically discussed the resolution ability (especially the space resolution ability) of different dataset for the first time; and then we developed, improved and optimized several efficient methods for rupture process analysis based on the existing methods; finally, we tested the methods for advantages by application to synthetic and observed data.
In order to obtain stable and reliable ASTFs, we introduced and improved the PLD (Projected Landweber Deconvolution) method, and newly constructed a genetic algorithm especially for ASTF deconvolution. Numerical tests and practical applications showed that both the methods have more advantages compared with traditional ones such as the water-level method. By the two methods, we retrieved the ASTFs of the 2005 Kashmir M_W7.6 earthquake from all phases and the ASTFs of the 2001 Kunlun M_W7.8 earthquake from Rayleigh waves only. The comparison with other results suggested that our results are highly reliable.
In order to get stable, reliable and more realistic inversion results using the ASTF method and direct-waveform method in case that focal mechanism is kept unchanged, we freed the precondition on the shape of sub-fault STF, imposed the smoothing constraints in time and space by adding Laplatian equations and the scalar-moment -minimum constraint, and constructed new equations of linear inversion. The practical applications to the 2005 M_W7.6 Kashmir earthquake, the 2001 Kunlun M_W7.8 earthquake and the 2007 Ning’er M_S6.4 earthquake indicated that this approach was very good.
In order to obtain the information about rakes' variation on the fault plane and insure the stability of inversion results, we improved the existing method by proposing a new way of constraining the slips in strike direction and dip direction to have the same time function. By the improved linear inversion method, we analysised the rupture process of the 2004 Sumatra—Andaman M_W9.3 earthquake. The comparison with the others results from different methods and data showed that the improvement of the method was very successful.
In order to get the information about focal-mechanism variation in earthquake rupture process and redisplay the mechanisms of different sub-events at different locations, for the first time, we developed a linear inversion technique for investigating the mechanism variation and rupture process. By this method, we can also obtain the estimation of the variable rupture velocity by grid-searching process beside the information about variable mechanisms in the earthquake process. The advantages of this method and technical way were illustrated adequately in the application to the 2001 Kunlun M_W7.8 earthquake.
At last, for the Wenchuan huge earthquake, we carried rupture process inversions with all methods in this paper after the fast estimations, and finally obtained many rupture details for the earthquake.
本文首先从位移表示定理出发,推导了用于地震震源破裂过程反演分析的基本方程,构建了视震源时间函数反演方法和直接波形反演方法的一般形式,并首次从理论上分析讨论了不同的资料组合对反演结果的分辨能力的影响(尤其是空间分辨能力);然后,在前人工作的基础上,优化、改进和发展了多种用于震源破裂过程反演分析的方法,并通过数值试验和实际震例检验了这些方法的优越性。
为了获取稳定可靠的视震源时间函数,本文引入了PLD(映射Landweber反褶积: Projected Landweber Deconvolution)方法,并专门针对视震源时间函数的提取构造了遗传算法。数值试验和对实际资料的应用结果表明,相对于传统的水平线方法,这两种方法都有着相当的优越性。利用这两种方法,本文提取了2005年克什米尔M_W7.6地震各个震相的视震源时间函数和2001年昆仑山口西M_W7.8地震的瑞雷波视震源时间函数。与其它研究结果的比较表明,本研究得到的结果是十分可信的。
为了在震源机制固定的情况下利用视震源时间函数或直接利用波形资料获取稳定可靠且符合实际的反演结果,本文放开对子断层时间函数的形状的前提假设,引入拉普拉斯方程实现了破裂在时间上和空间上的光滑约束,以及标量地震矩最小约束,实现了约束条件的合理且高效化,构建了新的反演方程。对2005年克什米尔M_W7.6地震、2001年昆仑山口西M_W7.8地震和2007年宁洱M_S6.4地震的应用表明,本文提出的方法效果甚佳。
为了获取滑动方向在地震断层面上的变化信息,同时保证反演结果的稳定性,在保持线性反演的前提下,本文找到了约束子断层在走向和倾向上具有相同时间过程的技术途径。利用这种方法,本文分析了2004年苏门答腊—安达曼M_W9.3地震的时空破裂过程。分析结果和其它研究结果的比较表明,这种方法的应用是非常成功的。
为了获取震源机制在地震过程中的变化信息,实现对震源区不同空间位置子事件不同震源机制的再现,本文首次提出通过线性反演过程对地震破裂过程成像的方法和技术途径。利用这种方法,不但可以得到震源机制随空间的变化,而且可以通过逐步搜索法估计地震的最佳破裂速度。这种方法和技术途径的优越性在对2001年昆仑山口西M_W7.8地震的应用中得到了充分的体现。
最后,针对2008年发生在四川的汶川M_W7.9地震,除震后的快速响应外;我们还采用本文中介绍的多种方法进行综合细致的分析,得到了此次地震较为详细的破裂过程解。
Study on the earthquake rupture process based on the theory of seismic source, seismic waveform data and inversion technology is the most efficient way to quantitatively understanding the kinematical characteristics of earthquake sources. Thus, inversion or imaging of the earthquake rupture process using digital waveforms has been frontier and highlight issue of seismological study in recent years. Development of the study on kinematics of earthquake source is very important theoretically and realistically to the study on dynamics of earthquake source, earthquake prediction and earthquake hazard reduction. Therefore, to obtain more and more information about the details of earthquake kinematics from observed seismic data for describing source rupture complexity becomes a direction of this kind study. However, uncertainty of solution will be getting higher with the number of unknown parameters increasing. Therefore, it becomes a difficult problem how to obtain the information as much as possible about kinematical information of earthquake source from digital seismic waveform data analyzing the complexity of rupture process under a precondition that certainty or stability of solutions is guaranteed. For example, in most of the current research works, value of rupture velocity, shape of the sub-fault source time function and focal mechanism are kept fixed artificially as preconditions in performing inversion process in order to stabilize solution. As we know, improper precondition usually results in distorted solutions. So the task of this study is to develop, improve and optimize the methods for investigating the source kinematical issues using seismic waveform data on a basis of seismic source theory. The goal is to reduce artificial preconditions and obtain more information about earthquake source under condition of insuring inversion stable.
In this paper, at first, we derived the basic equations for rupture process inversion from the law of displacement representation, got the general forms for the methods of the apparent-source-time-function (ASTF) inversion and the direct-waveform inversion, and theoretically discussed the resolution ability (especially the space resolution ability) of different dataset for the first time; and then we developed, improved and optimized several efficient methods for rupture process analysis based on the existing methods; finally, we tested the methods for advantages by application to synthetic and observed data.
In order to obtain stable and reliable ASTFs, we introduced and improved the PLD (Projected Landweber Deconvolution) method, and newly constructed a genetic algorithm especially for ASTF deconvolution. Numerical tests and practical applications showed that both the methods have more advantages compared with traditional ones such as the water-level method. By the two methods, we retrieved the ASTFs of the 2005 Kashmir M_W7.6 earthquake from all phases and the ASTFs of the 2001 Kunlun M_W7.8 earthquake from Rayleigh waves only. The comparison with other results suggested that our results are highly reliable.
In order to get stable, reliable and more realistic inversion results using the ASTF method and direct-waveform method in case that focal mechanism is kept unchanged, we freed the precondition on the shape of sub-fault STF, imposed the smoothing constraints in time and space by adding Laplatian equations and the scalar-moment -minimum constraint, and constructed new equations of linear inversion. The practical applications to the 2005 M_W7.6 Kashmir earthquake, the 2001 Kunlun M_W7.8 earthquake and the 2007 Ning’er M_S6.4 earthquake indicated that this approach was very good.
In order to obtain the information about rakes' variation on the fault plane and insure the stability of inversion results, we improved the existing method by proposing a new way of constraining the slips in strike direction and dip direction to have the same time function. By the improved linear inversion method, we analysised the rupture process of the 2004 Sumatra—Andaman M_W9.3 earthquake. The comparison with the others results from different methods and data showed that the improvement of the method was very successful.
In order to get the information about focal-mechanism variation in earthquake rupture process and redisplay the mechanisms of different sub-events at different locations, for the first time, we developed a linear inversion technique for investigating the mechanism variation and rupture process. By this method, we can also obtain the estimation of the variable rupture velocity by grid-searching process beside the information about variable mechanisms in the earthquake process. The advantages of this method and technical way were illustrated adequately in the application to the 2001 Kunlun M_W7.8 earthquake.
At last, for the Wenchuan huge earthquake, we carried rupture process inversions with all methods in this paper after the fast estimations, and finally obtained many rupture details for the earthquake.
引文
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Gutenberg B. 1945. Amplitudes of P,PP,and S and magnitude of shallow earthquaks. Bull. Seism. Soc. Am. 35:57-69
Gutenberg B. and Richter C. F. 1942. Earthquake magnitude, intensity, energy and acceleration. Bull. Seism. Soc. Am. 32:163-191
Gutenberg B. and Richter C. F. 1944. Frequency of earthquakes in California. Bull. Seism. Soc. Am. 34:185-188
Hartzell S. H. 1978. Earthquake aftershocks as green's functions. Geophys. Res. Lett. 5:1-4.
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Hartzell S. H. and Heaton T. H. 1986. Rupture history of the 1984 Morgan Hill, California, earthquake from the inversion of strong motion records. Bull. Seism. Soc. Am. 76:649-674.
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Gutenberg B. 1945. Amplitudes of P,PP,and S and magnitude of shallow earthquaks. Bull. Seism. Soc. Am. 35:57-69
Gutenberg B. and Richter C. F. 1942. Earthquake magnitude, intensity, energy and acceleration. Bull. Seism. Soc. Am. 32:163-191
Gutenberg B. and Richter C. F. 1944. Frequency of earthquakes in California. Bull. Seism. Soc. Am. 34:185-188
Hartzell S. H. 1978. Earthquake aftershocks as green's functions. Geophys. Res. Lett. 5:1-4.
Hartzell S. H. 1989. Comparison of seismic waveform inversion results for the rupture history of a finite fault: application to the 1986 North Palm Springs, earthquake. J. Geophys. Res. 94:7515-7534.
Hartzell S. H. and Heaton T. H. 1983. Inversion of strong ground motion and teleseismic waveform data for the fault rupture history of the 1979 Imperial Valley, California,earthquake. Bull. Seism. Soc. Am. 73:1553 -1583.
Hartzell S. H. and Heaton T. H. 1986. Rupture history of the 1984 Morgan Hill, California, earthquake from the inversion of strong motion records. Bull. Seism. Soc. Am. 76:649-674.
Hartzell S. H. and Liu P. C. 1996. Calculation of earthquake rupture histories using a hybrid global search algorithm:application to the 1992 Landers,California,earthquake. Phys Earth Planet Inter 95:79-99.
Hartzell S. H., Liu P., Mendoza C., Ji C. and Larson K. M. 2007. Stability and uncertainty of finite-fault slip inversion: application to the 2004 Parkfield, California, earthquake. Bull. Seis. Soc. Am. 97:1911-1934, doi:1910.1785/0120070080.
Horikawa H. 2001. Earthquake doublet in Kagoshima, Japan: rupture of asperities in a stress shadow. Bull. Seism. Soc. Am. 91:112-127.
Hutchings L. 1991. "Prediction" of strong ground motion for the 1989 Loma Prieta earthquake using empirical green's functions. Bull. Seism. Soc. Am. 81:1813-1837.
Hutchings L. 1994. Kinematic earthquake models and synthesized ground motion using empirical Green's functions. Bull. Seism. Soc. Am. 84:1028-1050.
Ji C. 2006. Finite-fault slip model preliminary result for the 05/10/08 PAKISTAN earthquake. http://earthquake.usgs.gov/eqcenter/eqinthenews/2005/usdyae/finitefault/.
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. 92:1192-1207.
Ji C., Wald D. J. and Helmberger D. V. 2002. Source description of the 1999 Hector Mine, California, earthquake, part II: conplexity of slip history. Bull. Seism. Soc. Am. 92:1208-1226.
Kanamori H. 1977. The energy release in great earthquakes. J. Geophys. Res. 82:2981-2987.
Kaneda H. 2006. Surface Rupture of the 2005 Kashmir, Pakistan, Earthquake and its Active Tectonic Implications. AGU Fall Meeting 87.
Kikuchi M. and Kanamori H. 1982. Inversion of complex body waves. Bull. Seism. Soc. Am. 72: 491-506.
Kikuchi M. and Kanamori H. 1986. Inversion of complex body waves —II. Phys. Earth Planet. Interiors 43:205-222.
Kikuchi M. and Kanamori H. 1991. Inversion of complex body waves —III. Bull. Seism. Soc. Am. 81:2335-2350.
Kraeva N. 2004. Tikhonov's regularization for deconvolution in the empirical Green function method and vertical directivity effect. Tectonophysics 383:29-44.
Lanza V., Spallarossa D., Cattaneo M., Bindi D. and Augliera P. 1999. Source parameters of small events using constrained deconvolution with empirical Green's functions. Geophys.J.Int. 137:651-662.
Lawson C. L. and Hanson R. J. 1974. Solving Least Squares Problems. Prentice-Hall, Englewood Cliffs, New Jersey.
Lay T. and Wallace T. C. 1995. Modern Global Seismology.
Lin A. M., Kikuchi M. and Fu B. H. 2003. Rupture Segmentation and Process of the 2001 Mw 7.8 Central Kunlun, China, Earthquake. Bull. Seis. Soc. Am. 93:2477-2492.
Mendoza C. and Hartzell S. H. 1989. Slip distribution of the 19 September 1985 Michoacan, Mexico, earthquake: near-source and teleseismic constraints. Bull. Seism. Soc. Am. 79:655-669.
Mori J. and H.Hartzell S. 1990. Source inversion of the 1988 upland, California, earthquake: determination of a fault plane for a small event. Bull. Seism. Soc. Am. 80:507-517.
Mueller C. S. 1985. Source pulse enhancement by deconvolution of an empirical Green's function. Geophys. Res. Lett. 12:33-36.
Ni S. D., Knamori H. and Helmberger D. 2005. Energy radiation from the Sumatra earthquake. Nature 434:582.
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.
Parsons T., Yeats R. S. and Yagi Y. 2006. Hussain A. Static stress change from the 8 October, 2005 M = 7.6 Kashmir earthquake. Geophysical Research Letters 33:L06304, doi:06310.01029/02005GL025429.
Pathier E., Fielding E. J., Wright T. J., Walker R., Parsons B. E. and Hensley S. 2006. Displacement field and slip distribution of the 2005 Kashmir earthquake from SAR imagery. Geophysical Research Letters 33, L20310, doi:20310.21029/22006GL027193.
Plicka V. and Zahradnik J. 2002. The EGf method for dissimilar focal mechanisms: the Athens 1999 earthquake. . Tectonophysics 359:81-95
Popescu E. and Radulian M. 2001. Source characteristics of the seismic sequences in the Eastern Carpathians foredeep region(Romania). Tectonophysics 338:325-337.
Pujol J. 2003. Elastic wave propagation and generation in seismology.
Radulian M. and Popa M. 1996. Scaling of source parameters for Vrancea (Romania) intermediate depth earthquake. Tectonophysics 261:67-81.
Reid H. F. 1911. The elastic-rebound theory of earthquakes. University of California Department of Geology Bulletin 6(19): 413-444.
Richard C. A., Brian B. and Clifford H. T. 2005. Parameter Estimation and Inverse Problems. International Geophysics Series 90.
Richter C. F. 1935. An instrumental earthquake magnitude scale. Bull. Seism. Soc. Am. 25:1-32
Roumelioti Z., Dreger D., Kiratzi A. and Theodoulidis N. 2003. Slip distribution of the 7 September 1999 Athens Earthquake Inferred from an Empirical Green's Function Study. Bull. Seism. Soc. Am. 93:775-782.
Roumelitoi Z., Kiratzi A. and Dreger D. 2004. The source process of the 2001 July 26 Skyros Island(Greece) earthquake. Geophys. J. Int. 156:541-548.
Saraò A., Das S. and Suhadolc P. 1998. Effect of non-uniform station coverage on the inversion for earthquake rupture history for a Haskell-type source model. Journal of Seismology 2:1-25.
Sekiguchi H. and Iwata T. 2002. Rupture process of the 1999 Kocaeli, turkey, earthquake estimated from strong-motion waveforms. 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.
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