分层均匀介质中有限震源引起的地面运动计算
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摘要
首先,学习掌握了分层均匀介质中地震波传播的基本理论、采用广义反射透射系数矩阵方法计算单一点源引起的地面运动的基本原理以及数值计算问题中的经典技术难题及其解决方法；然后,基于分层均匀介质中地震波计算的基本原理,考虑有限震源的任意几何特征、有限震源的震源机制随时间和空间发生变化的可能性以及并行计算的发展方向,参考现有的计算程序,利用具有矩阵计算与数据可视化优势的Matlab高级编程语言,重新设计编写了计算程序,使其不但适用于点震源的简单情况,也适用于任意几何形状的、震源机制随时间和空间发生变化的有限震源的复杂情况。
考虑到有限震源在深度方向的分布特点,论文在计算广义反射透射系数矩阵的环节上,采用单循环同时计算不同深度震源界面情况下的广义反射透射系数矩阵的方案,大大提高了计算效率；考虑到震源过程中震源机制不但随时间发生变化而且随空间发生变化的可能性,在计算震源作用的环节上,采用预先计算6个基本震源(地震矩张量)的技术路线,也大大提高了计算效率。
为了适应并行计算的发展趋势,论文重点在两个环节上设计了并行计算。第一个环节是极其耗时的广义反射透射系数矩阵的计算环节。在这个环节上,本程序采用了同时计算上行波和下行波的广义反射透射系数矩阵的技术路线。第二个环节是有限震源的地面运动的合成环节。在这个环节上,本程序采用了同时计算一组震源-多组观测点的计算方案。
为了检验计算程序的可靠性、计算效率和适用性(功能),论文分别设计了远场情况、近场情况、点源情况和有限震源情况下的多组数值实验,对比分析了该程序与现有程序的计算结果和计算时间,检验了程序可靠性、计算效率以及适用能力。
最后,为了检验论文设计编写的程序的应急效能,将程序应用于2008年5月12日四川汶川Ms8.0地震和2010年4月14日青海玉树Ms7.1地震的近断层的地面运动(位移和速度)的计算,结果表明,该程序可以在较短时间内再现地震现场的、有助于判定灾情分布的地面运动。
At first, the fundamental theories of the seismic wave propagation in stratified media, the basic principles of calculating ground motion caused by a point source using the method of generalized reflection and transmission matrices, and several classical technical problems in calculation as well as their typical solutions to those problems are learned. Then, on the basis of the fundamental theory of seismic wave calculation in stratified media, with consideration of arbitrary geometry and tempo-spatially variable focal mechanisms of finite sources, as well as development trend of parallel computation, and with reference to the programs already developed for calculating point-source-caused ground motion, using Matlab programming language with great advantages of matrix computing and data visualization, this paper focuses on improvement of computing-flow in the point-source case and development of a new program to be suitable for both point sources and finite sources with arbitrary geometries and tempo-spatially variable mechanisms.
With Consideration of characteristics of the distribution of finite sources in depth direction, the same single-loop is adopted to compute generalized reflection and transmission matrices for all the source depths, which largely raises the computing efficiency; and with consideration of the possibilities of the variation of focal mechanisms of finite sources with both time and space, source contribution of the six basic types of sources(seismic moment tensors) are pre-calculated, which also helps to raise computing efficiency.
Meanwhile, in order to adapt the development trend of parallel computation, parallel computation is applied to two steps, one for calculating the extremely time-consuming generalized reflection and transmission matrices, in which generalized reflection and transmission matrices for the up-going and down-going waves are simultaneously computed; the other for summing the ground motions caused by finite source, in which the ground motions at a number of observation stations caused by the finite source are simultaneously summed.
In order to investigate reliability, computing efficiency and functions of the program, enough numerical tests in cases of far field, near field, point sources and finite sources are designed, and the test results and computing time are compared with those from already developed applications. The comparison indicates that the application developed in this study is reliable, rather more efficient and applicable.
At last, in order to evaluate the emergency function of the application developed in this study, the application is applied to the 2008 Wenchuan Ms8.0 earthquake and the 2010 Yushu MS7.1 earthquake. The results indicate that the application could reconstruct the image of ground motion which could well explain the spatial distribution of main disaster across the epicentral areas.
考虑到有限震源在深度方向的分布特点,论文在计算广义反射透射系数矩阵的环节上,采用单循环同时计算不同深度震源界面情况下的广义反射透射系数矩阵的方案,大大提高了计算效率；考虑到震源过程中震源机制不但随时间发生变化而且随空间发生变化的可能性,在计算震源作用的环节上,采用预先计算6个基本震源(地震矩张量)的技术路线,也大大提高了计算效率。
为了适应并行计算的发展趋势,论文重点在两个环节上设计了并行计算。第一个环节是极其耗时的广义反射透射系数矩阵的计算环节。在这个环节上,本程序采用了同时计算上行波和下行波的广义反射透射系数矩阵的技术路线。第二个环节是有限震源的地面运动的合成环节。在这个环节上,本程序采用了同时计算一组震源-多组观测点的计算方案。
为了检验计算程序的可靠性、计算效率和适用性(功能),论文分别设计了远场情况、近场情况、点源情况和有限震源情况下的多组数值实验,对比分析了该程序与现有程序的计算结果和计算时间,检验了程序可靠性、计算效率以及适用能力。
最后,为了检验论文设计编写的程序的应急效能,将程序应用于2008年5月12日四川汶川Ms8.0地震和2010年4月14日青海玉树Ms7.1地震的近断层的地面运动(位移和速度)的计算,结果表明,该程序可以在较短时间内再现地震现场的、有助于判定灾情分布的地面运动。
At first, the fundamental theories of the seismic wave propagation in stratified media, the basic principles of calculating ground motion caused by a point source using the method of generalized reflection and transmission matrices, and several classical technical problems in calculation as well as their typical solutions to those problems are learned. Then, on the basis of the fundamental theory of seismic wave calculation in stratified media, with consideration of arbitrary geometry and tempo-spatially variable focal mechanisms of finite sources, as well as development trend of parallel computation, and with reference to the programs already developed for calculating point-source-caused ground motion, using Matlab programming language with great advantages of matrix computing and data visualization, this paper focuses on improvement of computing-flow in the point-source case and development of a new program to be suitable for both point sources and finite sources with arbitrary geometries and tempo-spatially variable mechanisms.
With Consideration of characteristics of the distribution of finite sources in depth direction, the same single-loop is adopted to compute generalized reflection and transmission matrices for all the source depths, which largely raises the computing efficiency; and with consideration of the possibilities of the variation of focal mechanisms of finite sources with both time and space, source contribution of the six basic types of sources(seismic moment tensors) are pre-calculated, which also helps to raise computing efficiency.
Meanwhile, in order to adapt the development trend of parallel computation, parallel computation is applied to two steps, one for calculating the extremely time-consuming generalized reflection and transmission matrices, in which generalized reflection and transmission matrices for the up-going and down-going waves are simultaneously computed; the other for summing the ground motions caused by finite source, in which the ground motions at a number of observation stations caused by the finite source are simultaneously summed.
In order to investigate reliability, computing efficiency and functions of the program, enough numerical tests in cases of far field, near field, point sources and finite sources are designed, and the test results and computing time are compared with those from already developed applications. The comparison indicates that the application developed in this study is reliable, rather more efficient and applicable.
At last, in order to evaluate the emergency function of the application developed in this study, the application is applied to the 2008 Wenchuan Ms8.0 earthquake and the 2010 Yushu MS7.1 earthquake. The results indicate that the application could reconstruct the image of ground motion which could well explain the spatial distribution of main disaster across the epicentral areas.
引文
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胡幸平,俞春泉,陶开,崔效锋,宁杰远,王艳华.2008.利用P波初动资料求解汶川地震及其强余震震源机制解[J].地球物理学报.51(6)：1711-1718.
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刘超,张勇,许力生等.2008.一种矩张量反演新方法及其对2008年汶川Ms8.0地震序列的应用[J].地震学报.30(4)：329-339.
刘超,许力生,陈运泰.2010.2010年4月13日青海玉树地震快速矩张量解[J]。地震学报.32(3),362-364.
刘启方.2001.断层附近强地面运动的初步研究[D].哈尔滨：中国地震局工程力学研究所：1-16.
四川大学数学系高等数学与微分方程教研室.1985.高等数学[M].北京：高等教育出版社：355-387.
王为民,赵连锋,李娟.2008.四川汶川8.0级地震震源过程[J].地球物理学报.51(5)：329-339.
王为民,赵良峰,姚振兴.2010.2010年4月14日玉树7.1级地震震源破裂过程初步结果. http://www.csi.ac.cn/manage/html/4028861611c5c2ba0111c5c558b00001/_content/10 04/14/1271250817270.html
王勤彩,陈章立,郑斯华.2009.汶川大地震余震序列震源机制的空间分段特征[J].科学通报.54(16)：2348-2354.
闻学泽,徐锡伟,郑荣章.2003.甘孜-玉树断裂的平均滑动速率与近代大地震破裂[J].中国科学D辑.33：199-208.
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许力生,邸海滨,冯万鹏等.2010.2010年青海玉树Ms7.1地震近断层地面运动估计[J].地球物理学报.53(6)：1366-1373
徐彦,张俊伟,苏有锦.2011.反投影全球子台网P波记录研究2010年4月14日玉树地震破裂过程[J].地球物理学报54(5)：1243-1250.
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陈运泰,吴忠良,王培德等.2000.数字地震学[M].北京：地震出版社：15-127.
杜海林.2007.2004年苏门答腊-安达曼大地震能量辐射源的时间域台阵技术分析[D].北京：中国地震局地球物理研究所：1-6.
胡幸平,俞春泉,陶开,崔效锋,宁杰远,王艳华.2008.利用P波初动资料求解汶川地震及其强余震震源机制解[J].地球物理学报.51(6)：1711-1718.
李闽锋,刑成起,蔡长星.1995.玉树断裂活动性研究[J].地震地质.17(3)：218-224.
李旭.1993.用地震波形资料反演1990年青海共和地震的震源过程[D].北京：国家地震局地球物理研究所：1-45.
李旭,陈运泰,王培德.1994.水平分层均匀介质中理论地震图计算程序的使用说明.北京：国家地震局地球物理研究所：1-20.
李旭,陈运泰.1996.用长周期地震体波波形资料反演1990年青海共和地震的震源过程[J].地震学报.18(3)：279-286.
刘超,张勇,许力生等.2008.一种矩张量反演新方法及其对2008年汶川Ms8.0地震序列的应用[J].地震学报.30(4)：329-339.
刘超,许力生,陈运泰.2010.2010年4月13日青海玉树地震快速矩张量解[J]。地震学报.32(3),362-364.
刘启方.2001.断层附近强地面运动的初步研究[D].哈尔滨：中国地震局工程力学研究所：1-16.
四川大学数学系高等数学与微分方程教研室.1985.高等数学[M].北京：高等教育出版社：355-387.
王为民,赵连锋,李娟.2008.四川汶川8.0级地震震源过程[J].地球物理学报.51(5)：329-339.
王为民,赵良峰,姚振兴.2010.2010年4月14日玉树7.1级地震震源破裂过程初步结果. http://www.csi.ac.cn/manage/html/4028861611c5c2ba0111c5c558b00001/_content/10 04/14/1271250817270.html
王勤彩,陈章立,郑斯华.2009.汶川大地震余震序列震源机制的空间分段特征[J].科学通报.54(16)：2348-2354.
闻学泽,徐锡伟,郑荣章.2003.甘孜-玉树断裂的平均滑动速率与近代大地震破裂[J].中国科学D辑.33：199-208.
谢毓寿,蔡美彪.1987.中国地震历史资料汇编第三卷(下)[M].北京：科学出版社：235-236.
徐果明,周蕙兰.1982.地震学原理[M].北京：科学出版社：38-75.
许力生,邸海滨,冯万鹏等.2010.2010年青海玉树Ms7.1地震近断层地面运动估计[J].地球物理学报.53(6)：1366-1373
徐彦,张俊伟,苏有锦.2011.反投影全球子台网P波记录研究2010年4月14日玉树地震破裂过程[J].地球物理学报54(5)：1243-1250.
姚振兴,郑天愉.1985.对二滩水电站坝区场地地面运动的估计[J].地球物理学报.28(2)：170-180.
张勇,冯万鹏,许力生等.2008.2008年汶川大地震的时空破裂过程[J].中国科学D辑:地球科学.38(10)：1186-1194.
张勇.2008.震源破裂过程反演方法研究[D].北京：北京大学：1-16.
张勇,许力生,陈运泰.2010.2010年4月14日青海玉树地震破裂过程快速反演[J].地震学报.32(3)：361-365.
张勇,许力生,陈运泰.2010.2010年青海玉树地震震源破裂过程[J].中国科学D辑.40(7)：819-821.
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