仿真地震图
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摘要
运用动力有限元方法得到一种数值模拟的地震图。动力有限元方法在计算中涉及时间,因此它不同于传统的静态有限元方法,也不同于后来有人用过的伪动态模拟(一系列时间的静态结果,连接起来看,在一定程度上反映变化趋势);动力学有限元是考虑了加速度和惯性影响的。借鉴理论地震图思想,提出仿真地震图概念,采取非线性动力学有限元方法,得到地学模型的仿真地震图,运用反演方法,通过对比仿真地震图与实际地震图,得出地球介质或者震源的物理图景。考虑燕山断层带、太行山山前断层带、郯庐断层带以及海岸线,建立中国中、中北部地壳有限元模型,地壳底部采用无反射边界,相当于无限延拓。在对应唐山的单元(节点)上加载一个爆炸源,在对应于兰州、西安、上海地震台的单元(节点)上,得到应力随时间变化的时间历程,也就是数值模拟的地震图。在示例中,按照反演步骤,调整了地壳模型的物理参数,并由此提出仿真地震图的原理。较之理论地震图,仿真地震图物理上更加真实。
In this paper,we use non-linear dynamic Finite Element Method(FEM)to obtain a simulation seismogram.Here,the dynamic FEM is a time-related simulation.Thus,dynanic FEM is quite different from the traditional FEM,and also different from the pseudo-dynamic simulation that is a set of static simulations at a series of time.Contrastingly,dynamic FEM takes every element's(node's)acceleration and its inertia into consideration.On the basis of theoretical seismogram,we proposed the concept of the simulation seismogram.Using non-linear dynamic FEM we got the simulated seismogram of a FEM model.With inversion steps and by comparing the simulation seismogram and the real seismogram,we approached the physics of the earth media and the physics of the focus of an earthquake.As an example,taking the Yanshan fault zone,Taihangshan Mountain Front fault zone,and Tan-Lu fault zone into consideration for the modeling,we built the FEM model for the crust of the north and middle of China.In addition,the model takes the coastline into consideration and the bottom of the crust is set to be the non-reflection boundary,which is equal to an infinitely continued media.When running the model,we applied an explosive load on the element where geographically matches to Tangshan City.As the model was running,we got three time-courses of stress at the elements matching to Lanzhou,Xi'an,and Shanghai Station,respectively.These time courses of stress are the simulated seismograms.By practicing the inversion methodology,we adjusted the physical parameters of the model.Compared to the theoretical seismogram,the simulation seismogram is more close to the physical reality.
In this paper,we use non-linear dynamic Finite Element Method(FEM)to obtain a simulation seismogram.Here,the dynamic FEM is a time-related simulation.Thus,dynanic FEM is quite different from the traditional FEM,and also different from the pseudo-dynamic simulation that is a set of static simulations at a series of time.Contrastingly,dynamic FEM takes every element's(node's)acceleration and its inertia into consideration.On the basis of theoretical seismogram,we proposed the concept of the simulation seismogram.Using non-linear dynamic FEM we got the simulated seismogram of a FEM model.With inversion steps and by comparing the simulation seismogram and the real seismogram,we approached the physics of the earth media and the physics of the focus of an earthquake.As an example,taking the Yanshan fault zone,Taihangshan Mountain Front fault zone,and Tan-Lu fault zone into consideration for the modeling,we built the FEM model for the crust of the north and middle of China.In addition,the model takes the coastline into consideration and the bottom of the crust is set to be the non-reflection boundary,which is equal to an infinitely continued media.When running the model,we applied an explosive load on the element where geographically matches to Tangshan City.As the model was running,we got three time-courses of stress at the elements matching to Lanzhou,Xi'an,and Shanghai Station,respectively.These time courses of stress are the simulated seismograms.By practicing the inversion methodology,we adjusted the physical parameters of the model.Compared to the theoretical seismogram,the simulation seismogram is more close to the physical reality.
引文
[1]姚振兴,王凯,郑天愉.理论地震图应用研究[G]∥中国科学院地球物理研究所40周年所庆论文集.北京:《中国学术期刊(光盘版)》电子杂志社,1990,76-80.
[2]郑文衡,曾佐勋.非线性动力学有限元在地震学中的应用[M].武汉:中国地质大学出版社有限公司,2012.
[3]Krishna V G,Rao C V R K,Gupta H K,et al.Crustal seismic velocity structure in the epicentral region of the Latur earthquake(September 29,1993),southern India:Inferences from modelling of the aftershock seismograms[J].Tectonophysics,1999,304(3):241-255.
[4]Zheng W,Wang C,He Z,et al.Response of crust to ocean tide[J].大地测量与地球动力学,2002,22(2):41-46.
[5]郑文衡,王乘,陈湘鹏.地壳块体脉冲相应的时间反转效应研究[J].地震学报,2001,23(4):370-379.
[6]Larmat C,Montagner J P,Capdeville Y,et al.Numerical assessment of the effects of topography and crustal thickness on martian seismograms using a coupled modal solution-spectral element method[J].Icarus,2008,196(1):78-89.
[7]Jobert N.Contribution of some particularities in the dispersion curves to numerical seismograms computed by normal modes[J].Journal of Computational Physics,1978,29(3):404-411.
[8]Chiaruttini C,Salemi G.Artificial intelligence techniques in the analysis of digital seismograms[J].Computers&Geosciences,1993,19(2):149-156.
[9]Nur A.Dilatancy Pore fluids and premonitory variations of ts/tp traval times[J].Bulletin of Sensmological Society of America,1972,62(5):1217-1222.
[10]Myachkin V I,Brace W F,Sobolev G A,et al.Two models for earthquake forerunners[J].Pure and Applied Geophysics,1975,113(1/2):169-182.
[2]郑文衡,曾佐勋.非线性动力学有限元在地震学中的应用[M].武汉:中国地质大学出版社有限公司,2012.
[3]Krishna V G,Rao C V R K,Gupta H K,et al.Crustal seismic velocity structure in the epicentral region of the Latur earthquake(September 29,1993),southern India:Inferences from modelling of the aftershock seismograms[J].Tectonophysics,1999,304(3):241-255.
[4]Zheng W,Wang C,He Z,et al.Response of crust to ocean tide[J].大地测量与地球动力学,2002,22(2):41-46.
[5]郑文衡,王乘,陈湘鹏.地壳块体脉冲相应的时间反转效应研究[J].地震学报,2001,23(4):370-379.
[6]Larmat C,Montagner J P,Capdeville Y,et al.Numerical assessment of the effects of topography and crustal thickness on martian seismograms using a coupled modal solution-spectral element method[J].Icarus,2008,196(1):78-89.
[7]Jobert N.Contribution of some particularities in the dispersion curves to numerical seismograms computed by normal modes[J].Journal of Computational Physics,1978,29(3):404-411.
[8]Chiaruttini C,Salemi G.Artificial intelligence techniques in the analysis of digital seismograms[J].Computers&Geosciences,1993,19(2):149-156.
[9]Nur A.Dilatancy Pore fluids and premonitory variations of ts/tp traval times[J].Bulletin of Sensmological Society of America,1972,62(5):1217-1222.
[10]Myachkin V I,Brace W F,Sobolev G A,et al.Two models for earthquake forerunners[J].Pure and Applied Geophysics,1975,113(1/2):169-182.
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