【作者】 王大伟；

【导师】 孟凡顺；

【作者基本信息】 中国海洋大学 ， 地球探测与信息技术， 2011， 硕士

【摘要】 地震和断层的关系错综复杂。地震可能导致断层的生成,而断层的活动也会引发地震。实际上,断层的产生或地震的发生都和地下的构造应力有密切的联系。从断层处考虑,断层的破裂直接影响着地震波的形成,而断层处各介质的物理状态决定了断层未来的运动状态,弹性动力学正是研究弹性物体对动力载荷的响应。在早期的研究中,地震波理论是基于理想化的地层:均匀的或具有层状结构的。在实际断层情况下,需要我们考虑实际的地球介质:非均匀各向异性。就讨论地震波入射到断层面而言,断层面是一个特殊的应力间断反射界面,两侧介质间的关系是一个弹性接触关系。从数学力学角度观察,地震波入射到断层面可以归结为一个弹性动力学问题,即研究弹性体在外力的作用下,弹性体瞬态变形和应力变化的规律。地震波的传播在断层处我们可以归结为波动方程的边界问题,分界面的作用在于提供了某些边值条件,也就是常说的不连续分布问题。对复杂介质建模和数值模拟随着计算机技术的发展越来越成熟,间接导致了现代弹性波理论的飞速发展。要建立更加适用的模型就需要对介质的参数有一定的了解。通过研究地震波,利用现有的介质理论,可以得到断裂走向,介质密度等重要参数,而用数值方法模拟弹性波在复杂介质中的传播,研究弹性波的传播特性,对复杂介质的某些参数对波传播的影响的认识将会有很大的帮助。本文从弹性介质的体积元出发,探讨了体积元的弹性力学、动力学,并由此推导弹性介质在力学上的微分型理论,进而从连续介质力学的质量守恒,线动量守恒,角动量守恒以及能量守恒出发,研究出弹性介质瞬态变形和应力变化的规律,从而进一步研究了弹性波在地下介质中的弹性动力学理论,并借助计算机手段实现了波场的正演模拟,得出地震波在断层处的弹性动力学特征。本文总结了研究断层地震波的现状,从弹性波动力学方程及其核心问题的角度出发,分析了弹性波在均匀和非均匀各向同性介质中的波场,在掌握了正演原理及正演模型建立技术的基础上,通过Tesseral 2-D正演模拟软件,探讨了影响弹性动力学方程解的精确性的因素,并建立多个模型,深入研究了实际地层中含有破碎带的地层对弹性波传播的影响,验证了弹性动力学方程的解的有关理论。本文在数值计算上是基于弹性波动方程的有限差分数值解,求得基本模型的断层处弹性波动力学方程的解,通过各种介质的比较,分析在断层处,有限差分法的不足和改进的方法,以求得更精确的方程的解。更多还原

【Abstract】 The relationship between seismic fault is very Intricate. Earthquakes can lead to fault,the fault activity can also cause the earthquakes Tectonic stress bring on the shaping of the fault,the cracking of the fault take effect on the shaping of the seismic wave, and the physical state of the media on the fault determine the state of motion of the fault in future, The elastodynamics just devote itself to study the answerback of the dynamic loading in elastic substance.In the early research,the seismic wave theory is based on the idealized stratum: uniform or with the layer structure .But we will consider the actual earth medium: non-uniform anisotropy. To discuss the seismic wave incident to the fault plane waves concerned, the fault plane is a special reflecting interface with stress discontinuity and it is a elastic contact relationship between both sides of medium. From the angle of mathematics and mechanics, we can take it as an elastic dynamics problems.That is we research elasto’s transient deformation and stress variation under the influence of the outside. On the fault, we can attribute it as boundary problem of the wave equation the role of boundary is providing some boundary value conditions, also is often said as discontinuous distribution problem. The method of modeling of complex medium is more and more mature as the With the development of computer technology which indirectly lead to the rapid development of elastic wave theory.To build more applicable model we need to understand the parameters of the medium, and we can get the fracture toward, medium density and other important parameters. By using numerical method to simulation the elastic wave spreading in complex medium, and researching it’s propagation, we can get more about the parameters on the influence of wave propagation.In this text, we begin with element of volume of elastic substance, take the research into the elasticity and dynamics of it, and derive the differential theory of the elastic medium basing on the point of mechanics, then we develop the regular of the momentary deform state and the stress movement basing on the consertvation of mass, linear momentum, angular momentum and energy which contribute to the work about the next step: the theory of the elastodynamics about elastic wave in interior medium of the earth. And we achieve the forward modeling of the wave field by computer. At last we gain the characteristic of the elastodynamics of seismic wave on fault zone.The paper sum up the present situation of the research of the seismic wave on fault zone. After the researching of the equation of the dynamics of the elastic wave, we analyze the wave field which own the homogeneity or nonhomogeneity isotropic medium. And we master the method of the forward modeling and build up the forward model ,basing of which we probe into the accuracy element which can affect the answer of the equation of the dynamics of the elastic wave by Tesseral 2-D.And we develop some models which can contribute on the researching of the actual layer containing the fracture zone, and give us the result of the verification of the equation of the dynamics of the elastic wave in the fracture zone.The paper is base on the finite difference numerical solution of the equation of the dynamics of the elastic, and find the solution of the equation of the dynamics of the elastic on the fault by the basic model. Bying comparing the different media, we find the defect of the FDM and propose the modify, and we expect that we can get more accuracy answer.更多还原