近地表面波的散射研究

【作者】 鲁来玉；

【导师】 曾融生； 丁志峰；

【作者基本信息】 中国地震局地球物理研究所 ， 地球物理， 2007， 博士

【摘要】 利用地震面波信息来反演推断介质物性，在全球地震学，岩土工程，超声无损检测等领域获得了广泛的应用。然而，目前的方法都潜在假定所探测的对象是横向均匀的，即介质是水平分层介质，没有考虑介质横向非均匀性的影响，而实际中经常遇到介质是横向非均匀性的情况。对于横向非均匀性的情况，面波的传播受三维非均匀结构的影响而产生散射，这在上述三种不同尺度的应用中都获得了广泛的关注。本文则主要研究近地表地球物理领域面波的散射理论。 本文共分六章。第一章和第二章讨论了本研究的背景，研究意义及国内外的研究现状，对复杂介质和结构中地震波的传播和散射进行了综述。第三章讨论了弹性波散射的一般理论，给出了弹性波散射的Lippman-Schwinger方程，并分析了体波散射的特点。 第四章和第五章是本文的主要工作。第四章介绍了模拟面波在横向非均匀性介质中传播的局部模式耦合和参考模式耦合方法，采用参考模式耦合方法分析了面波的散射特征。该方法仍然利用沿分层介质中传播的模式来表示波场，和横向均匀介质不同的是，此时各模式由于非均匀体的存在不是独立传播的，而是相互耦合在一起，通过计算模式的耦合系数，可以得到散射面波的表达式。该方法可以考虑任意阶数的散射。本章针对不同的参考模型，在时间和频率域中，分析了波速的扰动引起的三维非均匀体对面波的散射特点。 第五章采用积分方程法研究面波的散射，和第四章的不同在于，我们利用此方法可以分析三维非均匀体对不同点源激发的面波的散射。首先将观察点置于非均匀体内部，利用Hankel函数的附加定理，可以将面波格林函数对非均匀体的积分解析地给出。求得非均匀体内部的场之后，即可求得任意一点的散射场。本章也针对不同的参考模型，对平面波入射以及不同点源激发的情形，在时间和频率域中分析了散射面波的特点。 第六章是本文的结论和讨论。总结了本文结论之后，对未来面波散射与应用的研究方向进行了展望，特别地，在附录中讨论了散射引起的地震尾波在推断介质随时间变化方面的应用。更多还原

【Abstract】 The seismic surface waves are widely used to infer the properties of the media in different fields ranged from global seismology and geotechnical engineering to ultrasonic Nondestructive test(NDT). However, in current analysis of the surface waves the structure to be inferred are usually assumed isotropic and homogeneous transversely, and which does not vary laterally, but only with depth. This assumption is valid only for small lateral variations in the structure. When large variations (which is often seen in practice) occur, the wavefield becomes more complex, and we have to consider the scattering of the surface waves caused by the 3D heterogeneities. This is paid attention by many researchers in the fields at different scales described above. This paper mainly focus on the scattering of the surface waves in the near surface geophysics.Six chapters are included in this paper. Background and introduction are given in chapter 1. Chapter 2 presents a review on the propagation and the scattering of the seismic waves in complex media. Chapter 3 is the general theory about the scattering of the elastic waves, and the analysis of the scattering characteristics of the body waves is also presented in this chapter.Chapter 4 and 5 are the main work of the paper. Mode coupling method for surface waves propagated in the laterally heterogeneous structure are studied in chapter 4. Reference mode coupling method is used to analyze the characteristics of the scattering surface waves in this chapter. This method also use the modes in reference model as the basis to represent the wavefield. However, the Rayleigh and Love modes propagated independently in the laterally homogeneous reference structure will not independent any more due to the 3D heterogeneity and are said to be coupled. The expression of the wavefield can be given by calculating the coupling coefficients between the modes. Single- and Multi-scattering of the surface waves can be achieved by this method. For different laterally heterogeneous structures, the scattering of the surface waves are investigated in this chapter, both in frequency and time domain.Integral equation method is used to calculate the scattering of the surface waves in chapter 5. Different from the chapter 4, this method can handle the situation of the point sources. The wavefield is represented by the Fredholm integral equation. To solve the integral equation, we discretize the heterogeneity to many cells, and replacing the cubic cell by a cylinder with equal volume to calculate the volume integration since the shape of the cell is not important. The volume integration is formed by a surface integration in the horizontal plane and a depth integration in vertical direction. The surface integration of the Green’s elements to a circle can be given analytically after replacing the cubic cell by a cylinder. We firstly get the wave field inside the heterogeneity by put the observe point inside. Then the scattered field at arbitrary point can be given by taking the heterogeneity as the secondary source. We investigate the characteristics of the scattering of the surface waves propagated更多还原