And then the solutions for displacement mode of scattering wave at far field and scattering cross - section are provided at the interface cavity when it is ellipse and diamond 在求解了界面孔对sh波散射的近场解的基础上，进一步研究了其远场特性。给出了界面椭圆孔和方孔的远场位移模式和散射截面的解答。
Using this scattered wave function and moving coordinate system , the problem can be summarized to scattering of sh - wave by multiple circular cavities in infinite space and the boundary conditions can be satisfied 利用这一波函数，则可将该问题转化成为一个对无限空间中相邻多个圆形孔洞对sh波散射的求解问题。
An analytic method is developed for the problem of scattering of steady sh - wave and dynamic analysis of a shallow - embedded circular lining structure in the field of linearly elastic dynamic mechanics in this paper 本文在线弹性力学范畴内，建立了求解半无限空间中界面附近圆形衬砌结构对sh波散射与动应力集中问题的解析方法。
The method of crack - division is used to make radial cracks at the edge of cavity . a series of integral equations for determining the dsif at tips of anti - plane crack are set up in terms of the green ' s function 按“契合”的方式和采用裂纹切割技术构造出孔边径向界面裂纹对sh波散射的模型，利用green函数建立直接求解m型裂纹尖端动应力强度因子的定解积分方程组。
Scattering of sh - wave by collinear cracks of any limited length originating diametrecally at the boundary of circular lining which has cracks in homogeneous medium is investigated , and solution of dynamic stress intensity factors in mode at crack tip are obtained 按“契合”方式并采用裂纹切割技术构造含径向裂纹圆环形衬砌对sh波散射的模型，利用green函数将问题归结为求解第一类fredholm积分方程组。
In the course of scattering with the same energy , the excited probabilities of lower exciting states are far off bigger than ones of higher exciting states . all in all , the adapted ms potential has advantages of concision form , less adjustable parameters , convenient for applicant 当体系能量一定时，不管是微分散射截面还是分波散射截面，弹性散射的几率大，对总的散射截面贡献最大；非弹性散射的几率小，对总的散射截面的贡献也小。
The main achievements of this paper could be summarized as follows : ( 1 ) wave function expansion method involved in the scattering problem of elastic wave is summarized , and key points of the wave function expansion method and its application in the elastic wave scattering problem of local sites are studied 本文所做的主要工作摘要如下： ( 1 )对弹性波散射问题中的波函数展开方法做了总结，研究了波函数展开法在求解局部场地弹性波散射问题时的要点。
By means of " conjunction " , the model of this problem is established . and then a series of fredholm integral equations of first kind can be set up in terms of the green ' s function , furthermore the scattering problem of sh - wave by cavity in the interface is transformed into a series of algebraic equations based on the direct - discrete method 按“契合”的方式构造出在两个性质不同的弹性半空间交界面上的任意形孔洞对sh波散射的模型，利用green函数建立求解问题的定解积分方程组，并用直接离散的方法将其转化为代数方程组进行求解。
Then we consider the problem as a " conjunction " problem : according to the solutions for wave problem in interface between two conjunctive homogeneous elastic half - spaces as well as the scattering problem of sh - waves by an arbitrary - shape - cavity in homogeneous material , we divide the elastic space with an interface cavity into two parts along the interface , each is elastic half space with an arbitrary - shape - canyon . and then dividing surfaces are loaded with undete rmined antiplane forces , and with some antiplane reacting forces to appear cracks 然后将界面任意形孔洞和孔边裂纹对sh波的散射问题视为“契合”问题：即从两个相互契合的完整弹性半空间的界面波动问题和弹性均匀介质中任意形孔洞对sh波散射的解答出发，沿界面处将含孔洞的弹性空间剖分为两个含有任意形凹陷的弹性半空间，在其剖分表面上加置未知的反平面荷载，在出现裂纹的位置加置反平面反力构造出裂纹。
Several typical sites are chosen in this paper in order to investigate the main points of wave function expansion method applied to elastic wave scattering problems . antiplane scattering analytical solution for the alluvial valley of shallow circular - arc cross - section is investigated , which has practical engineering value 本文选择了几种典型场地，研究了波函数展开法在求解其中局部场地弹性波散射问题时的要点，对更有工程实际意义的浅圆弧型沉积盆地，研究了其出平面散射解析解答的收敛性和精度。
