积分方程法模拟三维体对面波的全散射

Full-Scattering of Surface Waves Modeled by Integral Equation Method

采用积分方程法模拟三维非均匀结构中面波的传播,首先将波场表示成Fredholm积分方程的形式,将观察点置于非均匀体内部,求得非均匀体内部的波场,然后根据积分方程,求得任意一点的散射场。通过背景介质中面波格林函数的适当表示,以及Hankel函数的附加定理,解析地给出了格林函数元素的体积分表达式,避免了Hankel函数的积分奇异问题。最后给出了三维非均匀体对点源激发的基阶瑞利波模式的散射实例。

Integral equation method is used to model the propagation of the surface waves in three--dimensional structure. We first get the wave field inside the heterogeneity by putting the observed points in the heterogeneity, and then the wave field at the arbitrary point can be given by taking the heterogeneity as the secondary source. The volume integration of the Green＇s function elements is given analytically by treating the singularity of the Hankel function atR = 0 , based on the proper expression of the Green＇s element and the additional theorem of the Hankel function. We investigate the scattering of the fundamental surface mode, excited by a single force, propagated in the layered reference models imbedding beterogeneity with different velocity contrast.