一种求解瑞利波散射问题的修正边界元方法

边界元法的一大优势是用于求解半空间等无限域问题，然而对于弹性波的传播问题，传统边界元法在采用全平面或全空间格林函数时，在截断边界处仍会产生虚假的反射回波，直接影响到散射场的求解准确性。因此，本文在传统边界元法基础上提出一种修正边界元法，用于计算无限大半平面中的弹性波场问题。该方法以瑞利波形式的远端散射场代替原本因截断而舍去的部分，通过互易定理建立单位瑞利波和全平面格林函数的积分方程，求得修正系数，并代入修正边界元矩阵，计算出瑞利波的散射场。为验证本文所提方法，文中将多个算例的结果与解析解对比，并用该方法计算了不同缺陷的散射场。这些对比结果表明，本文所提修正边界元法可准确求解瑞利波散射场，为基于表面波的缺陷反演问题研究提供了有效的正演途径。

A modified boundary element method for scattering problem of Rayleigh wave

Boundary element method (BEM) has the advantage in solving infinite field problems such as those concerning half-spaces. However, for elastic wave propagation problem, spurious reflected waves will occur at the truncation points by the conventional BEM if full space Green’s function is adopted, which directly affects the accuracy in solving scattering fields. In light of this, a modified BEM method is proposed to analyze scattered fields of the two dimensional Rayleigh waves in 2-D half-plane based on the conventional BEM. We calculated the correction factors by reciprocity relations between the unit Rayleigh wave and the full plane Green’s function. Meanwhile, by substituting the correction factors into the modified BEM method, we can calculate the scattered field of Rayleigh wave. The method is varified by comparing the numerical results with analytical solutions and calculating scattering fields of different flaws. Those comparison results show that the modified BEM proposed in the paper can accurately solve the scattering problem of Rayleigh waves, which provides an effective forward simulation way for further investigating inverse problem of flaw reconstruction based on surface waves.