圆弧形沉积谷地对平面SV波三维散射解析解

3D scattering of plane SV waves by a circular-arc alluvial valley

采用大圆弧面来模拟半空间表面,利用波函数展开法和有限项Fourier展开技术,在频域内给出了圆弧形沉积谷地对平面SV波三维散射的一个解析解。并以此解答为基础,进一步分析了入射波频率和入射角度对圆弧形沉积谷地场地反应的影响。研究表明,圆弧形沉积谷地对平面波的三维散射比二维散射更加复杂;将三维散射问题分解为两个主平面入射的简化处理存在较大的误差;入射波的频率和入射角度对圆弧形沉积谷地场地反应均有重要影响。

The 3D scattering of plane SV waves by circular-arc alluvial valleys is studied. The circular surface assumption is used to simulate the half-space surface. The wave function expansion method and the finite item Fourier series expansion technique are used to give the analytical solution in the frequency domain. Based on the solution, the effects of the incident frequencies and incident angles of the plane SV waves on the dynamic response of circular-arc alluvial valleys are discussed. The study shows that the 3D scattering of plane SV waves by circular-arc alluvial valleys are more complicated than the 2D scattering problem. The simplified decomposition of separating the 3D scattering problem into two main planes may lead to error. Both the incident angles and the incident frequencies of the incident SV waves have important effects on the surface displacement amplitudes.