半球形沉积谷场地对入射平面Rayleigh波的三维散射解析解

Analytical solution of three-dimensional scattering and diffraction of plane Rayleigh-waves bya hemispherical alluvial valley with saturated soil deposit

把半球形沉积谷和周围半空间场地分别用具有不同弹性模量和不同半径的球坐标描述。利用Fourier-Bessel级数展开法,在频域内给出了半空间中半球形沉积谷场地在平面Rayleigh波入射下三维散射问题的解析解。利用这一解析解计算分析了入射波频率、场地软硬对场地内地表位移幅值的影响。

The three-dimensional scattering and diffraction of plane Rayleigh-waves by a hemispherical valley is studied. The deposit and the half space is simulated by elastic single-phase media. The Fourier-Bessel series expansion technique is used to get the analytical solution for the first time. The results of surface displacement amplitudes are presented; and the effects of frequency and angle of incident waves on the surface displacement amplitudes are discussed.