三维半球形凹陷饱和土场地对平面P波散射问题的解析解

An analytic solution for the diffraction of plane P-wave by three-dimensional hemispherical canyons in a fluid-saturated porous media half space

以Biot饱和多孔介质动力学理论为基础,利用Fourier Bessel级数展开法,得到饱和多孔介质半空间中半球形凹陷地形对入射平面P波三维散射问题的解析解.利用这一解析解数值计算给出地表位移幅值,分析入射角、入射波频率对地表位移幅值的影响,并与现存的单相介质情况下三维半球形凹陷问题和两相介质情况下二维圆弧形凹陷问题得到的结论进行对比.

On the basis of the Biot dynamic theory, we obtain an analytic solution of three-dimensional scattering and diffraction by hemispherical canyons in a fluid saturated porous media half space to plane P-wave incidence. The Fourier-Bessel series expansion technique is used to get the analytic solution for the first time. The results of surface displacement amplitudes are presented, and the effects of frequency and angle of incident wave on the surface displacement amplitudes are discussed. These results are compared with those for the same situation but with an elastic one-phase media and two-dimensional circular cylindrical canyons regarded as two-phase media, respectively.