A Note On The Scattering Of Elastic Plane Waves By A Hemispherical Canyon

In the homogeneous elastic half space, hemispherical canyon will affect the three-dimensional scattering and diffraction of plane waves, which will lead to the change of the ground near the canyon. Using the series solution for a general angle of wave incidence, the exact solution of the ground motion near the canyon has been drawn. Since the existence of physiognomy that can be simulated by hemispherical canyon, the displacement of the ground will be magnified, which can be used as a factor in practical project. At the same time, the result gained by analysis can be used to testify other results obtained by numerical methods such as FEM and BEM. The nature of ground motion depends on three key parameters:(1), the angle of incidence,(2), a dimensionless frequency of wave number proportional to the ratio of the diameter of the canyon to wavelength of the incident wave,(3), the ratio of longitudinal to transverse wave speeds.The displacement amplitudes and phases of nearby ground surface show significant difference from the uniform half-space motions. The angle of incidence determines the overall trends of motion amplitudes. For oblique incidence, considerable amplification is observed in front of the canyon, and a prominent shadow zone is realized behind the canyon.