Abstract
The three-dimensional scattering and diffraction of plane waves by a hemispherical canyon in the homogeneous elastic half-space has been analyzed. Using the series solution for a general angle of wave incidence, ground motion near the canyon has been studied. The nature of ground motion has been found to depend on three key parameters: 1. (1) γ, the angle of incidence, 2. (2) ν, a dimensionless frequency of wave number proportional to the ratio of the diameter of the canyon to wavelength of the incident P-wave, and 3. (3) κ, the ratio of longitudinal to transverse wave speeds. The displacement amplitudes and phases on nearby ground surface show significant departure from the uniform half-space motions. The angle of incidence γ determines the overall trends of motion amplitudes. For oblique incidence, for example, considerable amplification is observed in front of the canyon, and a prominent shadow zone is relaized behind the canyon.
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