Scattering and differaction of plane P waves by circular cylindrical canyons with variable depth-to-width ratio

Abstract

The scattering and diffraction of plane ( P ) waves by a circular canyon with variable width-to-depth ratio has been studied in this paper. Series of Bessel function expansions have been used to solve the problem. To illustrate the results, the surface displacement amplitudes and phases are presented. The following parameters are found to affect the results: o 1. The angle of incidence, α , 2. The ratio of the canyon depth to canyon width, h/a , 3. The dimensionless frequency of the incident P wave, ν and 4. The Poisson's ratio, v The displacement amplitudes and phases on the ground surface show significant deviation from those of the uniform half-space motions, especially at high frequencies, when the wavelengths of the incident and scattered waves are small compared to the size of the canyon.