Diffraction of SV Waves by Circular Canyons of Various Depths

Abstract

The scattering and diffraction of plane SV waves by circular cylindrical canyons of various depths in an elastic half space is studied in this paper. The canyons studied here range from shallow circular to semicircular canyons in an elastic half-space. The series of Bessel function expansions is used to solve the problem. For incidence beyond critical angle, the surface waves generated are expanded in terms of finite Fourier series that also involve Bessel functions. The number of steps and operations involved in the calculations is small and the method is applicable to a wide range of frequencies, thus making it preferable to the presently available numerical techniques. The surface displacement amplitudes and phases that are presented shows that the results depend on the following parameters; (1) The angle of incidence, θ\Gβ\N; (2) the ratio of canyon depth to its half width, \Ih\N/\Ia\N; (3) the dimensionless frequency of the incident SV wave, \Ighn; and (4) Poisson’s ratio, \Nν\N. The presence of the canyon in the elastic half space results in significance deviation of both the displacement amplitudes and phases on nearby ground surface from that of uniform half space motions, especially at high frequencies.