Shear wave scattering generated by the interaction of a circular half-cylinder with a wavefield originated by a line source.

Abstract

The problem of shear wave diffraction caused by a circular half-cylinder was considered. In this case, the incident field was assumed to be generated by a line source, which was set to be parallel to the axis of the cylinder. The solution of this eigenvalue problem was obtained through the application of the superposition principle. In this case, the wavefield outside of the half-cylinder was expressed in terms of the free field and the diffracted field. On the other hand, the wavefield inside of the cylinder was defined in terms of refracted fields. Since the scatterer and the source possess cylindrical symmetry, all the wavefields could be expressed in terms of series of Bessel and Hankel functions. The unknown coefficients of these series were obtained by evaluating boundary conditions. With the solution of this problem, the seismic response of a semi-circular alluvial valley was studied.