Soil and topographic effects on ground motion of a surficially inhomogeneous semi-cylindrical canyon under oblique incident SH waves

To elucidate the ground motion amplification due to combined soil and topographic effects, an analytical formulation in the framework of classical elastodynamics is derived for the scattering of oblique incident plane SH waves by a semi-cylindrical canyon covered by a local inhomogeneous soil layer with a radially-varying modulus. Allowing the shear modulus of the finite soil layer covering the circular surface of the canyon as a power of the radial distance, the governing equation of motion for the anti-plane shear problem is derived and solved analytically by the method of wave function expansion. The ground motions for both of the homogeneous and inhomogeneous canyons under oblique incident waves can be computed efficiently and a comprehensive set of numerical examples are presented as illustrations. The degree of inhomogeneity of the soil layer and its thickness are found to affect the magnitude and the pattern of ground motion amplification of the cylindrical canyon surface depending on the frequency content, the irregular topography and obliquity of the wave incidence.