An exact solution for<i>SH</i>-wave scattering by a radially multilayered inhomogeneous semicylindrical canyon

Abstract

An analytical treatment of the seismic response of a cylindrical canyon with a radially piecewise inhomogeneous arbitrary multilayered profile to a finite depth on a homogeneous half-space under obliquely incident plane SH waves is presented. In terms of a radial wave function expansion and a transfer matrix approach, a rigorous approach is formulated for general computation for the elastodynamic plane problem. Upon confirmation of its accuracy with past exact solutions for a canyon covered by a single surficial layer with a homogeneous and a power-law modulus variation by suitable depth-wise discretization, the proposed solution is extended to the case of a canyon covered by a discretely inhomogeneous surficial zone containing three power-law layers as well as the case of a canyon covered by a continuously inhomogeneous surficial zone with a three-parameter exponential shear wave velocity model as a generalized class of smooth in situ variations. A comprehensive set of numerical examples are presented to illustrate the sensitivity of the ground motion to the canyon geometry, the inhomogeneity profile of the top zone, the frequency content and the angle of the seismic wave incidence.