Interaction of two semi-cylindrical canyons excited by sh waves

The spectral analysis of strong earthquake ground motion needs detailed understanding of transfer function properties and source radiation along the wave propagation path. The main goal of this study is to evaluate the interaction of two semi-cylindrical canyons, which are subjected to the horizontally polarized shear-wave (SH-wave) and to find the transfer function properties of two canyons. In this study, the interaction of two semi-cylindrical canyons subjected to SH waves are considered and evaluated for a general angle of wave incidence. The method of Wave Function Expansion is derived, and the infinite series solution is obtained. Due to the complexity and convergence of infinite series including Bessel functions, the numerical results are limited. The convergence of the solution for the high frequencies requires the high order term. Moreover, the difficulties of this study come from convergence of the solution owing to interaction of two canyons having various dimensions and material properties. The closed-form solution of the problem shows that the surface topography can have prominent effects on incident waves when the wavelengths of incident motion are short compared to the radius of a canyon. The parameters, dimensions of the canyons, distance between two canyons, and the amplifications of the displacement amplitudes are obtained with respect to the incident angles of the waves and dimensionless frequency.