An analytical approach for the scattering of SH waves by a symmetrical V-shaped canyon: shallow case

Based on the application of the region-matching technique, an analytical approach is presented for the scattering of plane SH waves from a shallow symmetrical V-shaped canyon, and then a series solution is derived. The analysed region is divided into an enclosed and an open region by introducing a semi-circular auxiliary boundary. In each region, the displacement field can be expressed as infinite sum of appropriate wavefunctions satisfying partial boundary conditions, respectively. The unknown coefficients can be determined by enforcing the continuity conditions in connection with the Graf's addition formula. The frequency- and time-domain responses are both evaluated and displayed for several physical parameters. From graphical results, the effects of the canyon depth on surface ground motion are conspicuous. The proposed series solutions can serve as benchmark for numerical methods, in particular for those at much higher frequencies.