Scattering of plane P waves by canyons containing multiple circular-arc-shaped layers

By expressing the wave functions in the form of Fourier-Bessel series, the analytical solution for the two-dimension scattering problem of plane P waves by the cylindrical canyon topography that contains arbitrary number of circular-arc-shaped layers is presented firstly. And then, the convergence of the proposed series solution with the truncation number of terms is discussed, which demonstrates that the analytical solution can converge even for very high frequencies of the incident P wave. Finally, using this solution, the influences that are imposed on the stationary ground motion by the number and the sequence of alluvial layers, as well as the stiffness of soft interlayer contained in the canyon, are studied.