Dynamic response of arc-layered alluvial valley under incidence of plane SH waves

For the two-dimensional scattering problem of plane SH waves in alluvial valley with a circular-arc section, some researchers proposed a type of closed-form analytical solution, which reduced the scattering problem into the solution of an infinite-dimensional algebraic equation system. The high incident frequency will cause the system coefficient matrix to be ill-conditioned, which limits the usable frequency band of the analytical solution. Here, the method of this solution is followed, however, in the solving procedure, the solution of linear equation system is avoided by selecting coordinate system, with the undetermined coefficients of scattering wave functions possessing definite analytical expressions. As a result, the analytical solution to this scattering problem is presented in a very broad frequency band, and the influence of the properties of the incident wave as well as the valley on the ground motion is discussed.