AbstractA closed‐form solution of two‐dimensional scattering of plane SH waves by a cylindrical alluvial valley of circular‐arc cross‐section in a half‐space is presented using the wave functions expansion. The solution is reduced to solving a set of infinite linear algebraic equations using the exterior region form of Graf's addition theorem. Numerical solutions are obtained by truncation of the infinite equations and their accuracies are demonstrated by convergence of the numerical results to the exact boundary condition with the increasing of the truncation order. The present solution is compared with the existing one presented by Todorovska and Lee for the same problem and their differences are analysed. Complicated effects of the depth‐to‐width ratio of the alluvial valley on surface ground motion are finall
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