Scattering of SH waves by a scalene triangular hill

The influence of local landforms on ground motion is an important problem. The antiplane response of a scalene triangular hill to incident SH waves is studied in this paper by using a complex function, moving coordinates and auxiliary functions. First, the model is divided into two domains: a scalene triangular hill with a semi-circular bottom; and a half space with a semi-circular canyon. Wave functions that satisfy the zero-stress condition at the triangular wedges and at the horizontal surface are constructed in both domains. Then, considering the displacement continuity and stress equilibrium, algebraic equations are established. Finally, numerical examples are provided to illustrate the influence of the geometry of the hill and the characteristics of the incident waves on the ground motions.