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Results of an extensive numerical study on two-dimensional wave scattering by valleys of semi-elliptical cross-section due to incident SH, SV and P waves are presented. The investigation has been conducted using a rigorous boundary element algorithm. The influence of key parameters, such as, valley depth, impedance ratio, frequency, and angle of incidence on surface ground motion are studied in detail. Furthermore, the case of a valley within a layered half-space is analyzed and results compared with those obtained for a valley within a homogeneous half-space.