Influence of a Steepened Hill on the Surface Displacement Amplitudes

This paper presents a theoretical approach to study the surface motion of a steepened hill impacted by incident SH waves. A rigorous solution has been derived by applying an accurate region-matching technique. According to the continuity condition at the auxiliary boundary, surface displacements are expressed in series of infinite algebraic equations, and the unknown coefficients of the series can be determined by Fourier series expansion technique in complex domain. Numerical results demonstrate the analytical results depend on some key parameters.