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Scattering of plane P waves by a semi-cylindrical hill: analytical solution

Liang Jianwen (梁建文)1, Zhang Yanshuai (张彦帅) 1 and Vincent W Lee2

1. Department of Civil Engineering, Tianjin University, Tianjin 300072, China
2. Department of Civil Engineering, University of Southern California, Los Angeles, CA 90089-2531, USA

Abstract: An analytical solution for scattering of plane P waves by a semi-cylindrical hill was derived by using the wave function expansion method, and convergence of the solution and accuracy of truncation were verified. The effect of incident frequency and incident angle on the surface motion of the hill was discussed, and it was shown that a hill greatly amplifies incident plane P waves, and maximum horizontal displacement amplitudes appear mostly at the inclined incidence of waves, which are located at the half-space; and maximum vertical displacement amplitudes emerge mostly at the vertical incidence of waves, which are situated at the hill.

Keywords: hill; plane P waves; scattering; analytical solution; amplification moment