The seismic activity is a matter of concern in the safety of human life and property. The surface irregularities commonly on the earth can affect seismic wave propagation and cause the amplification of ground motions to aggravate the damage of buildings. Therefore, it is significant to investigate the scattering of seismic waves by surface irregularities. In this paper, the scattering problem of plane SH waves by a triangular hill in a rocky half-space is studied. Based on the equivalent viscoelastic medium model, the rocky material is equivalent as a viscoelastic, isotropic and homogeneous medium. Then, a series solution of wave functions is derived using the wavefunction expansion method combining with the conjunction concept and the Graf's addition formula. The wave field in every domain of interest is calculated. Comparisons of results from the present research and the existing pieces of literature are carried out to confirm the validity of the deriving process. Finally, parametric studies are conducted to evaluate the effects of the viscous property of the rocky material, the frequency and angle of the incidence, and the shape of the triangular hill on the seismic responses of the hill.

1 Introduction

A large number of earthquakes take place every year all over the world. An enormous amount of energy released by an earthquake threatens human life and property safety, and triggers many geological disasters, especially, in the region with topographic irregularities, such as hills, ridges and slopes. Observational evidence reveals that buildings situated on the tops of convex topographies suffer more severe damage than those located at base during past events (Hough et al. 2010). Over the last decades, topographic amplification of ground motions has attracted considerable attention in several branches of geophysics and engineering. Some analytical methods and numerical approximation approaches have been devised to investigate the role of topographic amplification. Representative numerical tools include: (a) finite difference method (Asimaki and Mohammadi 2018), (b) finite element method (Glinsky et al. 2019), (c) boundary element method (Panji et al. 2014). In contrast to the numerical approaches, analytical approaches are limited to deal with linearly-elastic or viscoelastic media and simple geometries, typically such as circular-arc ridges (Yuan and Liao 1996; Li et al. 2019), semi-elliptic ridges (Tsaur 2011), isosceles triangular hills (Qiu and Liu 2005). However, closed-form solutions can be derived through analytical approaches, and relatively simpler numerical implementation is required for analytical approaches.

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