Determining anti-plane responses induced by oblique-truncated semicircular canyon using systematic hybrid method with mapping function

This paper proposes a novel strategy for the investigation of displacement amplitude ($\left|u_y\right|$) near and along an oblique-truncated semicircular canyon subjected to shear horizontal (SH) waves. Transfinite interpolation (TFI) was used to obtain the coordinates of nodes and determine the sequence of node numbering in the inner finite region including the canyon. The hybrid method, comprising finite element method and a Lamb series, was applied in conjunction with TFI to study the effects of canyon geometry, incident angle of SH waves ($\theta$), and dimensionless frequency ($\eta$) on $\left|u_y\right|$. We detailed the amplification of $\left|u_y\right|$ in the illuminated zone and variations in $\left|u_y\right|$ due to canyon-decay-effect along the canyon surface as well as the decay of $\left|u_y\right|$ resulting from the shield effect in the shadow zone. Interestingly, oblique-effects play an important role in the magnification of $\left|u_y\right|$ along the inclined bottom of canyons, and variations in $\theta$ and $\eta$ dominate the patterns of $\left|u_y\right|$.