Plane P-wave scattering by a circular-arc canyon with an unsaturated covering layer over an unsaturated half-space

This study presents a semi-analytical Fourier–Bessel solution, based on unsaturated porous-media theory, for plane P-wave scattering by a circular-arc canyon with an unsaturated covering layer over an unsaturated half-space. Parametric analyses are performed to examine the effects of half-space saturation, covering-layer saturation, covering-layer thickness, incident frequency, and canyon geometry on surface displacement amplitudes. The results show that half-space saturation and covering-layer saturation influence the response in different ways, while covering-layer thickness has a generally strengthening but not purely monotonic effect on amplification because of thickness-dependent interference and resonance. Increasing frequency enhances multiple scattering and local interference, leading to more oscillatory and asymmetric displacement patterns. Compared with shallow canyons, semi-circular canyons exhibit stronger vertical amplification, whereas shallow canyons favor horizontal amplification.