Analytical Solution for the Topographic Effect of an Offshore Circular‐Arc Canyon Under P‐Wave Incidence

Abstract

This paper studies the dynamic response of a circular‐arc canyon topography in the seabed under a seawater layer subjected to vertically and obliquely incident P‐wave excitations. The seabed is assumed to be an isotropic elastic medium. The analytical solution of the problem is developed using the large circular arc assumption and the Fourier–Bessel series expansion technique. This study focuses mainly on analysing the influence of seawater on the topographic amplification effect of the canyon. The differences between offshore and onshore canyons are compared in both the frequency and time domains. In the frequency domain, the presence of a layer of water will amplify or suppress the vertical response of the canyon, depending on the frequencies of the incident P‐waves and the detailed point location within the canyon. This is in contrast to the flat seabed model. In addition, the effects of water depth, canyon depth‐to‐width ratio, and angle of incidence of the P‐waves on the W/L (water/land) spectral ratio are further analysed. The time domain results under both simple Ricker wavelets and real earthquake waves are then obtained, which show that the seawater layer amplifies the responses near the canyon edge, and the amplification effect mainly depends on the canyon depth‐to‐width ratio and incidence frequency.