Analytical Solution for the Transient Response of A Sloping Seabed Induced by A P-Wave Line Source

Many offshore marine structures are built on the seabed that are slightly or considerably sloping. To study the sloping seabed transient response during marine earthquakes, an analytical solution induced by a P-wave line source embedded in the solid is presented. During the derivation, the wave fields in the fluid layer and the semi-infinite solid are firstly constructed by using the generalized ray method and the fluid‒solid interface reflection and transmission coefficients. Then, the analytical solution in the transformed domain is obtained by superposing these wave fields, and the analytical solution in the time domain by applying the analytical inverse Laplace transform method. The the head wave generation conditions and arrival times at the fluid‒solid interface are derived through this solution. Through the use of numerical examples, the analytical solution is proved right and the impacts of the sloping angle on the hydrodynamic pressure in the sea, the seismic wave propagation in the seabed, the head wave, and the Scholte wave at the seawater-seabed interface are also addressed.