Near-fault seafloor ground motions: A pure time-domain analytical solution to the 2D marine Lamb problem

This study investigates the two-dimensional marine Lamb problem and near-field wavefield mechanisms based on a pure time-domain analytical solution. First, utilizing the Cagniard-de Hoop method, the closed-form pure time-domain displacement Green's functions excited by a 2D point dislocation source in a water-covered elastic half-space model are rigorously derived. Second, to address the severe singularity issue inherent in the spatial derivatives of the impulse Green's functions, a time-domain order-reduction integration strategy is proposed by transferring the time derivative to the source function. This facilitates the construction of an efficient discrete convolution numerical framework based on the ramp response and historical slip rate. The ultra-high theoretical accuracy of the proposed analytical framework is thoroughly verified by degrading it to the classical waterless Lamb problem. Building upon this and incorporating a kinematic finite fault model, the near-field effects of seafloor ground motions are systematically analyzed. The spatiotemporal evolution patterns of the Fling Step and strong velocity pulses on the near-fault seafloor are explored, and the intense coupling mechanisms between rupture directivity and geometric hanging-wall effects in the near field are quantitatively revealed. The results demonstrate that, although the fluid layer has no impact on the static permanent displacement of the seabed, it exerts a significant duration-prolonging and spectrum-modulating effect on the near-fault broadband dynamic wavefield through water-layer multiples and notch mechanisms. This study provides a solid theoretical foundation and high-precision computational tools for the simulation of seafloor strong ground motions.