Abstract In this study, the propagation of surface water waves initially displaced by a tectonic seafloor deformation of arbitrary geometry was obtained considering the rupture kinematics. The developed solution was applied to a set of problems for wave generation by bottom motion with arbitrary spatiotemporal variations. First, a single bottom motion with different uplift speeds was considered; results showed that relatively fast uplift speed produces increased free surface elevation at the center of the movable bottom. For dual bottom motion with spatial and temporal intervals, the free surface elevation at the end of entire uplift motion has different maxima at different positions depending on their intervals. Then, the bottom motion subdivided into 10 sub-regions with rupture velocity and uplift speed was considered. The result implies that when the rupture process is introduced in the solution, the wave energy in the direction opposite to rupture decreases, while it is enhanced in the rupture direction with higher-frequency components. The solution was applied to the dual-Gaussian-shaped bottom motion with various rupture velocities and directions to demonstrate its prospective use in the numerical models for real tsunami events. Depending on the rupture direction, surface wave propagation exhibits distinct patterns.

中文翻译：

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考虑破裂运动学的任意几何形状的海底构造变形产生的活跃海啸

摘要 在这项研究中，考虑到破裂运动学，获得了最初被任意几何形状的海底构造变形位移的地表水波的传播。开发的解决方案被应用于通过具有任意时空变化的底部运动产生波浪的一组问题。首先，考虑了具有不同上升速度的单一底部运动；结果表明，相对较快的抬升速度会增加活动底部中心的自由表面高程。对于具有时空间隔的双底运动，整个抬升运动结束时的自由面高程在不同位置具有不同的最大值，取决于它们的间隔。然后，将底部运动细分为具有破裂速度和隆起速度的10个子区域。结果表明，当溶液中引入破裂过程时，与破裂相反方向的波能减小，而在破裂方向上的波能随着高频分量而增强。该解被应用于具有各种破裂速度和方向的双高斯形底部运动，以证明其在真实海啸事件的数值模型中的预期用途。根据破裂方向，表面波传播表现出不同的模式。该解决方案应用于具有各种破裂速度和方向的双高斯形底部运动，以证明其在真实海啸事件的数值模型中的预期用途。根据破裂方向，表面波传播表现出不同的模式。该解被应用于具有各种破裂速度和方向的双高斯形底部运动，以证明其在真实海啸事件的数值模型中的预期用途。根据破裂方向，表面波传播表现出不同的模式。