There are only a few analytical 2+1D models for tsunami propagation, most of which treat tsunami generation from a static deformation field isolated from the kinematics of the rupture. This work examines the behavior of tsunami propagation in a simple setup including a source time function which accounts for a time description of the rupture process on the tsunami source. An analytical solution is derived in the wavenumber domain, which is quickly inverted to space with the fast Fourier transform. The solution is obtained in closed form in the 1+1D case. The inclusion of temporal parameters of the source such as rise time and rupture velocity reveals a specific domain of very slow earthquakes that enhance tsunami amplitudes and produce non-negligible shifts in arrival times. The results confirm that amplification occurs when the rupture velocity matches the long-wave tsunami speed, and the static approximation corresponds to a limit case for (relatively) fast ruptures.

中文翻译：

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包括震源运动学在内的海啸传播分析模型

只有少数用于海啸传播的 2+1D 分析模型，其中大部分是从与破裂运动学分离的静态变形场中处理海啸产生的。这项工作在一个简单的设置中检查海啸传播的行为，包括一个源时间函数，该函数解释了海啸源破裂过程的时间描述。在波数域中推导出解析解，该解通过快速傅立叶变换快速反转到空间。该解是在 1+1D 情况下以封闭形式获得的。将震源的时间参数（如上升时间和破裂速度）包括在内，揭示了非常缓慢的地震的特定领域，这些地震增强了海啸振幅并在到达时间上产生了不可忽视的变化。