Based on a simple physical model, we derive a formula for the energy radiated into a tsunami by a dynamic deformation of the ocean floor. We use the analytical solutions developed by J.L. Hammack, Jr. (1972, Tsunamis – A model of their generation and propagation, Ph.D. Dissertation, 261 pp., California Institute of Technology, Pasadena) to show that, in addition to its expected dependence on the source rise time, and even in the limiting case of an instantaneous source, the energy of the tsunami is controlled by the ratio of water depth to source size. For very large earthquakes, these results have no impact on the time-honored approximation which uses the static deformation of the ocean floor as a set of initial conditions of the surface displacements for numerical simulations, but they provide insight into the theoretical limits of this practice.

基于一个简单的物理模型，我们推导出了海底动态变形辐射到海啸中的能量的公式。我们使用 JL Hammack, Jr. (1972, Tsunamis – A model of their generation and spread, Ph.D. Dissertation)开发的分析解决方案, 261 pp., California Institute of Technology, Pasadena) 表明，除了对震源上升时间的预期依赖性外，即使在瞬时震源的极限情况下，海啸的能量也受以下比率控制水深到水源大小。对于非常大的地震，这些结果对历史悠久的近似没有影响，该近似使用海底的静态变形作为数值模拟的表面位移的一组初始条件，但它们提供了对这种做法的理论限制的深入了解.