Japan's 2011 Tsunami: Characteristics of Wave Propagation from Observations and Numerical Modelling

We use a numerical tsunami model to describe wave energy decay and transformation in the Pacific Ocean during the 2011 Tohoku tsunami. The numerical model was initialised with the results from a seismological finite fault model and validated using deep-ocean bottom pressure records from DARTs, from the NEPTUNE-Canada cabled observatory, as well as data from four satellite altimetry passes. We used statistical analysis of the available observations collected during the Japan 2011 tsunami and of the corresponding numerical model to demonstrate that the temporal evolution of tsunami wave energy in the Pacific Ocean leads to the wave energy equipartition law. Similar equipartition laws are well known for wave multi-scattering processes in seismology, electromagnetism and acoustics. We also show that the long-term near-equilibrium state is governed by this law: after the passage of the tsunami front, the tsunami wave energy density tends to be inversely proportional to the water depth. This fact leads to a definition of tsunami wave intensity that is simply energy density times the depth. This wave intensity fills the Pacific Ocean basin uniformly, except for the areas of energy sinks in the Southern Ocean and Bering Sea.