Sequencing of tsunami waves: why the first wave is not always the largest

This paper examines the factors contributing to the ‘sequencing’ of tsunami waves in the far field, that is, to the distribution of the maximum sea surface amplitude inside the dominant wave packet constituting the primary arrival at a distant harbour. Based on simple models of sources for which analytical solutions are available, we show that, as range is increased, the wave pattern evolves from a regime of maximum amplitude in the first oscillation to one of delayed maximum, where the largest amplitude takes place during a subsequent oscillation. In the case of the simple, instantaneous uplift of a circular disk at the surface of an ocean of constant depth, the critical distance for transition between those patterns scales as $r_{0}^{3} / h^{2}$ where r0 is the radius of the disk and h the depth of the ocean. This behaviour is explained from simple arguments based on a model where sequencing results from frequency dispersion in the primary wave packet, as the width of its spectrum around its dominant period T0 becomes dispersed in time in an amount comparable to T0, the latter being controlled by a combination of source size and ocean depth. The general concepts in this model are confirmed in the case of more realistic sources for tsunami excitation by a finite-time deformation of the ocean floor, as well as in real-life simulations of tsunamis excited by large subduction events, for which we find that the influence of fault width on the distribution of sequencing is more important than that of fault length. Finally, simulation of the major events of Chile (2010) and Japan (2011) at large arrays of virtual gauges in the Pacific Basin correctly predicts the majority of the sequencing patterns observed on DART buoys during these events. By providing insight into the evolution with time of wave amplitudes inside primary wave packets for far field tsunamis generated by large earthquakes, our results stress the importance, for civil defense authorities, of issuing warning and evacuation orders of sufficient duration to avoid the hazard inherent in premature calls for all-clear.