Tsunamigenesis revisited

When modelling tsunamis, it is frequently necessary to make simplifying assumptions in order to reduce the problem to one that is computationally tractable. Here, we examine the key factors controlling the generation of the initial sea surface wave and present a series of clear and simple guidelines for real-world problems. Most tsunami modelling codes assume the initial sea surface wave is identical to the seafloor perturbation. However, this is only true for large tsunami sources (Kajiura 1963). We model the tsunamigenesis process and the formation of the initial sea-surface wave, taking into account elastic deformation and the diffusive effect of the water column above the deforming seafloor. These can result in a substantial decrease in the energy in the initial sea-surface wave, particularly critical for small uplift patches, e.g. on the scale of splay faults or advecting bathymetry. In particular, slip on frontal thrusts has been proposed as a way to maximise wave heights in tsunami earthquakes, which generate larger than expected tsunamis given their seismic shaking, but the impact of this mechanism has thus far not been quantified. Here, we explore how frontal thrust slip can contribute to tsunami wave generation by modeling the resulting seafloor deformation using fault-bend folding theory. We present an analytical solution for the damping effect of the water column, and show that since the narrow band of seafloor uplift produced by frontal thrust slip is damped, initial tsunami heights and resulting energies solely due to thrust ramps are relatively low. More generally, consider an uplifting patch on the seafloor below 4 km of water. For a 4 km x 4 km square patch, the diffusive effect will result in an energy reduction in the initial wave of 90%. For rectangular patches with one long and one short dimension, this effect still holds: for a relatively large 400 km x 4 km uplifting region, the energy reduction is 70%. We find that the shortest dimension of the uplifting patch strongly controls the energy of the initial sea-surface wave, and the consequential tsunami. Even for larger patches, this effect is still important: for a 40 kmx40 km square patch, the reduction is 20%, and for a 400 km x 40 km patch, it is a non-negligible 12%. Currently implemented for fault sources, we are working to include landslide and volcanic sources.