On the relation between seismic source dynamics, tsunami generation and propagation, and numerical modelling complexity in subduction zones

The features of the seismic ruptures, such as the duration of shallow earthquakes in subduction zones, may affect the tsunami generation and the inundation intensity. Numerical and experimental results have shown how the interaction between the shallow part of the fault and the seismic radiation trapped in the hanging wall, can lead to enhanced up-dip rupture propagation. This in turn may result in shallow slip amplification producing larger vertical displacement, and even transient ground motion that is larger than the final static displacement. On the other hand, tsunami modelling for hazard assessment and early warning is generally based on static sea-floor displacement obtained with an instantaneous elastic dislocation (without shallow slip amplification) on a simplified hydrostatic model for tsunami generation and propagation. Here, we aim to analyze the relative importance of these effects and the optimal modelling strategy for the tsunami generation. Using a Tohoku-like setting, we impose time dependent initial conditions as computed from 1-D dynamic rupture simulations, by varying the rupture extent and duration over a wide range of stress-drop, rigidity and average slip values (corresponding to earthquake magnitudes between 7.5 and 9, approximately). We performed 1-D numerical tsunami simulations using both the hydrostatic and the multi-layer non-hydrostatic versions of Tsunami-HySEA. We also account for different coastal morphologies, modelling the presence of shelf and/or fjords and variable slope bathymetry. We address, first, how the time-dependent sea-floor displacement characteristics effects may affect (enhancing or reducing) the tsunamigenic potential. To do this, we investigated the resulting tsunami features, in terms of maximum wave height above sea level (also seaward) and maximum run-up, in relation to the spatial and temporal characteristic scales of the transient sea floor displacement. We also compare the simulations with a time-dependent initial condition against those where a static sea-floor displacement is used. We show that the use of a static source systematically overestimates the tsunami effects on the mainland, with the more realistic tsunami reduced due to the seaward seismic rupture (up-dip) directivity, opposite to the direction of the tsunami propagation. Moreover, the slower the rupture, the larger the overestimation. Conversely, as the rupture slows down, the seismic rupture propagating in the same direction of the tsunami increases the tsunami amplitude toward the open ocean. Second, we wish to assess in which conditions and to what extent it is enough to use a shallow-water tsunami model and when, instead, a more complex tsunami modelling scheme is required. The hydrostatic simulations lead to overestimate the inundation, although less significantly with respect to the static/dynamic comparison. We finally investigate how the discrepancy between simplified and complex modelling is controlled by different trench, shelf, and coastal morphologies.