Generation of tsunamis by a slowly spreading uplift of the sea floor

Generation of tsunamis by slow submarine processes (faulting, slumps or slides) is investigated, in search for possible amplification mechanisms resulting from lateral spreading of the sea floor uplift. A linearized solution for constant water depth is derived by transform methods (Laplace in time and Fourier in space), for sea floor uplift represented by a sliding Heaviside step function (i.e. a simplified Haskell source model, with zero rise time). The model is used to study the tsunami amplitude amplification (wave amplitude normalized by the final sea floor uplift) as a function of the model parameters. The results show that, above the source, the amplification is larger for larger uplifted area and for smaller water depth, and is the largest in the direction of uplift spreading, for velocity of spreading comparable to the long period tsunami velocity. Near the source, this amplification could be one order of magnitude. This amplification mechanism seen in the near-field is a form of wave focusing, and is manifested by a high frequency pulse, with amplitude attenuating with distance due to dispersion and geometric spreading. In the far-field, the linear theory predicts maximum amplification equal to one, as predicted by point source models. An analogy between this form of focusing and resonance of a single-degree-of-freedom oscillator, and near-field radiation patterns are discussed. The magnitudes, seismic movements and source durations of selected earthquakes which generated tsunamis are cited in search of conditions which could lead to slow rupture and unusually large near-field amplification.