Tsunami Generation and Propagation by a Curvilinear Stochastic Spreading Seismic Faulting in Linearized Water Wave Theory

Abstract

The generation and propagation of tsunami caused by a curvilinear stochastic seismic faulting driven by two Gaussian white noise processes in the [Formula: see text]- and [Formula: see text]-directions are investigated. This model is used to study the tsunami build up and propagation during and after a realistic curvilinear source model represented by a random spreading slip-fault model. The amplification of tsunami amplitudes builds up progressively as time increases during the generation process due to wave focusing while the maximum wave amplitude decreases with time during the propagation process due to geometric spreading and dispersion. The increase of the normalized noise intensities on the random bottom leads to an increase in oscillations and amplitude of the free surface elevation. Tsunami waveforms using linearized shallow water theory for constant water depth are analyzed analytically by transform methods. The mean and variance of the random tsunami waves are derived and analyzed as a function of the noise intensities, propagated uplift length and the average depth of the ocean along the generation and propagation path.