Modeling of tsunami generation and propagation under the effect of stochastic submarine landslides and slumps spreading in two orthogonal directions

Tsunami generation and propagation caused by stochastic submarine landslides and slumps driven by a Gaussian white noise in the x-and y-direction are investigated. This model is used to study the tsunami amplitude amplification under the effect of the noise intensities, spreading velocities, length and width of sliding and times of the stochastic landslides and slumps in the two-dimensional movements. This study shows that focusing and amplification of tsunami amplitudes can occur in an arbitrary direction, determined by the velocities of spreading. Tsunami waveforms within the frame of the linearized shallow water theory for constant water depth are analyzed analytically by transform methods (Laplace in time and Fourier in space) for the stochastic source model. We derived and analyzed the mean and variance of the random tsunami waves in the two orthogonal directions as a function of the propagated uplift length and width, noise intensities of the stochastic source model and the average depth of the ocean along the generation and propagation path.