Three-Dimensional Modeling of Tsunami Generation and Propagation under the Effect of Stochastic Seismic Fault Source Model in Linearized Shallow-Water Wave Theory

Abstract

Tsunami generation and propagation caused by stochastic seismic fault driven by two Gaussian white noises in the x- and y-directions are investigated. This model is used to study the tsunami amplitude amplification under the effect of the noise intensities, spreading uplift length and rise times of the three-dimensional stochastic fault source model. 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). 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 the geometric spreading and also due to dispersion. The maximum amplitude amplification is proportional to the propagation length of the stochastic source model and inversely proportional to the water depth. The increase of the normalized noise intensities on the bottom topography leads to an increase in oscillations and amplitude in the free surface elevation. We derived and analyzed the mean and variance of the random tsunami waves as a function of the propagated uplift length, noise intensities, and the average depth of the ocean along the generation and propagation path.

Near- and far-field tsunami waves, displaced water volume, potential energy and velocity flow rates by a stochastic submarine earthquake source model

“…Submarine earthquakes are often represented as random phenomena, where white noise stochastic processes are 45 adopted to properly model their frequency content (Greco et al 2014). Numerous studies used Gaussian white noise stochastic processes to account the random components of bottom deformation in tsunami simulation, see (Omar et al 2012;Allam et al 2014;Ramadan et al 2015;Ramadan et al 2017). Dynamic bottoms are often used to model the waves generated by some type of bottom motion.…”