Three-Dimensional Modeling of Tsunami Generation and Propagation under the Effect of Stochastic Seismic Fault Source Model in Linearized Shallow-Water Wave Theory
Tsunami generation and propagation caused by stochastic seismic fault driven by two Gaussian white noises in the - and -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. 1. Introduction A tsunami is most often triggered by undersea earthquakes that cause massive changes to the ocean floor. Tsunami can also be caused by other undersea events such as volcanoes or landslides. When an undersea earthquake or another major disturbance causes a section of the ocean floor to suddenly rise or sink, the mass of water above the affected area also rises or sinks. This unexpected movement of the water creates a series of powerful waves. Undersea earthquakes that cause massive changes to the ocean floor and the displacement of a large volume of water are the most common cause of a tsunami. In recent years, there have been a number of subduction zone earthquakes that have generated unexpectedly large local tsunamis, for example, Papua New Guinea tsunami, 17 July, 1998, Sumatra earthquake and tsunami, 26 December, 2004, Solomon Islands tsunami, 2 April, 2007, Samoa tsunami, 29 September, 2009, the Chile tsunami, 27 February, 2010, and the Fukushima Prefecture, Japan, 11 March, 2011. The investigation of the tsunami waves has become of great practical interest that attracts nowadays a lot of attention due in part to the intensive human activity in coastal areas. The evaluation of a local tsunami threat is useful to get
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