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.
Highlights
A tsunami is most often triggered by undersea earthquakes that cause massive changes to the ocean floor
The process of tsunami generation and propagation was investigated over a stochastic bottom topography represented by a sliding Heaviside step function under the influence of two independent Gaussian white noise processes in the x- and y-directions, respectively
We demonstrated the waveform amplification resulting from stochastic source spreading and wave focusing and the tsunami propagation in the far-field
Summary
A tsunami is most often triggered by undersea earthquakes that cause massive changes to the ocean floor. 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 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. Numerical models based on the nondispersive shallow-water equations are often used to simulate tsunami propagation and run-up (e.g., [4, 5]) The propagation of these waves is strongly influenced by the shape of the bottom. The problem of tsunami source reconstruction is a key concern of tsunami
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