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.
Tsunami generation and propagation resulting from lateral spreading of a stochastic seismic fault source model driven by two Gaussian white noises in the x- and y- directions are investigated. 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 random sea floor uplift represented by a sliding Heaviside step function under the influence of two Gaussian white noise processes in the x- and y- directions. This model is used to study the tsunami amplitude amplification under the effect of the noise intensity and rise times of the stochastic fault source 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 the geometric spreading and also due to dispersion. We derived and analyzed the mean and variance of the random tsunami waves as a function of the time evolution along the generation and propagation path.
Abstract. Sources of tsunamis are non-uniform and commonly uncorrelated and very difficult to predict. The best ideal way to appear their aspects is through heterogeneous or stochastic source models which are more realistic. The effect of random fluctuation of submarine earthquake modeled by vertical time-dependent displacement of a stochastic source model is investigated on the tsunami generation and propagation waves. The noise intensity parameter controls the increase of the stochastic bottom amplitude which results in increasing the oscillations and amplitude in the free surface elevation which provides an additional contribution to tsunami waves. The L2 norm of the free surface elevation, the displaced water volume and the potential energy are examined. These quantitative information about predicting tsunami risk are useful for risk managers who decide to issue warnings and evacuation orders. The horizontal average velocity flow rates of the tsunami wave are investigated. The average velocity flow rates can provide valuable information about the stochastic bottom topography by the distinctive velocity oscillations. Flow velocity is of importance in risk assessment and hazard mitigation which may provide a clear signal of tsunami flows. Time series of the flow velocities and wave gauges under the effect the water depth of the ocean are investigated.
The processes of tsunami evolution during its generation in search for possible amplification mechanisms resulting from unilateral spreading of the sea floor uplift is investigated. We study the nature of the tsunami build up and propagation during and after realistic curvilinear source models represented by a slowly uplift faulting and a spreading slip-fault model. The models are used to study the tsunami amplitude amplification as a function of the spreading velocity and rise time. 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 movable source models. We analyzed the normalized peak amplitude as a function of the propagated uplift length, width and the average depth of the ocean along the propagation path.
The process of tsunami evolution during its generation under the effect of the variable velocities of realistic submarine landslides based on a two-dimensional curvilinear slide model is investigated. Tsunami generation from submarine gravity mass flows is described in three stages. The first stage represented by a rapid curvilinear down and uplift faulting with rise time. The second stage represented by a unilaterally propagation in the positive x direction to a significant length to produce curvilinear two-dimensional models represented by a depression slump, and a displaced accumulation slide model. The last stage represented by the time variation in the velocity of the accumulation slide (block slide). By using transforms method, Laplace in time and Fourier in space, tsunami waveforms within the frame of the linearized shallow water theory for constant water depth are analyzed analytically for the movable source model. Effect of the water depths on the amplification factor of the tsunami generation by the submarine slump and slide for different propagation lengths and widths has been studied and the results are plotted. Comparison of tsunami peak amplitudes is discussed for different propagation lengths, widths and water depths. In addition, we demonstrated the tsunami propagation waveforms after the slide stops moving at different propagation times.