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 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...

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Bibliographic Details
Published in:ISRN applied mathematics 2014-01, Vol.2014, p.1-27
Main Authors: Allam, Allam A., Omar, M. A., Ramadan, Khaled T.
Format: Article
Language:English
Subjects:
Amplification
Amplitudes
Deformation
Earthquakes
Investigations
Kinematics
Landslides & mudslides
Mathematical analysis
Mathematical models
Noise
Noise intensity
Propagation
Ramadan
Stochasticity
Studies
Theory
Tidal waves
Topography
Tsunamis
Velocity
Water waves
Wave propagation
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Summary: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.
ISSN:2090-5572
2090-5564
2090-5572
DOI:10.1155/2014/874230