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Abstract
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Article Information:
Linearized Shallow-water Wave Theory of Tsunami Generation and Propagation by Three-dimensional Stochastic Seismic Bottom Topography
M.A. Omar, Khaled T. Ramadan and Allam. A. Allam
Corresponding Author: M.A. Omar
Submitted: November 20, 2013
Accepted: December 29, 2013
Published: May 15, 2014 |
Abstract:
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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.
Key words: Bottom topography, Gaussian white noise, Itô integral, Laplace and Fourier transforms, shallow water theory, stochastic process, tsunami modeling
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Cite this Reference:
M.A. Omar, Khaled T. Ramadan and Allam. A. Allam, . Linearized Shallow-water Wave Theory of Tsunami Generation and Propagation by Three-dimensional Stochastic Seismic Bottom Topography. Research Journal of Applied Sciences, Engineering and Technology, (19): 4035-4055.
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ISSN (Online): 2040-7467
ISSN (Print): 2040-7459 |
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