Table of Contents
ISRN Applied Mathematics
Volume 2014, Article ID 874230, 27 pages
Research Article

Three-Dimensional Modeling of Tsunami Generation and Propagation under the Effect of Stochastic Seismic Fault Source Model in Linearized Shallow-Water Wave Theory

Department of Basic and Applied Science, College of Engineering and Technology, Arab Academy for Science, Technology and Maritime Transport, P.O. Box 1029, Abu Quir Campus, Alexandria, Egypt

Received 12 September 2013; Accepted 27 November 2013; Published 19 March 2014

Academic Editors: Z. Hou, J. Shen, H. C. So, and X. Wen

Copyright © 2014 Allam A. Allam et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.