Modeling of Tsunami Generation and Propagation by a Spreading Seismic Faulting in two Orthogonal Directions in Linearized Shallow-Water Wave Theory

Abstract

The process of tsunami evolution during its generation in search for possible amplification mechanisms resulting from spreading of the sea floor uplift in the x-and y-direction is investigated under the effect of rupture velocities, uplift length and width and rise times. This study shows that focusing and amplification of tsunami amplitudes can occur in an arbitrary direction, determined by the velocities of spreading. 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 spreading source model. We analyzed the normalized peak amplitude as a function of the propagated uplift length, width and the average depth of the ocean along the generation path. 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 normalized peak amplitudes were smaller when the slip-fault spreads in two orthogonal directions than the numerical values for one dimensional solution because of the interaction of the velocities. The maximum amplitude amplification is proportion to the propagation length and the width of the source model and inversely proportional with the water depth.