Submarine earthquakes generate tsunamis through the hydrodynamic response to the sea floor deformation, or indirectly through triggering of submarine slides. Most earthquakes can be associated with interaction of moving plates at the earth's surface. When they make contact at the boundary the motion may be obstructed and tension builds up until released through an earthquake. The relative motion between the plates may be parallel to the boundary (strike-slip), normal (dip-slip) or a combination. It is the vertical, permanent displacement of the sea bottom that is important for tsunami generation. Largest vertical motions are found with earthquakes having a dominant dip-slip component. In the figure we have depicted a cross-section of an inverse trust fault, where two plates converge, one (dark green) subducting the other (light green).
After the initial rise of the sea surface waves propagates away from the source region. To give an idea of the effect of wave dispersion we have performed two dimensional calculations, solving the linear hydrostatic equations, the linear Boussinesq equations and a linear, but otherwise fully inviscid, set of equations.
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An mpeg animation of tsunami wave propagation from an earthquake. All the results are linear and "Laplace" correponds to full potential theory. |
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Starting from t=2 min we focus on the part of the wave system going to the right. The key point is the approach to the asymptotic solution. Click for more details on this solution. |
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Wave propagation as computed by a hydroststatic finite difference model. The bottom deforamtion are indicated, but is depicted with a smaller scale than the surface. The numerical solution is carefully checked for convergence. See grid refinement for a cross section. Note the strong numerical dispersion for coarse grid with 5 km increment. |
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Wave propagation as computed by a Boussinesq finite difference model. For better quality for click for an integrated
quicktime animation. Grid refinement. |
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An mpeg animation of a cross-section normal to the fault. |
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First phase: dispersion in deep waterThe wave system is divided and spread out by dispersion. Note that the surface elevation and the depth are in different scales and vertically translated relative to each other. |
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Second phase: Amplification in shoaling waterThe wave system encounters the slope of the continental shelf and is amplified, while the wavelength is reduced. |
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Second phase: Amplification in shoaling waterA close up of nearshore region. At the end we may observe a steepening of the wavefronts. |
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Third phase: Bore formationNonlinear effects causes the wave front to break. In this case the amplitude is then reduced due to a very slow rate of shoaling. For a steeper bottom gradient the amplitude loss due to dissipation in breaking would compete with amplification due to shoaling. Also the second crest breaks. In the present long wave models the bore (breaking wave) is represented by a jump in the surface. In reality we have a turbulent wave front of finite, but small, width. |
A complete story, from generation to breaking, is available as a quicktime animation. Note: The animation is large (100 M) and includes speech.
Author of page: Geir Pedersen <geirkp@math.uio.no>
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