Displaced Water Volume, Potential Energy of Initial Elevation, and Tsunami Intensity: Analysis of Recent Tsunami Events

摘要

We consider recent ocean-bottom earthquakes for which detailed slip distribution data are available. Using these data and the Okada formulae, we calculate the vector fields of coseismic bottom deformations, which allow us to determine the displaced water volume and the potential energy of initial elevation of the tsunami source. It is shown that, in the majority of cases, the horizontal components of bottom deformation provide an additional contribution to the displaced water volume and virtually never diminish the contribution of the vertical component. The absolute value of the relative contribution of the horizontal components of bottom deformation to the displaced volume varies from 0.07 to 55 %, on average amounting to 14 %. The displaced volume and the energy of initial elevation (tsunami energy) are examined as functions of the moment magnitude, and the relevant regressions (least-squares fits) are derived. The obtained relationships exhibit good correspondence with the theoretical upper limits that had been obtained under the assumption of uniform slip distribution along a rectangular fault. Tsunami energy calculated on the basis of finite fault model data is compared with the earthquake energy determined from the energy-magnitude relationship by Kanamori. It is shown that tsunami takes from 0.001 to 0.34 % of the earthquake energy, and on average 0.04 %. Finally, we analyze the Soloviev-Imamura tsunami intensity as a function of the following three quantities: (1) the moment magnitude, (2) the decimal logarithm of the absolute value of displaced volume, and (3) the decimal logarithm of the potential energy of initial elevation. The first dependence exhibits rather poor correlation, whereas the second and third dependences demonstrate noticeably higher correlation coefficients. This gives us grounds to suggest considering the displaced volume and the energy of initial elevation as measures of the tsunamigenic potential of an earthquake.