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The early tsunami warning is normally issued on the base of the magnitude-geographic criterion. The decision to issue a tsunami alert is taken when the magnitude of a seismic event exceeds a certain threshold value for the region. The practice of using the magnitude-geographical criterion exhibits its imperfection, which manifests itself in a significant number of false alarms. The imperfection of the criterion is explained by the complexity of the connection between the tsunami wave and the earthquake that generated it. Magnitude is an important, but far from the only factor influencing the strength of a tsunami. Differences in the mechanisms of earthquake and focal depths, the features of the bottom topography and the flooded area, the possible contribution to the tsunami energy from secondary sources - landslides triggered by an earthquake - all this does not allow unambiguously linking the tsunami intensity with the earthquake magnitude. It is possible to increase the accuracy of the early tsunami warning by taking into account the mechanism of the earthquake source and its depth. In January 2018, the automatic system "Tsunami-Observer" was launched into test operation, which implements the indicated opportunity. As a measure of the tsunamigenicity of an earthquake in the Tsunami-Observer system, an estimate of the potential energy of the initial rise of the water surface in the tsunami source (tsunami energy) is used. A feature of the data on the earthquake mechanism is the coexistence of two possible solutions. Choosing one of these solutions, under time pressure conditions, is difficult or impossible. The aim of this work is to study how strongly the choice of the nodal plane influences the estimation of the potential energy of the initial elevation in the tsunami source. The second goal is to identify conditions under which the choice of the nodal plane is guaranteed to have little effect on the energy estimate. The study was carried out using data on the earthquake mechanisms from the Bulletin of the International Seismological Center (ISC). It is shown that for the majority of seismic events the energy estimate weakly depends on the choice of the nodal plane. But in some rare cases, the energy estimates can differ significantly - up to one order of magnitude. As a rule, such significant differences are peculiar to strong shallow earthquakes, i.e., precisely those seismic events that are able to effectively excite tsunami waves. It was found that in all cases when the ratio of the length of the rupture area to the source depth is small, the choice of the nodal plane practically does not affect the energy estimate. The authors are grateful to the International Seismological Center for the data provided. This work was supported by the Russian Foundation for Basic Research (grants 19-05-00351, 20-07-01098, 20-35-70038).