Analytical Model for Gravity and Rayleigh-Wave Investigation in the Layered Ocean–Earth Structure

In terms of the linear theory of elasticity we analyze the gravity and Rayleigh-wave excitation and propagation process in a three-layered ocean–Earth model, which includes a superficial liquid layer and two layers of sediments—soft and hard. To compute the oceanic surface-wave dispersion function, the Thomson-Haskell matrix method is used. The solution is obtained by applying the normal mode formalism to the flat, homogeneous, layered ocean–Earth structure. Based on this theory, the spectra of the excitation functions are investigated in detail for 45° thrust, dip-slip, and strike-slip point sources in the half-space. A numerical experiment reveals that the rigidity of the rock exerts a strong influence on both gravity and Rayleigh waves. In the case of Rayleigh waves, a layered structure of the bottom strongly affects the propagation process. The main focus of the present study is to model tsunami and tsunamigenic events. It is well known from observations that earthquakes that generate abnormally large tsunamis are mostly thrust events, characterized by long source duration (2–4 times longer than typical earthquakes of similar moment) and shallow source depth, and are located near the trench axis. Meanwhile, typical tsunamigenic earthquakes are generally dip-slip and thrust events with depths between 15 and 50 km. On this basis, and using the distributed model of seismic source, the influence of source mechanism, location, and source duration on the tsunami-wave amplitude are investigated here. The results of our model computations of the seismic sea waves from tsunami- and tsunamigenic earthquake are in good agreement with real observation data.