Physical Processes at the Source of a Tsunami of Seismotectonic Origin

Abstract

Modern ideas are presented concerning the source of an earthquake and the seismotectonic source of a tsunami. The main physical processes taking place at a tsunami source are described. Estimation is performed of the role of secondary effects: displacements of the bottom, occurring in its own plane, Coriolis force, and density stratification of the water. The Okada formulae are presented, and the technique is exposed for calculating residual bottom deformations caused by an underwater earthquake. Within the framework of linear potential theory of an in-compressible liquid in a basin of fixed depth, the general analytical solution is constructed for the two-dimensional (2D) and three-dimensional (3D) problems of tsunami generation by bottom deformations of small amplitudes. The solution of the 3D problem is constructed in both Cartesian and cylindrical coordinates. For a series of model bottom deformation laws (piston, membrane and running displacements, bottom oscillations and alternating-sign displacement) physical regularities are revealed that relate the amplitude, energy and direction of tsunami wave emission to peculiarities of the bottom deformation at the source. In some cases, the theoretical regularities, obtained within potential theory, are compared with dependences following from the linear theory of long waves and, also, with the results of laboratory experiments. Keywords Tsunami source · tsunami generation · earthquake · seismic moment · magnitude · tsunami earthquake · fault · residual deformation · initial elevation · bottom displacement · time scale · period of tsunami · duration of earthquake · Coriolis force · vortex · kinetic energy · potential energy · internal waves · Burger's vector · strike-slip fault · dip-slip fault · tensile fault · Lame constants · strike angle · dip angle · rake(slip) angle · slip distribution · linear potential theory · velocity potential · Laplace transformation · Fourier transformation · analytical solution · dispersion · directional diagrams The following three stages are traditionally distinguished in the life of a tsunami: generation of the wave, its propagation in open ocean and its interaction with the coast (its uprush or run-up). Such a division is related to the existence of B. Levin, M. Nosov, Physics of Tsunamis, 31