Mikhail A. Nosov

Physics of tsunamis

General Information on Tsunami Waves, Seaquakes and Other Catastrophic Phenomena in the Ocean.- Physical Processes at the Source of a Tsunami of Seismotectonic Origin.- Role of the Compressibility of Water and of Non-linear Effects in the Formation of Tsunami Waves.- The Physics of Tsunami Formation by Sources of Nonseismic Origin.- Propagation of a Tsunami in the Ocean and Its Interaction with the Coast.- Methods of Tsunami Wave Registration.- Seaquakes: Analysis of Phenomena and Modelling.

On the near-bottom pressure variations in the region of the 2003 Tokachi-Oki tsunami source

The Tokachi-Oki earthquake was the strongest seismic event in 2003. The tsunami caused by the earthquake reached a height of four meters at the northeastern coast of Hokkaido. The JAMSTEC successfully recorded the variations of the near-bottom pressure in the region of the tsunami source. An analysis of the data reveals low-frequency (∼ 0.15 Hz) elastic vibrations of the water layer. Estimates of the amplitude, velocity, and duration of the bottom deformation at the tsunami source were obtained.

Tsunami waves of seismic origin: The modern state of knowledge

This review summarizes the concepts of seismogenic tsunami waves. Principles of short-term tsunami forecasting and tsunami recording systems are discussed. The traditional approach to describing tsunami generation by earthquakes is outlined and its drawbacks are analyzed. The main and secondary effects are distinguished which are responsible for the formation of waves by underwater earthquakes. The existing numerical codes of tsunami dynamics are described.

Contribution of horizontal deformation of the seafloor into tsunami generation near the coast of Japan on March 11, 2011

Based on the USGS slip distribution data (Finite Fault Model), the vector field of the seafloor deformation in the source of the tsunami that occurred on March 11, 2011, was calculated. The field of seafloor deformation and distribution of depths in the area of the source were used for reconstruction of the initial elevation of the water surface in the tsunami source. It was found that the contribution of horizontal deformations into the amplitude of the initial elevation, into the displaced water volume, and into the potential energy of the initial elevation is at about 20–25%. Within the framework of the linear theory of long waves, numerical simulation of evolution of the initial elevation was made. The simulation results were compared to the signals recorded by the four deep water stations DART which were the nearest to the source. It was shown that account of the horizontal deformation of the seafloor provides a more precise coincidence between the model and real data. Insignificant differences in arrival times of the model and real signals were interpreted as manifestation of phase dispersion and finite duration for the seafloor deformation to form.

Residual Hydrodynamic Fields near a Tsunami Source

The strong dependence of the tsunami characteris tics on the mechanism of the earthquake source and its depth [3] leads to the fact that not every underwater earthquake with magnitude M ≥ 7 is accompanied by the generation of waves that cause a real danger. An exact calculation of the bottom deformation in the tsunami source is not possible in an operative regime. Therefore, confirmation or cancellation of a tsunami alarm requires objective information about the fact of wave generation. Such information can be obtained when the wave is recorded at the bottom of the coastal sea level station closest to the source.

The Physics of Tsunami Formation by Sources of Nonseismic Origin

The physics is described of tsunami formation by sources of nonseismic origin: landslides, volcanic eruptions, meteorological causes, and cosmic bodies falling into the ocean. Short descriptions are given of certain remarkable historical events (with the exception of cosmogenic tsunamis). Approaches to the mathematical description of tsunami generation by these sources are expounded. Basic regularities, relating parameters of a source and of the tsunami wave generated by it are presented.

Tsunami Forecasting Based on Deepwater-Station Data

Short-term forecasting of tsunamis is proposed by sea-level prediction based on the data of a dense network of deepwater stations. This approach was applied to calculate tsunami waves on March 11, 2011 in the Kii Peninsular coast (Japan). Variations in bottom pressure recorded by DONET stations were used as the input data. The calculation results were compared with the data of JMA coastal tide gauges. Only the two to three first waves that were recorded with coastal tide gauges that were closest to the DONET system were reconstructed with sufficient accuracy. The reasons for the inconsistency between the measured and predicted sea-level variations are discussed. Principles of optimal layout of deep-water stations for tsunami forecasting are suggested.

The properties of co-seismic deformations of the ocean bottom as indicated by the slip-distribution data in tsunamigenic earthquake sources

In this study we consider 75 ocean-bottom earthquakes that occurred during the 1923–2013 period. Based on the slip-distribution data from the Finite-Source Rupture Model Database (SRCMOD) and Okada formulas, the vector fields of co-seismic bottom deformations were calculated. It is shown that, as a rule, the horizontal components of the sloping bottom deformation make an additional and essential contribution to the water displacement and the potential energy of the water-surface elevation that is similar in shape to the bottom surface displacement (the tsunami energy). On the basis of the analyzed relationships between the bottom deformation amplitude, the displaced water volume, tsunami energy, and the earthquake moment magnitude the corresponding regression dependencies were constructed. It is shown that the fraction of the potential energy of an earthquake that is converted into a tsunami increases with the increasing moment magnitude, but even during catastrophic earthquakes it is less than 0.1% of the total earthquake energy.

Residual hydrodynamic fields after tsunami generation by an earthquake

The linear theory of long waves was applied to study horizontal motions of the water layer in a rotating ocean which appear after tsunami generation by an earthquake. The structures of residual potential and eddy fields are analyzed on the basis of the analytical solution of a model axisymmetric problem for an ocean of constant depth. The estimates of the horizontal displacements of water particles, velocity of the eddy current, and energy of the geostrophic eddy are calculated for typical conditions of the tsunami source. Particular features of the residual fields related to the existence of stable stratification are considered. Static and dynamic numerical models are described that allow us to calculate the residual potential field and its evolution related to the realistic events. The field of residual horizontal displacements of water particles for the catastrophic earthquake near the coasts of Japan on March 11, 2011, is calculated and analyzed.

Propagation of a Tsunami in the Ocean and Its Interaction with the Coast

Traditional ideas of tsunami propagation in the open ocean are dealt with. The significance is estimated of manifestations of phase and amplitude dispersions. Classical problems are considered, concerning variation of the amplitude of a long wave in a basin with gently varying depth (the Green’s law) and the reflection of a wave from a step and from a rectangular obstacle. Formulae of the ray method are presented in Cartesian and spherical coordinate systems. Phenomena of long-wave refraction and capture by underwater ridges and the shelf are described. Estimation is performed of linear (viscous) and nonlinear (turbulent) dissipation of the energy of long waves. The effect of a wave amplitude being reduced by scattering on bottom irregularities is considered. Approaches to the numerical simulation of tsunami wave propagation are described. Conventionally applied equations of nonlinear long-wave theory, taking into account the Coriolis force and bottom friction, are presented both in Cartesian and spherical coordinate systems. The technique for formulating initial and boundary conditions in the tsunami propagation problem is described. Brief information is given on certain tsunami models (codes), that are actively applied, at present. Features of transoceanic wave propagation are considered, taking advantage of the December 26, 2004 tsunami as an example. The main results, due to investigation of the issues of a tsunami run-up on the shore, are presented.