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A theoretical analysis of wave motions that arise in the ocean under the action of traveling disturbances of atmospheric pressure is presented. Formulas for a fixed-depth ocean have been obtained to describe the manifestations of traveling disturbances of atmospheric pressure in bottom pressure variations. Formulas have been obtained for estimating the amplitude of free gravity waves generated in the ocean by a traveling atmospheric disturbance in the region of a sharp change in depth. Data from IRIS ground-based barographs and DART (Deep-ocean Assessment and Reporting of Tsunami) stations recording wave disturbances in the atmosphere and ocean caused by the explosive eruption of the Hunga Tonga–Hunga Ha'apai volcano on January 15, 2022 have been used to study the atmospheric Lamb wave manifestations in bottom pressure variations. A Lamb wave was shown to be manifested in bottom pressure variations with amplification and identical waveforms recorded by ground-based barographs and bottom pressure sensors. A Lamb wave with an amplitude of 500 Pa can excite surface gravity waves with an amplitude of 0.5 m in the region of a deepwater trench. [ABSTRACT FROM AUTHOR]

A physical analysis of the generation of tsunami waves by seismic movements of the ocean floor is presented. For a set of strong underwater earthquakes, the work done against hydrostatic pressure during coseismic displacements of the ocean floor and the available potential energy, tsunami energy, are estimated. It is shown that an insignificant part of the earthquake energy (from 0.004% for Mw = 7 to 0.16 % for Mw = 9) is transferred to the tsunami waves, while the work done against the hydrostatic pressure is comparable in absolute value to the earthquake energy estimated by the Kanamori formula. [ABSTRACT FROM AUTHOR]

Tsunami propagation in the open ocean is most commonly modeled by solving the shallow water wave equations. These equations require initial conditions on sea surface height and depth-averaged horizontal particle velocity or, equivalently, horizontal momentum. While most modelers assume that initial velocity is zero, Y.T. Song and collaborators have argued for nonzero initial velocity, claiming that horizontal displacement of a sloping seafloor imparts significant horizontal momentum to the ocean. They show examples in which this effect increases the resulting tsunami height by a factor of two or more relative to models in which initial velocity is zero. We test this claim with a 'full-physics' integrated dynamic rupture and tsunami model that couples the elastic response of the Earth to the linearized acoustic-gravitational response of a compressible ocean with gravity; the model self-consistently accounts for seismic waves in the solid Earth, acoustic waves in the ocean, and tsunamis (with dispersion at short wavelengths). Full-physics simulations of subduction zone megathrust ruptures and tsunamis in geometries with a sloping seafloor confirm that substantial horizontal momentum is imparted to the ocean. However, almost all of that initial momentum is carried away by ocean acoustic waves, with negligible momentum imparted to the tsunami. We also compare tsunami propagation in each simulation to that predicted by an equivalent shallow water wave simulation with varying assumptions regarding initial velocity. We find that the initial horizontal velocity conditions proposed by Song and collaborators consistently overestimate the tsunami amplitude and predict an inconsistent wave profile. Finally, we determine tsunami initial conditions that are rigorously consistent with our full-physics simulations by isolating the tsunami waves from ocean acoustic and seismic waves at some final time, and backpropagating the tsunami waves to their initial state by solving the adjoint problem. The resulting initial conditions have negligible horizontal velocity. [ABSTRACT FROM AUTHOR]

The generation of surface waves by seafloor displacement is a classic problem that arises in the study of tsunamis. The generation of waves in a two-dimensional domain of uniform depth by uplift or subsidence of a portion of a flat bottom boundary has been elegantly studied by Hammack (Tsunamis: a model of their generation and propagation, Ph.D. thesis, California Institute of Technology, ), for idealized motions. The physical problem of tsunami generation is more complex; even when the final displacement is known from seismic analysis, the deforming seafloor includes relief features such as mounts and trenches. Here, following Kajiura (J Oceanogr Soc Jpn 28:260-277, ), we investigate analytically the effect of bathymetry on the surface wave generation, by solving the forced linear shallow water equation. While Kajiura's geometry consisted of a step-type bottom bathymetry with a rectangular uplift to understand the effect of the continental shelf on tsunami generation, our model bathymetry consists of an uplifting cylindrical sill initially resting on a flat bottom, a geometry which helps evaluate the effect of seamounts on tsunami generation. We find that as the sill height increases, partial wave trapping reduces the wave height in the far field, while amplifying it above the sill. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We have obtained an analytical solution to the problem of determining the initial elevation at the tsunami source, which was formed by small residual deformations of a flat sloping bottom. This solution, which is newly derived, is compared with the known analytical solution of an equivalent problem over a horizontal bottom. It is shown that applying an analytical solution over a horizontal bottom for calculating the initial perturbations in the sources of realistic tsunami provides sufficient accuracy. [ABSTRACT FROM AUTHOR]

Within shallow water equations, the numerical simulation problem of the generation and propagation of shallow waves caused by a running bottom rupture is considered. The rupture is a trench with a width increasing with time. As a result of fluid drainage into the trench, waves are formed. The basic problem parameters influencing the characteristics of the formed waves are found. [ABSTRACT FROM AUTHOR]

In the framework of the linear long-wave theory, we derive a system of equations that describe the potential and vortex residual hydrodynamic fields that arise in a rotating stratified (two-layer) ocean during tsunami generation by coseismic deformations of the ocean bottom. For the model case of a cylindrically symmetric ocean bottom deformation, we find an approximate analytical solution of the problem. Based on this solution, we analyze the specific features of residual fields due to the presence of stratification for conditions that are typical of real tsunami sources. [ABSTRACT FROM AUTHOR]

A numerical model of the wave dynamics in Chenega Cove, Alaska during the historic M9.2 megathrust earthquake is presented. During the earthquake, locally generated waves of unknown origin were identified at the village of Chenega, located in the western part of Prince William Sound. The waves appeared shortly after the shaking began and swept away most of the buildings while the shaking continued. We model the tectonic tsunami in Chenega Cove assuming different tsunami generation processes. Modeled results are compared with eyewitness reports and an observed runup. Results of the numerical experiments let us claim the importance of including both vertical and horizontal displacement into the 1964 tsunami generation process. We also present an explanation for the fact that arrivals of later waves in Chenega were unnoticed. [ABSTRACT FROM AUTHOR]

The present study is devoted to the problem of tsunami wave generation. The main goal of this work is twofold. First of all, we propose a simple and computationally inexpensive model for the description of the sea bed displacement during an underwater earthquake, based on the finite fault solution for the slip distribution under some assumptions on the dynamics of the rupturing process. Once the bottom motion is reconstructed, we study waves induced on the free surface of the ocean. For this purpose, we consider three different models approximating the Euler equations of the water wave theory. Namely, we use the linearized Euler equations (we are in fact solving the Cauchy-Poisson problem), a Boussinesq system, and a novel weakly nonlinear model. An intercomparison of these approaches is performed. The developments of the present study are illustrated on the July 17, 2006 Java event, where an underwater earthquake of magnitude 7.7 generated a tsunami that inundated the southern coast of Java. [ABSTRACT FROM AUTHOR]

An equation system that describes the potential and vortex residual hydrodynamical fields that emerge in the rotating ocean during tsunami generation by co-seismic deformations of the bottom was obtained in terms of linear long-wave theory. For the model case of a cylindrically symmetrical deformation of the bottom, a completely analytical solution was found. On the basis of this solution, the structure of residual fields was analyzed and estimates of the residual horizontal displacements of water particles, of the speed of the vortex current, and of the energy of a geostrophic vortex were obtained under typical tsunami source conditions. [ABSTRACT FROM AUTHOR]

Numerical simulation of seismotectonic tsunamis usually starts with specification of the initial elevation of the water surface in the tsunami source. The initial elevation is traditionally set equal to the vertical residual bottom deformation resulting from earthquakes. We discuss the imperfectness of the traditional approach and suggest an improved practical method of calculating the initial elevation from the solution of the 3D problem in the framework of potential theory. The method takes into account horizontal and vertical components of bottom deformation and bathymetry in the source area. Within the assumption of instant tsunami generation the suggested method represents the optimal way to specify the initial condition in the tsunami propagation problem. The tsunamis in the Central Kuril Islands on 15 November 2006 and 13 January 2007 are taken as examples to demonstrate the efficiency of the new method. [ABSTRACT FROM AUTHOR]

A new method for the specification of initial conditions in the tsunami problem is suggested. The initial elevation of a water surface is determined from the solution of the three-dimensional problem in the framework of potential theory with account for both the horizontal and vertical components of the bottom deformations and the distributions of depths in the vicinity of the source. The tsunamigenic Central Kuril Islands earthquakes in 2006 and 2007 are taken as examples to demonstrate the efficiency of the new method. [ABSTRACT FROM AUTHOR]

The modeling of tsunami generation is an essential phase in understanding tsunamis. For tsunamis generated by underwater earthquakes, it involves the modeling of the sea bottom motion as well as the resulting motion of the water above. A comparison between various models for three-dimensional water motion, ranging from linear theory to fully nonlinear theory, is performed. It is found that for most events the linear theory is sufficient. However, in some cases, more-sophisticated theories are needed. Moreover, it is shown that the passive approach in which the seafloor deformation is simply translated to the ocean surface is not always equivalent to the active approach in which the bottom motion is taken into account, even if the deformation is supposed to be instantaneous. [ABSTRACT FROM AUTHOR]

The 1771 Yaeyama tsunami is successfully reproduced using a simple faulting model without submarine landslide. The Yaeyama tsunami (M 7.4), which struck the southern Ryukyu Islands of Japan, produced unusually high tsunami amplitudes on the southeastern coast of Ishigaki Island and caused significant damage, including 12,000 casualties. Previous tsunami source models for this event have included both seismological faults and submarine landslides. However, no evidence of landslides in the source has been obtained, despite marine surveying of the area. The seismological fault model proposed in this study, describing a fault to the east of Ishigaki Island, successfully reproduces the distribution of tsunami runup on the southern coast of the Ryukyu Islands. The unusual runup heights are found through the numerical simulation attributable to a concentration of tsunami energy toward the southeastern coast of Ishigaki Island by the effect of the shelf to the east. Thus, the unusual runup heights observed on the southeastern coast of Ishigaki Island can be adequately explained by a seismological fault model with wave-ray bending on the adjacent shelf. [ABSTRACT FROM AUTHOR]

The immediate impulsive flow of an incompressible fluid due to a concentrated flux through an otherwise impermeable boundary is investigated analytically in three dimensions. The flow is inviscid and irrotational, and obeys the equipotential condition at the free surface, which is initially horizontal. Various elementary bottom geometries are analyzed: rectangular basins, sloping beaches, semi-cylindrical and hemispherical basins. Special attention is paid to the case of impulsive free-surface flows generated on a uniform sloping beach. A general integral solution is presented and compared against a series solution found for a discrete set of angles. The results are relevant for the modeling of tsunami generation due to rapid bottom deflections. [ABSTRACT FROM AUTHOR]

Tsunami waveforms recorded on tide gauges, like seismic waves recorded on seismograms, can be used to study earthquake source processes. The tsunami propagation can be accurately evaluated, since bathymetry is much better known than seismic velocity structure in the Earth. Using waveform inversion techniques, we can estimate the spatial distribution of coseismic slip on the fault plane from tsunami waveforms. This method has been applied to several earthquakes around Japan. Two recent earthquakes, the 1968 Tokachi-oki and 1983 Japan Sea earthquakes, are examined for calibration purposes. Both events show nonuniform slip distributions very similar to those obtained from seismic wave analyses. The use of tsunami waveforms is more useful for the study of unusual or old earthquakes. The 1984 Torishima earthquake caused unusually large tsunamis for its earthquake size. Waveform modeling of this event shows that part of the abnormal size of this tsunami is due to the propagation effect along the shallow ridge system. For old earthquakes, many tide gauge records exist with quality comparable to modern records, while there are only a few good quality seismic records. The 1944 Tonankai and 1946 Nankaido earthquakes are examined as examples of old events, and slip distributions are obtained. Such estimates are possible only using tsunami records. Since tide-gauge records are available as far back as the 1850s, use of them will provide unique and important information on long-term global seismicity. [ABSTRACT FROM AUTHOR]