The potential and vortex traces of a tsunamigenic earthquake in the ocean

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.     

Scattering in a Pekeris waveguide from a rough bottom using a two-way coupled mode approach

Scattering from a rough ocean bottom is described numerically with a two-way coupled-mode formalism that contains scattering effects to all orders and provides an exact solution to the wave equation. Both scattered field and direct blast components are computed within the formalism framework. A comparison of the scattered component solution from the coupled mode with the Born approximation (BA) solution for scattering from a rough bottom Pekeris waveguide shows that the BA predicts correctly the scattered field levels but not detailed structure. The transition from direct blast to scattered field dominance is identified in the total field time series.     

Application of the Block Element Method to the Problem of Predicting the Preparation of a Tsunami

Doklady Physics - A model of preparation of an initial ocean earthquake is created for vertical impacts on the ocean layer and lithospheric plates, and the conditions of tsunami generation are found.     

Geoacoustic Inversion for Bottom Parameters via Bayesian Theory in Deep Ocean

We develop a new approach to estimating bottom parameters based on the Bayesian theory in deep ocean.The solution in a Bayesian inversion is characterized by its posterior probability density(PPD),which combines prior information about the model with information from an observed data set.Bottom parameters are sensitive to the transmission loss(TL)data in shadow zones of deep ocean.In this study,TLs of different frequencies from the South China Sea in the summer of 2014 are used as the observed data sets.The interpretation of the multidimensional PPD requires the calculation of its moments,such as the mean,covariance,and marginal distributions,which provide parameter estimates and uncertainties.Considering that the sensitivities of shallowzone TLs vary for different frequencies of the bottom parameters in the deep ocean,this research obtains bottom parameters at varying frequencies.Then,the inversion results are compared with the sampling data and the correlations between bottom parameters are determined.Furthermore,we show the inversion results for multifrequency combined inversion.The inversion results are verified by the experimental TLs and the numerical results,which are calculated using the inverted bottom parameters for different source depths and receiver depths at the corresponding frequency.     

Analytical study of a potential model of tsunami with a simple source of piston type. 1. Exact solution. Creation of tsunami

A linear hydrodynamic problem concerning the generation of gravitational waves on the free surface of a liquid by a source (defined as an initial instant vertical displacement of the bottom of the basin) is studied, where the displacement is defined by a rather simple axially symmetric function of the horizontal coordinates. A solution to the problem is obtained in the form of single integrals and is regarded as a distribution (a ??generalized function??) with respect to time. These integrals are evaluated numerically and asymptotically. In this part of the paper, using the results of numerical evaluation carried out for each source (having a given characteristic radius in a wide range of values), we find the initial instantaneous displacement of the fluid, determine the parameters of the leading crest of the created surface wave, and estimate the minimal radius which a source must have to be referred to tsunami generators.     

海啸的物理

地震海啸的产生是地球表面固体层和流体层相互作用的结果.文章介绍了这种相互作用的物理过程,讨论了海啸的大小、能量、传播速度.指出：建立早期预警系统是减少海啸灾害的重要措施,目前的预警系统虚报率很高的问题,仍需要通过加强地球表层系统相互作用的研究来解决.     

Underwater acoustic scattering from a radially layered cylindrical obstacle in a 3D ocean waveguide

A solution based on coupled mode expansions is presented for the 3D problem of acoustic scattering from a radially layered penetrable cylindrical obstacle in a shallow-water plane-horizontal waveguide. Each cylindrical ring is characterized by a general, vertical sound speed and density profile (ssdp), the ocean environment around the obstacle can be also considered horizontally stratified with a depth-arbitrary ssdp, and the bottom is assumed to be rigid. The total acoustic field generated by an harmonic point source is represented as a normal-mode series expansion. The expansion coefficients are calculated exploiting the matching conditions at the cylindrical interfaces, which results in an infinite linear system. The system is appropriately truncated and numerically solved by using a recursive relation, which involves the unknown coefficients of two successive rings. Results concerning the transmission loss outside and inside obstacles consisting of three cylindrical rings are given for a typical depth-dependent ocean sound-speed profile. The presented solution can serve as a benchmark solution to the general problem of 3D acoustic scattering from axisymmetric inhomogeneities in ocean waveguides at low frequencies.     

On the numerical simulation of the propagation of the wave front of a tsunami wave in a pool of variable depth with run-up on the beach

The aim of this work is the numerical-analytical modelling of the wave front of tsunami caused by the momentary lifting of a small bottom area in a pool of variable depth with a smooth coastline.     

Numerical tsunami modeling and the bottom relief

The effect of the quality of bathymetric data on the accuracy of tsunami-wave field calculation is considered. A review of the history of the numerical tsunami modeling development is presented. Particular emphasis is made on the World Ocean bottom models. It is shown that the modern digital bathymetry maps, for example, GEBCO, do not adequately simulate the sea bottom in numerical models of wave propagation, leading to considerable errors in estimating the maximum tsunami run-ups on the coast.     

平面波与线性粘弹海底的反射和折射

采用基于广义标准线性体Boltzmann叠加原理的固体流变模型来描述粘弹性海底底质结构,分析了沉积层和基岩的纵、横波速度频散和衰减的特点,计算了海水沉积层界面和沉积层基岩界面位移势反射和折射系数和能量反射和折射系数。结果表明,采取本模型的粘弹性海底的速度频散、衰减和已有文献的实验数据符合较好,能准确的描述海底底质的主要性质,反射和折射系数和声波的频率有关。     

On the possibility of using acoustic reverberation for remote sensing of ocean dynamics

The two-point correlation function of diffuse noise fields produced by distributed random sound sources carries useful information on the medium of sound propagation. Such information can be used for performing passive acoustic tomography of the ocean. In a number of cases that are important for practice, the noise field in the ocean is predominated by contributions of individual point sources. Here, a theoretical study is presented on the possibility of determining the sound speed and current velocity in the water column by the correlation processing of reverberation signals measured by two vertical receiving arrays. In other words, we study the possibility of replacing the diffuse noise produced by a great number of delta-correlated sources by waves generated by a localized source and scattered at the rough surface and bottom of the ocean for sensing the medium. The correlation function of scattered waves is calculated by using the method of small perturbations. It is shown that the correlation processing of the scattered waves offers an opportunity of measuring the acoustic nonreciprocity and reconstructing the field of sound speed in the fluid, without using any acoustiLc transceivers.     

“Hot spots” in the field of internal waves in the ocean

A review of observations of high-amplitude internal waves is presented. These waves play an important role in the global scenario of water mixing in the world ocean and also cause a considerable variability of oceanographic fields, including the sound velocity field. The main sources of intense internal waves and the regions where such waves arise are considered. It is shown that, in addition to the much-investigated trains of soliton-like internal waves, which are formed near large-scale inhomogeneities of the bottom relief because of the nonlinear evolution of internal tides, internal waves encountered in the open ocean also possess considerable amplitudes and nonlinearity.     

Augmented Riemann solvers for the shallow water equations over variable topography with steady states and inundation

We present a class of augmented approximate Riemann solvers for the shallow water equations in the presence of a variable bottom surface. These belong to the class of simple approximate solvers that use a set of propagating jump discontinuities, or waves, to approximate the true Riemann solution. Typically, a simple solver for a system of m conservation laws uses m such discontinuities. We present a four wave solver for use with the the shallow water equations—a system of two equations in one dimension. The solver is based on a decomposition of an augmented solution vector—the depth, momentum as well as momentum flux and bottom surface. By decomposing these four variables into four waves the solver is endowed with several desirable properties simultaneously. This solver is well-balanced: it maintains a large class of steady states by the use of a properly defined steady state wave—a stationary jump discontinuity in the Riemann solution that acts as a source term. The form of this wave is introduced and described in detail. The solver also maintains depth non-negativity and extends naturally to Riemann problems with an initial dry state. These are important properties for applications with steady states and inundation, such as tsunami and flood modeling. Implementing the solver with LeVeque’s wave propagation algorithm [R.J. LeVeque, Wave propagation algorithms for multi-dimensional hyperbolic systems, J. Comput. Phys. 131 (1997) 327–335] is also described. Several numerical simulations are shown, including a test problem for tsunami modeling.     

Perturbation,symmetry analysis,B(a)cklund and reciprocal transformation for the extended Boussinesq equation in fluid mechanics

In this work,we study a generalized double dispersion Boussinesq equation that plays a significant role in fluid mechanics,scientific fields,and ocean engineeri...     

海底反射对水声射线混沌行为的影响

本文探讨非线性声速分布、内波扰动、和海底反射对哈密顿抛物射线方程动力学行为的影响。运用Poincaré映象、Lyapunov指数等非线性动力学方法对射线系统行为进行描述。结果显示水声射线在不发生海底反射的情况下,内波对声速扰动的增强将导致正的Lyapunov指数,使射线产生不规则的混沌运动并扩大射线系统的混沌区域。然而海底反射显著影响了声速分布、内波扰动和射线运动的非线性相互作用。海底深度的减小使声射线系统的混沌区域扩大,然而过小的深度减弱了声速分布和射线的非线性相互作用,使混沌区域缩小。因此,我们可以得出海底反射对于水声射线的混沌动力学行为有重要影响的结论。     

Sound wave propagation in a vertically inhomogeneous ocean

Propagation of sound waves generated by a time dependent acoustic source in a vertically inhomogeneous ocean is considered. The effect of the solid bottom is included so that both the longitudinal and shear waves can be excited inside the bottom. The possibility of exciting a lateral shear wave by the acoustic source is also discussed. Although the results presented here are formal and general, physical interpretations have been offered whenever possible.     

Comparison of solutions of a problem of Cauchy–Poisson type under discontinuous and smooth initial values with the marigrams of Tsunami 2011 obtained from DART stations

The problem of Cauchy–Poisson type is considered in the framework of potential tsunami model with impulse cylindical compactly supported source discontinuous with respect to the radial horizontal coordinate under the assumption that the depth of the liquid is constant. An analytical solution of the problem for a special choice of values of the parameters of the source is given. The connection the solution thus obtained with nonstandard characteristics introduced by Maslov is discussed. The graphs of the time history of the free surface elevation are compared with the marigrams, received for the 2011 tsunami from the DART stations 21418, 21413, and 51407, and also with graphs calculated for the well-known model with a “simple” source.     

Exact solution of the vectorial field structure of a light beam

An alternative way of finding electromagnetic solutions based on the closest solution defined by Martinez-Herrero et al. [J. Opt. Soc. Am. A 18, 1678 (2001)] has been proposed. It is found that by identifying the components of closest solution as the components of the planewave spectrum of realistic fields at z = 0, an exact solution of the electromagnetic fields satisfying the Maxwell equations can also be obtained. This solution is applied to calculate the fields of a radially polarized Laguerre-Gaussian laser beam. It shows that although both formalisms are correct ways of finding electromagnetic solutions, as the beam waist size is less than a laser wavelength, the longitudinal electric field near the focus obtained from our solution can be significantly larger than that by Martinez-Herrero et al.     

The method of multifrequency near-field acoustical tomography of bulk inhomogeneities of the sea bottom

In this work, we propose a method of near-field acoustical multi-frequency coherent tomography of spatially localized inhomogeneities of the shallow-sea bottom. In the framework of the developed method, two-dimensional spatial scanning of the radiating-receiving system along the bottom over the region of location of the inhomogeneities is performed at multiple frequencies. Using the Born approximation, the initial three-dimensional integral equation for the scattered field is reduced to one-dimensional Fredholm equation of the first kind with respect to the depth profile of the transverse spatial spectrum of the inhomogeneities. In the solution of this integral equation for each pair of spectral components, we use the method of generalized residual and obtain the sought three-dimensinal distribution via the inverse Fourier transform of the reconstructed spectrum. Results of numerical simulation of the tomography scheme and visualized inhomogeneities of shallow-sea bottom are presented.     

Simulation of the vector wave field of a low-frequency sound source in the ocean: Some important features

An approach to the simulation of low frequency vector wave fields in stratified media (mainly in the ocean) is considered. The approach is characterized by an improved stability with respect to dividing the medium into many layers of arbitrary thickness. The model for the sound field of a point source is based on an integral representation of two-dimensional, cylindrically symmetric vector wave fields in inhomogeneous media, so that the contributions of all types of waves are included automatically. The model medium is subdivided into N horizontally homogeneous layers for which 4(N?1) equations are formulated to satisfy the boundary conditions between adjacent layers. The method of the generalized Schmidt matrix is used to obtain the coefficients of the equations; these coefficients are substituted into the expressions (of the Fourier-Bessel integral type) for the local parameters of the field. The latter are calculated according to the numerical procedure, and the results are used to model the distributions of the acoustic pressure and the horizontal and vertical components of the particle velocity in liquid and elastic media. The instability of the calculation procedure may result in a disagreement between the model and the exact solution. However, the disagreement is shown to occur mainly in models containing excessively thick layers. A way for improving the stability of the numerical model is suggested. The simulation results are compared with the exact analytical solution for the simplest example and with the results obtained according to the commonly used generalized matrix procedure (the benchmark problem). The examples of the practical application of the model for investigating more complex seismoacoustic wave fields in the ocean are presented.