A numerical treatment of underwater wave propagation with arbitrary boundaries and boundary conditions

abstract The problem of the Rayleigh wave propagation in a solid layer overlying a solid half space separated by a sinusoidal interface is investigated. The amplitude of the interface is assumed to be small in comparison to the average thickness of the layer or the wave length of the interface. Either by applying Rayleigh's approximate method or by perturbating the boundary conditions at the sinusoidal interface, plane wave solutions for the equations which satisfy the given boundary conditions are found to form a system of linear equations. These equations may be expressed in a determinant form. The period (or characteristic) equations for the first and second approximation of the wave number k are obtained. The phase and group velocities of Rayleigh waves in the present case depend upon both frequency and distance. At a given point on the surface, there is a local phase and local group velocity of Rayleigh waves that is independent of the direction of wave propagation.

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Boundary conditions for the numerical solution of wave propagation problems

Geophysics ◽

10.1190/1.1440881 ◽

1978 ◽

Vol 43 (6) ◽

pp. 1099-1110 ◽

Cited By ~ 169

Author(s):

Albert C. Reynolds

Keyword(s):

Wave Propagation ◽

Reflection Coefficient ◽

Finite Difference ◽

Boundary Conditions ◽

Numerical Solution ◽

Neumann Boundary ◽

Synthetic Seismograms ◽

Neumann Boundary Conditions ◽

Numerical Calculations ◽

Reflection Coefficients

Many finite difference models in use for generating synthetic seismograms produce unwanted reflections from the edges of the model due to the use of Dirichlet or Neumann boundary conditions. In this paper we develop boundary conditions which greatly reduce this edge reflection. A reflection coefficient analysis is given which indicates that, for the specified boundary conditions, smaller reflection coefficients than those obtained for Dirichlet or Neumann boundary conditions are obtained. Numerical calculations support this conclusion.

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The Problem on Dynamical Loading of Plane Elastic Regions With Irregular Boundaries

Journal of Applied Mechanics ◽

10.1115/1.2789078 ◽

1998 ◽

Vol 65 (2) ◽

pp. 476-478

Author(s):

N. Morozov ◽

I. Sourovtsova

Keyword(s):

Wave Propagation ◽

Boundary Conditions ◽

The Body ◽

Single Type ◽

Edge Condition ◽

Special Boundary ◽

Elastic Wedge ◽

Surface Loading ◽

Special Surface ◽

Extension Of Operators

The study of the problem of wave propagation in elastic wedge meets considerable difficulties, which are intensified by the presence of waves of two types that interact with each other through boundary conditions. However, some special surface loading permits separation of the potentials in the boundary conditions, but even in this case the problem cannot be simply reduced to two acoustic ones. The reason for this is that the edge condition cannot be satisfied if the disturbances are limited to a single type (longitudinal or shear). In spite of this the problem, such a special boundary loading nevertheless turns out to be very similar to the acoustic one, which makes it possible to find a closed analytical solution by means of the modified Kostrov method (Kostrov, 1966) and the idea of extension of operators. A similar approach is used for the study of the general problem of loading of the body with several angles.

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Effect of an elastically restrained boundary on SV-wave radiation patterns

Bulletin of the Seismological Society of America ◽

10.1785/bssa0580020497 ◽

1968 ◽

Vol 58 (2) ◽

pp. 497-520

Author(s):

Y. T. Huang

Keyword(s):

Boundary Condition ◽

Wave Propagation ◽

Free Boundary ◽

Boundary Conditions ◽

Elastic Wave ◽

Solid Earth ◽

Elastic Constants ◽

Wave Radiation ◽

Free Boundary Conditions ◽

Elastically Restrained

Abstract In the solution of elastic wave propagation equations applied to solid earth, it is customarily assumed that free boundary conditions are satisfied at a surface which is in contact with the atmosphere. Situations which depart from this boundary condition have now been studied for arbitrary combinations of the Lamé elastic constants. The solutions are given for a homogeneous, isotropic half space.

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The effect of boundaries on wave propagation in a liquid-filled porous solid: V. Transmission across a plane interface

Bulletin of the Seismological Society of America ◽

10.1785/bssa0540010409 ◽

1964 ◽

Vol 54 (1) ◽

pp. 409-416

Author(s):

H. Deresiewicz ◽

J. T. Rice

Keyword(s):

Wave Propagation ◽

Boundary Conditions ◽

Body Waves ◽

Porous Solid ◽

Plane Interface ◽

Plane Body ◽

Cross Sectional ◽

Material Constants ◽

Transmitted Waves

abstract The passage of plane body waves across a plane interface from one to another, contiguous, porous aggregate is examined, with particular attention paid to motions involving wave lengths large in comparison with cross-sectional pore dimensions. The results are obtained for a rather general set of boundary conditions which take account of possible resistance to flow due to partial nonalignment of pores at the interface. It is found that when certain conditions of equality of material constants for the two media are met one or more of the reflected and transmitted waves are extinguished.

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