Surface Wave Problem Research Articles

Partial derivatives of surface wave phase velocity with respect to physical parameter changes within the Earth

By using energy equations, which are equivalent to fundamental equations and boundary conditions in surface wave problems, we can get analytical expressions for partial derivatives of phase velocity with respect to changes of physical parameters within the earth. These derivatives can be calculated by knowing only the eigenfunction corresponding to the phase velocity. Numerical examples are worked out for CANSD (a model proposed by Brune and Dorman for the Canadian shield), the Jeffreys model, and the Gutenberg model for crustmantle structure. An application of the present result to numerical inversion of surface wave data is demonstrated by an example.

Uniqueness theorem for a surface wave problem in electromagnetic diffraction theory

Communications on Pure and Applied MathematicsVolume 16, Issue 1 p. 45-56 Article Uniqueness theorem for a surface wave problem in electromagnetic diffraction theory Richard C. Morgan, Richard C. Morgan Currently instructor of mathematics at St. John's University.Search for more papers by this authorSamuel N. Karp, Samuel N. KarpSearch for more papers by this author Richard C. Morgan, Richard C. Morgan Currently instructor of mathematics at St. John's University.Search for more papers by this authorSamuel N. Karp, Samuel N. KarpSearch for more papers by this author First published: February 1963 https://doi.org/10.1002/cpa.3160160107Citations: 4 AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Citing Literature Volume16, Issue1February 1963Pages 45-56 RelatedInformation

On certain boundary-value problems for the equations of seepage of a liquid in fissured rocks

The focus of this paper is on the propagation of thermoelastic waves with assigned wavelength within the context of theory of thermoelasticity for materials with double porosity. It is shown that there exist two shear waves that are undamped in time, non-dispersive and that are unaltered by the presence of pore system or by thermal effects. Furthermore, there also exist other four longitudinal wave solutions that are dispersive and damped in time: one longitudinal quasi-elastic wave and two quasi-pore modes and one quasi-thermal mode. The dispersion relation is explicitly established like a fifth degree algebraic equation with real coefficients and hence it always allows some real roots, thus predicting existence of some standing waves. A numerical analysis for Berea sandstone shows that the speed of propagation of the longitudinal quasi-elastic wave is larger than the wave speed for its counterpart from the classical elastic model or that in the double porosity elastic model. The propagation of the Rayleigh surface waves is addressed and the corresponding secular equation is explicitly established. As an illustrative example it is used Berea sandstone when the secular equation is solved by means of the graphical method to prove that the Rayleigh surface wave problem admits a solution.

Study of shear velocity distribution in the upper mantle by mantle Rayleigh and Love waves

A method is proposed by which we can calculate group velocity in surface wave problems without using numerical differentiation. This method is applied to the study of shear velocity distribution in the upper mantle by mantle Rayleigh and Love waves. The present study gives preference to the 8099 model proposed by Dorman and to the Lehmann* model proposed here as the models of the upper mantle structure in the oceanic and the continental regions, respectively.

“Periodic Source and its Applications”

The author once published the tables of some integrals appearing in some problems of surface-waves. In the present paper, the applications of these tables are showed for some periodic motions that is : (i) Calculations of wave elevation and induced pressure by a periodic point source, (ii) Calculation of flap-type wave generater, (iii) Two-dimensional source distribution for the heaving motion.These examples show the Usefulness of application of periodic source distributions for some problems of surface waves.

密度, 弾性率が連続的に変化している半無限弾性体の表面を伝わる波 (第1報)

The variational calculus method is applied to the problem of surface waves propagating along a free surface of a semi-infinite elastic medium of variable density and elasticity.Numerical examples are worked out for Love (§ 3) and Rayleigh waves (§ 5) in a medium of constant density and elasticity increasing linearly with the depth from the free surface-

Note on waves on the surface of running water

The method for the solution of problems of surface waves on water with which this note is concerned can be sufficiently illustrated by a particular example given by Lamb (1). In Lamb's example it is supposed that a steady stream in which the x, y components of the velocity are U, 0, where U is constant, is slightly disturbed by the application of a constant pressure ρPU2 to a band of finite width 2a of the surface of the stream; ρ denotes the density of the water and P a non-dimensional constant. In the solution Lamb, using an artifice due originally to Rayleigh and widely used since, assumes that ‘the deviation of any particle of the fluid from the state of uniform flow is resisted by a force proportional to the relative velocity’, and states that this ‘law of friction does not profess to be altogether a natural one, but it serves to represent in a rough way the effect of small dissipative forces; and it has the great mathematical convenience that it does not interfere with the irrotational character of the motion’.

On the Problem of Surface Waves Produced by an Impulse upon the Fluid

On the Problem of Surface Waves Produced by an Impulse upon the Fluid

The method of images in some problems of surface waves

1. When a circular cylinder is submerged in a uniform stream, the surface elevation may be calculated, to a first approximation, by a method due originally to Lamb for this case, and later extended to bodies of more general form: the method consists in replacing the cylinder by the equivalent doublet at its centre and then finding the fluid motion due to this doublet. In discussing the problem some years ago, I remarked that if the solution so obtained were interpreted in terms of an image system of sources, we should then be able to proceed to further approximations by the method of successive images, taking images alternately in the surface of the submerged body and in the free surface of the stream. This is effected in the following paper for two-dimensional fluid motion, and the method is applied to the circular cylinder. It provides, theoretically at least, a process for obtaining any required degree of approximation but, of course, the expressions soon become very complicated. It is, however, of interest to examine some cases numerically so as to obtain some idea of the degree of approximation of the first stage. An expression is first obtained for the velocity potential of the fluid motion due to a doublet at a given depth below the surface of a stream, the doublet being of given magnitude with its axis in any direction. A transformation of this expression then gives a simple interpretation in terms of an image system. This system consists of a certain isolated doublet at the image point above the free surface, together with a line distribution of doublets on a horizontal line to the rear of this point; the moment per unit length of the line distribution is constant, but the direction of the axis rotates as we pass along the line, the period of a revolution being equal to the wave-length of surface waves for the velocity of the stream. The contribution of each part of the image system to the surface disturbance is indicated.