Showing papers on "Lamb waves published in 1970"
273 citations
TL;DR: In this article, the multidimensional scalar wave equation at a single frequency is split into two equations, one controlling the downgoing transmitted wave; the other controlling the upcoming reflected wave.
Abstract: The multidimensional scalar wave equation at a single frequency is split into two equations. One controls the downgoing transmitted wave; the other controls the upcoming reflected wave. The equations are coupled, but in many reflection seismology situations the transmitted wave may be calculated without consideration of the reflected wave. The reflected wave is then calculated from the transmitted wave and the assumed velocity field. The waves are described by a modulation on up‐ or downgoing plane waves. This modulation function is calculated by difference equations on a grid. Despite complicated velocity models (steep faults, buried focus, etc.), the grid may be quite coarse if waves of interest do not propagate at large angles from the vertical. A one‐dimensional grid may be used for a two‐dimensional velocity model. With approximations, a point source emitting waves spreading in three dimensions may be included on the one‐dimensional grid. Calculation time for representative models is a few seconds. P...
195 citations
TL;DR: In this article, a finite difference approximation to the elastic equations of motion is successfully used to solve various wave-propagation problems possessing analytical solutions, and the method is extended to the problem of Love waves propagating across an ocean-continent type boundary.
Abstract: A simple finite difference approximation to the elastic equations of motion is successfully used to solve various wave-propagation problems possessing analytical solutions. On this basis the method is extended to the problem of Love waves propagating across an ocean-continent type boundary. Numerical propagation of an initial transient solution results in seismograms at various distances. The Fourier transforms of these seismograms are used to calculate phase velocity, group delay, and amplitude-transfer coefficients for various seismometer combinations across the transition region. Some results are' the transition zone can have a small but noticeable effect on phase velocities measured between stations situated away from the zone; a phase-velocity anisotropy exists for waves propagating in opposite directions across the same array. In general, waves propagating into the region of thinning have anomalously high-phase velocities and vice versa. This is especially noticeable for velocities measured over the zone of transition, where the perturbations of the phase velocity of continent-to-ocean waves from the expected local phase velocity can exceed the variations expected from the continent-ocean structural differences. The behavior at a distance from the boundary justifies the well-established method of calculating effective group velocities by means of inverse averages of regional group velocities and also indicates a simple correction for the effect of the ocean-continent boundary that can be applied to calculations of earthquake-source mechanisms based on the method of amplitude equalization.
104 citations
TL;DR: In this paper, it was shown that rotation of volume elements within an acoustic wave can make a large contribution to the scattering of light from an acoustic shear wave in optically anisotropic media, thus removing the traditionally assumed symmetry between the last two (acoustic) indices of the usual photoelastic tensor.
Abstract: Rotation of volume elements within an acoustic wave can make a large contribution to the scattering of light from an acoustic shear wave in optically anisotropic media, thus removing the traditionally assumed symmetry between the last two (acoustic) indices of the usual photoelastic tensor ${p}_{\mathrm{ij}1}$.
96 citations
TL;DR: Nonlinear oscillations averaging method applied to resonant interactions of acoustic gravity waves is used in this paper for nonlinear oscillation averaging of gravity wave interactions with acoustic resonant interaction.
Abstract: Nonlinear oscillations averaging method applied to resonant interactions of acoustic gravity waves
30 citations
TL;DR: In this paper, the authors considered only wave propagation along a plane of symmetry of the medium and showed that the regions in which waves are possible in anisotropic media are similar in outline to those calculated by Scholte (1947) for isotropic media.
Abstract: A general anisotropic medium is characterized by 21 elastic constants. In this study we consider only wave propagation along a plane of symmetry of the medium. The maximum number of independent elastic constants is therefore reduced to 13. Stoneley waves at solid-solid interfaces are only possible for certain ranges of values of the elastic constant and density parameters. Considering certain of these parameters to be variables, regions in which waves are possible are calculated for waves traveling in various directions and for media possessing cubic, orthorhombic, and monoclinic symmetries. The results show that the regions in which waves are possible in anisotropic media are similar in outline to those calculated by Scholte (1947) for isotropic media. For certain values of the elastic constants, large variations of the regions from one direction of wave propagation to another are observed. For specific substances in the three symmetry classes given above, the phase velocities of solid-solid Stoneley waves, liquid-solid Stoneley waves, and Rayleigh waves as a function of direction of wave propagation are calculated.
24 citations
TL;DR: In this paper, travel-wave propagation, modal vibrations and elastic transmission medium studies from theoretical seismograms for realistic gravitating heterogeneous spherical earth model were performed for a real gravitating spherical earth.
Abstract: Traveling wave propagation, modal vibrations and elastic transmission medium studies from theoretical seismograms for realistic gravitating heterogeneous spherical earth model
20 citations
TL;DR: In this paper, an ultrasonic wave propagation guided by fluid layer between two elastic solids, plotting normalized velocities and layer thicknesses, is described in terms of wave propagation.
Abstract: Ultrasonic wave propagation guided by fluid layer between two elastic solids, plotting normalized velocities and layer thicknesses
18 citations
17 citations
TL;DR: In this article, the phase velocity of a wave at the edge of a thick plate under initial stress is derived, and the frequency equation for the phase velocities of the wave in a thin and an infinite-thick plate is derived.
Abstract: The frequency equation giving the phase velocity of a wave at the edge of a thick plate under initial stress is obtained. Some particular cases are discussed to derive (a) the velocity of edge waves in a thin plate and (b) the velocity of Rayleigh waves in a plate of infinite thickness under initial stress.
16 citations
TL;DR: In this article, a dispersion relation for waves in an extrinsic semiconductor plate or film with an applied electric field is derived, and an arbitrary perturbation can be expressed as a superposition of modes.
Abstract: A dispersion relation for waves in an extrinsic semiconductor plate or film with an applied electric field is derived. It is shown that there exists an infinite number of modes. An arbitrary perturbation can be expressed as a superposition of modes. Expressions for the expansion coefficients are derived. Finally, it is shown that a perturbation which is initially a plane wave in a thick plate, remains an approximate plane wave in a time interval corresponding to the decay time, except near the boundaries. Thus, an apparent discrepancy between the theories of infinite- and finite-dimension semiconductors is resolved.
TL;DR: In this paper, the angle of deviation of ray from wave normal for plane elastic waves whose normal lies in a zonal plane of a hexagonal (transversely isotropic) medium (or an equivalent plane) is presented.
Abstract: Expressions for the angle of deviation, Δ, of ray from wave normal for plane elastic waves whose normal lies in a zonal plane of a hexagonal (transversely isotropic) medium (or an equivalent plane) are presented. Although values of Δ have been calculated from general expressions for rays or energy-flux vectors, the present forms have some computational convenience and allow certain general conclusions about the variation of Δ with wave normal to be stated in terms of inequalities involving the elastic stiffnesses. The particular case of cubic crystals is illustrated. The findings have relevance to ultrasonic wave propagation in many elastically anisotropic solids including fibre composites.
TL;DR: In this paper, a LiNbO3 surface wave delay line has been used to probe surface wave mode conversion and up to 4% of the power present in a surface wave incident on a reactively loaded interdigital transducer has been observed to be scattered into shear waves.
Abstract: Diffraction of laser light from bulk waves present in a LiNbO3 surface wave delay line has been used to probe surface wave mode conversion. Up to 4% of the power present in a surface wave incident on a reactively loaded interdigital transducer has been observed to be scattered into shear waves. In addition, a driven interdigital transducer has been seen to radiate bulk waves with directivity properties well described by a phased array antenna model.
TL;DR: In this paper, the authors demonstrate that a finite-amplitude traveling cyclotron harmonic wave may decay into two similar waves by the process of resonant mode-mode coupling.
Abstract: Experimental results are presented which demonstrate that a finite‐amplitude traveling cyclotron harmonic wave may decay into two similar waves by the process of resonant mode‐mode coupling. The results presented here are restricted to cases where the group velocity of one of the perturbed waves is in the opposite direction from that of the other perturbed wave. The important feature of this process is that considerable growth, both in time and space, can occur for the perturbed waves. The spatial growth of these waves is observed, and the wave amplitudes are in qualitative agreement with theory. Furthermore, the experiments provide a quantitative measure of the resonant mode‐mode coupling coefficient for waves that propagate perpendicularly to the magnetic field in a warm plasma.
TL;DR: In this paper, the authors describe the drastic modifications that occur in the spin-acoustic Love-type surface wave when the ferrite substrate is mass-loaded with a nonmagnetic elastic layer.
Abstract: The letter describes the drastic modifications that occur in the spin-acoustic Love-type surface wave when the ferrite substrate is mass-loaded with a nonmagnetic elastic layer.
Abstract: A theoretical study of acoustic propagation in a fluid layer between two solid layers of different elastic properties is discussed. A selection of materials suitable for a pulse-compression filter is reported.
TL;DR: In this article, the wave-wave coupling among ion waves is investigated experimentally and theoretically, and the growing regions of the harmonic and f 1 − f 1 - f 2 are found to grow spatially in some region, on the contrary to those of f 1 and f 2 which decrease monotonously in the region.
Abstract: Wave-wave coupling among ion waves is investigated, experimentally and theoretically. When two ion waves of different frequencies of f 1 and f 2 are excited by one grid, the signals of the harmonic (2 f 1 ) and f 1 – f 2 are detected by another grid. They are found to grow spatially in some region, on the contrary to those of f 1 and f 2 which decrease monotonously in the region. The growing regions of the harmonic and f 1 – f 2 are in accord with those obtained from the theory of the wave-wave coupling among ion waves. The propagation of small-amplitude wave under the large-amplitude wave and the propagation of ion wave with large-amplitude are also investigated.
01 Jan 1970
TL;DR: In this paper, the attenuation coefficients associated with small variations in the elastic parameters of a solid medium give rise to scattering of elastic waves and hence to a reduction in their amplitudes.
Abstract: Small variations in the elastic parameters of a solid medium give rise to scattering of elastic waves and hence to a reduction in their amplitudes. The attenuation coefficients associated with this process have been calculated for surface waves. Expressions have been derived for waves with wavelengths long compared with the mean wavelength of the variation of the elastic parameters in space. The attenuation coefficients were found to be the same as if the attenuating mechanism were a particular type of visco-elasticity.
TL;DR: Bunney et al. as mentioned in this paper showed that it is possible to excite both the Rayleigh and Lamb wave types over a limited region of wall thickness by adjusting the angles of incidence of the projector and receiver.
Abstract: Recent experimental data presented by Bunney et al. indicate that, as an originally solid cylinder is progressively made hollow, the circumferential acoustic waves that can be excited on that cylinder progress from those having the characteristics of Rayleigh waves to those having the characteristics of Lamb waves. Similar measurements of circumferential wave velocity have been made on a different type of aluminum alloy, type 1100F, and it was found possible to excite both the Rayleigh‐type and the Lamb‐type waves, over a limited region of wall thickness, by adjusting the angles of incidence of the projector and receiver.
TL;DR: In this article, the dynamics of three interacting waves in a magnetoactive plasma is discussed using the methods of non-linear optics, where the frequencies of the transverse wave are assumed very large whereas the frequency of the longitudinal wave may be a frequency characteristic of the system.
Abstract: The dynamics of three interacting waves in a magnetoactive plasma is discussed using the methods of non-linear optics. The frequencies of the transverse wave are assumed very large whereas the frequency of the longitudinal wave may be a frequency characteristic of the system. A general formula for the length of the total conversion is given in terms of the longitudinal electron permeability. Two examples of conversion are discussed in detail, i.e. excitation of Bernstein modes and of ion cyclotron waves. It is shown that for sufficiently large but attainable amplitudes of the transverse waves the length of conversion may be of practical interest.
TL;DR: In this paper, it was shown that the energy conversion of the magnetostatic waves into the spin waves is possible only when the wave impedance of two magnetic oscillating systems are equal.
Abstract: The energy flow of the magnetostatic waves is derived from the Lagrangian intensity, and the wave impedances of the magnetostatic waves and the exchange spin waves are derived from the energy flow of those waves. It is shown in the present paper that the energy conversion of the magnetostatic waves into the spin waves is possible only when the wave impedance of two magnetic oscillating systems are equal.
TL;DR: In this paper, the interaction of nonlinear waves on a liquid surface is studied, and it may help to explain a great number of phenomena in wave dynamics of the sea, which is also relevant to capillary waves and the modelling of the nonlinear wave processes for dispersive media, which are of interest in nonlinear optics and electrodynamics.
Abstract: STUDY of the interaction of nonlinear waves on a liquid surface is of considerable interest1 because it may help to explain a great number of phenomena in wave dynamics of the sea. It is also relevant to capillary waves and the modelling of the nonlinear wave processes for dispersive media, which is of interest in nonlinear optics and electrodynamics. The study of nonlinear capillary waves is also important for capillary hydrodynamics.
TL;DR: In this article, the dispersion relation for straight-crested waves in an isotropic plate in a state of plane strain that is covered by a layer of an incompressible liquid is derived and investigated in the limits of very long wavelengths (thickness-stretch vibrations of the plate-liquid system) and of very short wavelengths (surface waves and the solid-liquid interface).
Abstract: The dispersion relation for straight‐crested waves in an isotropic plate in a state of plane strain that is covered by a layer of an incompressible liquid is derived and investigated in the limits of very long wavelengths (thickness‐stretch vibrations of the plate‐liquid system) and of very short wavelengths (surface waves and the solid‐liquid interface). In the case of surface waves, there are two dispersive modes, one predominantly elastic (analogous to Rayleigh waves) and the other essentially fluid, and in the thickness‐stretch case, there are an infinite number of essentially elastic modes and one fluid mode. An approximate version of the dispersion relation valid for arbitrary wavelength is obtained by using two nonclassical plate theories to account for the extensional and flexural deformations of the plate. This relation gives rise to five modes on the real branch, which are identified as being thickness‐stretch, thickness‐shear, flexural, extensional, and fluid in character, and three modes on th...