Showing papers on "Wave propagation published in 1984"

SH-wave propagation in heterogeneous media; velocity-stress finite-difference method

Abstract: A new finite-difference (FD) method is presented for modeling SH-wave propagation in a generally heterogeneous medium. This method uses both velocity and stress in a discrete grid. Density and shear modulus are similarly discretized, avoiding any spatial smoothing. Therefore, boundaries will be correctly modeled under an implicit formulation. Standard problems (quarter-plane propagation, sedimentary basin propagation) are studied to compare this method with other methods. Finally a more complex example (a salt dome inside a two-layered medium) shows the effect of lateral propagation on seismograms recorded at the surface. A corner wave, always in-phase with the incident wave, and a head wave will appear, which will pose severe problems of interpretation with the usual vertical migration methods.

Effective anisotropic elastic constants for wave propagation through cracked solids

Abstract: Summary. Theoretical developments of Hudson demonstrate how to calculate the variations of velocity and attenuation of seismic waves propagating through solids containing aligned cracks. The analysis can handle a wide variety of crack configurations and crack geometries. Hudson associates the velocity variations with effective elastic constants. In this paper we associate the variation of attenuation with the imaginary parts of complex effective elastic constants. These complex elastic constants permit the simulation of wave propagation through two-phase materials by the calculation of wave propagation through homogeneous anisotropic solids.

SH-wave propagation in heterogeneous media: velocity-stress finite-difference method

Abstract: A new finite-difference (FD) method is presented for modeling SH-wave propagation in a generally heterogeneous medium. This method uses both velocity and stress in a discrete grid. Density and shear modulus are similarly discretized, avoiding any spatial smoothing. Therefore, boundaries will be correctly modeled under an implicit formulation. Standard problems (quarter-plane propagation, sedimentary basin propagation) are studied to compare this method with other methods. Finally a more complex example (a salt dome inside a twolayered medium) shows the effect of lateral propagation on seismograms recorded at the surface. A corner wave, always in-phase with the incident wave, and a head wave will appear, which will pose severe problems of interpretation with the usual vertical migration methods.

The propagation of electromagnetic waves

Abstract: This chapter describes the propagation of electromagnetic waves. For a steady monochromatic wave, frequency is a constant. This chapter also discusses the surface impedance of metals. The permittivity of metals is large compared with unity at low frequencies. The wavelength in metals is small compared with the wavelength in vacuum. As the frequency increases, the depth of penetration becomes of the same order as the mean free path of the conduction electrons. The chapter also describes the propagation of electromagnetic waves in waveguides. A waveguide is a hollow pipe of infinite length, that is, a cavity infinite in one direction. The characteristic oscillations in a resonator are stationary waves; however, those in a waveguide are stationary only in the transverse directions; waves travelling in the direction along the pipe can be propagated. The scattering of electromagnetic waves by particles is accompanied by absorption. The absorption cross-section is given by the ratio of the mean energy dissipated in a particle per unit time to the incident-energy flux density.

Propagation of nonlinear compression pulses in granular media

Abstract: The study of mechanics of a granular medium is of substantial interest, both scientifically and for the solution of applied problems. Such materials are, for example, good buffers for shock loads. Their, study is important for the development of processes of the pulse deformation of several porous materials. A review of studies of small deformations and elastic wave propagation in these media was carried out in [i] on the basis of discrete models. The structure of a stationary shock wave was analyzed in [2] as a function of its amplitude. i. Statement of the Problem. The problem of nonstationary, nonlinear perturbations in one-dimensional granular media is stated in the present paper on the basis of the wellknown interaction between neighboring granules. As an interaction law we choose the Hertz law [3]

Turbulent Boundary Layer in Wave‐current Motion

Abstract: The mean current velocity profile in the combined wave‐current motion is calculated by use of the depth‐integrated momentum equation. The velocity distribution is assumed to be logarithmic inside as well as outside the wave boundary layer, but with different slopes. Hereby, it is possible to describe the flow in the whole range from the pure wave motion (without any mean current) to the pure current motion (without any waves). The theory covers an arbitrary angle between wave propagation direction and mean current direction.

A unified theory for elastic wave propagation in polycrystalline materials

Abstract: We have developed a unified approach to solve for the attenuation and phase velocity variations of elastic waves in single‐phase, polycrystalline media due to scattering. Our approach is a perturbation method applicable for any material whose single‐crystal anisotropy is not large, regardless of texture, grain elongation, or multiple scattering. It accurately accounts for the anisotropy of the individual grains. It is valid for time‐harmonic waves with all ratios of grain size to wavelength. It uses an autocorrelation function to characterize the geometry of the grains, and thereby avoids coherent artifacts that occur if the grains are assumed to have symmetrical shapes and suggests new methods for characterizing distributions of grains that are irregularly shaped. We have carried out numerical calculations for materials that are untextured and equiaxed, and have cubic‐symmetry grains and an inverse exponential spatial autocorrelation function. These calculations agree with the previous calculations which are valid in the Rayleigh, stochastic, and geometric regions, and show the transitions between these regions. The complex transition between the Rayleigh and stochastic regions for longitudinal waves, and the severe limitations of the stochastic region for grains with fairly large anisotropy are of particular interest.

The slab geometry laser - Part I: Theory

Abstract: Slab geometry solid-state lasers offer significant performance improvements over conventional rod geometry lasers. We present a detailed theoretical description of the thermal, stress, and beam propagation characteristics of a slab laser. Our analysis includes consideration of the effects of the zig-zag optical path which eliminates thermal and stress focusing and reduces residual birefringence.

Finite-Element Analysis of Optical and Microwave Waveguide Problems

Abstract: A vector H-field formulation is developed for electromagnetic wave propagation for a wide range of guided-wave problems. It is capable of solving microwave or optical waveguide problems with arbitrarily anisotropic materials. We have introduced infinite elements to extend the region of explicit field representation to infirdly, to consider open-type waveguides more accurately. Computed results are given for a variety of optical planar guides, image lines, and waveguides containing skew anisotropic dielectic.

Experimental and theoretical study of wave propagation phenomena in drop-on-demand ink jet devices

Abstract: This paper presents experimental observations and a theoretical analysis of the operation of drop-on-demand piezoelectric ink jet devices. By studying experimentally the dependence of several operating characteristics on the length of the cavity in the nozzle of an ink jet device, we have gained insight into the physical phenomena underlying the operation of such a device. It is concluded that drop-on-demand ink jet phenomena are related to the propagation and reflection of acoustic waves within the ink jet cavity. A simple analysis is carried out on the basis of linear acoustics which is in good agreement with the experimental observations.

Attenuation of coda waves in New England

Abstract: Seismic wave attenuation was measured in New England from the time domain decay of coda wave amplitudes on narrow bandpass-filtered seismograms of local earthquakes. The frequency band of interest was 0.75 to 10 Hz. Q c ( f ) was found to increase with frequency across this band, but there was also a difference between the Q c ( f ) values for short ( t t > 100 sec) lapse times of coda wave propagation. For the short-lapse time data, corresponding to wave paths primarily in the upper crust, Q c ( f ) increases from 400 at 3 Hz to 1300 at 10 Hz. For the large-lapse time data, corresponding to wave paths in the lower crust and upper mantle, Q c ( f ) was found to vary from 660 at 1 Hz to 1500 at 10 Hz. If we interpret this dataset in terms of a model incorporating both scattering and anelastic attenuation, we find that the mean free path of seismic waves over this frequency band is 80 km for short-lapse times, and 400 km for long-lapse times. If we assume that scattering is entirely responsible for the observed attenuation, we find that the minimum mean free path for short-lapse times is about 75 km over all frequencies, whereas for long-lapse times, the minimum mean free path decreases from 400 km at 0.75 Hz to 90 km at 10 Hz.

Optical Communication Systems

Abstract: Part 1 Elementary discussion of propagation in dielectric waveguides material dispersion total dispersion in multimode and monomode fibres attenuation mechanisms in optical fibres inelastic scattering and non-linear propagation effects system considerations electromagnetic wave propagation in step-index fibre wave and ray propagation in graded-index fibres single-mode fibres the fabrication of fibres, cables and passive components fibre parameters specification and measurement. Part 2 Sources and detectors basic semiconductor properties injection luminescence the design of LEDS for optical communication the basic principles of laser action semiconductor lasers semiconductor lasers for optical fibre communication systems semiconductor photodiode detectors avalanche photodiode detectors and photomultiplier tubes. Part 3 The receiver amplifier the regeneration of digital signals coherent systems unguided optical communication systems optical fibre communication systems.

Ultrahigh gradient particle acceleration by intense laser-driven plasma density waves

Abstract: Space-charge waves driven by resonantly beating two laser beams in a high-density plasma can produce ultrahigh electric fields that propagate with velocities close to c. By phase-locking particles in such a wave, particles may be accelerated to very high energies within a very short distance.

Wave‐equation datuming before stack

Abstract: This note describes the extension to unstacked seismic data of a computationally efficient form of the Kirchhoff integral published several years ago. In the previous paper (Berryhill, 1979), a wave‐equation procedure was developed to change the datum of a collection of zero‐offset seismic traces from one surface of arbitrary shape to another, even when the velocity for wave propagation is not constant. This procedure was designated “wave‐equation datuming,” and its applications to zero‐offset data were shown to include velocity‐replacement datum corrections and multilayer forward modeling. Extending this procedure to unstacked data requires no change in the mathematical algorithm. It is necessary only to recognize that operating on a common‐source group of seismic traces has the effect of extrapolating the receivers from one datum to another, and that, because of reciprocity, operating on a common‐receiver group changes the datum of the sources. Two passes through the data, common‐source computations, th...

Diffuse ions produced by electromagnetic ion beam instabilities

Abstract: The evolution of the electromagnetic ion beam instability driven by the reflected ion component backstreaming away from the earth's bow shock into the foreshock region is studied by means of computer simulation. The linear and quasi-linear stages of the instability are found to be in good agreement with known results for the resonant mode propagating parallel to the beam along the magnetic field and with theory developed in this paper for the nonresonant mode, which propagates antiparallel to the beam direction. The quasi-linear stage, which produces large amplitude delta B approximately B, sinusoidal transverse waves and 'intermediate' ion distributions, is terminated by a nonlinear phase in which strongly nonlinear, compressive waves and 'diffuse' ion distributions are produced. Additional processes by which the diffuse ions are accelerated to observed high energies are not addressed. The results are discussed in terms of the ion distributions and hydromagnetic waves observed in the foreshock of the earth's bow shock and of interplanetary shocks.

Instabilities in line-driven stellar winds. I - Dependence on perturbation wavelength

Abstract: An analytical study is presented of the stability of absorption line-driven flows, such as found in stellar winds, in the presence of small-amplitude disturbances. A generalized calculation of the perturbed direct extinction force is performed and the evolution of the perturbation into the nonlinear regime and the dynamical results of perturbation in the scattered radiation field are examined. An expression is derived for the wavenumber variation of the perturbed line force from the milieu of nonoverlapping lines which have a power-law distribution in opacity. A linear dispersion analysis is carried out to model the growth and propagation of radiative-acoustic waves in absorption line-driven flows, which are found unstable to perturbations that may be smaller than the Sobolev length. No damping mechanism was found that would eliminate the absorption line-driven flows.

Weak and strong interactions between internal solitary waves

Abstract: The interaction of weakly nonlinear long internal gravity waves is studied. Weak interactions occur when the wave phase speeds are unequal; this case includes that of a head-on collision. It is shown that each wave satisfies a Korteweg-de Vries equation, and the main effect of the interaction is described by a phase shift. Strong interactions occur when the wave phase speeds are nearly equal although the waves belong to different modes. This case is described by a pair of coupled Korteweg-de Vries equations, for which some preliminary numerical results are presented.

Parametrically excited solitary waves

Abstract: A modulated cross-wave of resonant frequencyω1, carrier frequencyω =ω1 {1 + O(e)}, slowly varying complex amplitude O(e½b), longitudinal scale b/e½ and timescale 1/eω is induced in a long channel of breadth b that contains water of depth d and is subjected to a vertical oscillation of amplitude O(eb) and frequency 2ω, where 0 0.045 for d/b [gsim ] 1. The corresponding cnoidal waves (of which the solitary wave is a limiting case) are considered in an appendix.

Theory of electromagnetic waves

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Acoustical wave propagation in cylindrical ducts: Transmission line parameter approximations for isothermal and nonisothermal boundary conditions

Abstract: Approximate expressions are given for the characteristic impedance and propagation wavenumber for linear acoustic transmission through a gas enclosed in a rigid cylindrical duct. These expressions are most complicated in the transition zone where the thermoviscous boundary layers are on the order of the tube radius. The approximations are accurate to within 1% for all frequencies and tube diameters except within the transition zone where the approximations are accurate to within 10%. A simple modification of the transmission line parameters is presented for the case where the tube walls are nonisothermal.

Periodic and aperiodic dynamo waves

Abstract: In order to show that aperiodic magnetic cycles, with Maunder minima, can occur naturally in nonlinear hydromagnetic dynamos, we have investigated a simple nonlinear model of an oscillatory stellar dynamo. The parametrized mean field equations in plane geometry have a Hopf bifurcation when the dynamo number D=1, leading to Parker's dynamo waves. Including the nonlinear interaction between the magnetic field and the velocity shear results in a system of seven coupled nonlinear differential equations. For D>1 there is an exact nonlinear solution, corresponding to periodic dynamo waves. In the regime described by a fifth order system of equations this solution remains stable for all D and the velocity shear is progressively reduced by the Lorentz force. In a regime described by a sixth order system, the solution becomes unstable and successive transitions lead to chaotic behaviour. Oscillations are aperiodic and modulated to give episodes of reduced activity.

An introduction to wave propagation in anisotropic media

Abstract: Summary. Wave motion in an anisotropic solid is fundamentally different from motion in an isotropic solid, although the effects are often subtle and difficult to recognize. There are such a wide range of three-dimensional variations possible in anisotropic media that it is difficult to understand the behaviour of wave motion without experimentation. Laboratory experiments are very difficult to construct and extensive numerical experiments have now given many theoretical insights so that the behaviour of waves in anisotropic media is now comparatively well understood. This introduction summarizes some of the relationships and insights required for this understanding.

The nonlinear gyroresonance interaction between energetic electrons and coherent VLF waves propagating at an arbitrary angle with respect to the Earth's magnetic field

Abstract: A theory is presented of the nonlinear gyroresonance interaction that takes place in the magnetosphere between energetic electrons and coherent VLF waves propagating in the whistler mode at an arbitrary angle psi with respect to the earth's magnetic field B-sub-0. Particularly examined is the phase trapping (PT) mechanism believed to be responsible for the generation of VLF emissions. It is concluded that near the magnetic equatorial plane gradients of psi may play a very important part in the PT process for nonducted waves. Predictions of a higher threshold value for PT for nonducted waves generally agree with experimental data concerning VLF emission triggering by nonducted waves.

A numerical method for ocean‐acoustic normal modes

Abstract: The method of normal modes is frequently used to solve acoustic propagation problems in stratified oceans. The propagation numbers for the modes are the eigenvalues of the boundary value problem to determine the depth dependent normal modes. Errors in the numerical determination of these eigenvalues appear as phase shifts in the range dependence of the acoustic field. Such errors can severely degrade the accuracy of the normal mode representation, particularly at long ranges. In this paper we present a fast finite difference method to accurately determine these propagation numbers and the corresponding normal modes. It consists of a combination of well‐known numerical procedures such as Sturm sequences, the bisection method, Newton’s and Brent’s methods, Richardson extrapolation, and inverse iteration. We also introduce a modified Richardson extrapolation procedure that substantially increases the speed and accuracy of the computation.

Effects of the free surface on shear wavetrains

Abstract: Summary. The behaviour of shear-waves is of great importance in identifying and investigating seismic anisotropy in the Earth. However, shear wavetrains recorded at the Earth's surface do not always reflect the motion at depth, introducing practical problems of interpretation. Shear wavetrains incident on the surface of an isotropic half-space at angles less than critical (about 35°) are broadly preserved, but at greater angles substantial distortions can occur. For stations situated close to the source, as in local earthquake studies, the local SP phase, a radially polarized precursor to S, may occur. The behaviour at the surface of an anisotropic half-space is further complicated by the divergence of phase and energy propagation vectors. All of these complications suggest that detailed seismogram modelling is essential to any study of shear wave propagation in the Earth, and in particular to investigations of anisotropy-induced shear-wave splitting.

A radiation boundary condition for multi-dimensional flows

Abstract: A radiation boundary condition designed for use at open or computational boundaries with multidimensional flows is formulated and tested on three two-dimensional problems. Two of the problems simulate a simple wave propagation and possess analytic solutions so that the effectiveness of the boundary condition can be measured in terms of a r.m.s. error. A more subjective analysis must be used in the final problem, which is the simulation of an atmospheric cold front. The proposed radiation boundary condition utilizes the phase velocity projection in each coordinate direction or equivalently a weighted configuration of the phase velocities. This approach greatly reduces the sensitivity on the spatial derivative normally displayed in the phase velocity calculations. Comparisons are made against the traditionally used Sommerfeld radiation condition and various numerical schemes are tested. For multi-dimensional flows the proposed radiation boundary condition is found to give significant improvement over the traditional Sommerfeld radiation condition.