Showing papers on "Group velocity published in 1991"

Speed of propagation of classical waves in strongly scattering media.

Abstract: We present results of optical experiments which demonstrate that in a strongly scattering medium containing resonant scatterers the velocity for electromagnetic energy may differ by an order of magnitude from the phase velocity. We derive a microscopic theory that yields an expression for this velocity. Discrepancies are removed, and excellent agreement is found between experiment and theory.

Complete synthetic seismograms for high-frequency multimode SH -waves

Abstract: We present an efficient scheme to compute high-frequency seismograms (up to 10 Hz) for SH-waves in a horizontally stratified medium with the mode summation method. The formalism which permits the computation of eigenvalues, eigenfunctions and related integral quantities is discussed in detail. Anelasticity is included in the model by using the variational method. Phase velocity, group velocity, energy integral and attenuation spectra of a structure enable the computation of complete strong motion seismograms, which are the basic tool for the interpretation of near-source broad-band data.

Bloch Wave Analysis of Dispersion and Pulse Propagation in Pure Distributed Feedback Structures

Abstract: The excitation and behaviour of monochromatic and pulsed optical Bloch waves in pure distributed feed-back structures are discussed and analysed. The Bloch wave approach, based on a detailed knowledge of the natural optical modes of the periodic structure, is complementary to the more commonly used coupled-wave approach. The inter-relationship between dispersion, field micro-structure and group velocity is discussed, and the effects of group-velocity and higher-order dispersion on pulse propagation treated. Questions about the usefulness of DFB structures for dispersion correction and soliton formation are addressed.

Accuracy and Resolution of Surface Wave Inversion

Abstract: Shear wave velocity profiles of soils and pavements may be evaluated nondestructively using surface wave tests such as the Spectral Analysis of Surface Waves (SASW) method. In these tests, dispersion data are measured in situ and inverted using least squares techniques to obtain the shear wave velocity profile. This paper examines the influence of the number of dispersion points, the maximum wavelength, and the distribution of dispersion data with wavelength on the accuracy and resolution of the shear wave velocity profile. The results indicated that the best overall accuracy and resolution is obtained when the dispersion data is evenly distributed between the minimum and maximum wavelengths and the maximum wavelength is one to two times the maximum desired depth of the shear wave velocity profile. The number of points did not appear to significantly influence the inverted profile as long as the number of points remains greater than the number of layers in the inversion profile.

Propagation of Lg waves in the North Australian Craton: Influence of crustal velocity gradients

Abstract: Aftershocks of three large earthquakes near Tennant Creek in the Northern Territory of Australia provide a unique opportunity to study regional seismic phases in the North Australian Craton. Three portable digital seismographs were operated near the source zone to provide control on earthquake locations, and seven recorders formed a line between Tennant Creek and the seismic array at Alice Springs, which is 430 km to the south. Eleven earthquakes of sufficient size for analysis were recorded during a one week deployment two months following the main shocks. The group velocity observed for Lg waves along this profile of 3.7 km / sec is at the high end of the normal range and appropriate for a stable continental interior. We estimate attenuation in discrete frequency bands by measuring the decay of amplitude as a function of distance from the source and assuming the common r −5/6 relationship for geometrical spreading. However, this assumption leads to frequency dependent Q values: Q = (230 ± 36) f (0.66 ± 0.12) that are abnormally low for a stable continental region. The apparent Q is also not consistent with other observations, such as the high Lg group velocity, the positive bias in M L estimates obtained for other parts of Australia using standard attenuation relations, the size of felt areas for large central Australian earthquakes, nor with the high frequency content of seismic reflection data collected near our profile. Some crustal models for northern Australia derived from seismic refraction work show a gradient zone between 30 and 55 km rather than a sharp Moho discontinuity. We therefore investigate the effect of gradient zones at the crust-mantle transition on the decay of Lg amplitudes using synthetic seismograms calculated with the wavenumber integral method. The modeling suggests that some of the S -wave energy that would be trapped in a crustal wave guide with a sharp lower boundary can leak out in the presence of a gradient and so enhance the attenuation. In addition, there are focusing effects due to the formation of caustics from the gradient zones which cannot be represented by a single analytic amplitude correction.

Surface polaritons in cylindrical optical fibers

Abstract: The properties of the polariton modes associated with a resonance in the dielectric function of an optical fiber are derived. Particular attention is given to the surface polaritons, whose energy densities and power flows are concentrated close to the interface of the fiber core and its cladding. The results are illustrated with a range of dispersion curves for the two most important cases, when the fiber dielectric function has the reststrahl and plasma forms. General expressions are given and illustrated graphically for the power flow and the power density. It is shown numerically that the energy velocity, or group velocity, can have opposite sign to the phase velocity of the surface polariton.

Envelope Soliton as an Intrinsic Localized Mode in a One-Dimensional Nonlinear Lattice

Abstract: An envelope soliton in a nonlinear lattice has been studied theoretically and numerically. First, the nonlinear Schrodinger equation describing a lattice wave with large wave number is derived and then the equation of motion for the nonlinear lattice is solved numerically taking the one envelope soliton solution of the nonlinear Schrodinger equation as an initial wave. It is shown that the envelope soliton with zero group velocity exists stably in the lattice and that the frequency of carrier wave is above the cut-off frequency of the lattice. An intrinsic localized mode in the nonlinear lattice developed by Takeno is pointed out to be the envelope soliton with zero group velocity.

Two-station measurements of Rayleigh wave group velocity along the Hawai'ian Swell

Abstract: Two-station measurements of Rayleigh wave group velocity between Midway Atoll and O'ahu provide a useful constraint on lithospheric thickness along the Hawai'ian Swell. Comparison of the observed dispersion curve with age-dependent, regionalized dispersion curves suggests that the swell acts as 50–110 m.y. old lithosphere, and not as 20–50 m.y. old lithosphere as is predicted by the currently favored hypothesis for the swell's formation. A preliminary isotropic shear velocity model for the swell suggests that the lithosphere may be as thick as 100 km. This value is difficult to reconcile with the lithosphere being substantially thinned during its passage over the Hawai'ian hotspot.

Experimental investigation of velocity coupling in combustion instability

Abstract: An investigation has been conducted of the velocity coupling phenomenon reported in acoustically unstable solid-propellant rocket motors. An innovative simulation facility has been built using solid carbon dioxide as the simulated propellant. Acoustic disturbances are introduced over the dry-ice surface by means of a mechanically driven piston. Experiments have been conducted with dry ice located near both a velocity antinode and a velocity node. Mass flow rate and acoustic pressure measurements indicate the existence of a coupling mechanism, strongly dependent on the acoustic velocity amplitude, between the acoustic disturbance and the dry-ice sublimation process. Flow visualization and hot-film anemometry both show that the flow is turbulent near resonance. Transition to turbulence near a velocity node appears to occur at a smaller critical acoustic velocity amplitude than that near a velocity antinode. Some preturbulent instability has also been observed. Acoustically induced, turbulent forced convection is believed to be responsible for the increase in the sublimation rate of the dry ice (simulated burning of the propellant). Turbulence is believed to be one of the principal mechanisms in the velocity coupling phenomenon. An empirical correlation was developed which appeared to apply to the real propellant cases.

Selective excitation of single‐mode acoustic waves by phase velocity scanning of a laser beam

Abstract: A novel method for selective generation of single‐mode acoustic waves in multimode media has been developed using a laser beam scanned at the phase velocity of a specified mode. In dispersive media, the acoustic frequency can be varied by changing the scanning velocity. The number of carriers in the generated wave packet is proportional to the difference between the phase and the group velocities. These features were experimentally verified in the fundamental symmetric and asymmetric Lamb waves on an aluminum plate generated by a long‐pulse Nd:YAG laser. Applications to anisotropy and thickness measurements are discussed.

Three-dimensional crust and upper mantle structure of the north china region

Abstract: The data of long period Rayleigh surface wave have been processed in the present study by the "Display-Equalized Filter Frequency-Time Analysis" technique The dispersion of the group velocity of surface waves have been obtained from 238 mixed-pathes travelling through China's continent and its surrounded area with the periods range from 105s till 113s Accordingly, the pure-path dispersions for 12 cells of 4°×4° in North China have been extracted by using the modified "grid-dispersion inversion" method from the mixed-path dispersion measurements, and an inversion has thus been made of the crust and upper mantle The results obtained show a noticeable leteral change in- the structure of crust and upper-mantle in North China The crust has been thickened gradually from the east to the west In the cells on the eastern North China there are low velocity layers existing generally at the depth of 20 km in the crust The low velocity layers in the upper-mantle of the whole North China area are relatively shallowly buried: generally at the depths from 55 km to 100 km The velocity of a low velocity layer somewhat differs for different cells

Adiabatic amplification of optical solitons.

Abstract: We study the adiabatic evolution of the fundamental nonlinear Schr\"odinger soliton under a general integro-differential perturbation. This perturbation is shown to model a saturable bandwidth-limited amplification of an optical soliton with a nonresonant carrier wave. We use the soliton perturbation theory to calculate the evolution of the amplitude, frequency, group velocity, and phase of the pulse. The perturbative analytical steady-state solution is obtained and its stability is studied using the phase-plane formalism.

On the Velocity Fields of Elliptical Galaxies

Abstract: A family of self-consistent maximum entropy dynamical models is presented for the triaxial 'perfect ellipsoids'. These models are projected in different viewing geometries to explore the possible morphologies of the 2D radial-velocity fields of elliptical galaxies. It is found that, typically, about half the time an 'ordinary' velocity field is seen with a mixture of major- and minor-axis rotation. For other lines of sight, the velocity fields are more complicated, showing multiple peaks, steep gradients, strongly twisted contours, or kinematically distinct or counter-rotating cores. The origin of each of these velocity field morphologies is explained in terms of competing contributions from the major families of tube orbits.

Characteristic Wave Surfaces in Anisotropic Laminated Plates

Abstract: A numerical method is used to determine the dispersion relation (an eigenvalue equation) of plane wave propagation in an anisotropic laminated plate. A phase velocity surface, phase slowness surface, phase wave surface, group velocity surface, group slowness surface, and group wave surface are defined and their formulae are deduced from the Rayleigh quotient and the orthogonality condition of the eigenvectors of the eigenvalue equation. The six characteristic surfaces can be used to illustrate the characteristics of plane waves and waves generated from a point source in an anisotropic laminated plate. As numerical examples, the characteristic surfaces are computed for graphite/epoxy angle ply laminated plates and for a hybrid one. The results for the graphite/epoxy laminated plates are compared with those obtained by Moon’s approximate theory.

Localized traveling-wave convection in binary-fluid mixtures.

Abstract: The structure and dynamics of both subcritical and supercritical localized traveling-wave (LTW) convective states with different extensions and uniquely selected width are determined by numerical integration of the proper hydrodynamic field-equations with realistic horizontal boundary conditions. A large-scale mean concentration current loop influences the LTW significantly. It generates a concentration distribution that hinders propagation of the LTW pulse, so that the group velocity is small but finite

Solution of Three-Constraint Entropy-Based Velocity Distribution

Abstract: A two-dimensional velocity profile based upon the principle of maximum entropy (POME) for wide open channel flows is presented. The derivation is based on the conservation of mass and momentum. The resulting profile involves three parameters that are determined from observations of mean velocity and the velocity at the water surface. The velocity profile is verified using field data in a river with a live bed. A comparison with three existing methods shows that the profile presented is the most accurate of the three, especially near the bed.

Symbiotic optical solitons and modulational instability

Abstract: The interaction due to cross phase modulation of dark and bright solitons propagating in optical fibers is studied analytically, within the frame work of a variational approach as well as numerically. It is demonstrated that the interaction of a bright soliton in the anomalous dispersion regime with a dark soliton in the normal dispersion regime is described by a repulsive effective potential. In the reverse case when a bright soliton in the normal dispersion regime intracts with a dark soliton in the anomalous dispersion regime, the dark and bright solitons may form a symbiotic soliton, which is stable with respect to small mismatches in group velocity and initial relative position of the separate solitons. The influence of the symbiotic soliton on the modulational instability of the carrier c.w. background is also analysed. Analytical results are in good agreement with numerical simulations.

Limits to wideband pulsed squeezing in a traveling-wave parametric amplifier with group-velocity dispersion.

Abstract: A theoretical method is developed to treat wideband pulsed squeezing in a traveling-wave parametric amplifier with group-velocity dispersion. Classical stochastic wave equations that are fully equivalent to operator equations of motion are developed and solved numerically. It is found that squeezing occurs over the entire phase-matching bandwidth, although the degree of squeezing decreases when the pump-pulse duration is shorter than the inverse of this bandwidth.

Effects of anisotropy upon the normal modes in a borehole

Abstract: Elastic anisotropy affects the modes generated during acoustic logging. To study these effects, the wave equation was solved using a variational method for a model consisting of a fluid-filled borehole through a solid whose anisotropy is defined in the Cartesian coordinate system. The solution for each normal mode includes its phase velocity, group velocity, pressures in the fluid, and displacements in the solid. The most significant findings are: (1) two quasiflexural waves exist and have different phase and group velocities; (2) for the slow quasiflexural wave, the particle displacements in the plane perpendicular to the borehole, when viewed together, are aligned with the polarization of the slow, planar qS wave whose wave-number vector is parallel to the borehole; and (3) for the fast quasiflexural wave, the particle displacements in the plane perpendicular to the borehole, when viewed together, are aligned with the polarization of the fast, planar qS wave whose wave-number vector is parallel to the b...

Convection velocity in supersonic turbulent boundary layers

Abstract: The convection velocity of large‐scale organized motions was measured in a Mach 3 boundary layer using streamwise‐separated hot wires. The broadband convection velocity, determined from space‐time correlations, is 0.9U∞ across the entire outer region of the boundary layer. The convection velocity of individual structures was deduced using a pattern recognition technique, and this revealed that the majority of the large‐scale structures convect at nearly the same velocity. A comparison of the present results to previous measurements indicates negligible Reynolds number and Mach number effects on convection velocity.

Billiard-ball soliton interaction gates.

Abstract: We demonstrate a cascadable, Boolean complete, conservative-logic interaction gate that is based on elastic collisions between temporal solitons in optical fibers. The two identical-frequency and polarization inputs are initially separated by 4.5 pulse widths, and they interact in a 7.5 walk-off length of polarization-maintaining fiber. The group velocity of one of the inputs is altered by passing the pulse through a beam splitter with a wavelength-dependent reflection coefficient. Although details within the interaction region depend on the phase between the two inputs, after the pulses separate the result is phase independent. We find that each of two 17-pJ solitons is displaced after interaction by 3.5 pulse widths so as to increase the pulses' separation.

On acoustic transmission in ocean-surface waveguides

Abstract: A sound speed profile which increases monotonically with depth below the ocean surface is upward-refractive, acting as a duct in which sound may be transmitted to long ranges with little attenuation A well-known example is the mixed layer, in which the temperature is uniform and the sound speed approximately scales with the hydrostatic pressure, increasing linearly with depth The depth of the mixed layer depends on surface conditions, but is of the order of 100 m Deeper channels are found in ice-covered polar waters, where the temperature and sound speed profiles both show a minimum at the surface A typical surface duct in the Arctic Ocean may extend to depths of 1000 m or more and is capable of supporting very-low-frequency (VLF) (1-50 Hz) acoustic transmissions with no bottom interactions On a depth scale that is smaller by several orders of magnitude, wave-breaking events create a bubbly layer one or two metres thick below the sea surface, with the highest concentration of bubbles, and correspondingly the lowest sound speed, at the surface The bubble layer acts as a waveguide for sound in the audio frequency range, above 2 kHz, although transmission may be severely attenuated due to absorption and scattering by the bubbles, as well as by the irregular geometry of the sea surface and the bubble clouds Most ocean-surface waveguides can be accurately represented by an inverse-square sound speed profile, which may be monotonic increasing (upward refracting) or decreasing (downward refracting) with depth, and whose detailed shape is governed by just three parameters An analysis of the sound field below the sea surface in the presence of such a profile shows that it consists of a near-field component, given by a branch-line integral, plus a sum of uncoupled normal modes representing the trapped radiation which propagates to longer ranges The modal contribution is identically zero in the case of the downward refracting profiles The properties of the modes emerge from a straightforward theoretical development involving first- and second-order asymptotics: each mode shows an oscillatory region immediately below the surface, terminating at the extinction depth, below which the mode decays exponentially to zero; the extinction depth increases rapidly with both mode number and the reciprocal of the acoustic frequency; a reciprocal relationship exists between the extinction depth and the mode strength; and there is no mode cutoff, nor are there any evanescent modes On applying the inverse-square theory to VLF Arctic Ocean transmissions, the spectral density of the modal field is found to show a steep positive gradient between 5 and 50 Hz, the rising level occurring as more modes make a significant contribution to the field This result is compared with observations of infra-sonic ambient noise that have been made in the marginal ice zone of the Greenland Sea, using surface suspended, flow-shielded hydrophones The measured spectra show a deep minimum at about 5 Hz, in accord with the theoretical prediction The inverse-square theory also has application to under-ice ocean-acoustic tomography, where the dispersive nature of the upward refractive channel governs the arrival times of the modes at the receivers A simple expression for the group velocity of the modes gives the arrival times More generally, the full modal structure of the field across the tomography array may be constructed from the theory Acoustic signatures of wave-breaking events have recently been observed in the ocean-suiface bubble layer by farmer & Vagle (1989) The spectra show well-defined peaks (La Perouse) or a broader-band structure (FASINEX), both of which are fully explained, in terms of intermode interference, by the inverse-square theory The differences between the two data-sets are attributed to the different sound speed profiles in the bubble layers at the two sites The spectral banding in fasinex is a modulation phenomenon, showing a strong dependence on the source depth A straightforward inverse calculation indicates that the bubble sources in fasinex are located at a depth of 15 m, corresponding roughly to the base of the bubble layer, this is a slightly unexpected conclusion, since acoustically active bubbles generated by spilling breakers under wind-free conditions in a laboratory tank are known to be located within a few millimetres of the surface However, aeration is much more pronounced at the wind-driven surface of the ocean than in a tank, which may be a factor in accounting for the deeper sources There are practical difficulties in measuring the source distribution using conventional techniques, but the inverse-square transmission theory in conjunction with near-surface measurements of wave-breaking signatures provides an effective means of making such a determination

An exact solution of solute transport by one-dimensional random velocity fields

Abstract: The problem of one-dimensional transport of passive solute by a random steady velocity field is investigated. This problem is representative of solute movement in porous media, for example, in vertical flow through a horizontally stratified formation of variable porosity with a constant flux at the soil surface. Relating moments of particle travel time and displacement, exact expressions for the advection and dispersion coefficients in the Focker-Planck equation are compared with the perturbation results for large distances. The first- and second-order approximations for the dispersion coefficient are robust for a lognormal velocity field. The mean Lagrangian velocity is the harmonic mean of the Eulerian velocity for large distances. This is an artifact of one-dimensional flow where the continuity equation provides for a divergence free fluid flux, rather than a divergence free fluid velocity.

Anisotropy From Polarization And Moveout

Abstract: Seismic waves propagate in an inhomogeneous and anisotropic earth. It is extremely difficult to separate the effects of inhomogeneity and anisotropy globally. However, plane wave polarization is a. local propert,y of the wave field in an anisotropic medium and ma.y be used to evaluate the elastic moduli of a compact, relatively homogeneous but anisotropic region of the subsurface. This region could be a reservoir intersected by a borehole with a clamped array of closely spaced three-component geophones. An estimate of the anisotropic elastic parameters can help in lithology identification, fracture characterization and, perhaps most importa.ntly, in giving a propagation model that can be used as a “best” anisotropic background model for use in migration and inversion of long offset vertical seismic profile (VSP) and surface seismic data in a wide region around the well. Decomposition of a wave field, at least partially, into a set of plane wave arrivals, including possible downgoing and upgoing, quasishear a.nd quasicompressional, direct and converted plane waves, is greatly facilitated by considering the full vector wave field (Esmersoy, 1990). Each time the surface source is moved to a different location, a different wave field is excited from which different plane waves may be extracted, although the general method in no way requires the sources to be located on the surface. Each plane wave is of the form Ae,f(s . x t), where A is the amplitude, e, the eigenvector of the Christoffel equations specifying the particle motion, or polarization, of the wave, f the wave shape, and s = s e, the slowness vector. Given e, and the local elastic stiffness moduli (normalized by the density so they are of dimension velocity’), one may readily calculate S, e, and the group velocity. In the decomposition, the polarization vectors and the apparent phase slownesses along the borehole, s, E s e,.e, for all the isolated plane waves (with e, the unit vector in the z direction pointing downward along the borehole) are found. These, then, are the data used in the inversion to

Turbulent acceleration of auroral electrons

Abstract: It is shown that the characteristic peak in the auroral electron velocity distribution can be generated stochastically through resonant interactions with lower hybrid electrostatic turbulence. The peak itself is shown to be a direct consequence of restrictions imposed on reflection of electron velocities in the frame of reference of individual wave packets by the limitation in group velocity. A Monte-Carlo model demonstrates how the various properties of the acceleration region are reflected in the resultant electron distribution. It is shown, in particular, that the width of the peak is governed by the amplitude of the turbulence, while the amplitude of the peak reflects the column density of wave energy. Electron distributions encountered within three auroral arcs are interpreted to yield order of magnitude estimates of the amplitude and rms electric field of lower hybrid wave packets. The velocities and frequencies of the resonant waves, the net electric field, the column density of wave energy, and the electric-field energy density are also estimated. The results are found to be consistent with available electric-field measurements. A general broadening of the electron distribution caused by less systematic interactions between electrons and wave packets is shown to have a negligible effect on the peak resulting from the reflection process; it does, though, lead to the creation of a characteristic high-energy tail.