Showing papers on "Phase velocity published in 1998"

Eurasian surface wave tomography: Group velocities

Abstract: This paper presents the results of a study of the dispersion characteristics of broadband fundamental surface waves propagating across Eurasia. The study is broader band, displays denser and more uniform data coverage, and demonstrates higher resolution than previous studies of Eurasia performed on this scale. In addition, the estimated group velocity maps reveal the signatures of geological and tectonic features never before displayed in similar surface wave studies. We present group velocity maps from 20 s to 200 s period for Rayleigh waves and from 20 s to 125 s for Love waves. Broadband waveform data from about 600 events from 1988 through 1995 recorded at 83 individual stations across Eurasia have produced about 9000 paths for which individual dispersion curves have been estimated. Dispersion curves from similar paths are clustered to reduce redundancy, to identify outliers for rejection, and to assign uncertainty estimates. On average, measurement uncertainty is about 0.030–0.040 km/s and is not a strong function of frequency. Resolution is estimated from “checker-board” tests, and we show that average resolutions across Eurasia range from 5° to 7.5° but degrade at periods above about 100 s and near the periphery of the maps. The estimated maps produce a variance reduction relative to the Preliminary Reference Earth Model (PREM) of more than 90% for Rayleigh waves below 60 s period but reduce to about 70% between 80 and 200 s period. For Love waves, variance reductions are similar, being above 90% for most periods below 100 s and falling to 70% at 150 s. Synthetic experiments are presented to estimate the biases that theoretical approximations should impart to the group velocity maps, in particular source group time shifts, azimuthal anisotropy, and systematic event mislocations near subducting slabs. The most significant problems are probably caused by azimuthal anisotropy, but above 100 s the effect of source group time shifts may also be appreciable. These effects are probably below the signal levels that we interpret here, however. Many known geological and tectonic structures are observed in the group velocity maps. Of particular note are the signatures of sedimentary basins, continental flood basalts, variations in crustal thickness, backarc spreading, downgoing slabs, and continental roots. Comparison of the estimated group velocity maps with those predicted by CRUST5.1/S16B30 is qualitatively good, but there are significant differences in detail which provide new information that should help to calibrate future crustal and upper mantle models of Eurasia.

Particle injection into the wave acceleration phase due to nonlinear wake wave breaking

Abstract: We present analytical results and computer simulations of the nonlinear evolution of wake field waves in inhomogeneous plasmas. The wake wave break that occurs due to the inhomogeneity of the Langmuir frequency makes it possible to inject electrons into the acceleration phase of the wave. Particle-in-cell simulations show that stable beams of energetic electrons are formed. These beams are well bunched in coordinate and velocity space and contain a considerable fraction of the pulse energy

Low frequency modes in strongly coupled dusty plasmas

Abstract: The influence of strong correlations on low frequency collective modes in a dusty plasma is investigated. The dust dynamics is modeled by the generalized hydrodynamics description. For the well known dust acoustic mode, strong correlations lead to new dispersive corrections, an overall reduction of the frequency and phase velocity and the existence of parameter regions where ∂ω/∂k<0. A novel result is the possibility of sustaining a low frequency transverse mode—a dust shear mode—in which the correlation energy acts as an effective bulk modulus. The influence of ion streaming and collisional interaction with a background of neutrals on the modes are also studied and it is shown that the longitudinal modes may be driven unstable by ion streaming.

On stability of streamwise streaks and transition thresholds in plane channel flows

Abstract: Streak breakdown caused by a spanwise inflectional instability is one phase of the following transition scenarios, which occur in plane Poiseuille and Couette flow. The streamwise vortex scenario is described byformula hereThe oblique wave scenario is described byformula hereThe purpose of this paper is to investigate the streak breakdown phase of the above scenarios by a linear stability analysis and compare threshold energies for transition for the above scenarios with those for transition initiated by Tollmien-Schlichting waves (TS), two-dimensional optimals (2DOPT), and random noise (N) at subcritical Reynolds numbers.We find that if instability occurs, it is confined to disturbances with streamwise wavenumbers α0 satisfying 0<αmin< [mid ]α0[mid ]<αmax. In these unstable cases, the least stable mode is located near the centre of the channel with a phase velocity approximately equal to the centreline velocity of the mean flow. Growth rates for instability increase with streak amplitude. For Couette flow streak breakdown is inhibited by mean shear. Using the linear stability analysis, we determine lower bounds on threshold amplitude for transition for scenario (SV) that are consistent with thresholds determined by direct numerical simulations.In the final part of the paper we show that the threshold energies for transition in Poiseuille flow at subcritical Reynolds numbers for scenarios (SV) and (OW) are two orders of magnitude lower than the threshold for transition initiated by Tollmien–Schlichting waves (TS) and an order of magnitude lower than that for (2DOPT). Scenarios (SV) and (OW) occur on a viscous time scale. However, even when transition times are taken into account, the threshold energy required for transition at a given time for (SV) and (OW) is lower than that for the (TS) and (2DOPT) scenarios at Reynolds number 1500.

Simultaneous Inversion of Rayleigh Phase Velocity and Attenuation for Near-Surface Site Characterization

Abstract: Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Georgia Institute of Technology Simultaneous Inversion of Rayleigh Phase Velocity and Attenuation for Near-Surface Site

Electromechanical wave propagation in large electric power systems

Abstract: An electrical power network consisting of generators and transmission lines is treated as a continuum system. The application of the limit of zero generator spacing, with finite rotor inertia and transmission line impedance per unit length, yields a nonlinear partial differential equation in time and two spatial dimensions for the rotor phase angle. The equation is a nonlinear version of the standard second-order wave equation which exhibits an explicit expression for the finite wave phase velocity. The electromechanical wave propagation characteristics, equilibrium solutions, and linear stability are investigated and some potentially important results are presented. Numerical simulations of the usual discrete generator model, based upon the swing equation, are presented and demonstrate the electromechanical wave propagation as having interesting properties. Numerical solutions of the analogous continuum model are compared to the discrete model and are found to be in excellent agreement. A numerical estimate of the wave phase velocity for the U.S. power grid is consistent with observations of the transient wave phenomena during staged fault events. The continuum model enables an array of alternative analytic and simulation methods to be applied to the study of global power system characteristics, such as stability and transient dynamics.

Electromechanical wave propagation in large electric power systems

Abstract: An electrical power network consisting of generators and transmission lines is treated as a continuum system. The application of the limit of zero generator spacing, with finite rotor inertia and transmission line impedance per unit length, yields a nonlinear partial differential equation in time and two spatial dimensions for the rotor phase angle. The equation is a nonlinear version of the standard second-order wave equation which exhibits an explicit expression for the finite wave phase velocity. The electromechanical wave propagation characteristics, equilibrium solutions, and linear stability are investigated and some potentially important results are presented. Numerical simulations of the usual discrete generator model, based upon the swing equation, are presented and demonstrate the electromechanical wave propagation as having interesting properties. Numerical solutions of the analogous continuum model are compared to the discrete model and are found to be in excellent agreement. A numerical estimate of the wave phase velocity for the U.S. power grid is consistent with observations of the transient wave phenomena during staged fault events. The continuum model enables an array of alternative analytic and simulation methods to be applied to the study of global power system characteristics, such as stability and transient dynamics.

Experimental study of interfacial solitary waves

Abstract: A small-scale experiment was conducted (in a 3 m long flume) to study interfacial long-waves in a two-immiscible-fluid system (water and petrol were used). Experiments and nonlinear theories are compared in terms of wave profiles, phase velocity and mainly frequency--amplitude relationships. As expected, the KdV solitary waves match the experiments for small-amplitude waves for all layer thickness ratios. The characteristics of 'large'-amplitude waves (that is when the crest is close to the critical level - approximately located at mid-depth) asymptotically tend to be predicted by a 'KdV-mKdV' equation containing both quadratic and cubic nonlinear terms. In addition a numerical solution of the complete Euler equations, based on Fourier series expansions, is devised to describe solitary waves of intermediate amplitude. In all cases, solitary interfacial waves in this numerical theory tally with the experimental data. When the layer thicknesses are almost equal (ratio of lower layer to total depth equal to 0.4 or 0.63) both the KdV-mKdV and the numerical solutions match the experimental points.

Velocity dispersion of acoustic waves in cancellous bone

Abstract: Measurement of ultrasonic attenuation and velocity in cancellous bone are being applied to aid diagnosis of women with high fracture risk due to osteoporosis. However, velocity dispersion in cancellous bone has received little attention up to now. The overall goal of this research was to characterize the velocity dispersion of human cancellous bone based on a spectral analysis of ultrasound transmitted through the bone specimens. We have followed a systematic approach, beginning with the investigation of a test material, moving on to the investigation of bone specimens. Particular attention is given to diffraction effect, a potential source of artifacts. Parametric images of phase velocity (measured at the center frequency of the pulse spectrum), slope of attenuation coefficient (dB/cm/MHz) and velocity dispersion were obtained by scanning 15 bone specimens. We have demonstrated that the diffraction effect is negligible in the useful frequency bandwidth, and that the ultrasonic parameters reflect intrinsic acoustic properties of bone tissue. The measured attenuation showed approximately linear behavior over the frequency range 200 to 600 kHz. Velocity dispersion of cancellous bone in the frequency range 200 to 600 kHz was unexpectedly found to be either negative or positive and not correlated with the slope of attenuation coefficient. There was a highly significant correlation between the slope of attenuation coefficient and phase velocity at the center frequency of the spectrum. This behavior contrasts with other biological or nonbiological materials where the local form of the Kramers-Kronig relationship provides accurate prediction of velocity dispersion from the experimental frequency dependent-attenuation for unbounded waves.

Velocity, acceleration and vorticity under a breaking wave

Abstract: The fluid particle velocities in the overturning jet of a breaking wave have been measured by the Particle Image Velocimetry (PIV) technique. Monochromatic waves with wave height of 14.5 cm and wavelength of 121 cm were generated in the water depth of 20 cm. The measured fluid particle velocity at the tip of the overturning jet reached 1.68 times of the phase velocity calculated from the linear wave theory. Fluid particle accelerations were estimated from the velocity data with the following results: The overturning jet enters the horizontal water surface with an acceleration of 1.1 g at an angle of 88° downward. The PIV technique was also used to measure the instantaneous vertical vorticities generated by breaking waves. The number and locations of the vortices on the horizontal plane appear to be random. The maximum instantaneous vorticity was in the order of magnitude of 20–30 s−1, whereas the ensemble-averaged vorticity was quite small.

Polarization, phase velocity, and NMO velocity of qP-waves in arbitrary weakly anisotropic media

Abstract: We present approximate formulas for the qP-wave phase velocity, polarization vector, and normal moveout velocity in an arbitrary weakly anisotropic medium obtained with first-order perturbation theory. All these quantities are expressed in terms of weak anisotropy (WA) parameters, which represent a natural generalization of parameters introduced by Thomsen. The formulas presented and the WA parameters have properties of Thomsen's formulas and parameters: (1) the approximate equations are considerably simpler than exact equations for qP waves, (2) the WA parameters are nondimensional quantities, and (3) in isotropic media, the WA parameters are zero and the corresponding equations reduce to equations for isotropic media. In contrast to Thomsen's parameters, the WA parameters are related linearly to the density normalized elastic parameters. For the transversely isotropic media with vertical axis of symmetry, the equations presented and the WA parameters reduce to the equations and linearized parameters of Thomsen. The accuracy of the formulas presented is tested on two examples of anisotropic media with relatively strong anisotropy: on a transversely isotropic medium with the horizontal axis of symmetry and on a medium with triclinic anisotropy. Although anisotropy is rather strong, the approximate formulas presented yield satisfactory results.

Evolution and persistence of 5-μm hot spots at the Galileo probe entry latitude

Abstract: We present a study on the longitudinal locations, morphology, and evolution of the 5-μm hot spots at 6.5°N latitude (planetocentric) from an extensive Infrared Telescope Facility-National Science Foundation Camera (IRTF-NSFCAM) data set spanning more than 3 years, which includes the date of the Galileo probe entry. A probabilistic analysis of the data shows that within periods of several months to even more than a year, there are eight or nine longitudinal areas with high likelihood of containing a 5-μm hot spot. These areas drift together with respect to System III at a rate which changes only slowly in time, and they are quasi evenly spaced, suggesting a wave feature. A spectral analysis of the radiance data reveals that planetary wavenumbers 8, 9, and 10 are predominant in the data, 10 having more spectral power in several time periods when the speed was 103.5–102.5 m/s, while planetary wavenumber 8 has much more power when the speed is (99.5±0.5) m/s. By using the Galileo probe zonal wind speed [Atkinson et al., 1997] at the level of the main cloud that is opaque to the radiation at 5 μm (∼2 bar), our drift corrections imply a westward phase speed for the proposed wave. The wavenumbers and phase speeds are found to be consistent with an equatorial Rossby wave, and the dispersive properties of this wave can account for the observed simultaneous changes in the dominant wavenumber and drift speed. We take advantage of this interpretation to infer properties of the vertical structure at 6.5°N.

Terminal damping of a solitary wave due to radiation in rotational systems

Abstract: The evolution of a solitary wave under the action of rotation is considered within the framework of the rotation-modified Korteweg–de Vries equation. Using an asymptotic procedure, the solitary wave is shown to be damped due to radiation of a dispersive wave train propagating with the same phase velocity as the solitary wave. Such a synchronism is possible because of the presence of rotational dispersion. The law of damping is found to be “terminal” in the sense that the solitary wave disappears in a finite time. The radiated wave amplitude and the structure of the radiated “tail” in space–time are also found. Some numerical results, which confirm the approximate theory developed here, are given.

Bubble counting using an inverse acoustic scattering method

Abstract: A nuclei size measurement technique is developed, based on a dispersion relation for propagation of sound waves through a bubbly liquid. This is used to relate the attenuation and phase velocity of a sound wave to the bubble population, leading to two integral equations. These equations are ill posed, and require special treatment for solution. Algorithms based on a minimization method that imposes a number of physical constraints on the solution, rendering the equation well posed, are developed. The procedure is first tested on analytical data with varying artificial noise added, and found to be successful in recovering the bubble density function, and to perform much better than other published solution techniques. Then, bubbles were generated using electrolysis and air injection through porous tubes, and bubble populations measured. Short monochromatic bursts of sound at different frequencies were emitted and received using hydrophones. The received signals were then processed and analyzed to obtain the attenuation and phase velocity. The void fraction and known experimental errors were also obtained and were fed as constraints to the inverse problem solution procedure. This resulted in bubble populations which compare favorably to those obtained by microphotography.

Inversion of composite material elastic constants from ultrasonic bulk wave phase velocity data using genetic algorithms

Abstract: In this paper, efforts on the reconstruction of material stiffness properties of unidirectional fiber-reinforced composites from obliquely incident ultrasonic bulk wave data, employing an inverse technique based on genetic algorithms, is described. Computer-generated ultrasonic phase velocity data, as a function of the angle of refraction in both symmetry and nonsymmetry through the thickness planes of unidirectional composites were used as the input to the genetic algorithm. A simple genetic algorithm, with optimal parameters chosen from the literature and numerical analysis (reported here), was implemented for the reconstruction. The inversion using this novel technique was found to be extremely promising in the characterization of the material stiffness properties. Stability to noise in the input phase velocity data set was also investigated. Advantages and disadvantages of the genetic reconstruction technique over conventional methods are also discussed.

Incoherent scatter radar observations of AGW/TID events generated by the moving solar terminator

Abstract: . Observations of traveling ionospheric disturbances (TIDs) associated with atmospheric gravity waves (AGWs) generated by the moving solar terminator have been made with the Millstone Hill incoherent scatter radar. Three experiments near 1995 fall equinox measured the AGW/TID velocity and direction of motion. Spectral and cross-correlation analysis of the ionospheric density observations indicates that ST-generated AGWs/TIDs were observed during each experiment, with the more-pronounced effect occurring at sunrise. The strongest oscillations in the ionospheric parameters have periods of 1.5 to 2 hours. The group and phase velocities have been determined and show that the disturbances propagate in the horizontal plane perpendicular to the terminator with the group velocity of 300-400 m s-1 that corresponds to the ST speed at ionospheric heights. The high horizontal group velocity seems to contradict the accepted theory of AGW/TID propagation and indicates a need for additional investigation. Key words. Ionosphere (wave propagation) · Meteorology and atmospheric dynamics (waves and tides)

Phase velocity structure from Rayleigh and Love waves in Tibet and its neighboring regions

Abstract: Deep geodynamic processes involved in the continental collision between India and Asia are still controversial. To address this issue, phase velocities of 619 Rayleigh waves and 254 Love waves have been inverted by using an anisotropic tomographic technique. Such a technique enables us not only to retrieve phase velocity distributions but also to map azimuthal anisotropy on a large scale. Only phase velocity anomalies, in the period range 50–200 s, are dealt with here, but the azimuthal anisotropy has been taken into account in the inversion process. Moreover, because of the important influence of shallow layers on the inversion results, an inversion of phase velocities corrected for shallow layers has been performed. To correct raw phase velocities, the 3SMAC crust (heterogeneous reference Earth model) has been used. The comparison of phase velocity distributions for Love and Rayleigh waves with and without corrections of surficial layers implies that much of the low-velocity zone, visible at short periods, in central Tibet, can be explained by unusually thick crust. At periods longer than 100 s, Tibet is, overall, characterized by high-velocity anomalies. Such anomalies seem to converge toward the center of the plateau as period increases. We conclude that the phase velocity structure beneath Tibet results, at short periods, from thick crust and possible partial melting in the uppermost lithosphere and, at long periods, from the inward plunge of the cold lithospheric mantle surrounding the high plateau.

Eurasian fundamental mode surface wave phase velocities and their relationship with tectonic structures

Abstract: We automatically analyzed 32,000 fundamental mode Love and Rayleigh wave signals with earthquake-station paths traversing Eurasia and Indonesia and obtained robust average phase velocity measurements between 20 s and 170 s periods along 4389 Love and 4020 Rayleigh paths. These were inverted to give phase velocity maps at 14 fixed periods. Resolution tests suggest that features with diameter >750 km and >500 km are resolved over most of Eurasia and central/SE Asia respectively. Low-period Love waves image areas with thick sedimentary cover as low-velocity zones, and almost all periods image mountainous regions since these have thick crust and hence low average lithospheric shear velocity. At long periods, both Love and Rayleigh waves define high phase velocity zones across shield and cratonic areas reflecting their deep lithospheric roots. We observe significant along-strike heterogeneity in the Zagros fold belt and Tien Shan-Altai system. Taking sections across Eurasian phase velocity space allows us to make approximate interpretations in terms of shear velocity structure directly. For example, the Red River and East Vietnam Boundary faults are traced on their eastern side by low velocities which extend at depth into Indonesia. We relate this to mantle upwelling associated with early Eocene rotation of Indochina and reversal of the sense of shear across the Red River fault post-20 Ma. We observe dipping subduction of the Mediterranean beneath the Aegean, of the Philippine Sea beneath Indonesia, and of the Indian shield beneath Tibet. We also image a fossil subducted plate beneath NE Borneo which we associate with subduction of the proto-South China Sea between 50 Ma and 15 Ma.

Accurate analysis of helix slow-wave structures

Abstract: In this paper, the helix slow wave structure (SWS) of traveling wave tubes (TWT's) has been analyzed. Dielectric supporting rods of arbitrary cross section have been considered in this analysis. The inhomogeneous dielectric loading factor has been accounted for by modeling the discrete support with a number of continuous dielectric tubes of appropriate effective dielectric permittivity. The helix tape model has been used for the field analysis. Furthermore the thickness of the helix tape has been considered. A rigorous solution of the field equations, including the contribution of the space harmonics, was performed to evaluate the phase velocity and the interaction impedance up to millimeter-wave frequencies. The nonuniformity of radial propagation constant over the structure cross section has been also included. With respect to other approaches, a closed-form expression of the field constants has been obtained. A study to choose the optimum number of space harmonics and dielectric tubes to be used in the analysis, has shown how the results are more sensitive to the number of space harmonics than to the number of dielectric tubes, beyond a certain number of the latter. The validity of this theory has been proved by comparison between measurements and simulations for helix SWS with different dimensions, rod shapes and operating frequency band.

Ground Roll As a Tool to Image Near-surface Anomaly

Abstract: On an uncorrelated field record obtained using a monotonic sweep, ground roll is displayed in increasing or decreasing order of frequency with each frequency well separated from all others Phase velocity and attenuation characteristics of each frequency contain the average elastic property of nearsurface materials down to approximately half the wavelength An uncorrelated field record, therefore, by itself can be associated with a two-dimensional display of the change in near-surface elastic property Through the redundancy in data acquisition and a simple data processing step, the uncorrelated field records can be transformed into a stacked section that can be correlated directly to the image of the change in elastic property of near-surface materials This method can be effectively used to detect near-surface anomalies of various kinds

Ion cyclotron waves in the Io torus: Wave dispersion, free energy analysis, and SO2 + source rate estimates

Abstract: As the Galileo spacecraft passed through the Io torus, ion cyclotron waves were observed near the sulfur dioxide ion gyrofrequency. The torus plasma is continually replenished by the ionization of neutral particles from Io. It is well known that sulfur dioxide dissociates rapidly, so that the corotating torus plasma consists of predominantly sulfur and oxygen ions. However, for the small fraction of molecules that become ionized before dissociation, the appearance of SO2+ gyroresonant waves near Io indicates that the wave growth timescale (or wave-particle scattering time) is short compared with the lifetime of these SO2+ ions. Newly created ions initially form “ring”-type ion distributions which are highly unstable and generate the observed ion cyclotron waves. A warm plasma dispersion analysis finds that growth at the SO2+ gyrofrequency dominates over that at the O+ and S+ gyrofrequencies, partly because the ring energy scales with ion mass, but mainly due to the absence of a thermalized “background” component of SO2+ which would otherwise damp these waves. At the growth rate peak, the wave frequency is just below the SO2+ gyrofrequency (0.4 Hz) and the phase velocity is ∼55 km/s. A free energy analysis for wave-particle scattering of ions toward a “bispherical” shell-type distribution suggests that the SO2+ density in the torus falls off steeply with distance from Io wake values. These density estimates obtained from the observed wave power do not rely on assumptions of the exact plasma composition, but require that the SO2+ wave dominates the spectrum and is not strongly damped (as verified by the dispersion analysis). From our density estimates, we infer an ion production rate for SO2+ of ∼8×1026/s, representing the small fraction of sulfur dioxide that survives in molecular form long enough to be ionized and generate waves before dissociation occurs. This is consistent with 5% of the total ion source at the time of the Galileo flyby but is less than 3% of the widely accepted total torus supply rate of ∼3×1028 particles/s from Io.

A model for calculating acoustic gravity wave energy and momentum flux in the mesosphere from OH airglow

Abstract: Acoustic gravity and tidal waves propagating in the mesosphere/lower thermosphere (80–110 km) perturb the airglow layer intensities. The OH airglow has recently been modeled to determine the relationship between the relative perturbed atmospheric density and temperature (ρ′/ρ, T′/T) to the OH intensity (I′OH/IOH) at the OH emission altitudes [Swenson and Gardner, 1997]. A model is presented here which relates wave perturbed OH airglow to the wave energy and momentum flux as they propagate through the emission layer. The model is dependent on the wave horizontal and vertical wavelengths (or phase speed as related through the dispersion relationship), and the relative perturbed airglow intensity, I′OH/IOH. The model can be used by optical experimenters to relate their measurements to wave energy and momentum flux in the stated altitude region.

Cherenkov radiation in coupled long Josephson junctions

Abstract: Cherenkov radiation exists if a particle moves with the velocity equal to the phase velocity of the emitted waves. Electromagnetic waves in a long Josephson junction ~LJJ! are described by the sine-Gordon equation which has, in particular, soliton ~Josephson vortex! and linear wave ~Josephson plasma! solutions. A soliton behaves as a quasiparticle with its own characteristic mass and velocity. The highest