Showing papers on "Phase velocity published in 1985"

Directional spectra of wind-generated waves

Abstract: From observations of wind and of water surface elevation at 14 wave staffs in an array in Lake Ontario and in a large laboratory tank, the directional spectrum of wind-generated waves on deep water is determined by using a modification of Barber's (1963) method. Systematic investigations reveal the following: (a) the frequency spectrum in the rear face is inversely proportional to the fourth power of the frequency $\omega $, with the equilibrium range parameter and the peak enhancement factor clearly dependent on the ratio of wind speed to peak wave speed; (b) the angular spreading $\theta $ of the wave energy is of the form sech$^{2}$ ($\beta \theta $), where $\beta $ is a function of frequency relative to the peak; (c) depending on the gradient of the fetch, the direction of the waves at the spectral peak may differ from the mean wind direction by up to 50 degrees, but this observed difference is predictable by a similarity analysis; (d) under conditions of strong wind forcing, significant effects on the phase velocity caused by amplitude dispersion and the presence of bound harmonics are clearly observed and are in accordance with the Stokes theory, whereas (e) the waves under natural wind conditions show amplitude dispersion, but bound harmonics are too weak to be detected among the background of free waves.

Lateral heterogeneity and azimuthal anisotropy of the upper mantle: Love and Rayleigh waves 100–250 s

Abstract: The lateral heterogeneity and apparent anisotropy of the upper mantle are studied by measuring Rayleigh and Love wave phase velocities in the period range 100-250 sec. Spherical harmonic descriptions of the lateral heterogeneity are obtained for order and degree up to 1=m=10. Slow regions are evident at the East Pacific rise, northeast Africa, Tibet, Tasman sea, southwestern North America and triple junctions in the Northern Atlantic and Indian oceans. Fast regions occur in Australia, western Pacific and the eastern Atlantic. Details which are not evident in previous studies include two fast regions in the central Pacific and the subduction zone in the Scotia Arc region. Inversion for azimuthal dependence showed (1) little correlation between the fast phase velocity directions and the plate motion vector in plate interiors, but (2) correlation of the fast direction with the perpendicular direction to trenches and ridges. Phase velocity is high when waves propagate perpendicular to these structures. Severe tradeoffs exist between heterogeneity and azimuthal dependence because of the yet unsatisfactory path coverage.

Strong ion acceleration by a collisionless magnetosonic shock wave propagating perpendicularly to a magnetic field

Abstract: A 2 1/2 ‐dimension, fully relativistic, fully electromagnetic particle code is used to study the time evolution of a nonlinear magnetosonic pulse propagating in a direction perpendicular to a magnetic field. The pulse is excited by an instantaneous piston acceleration, and evolves in a totally self‐consistent manner. A large amplitude pulse traps some ions and accelerates them parallel to the wave front. They are detrapped when their velocities become of the order of the sum of the E×B drift velocity and the wave phase velocity, where E is the electric field in the direction of the wave propagation. The pulse develops into a quasishock wave in a collisionless plasma because of dissipation caused by the resonant ion acceleration. A simple nonlinear wave theory for a cold plasma describes the shock properties observed in the simulation except for the effects of resonant ions. In particular, the magnitude of an electric potential across the shock region is derived analytically and is found to be in good agreement with our simulations. The potential jump is proportional to B2, and hence the E×B drift velocity of the trapped ions is proportional to B.

Azimuthal propagation and frequency characteristic of compressional Pc 5 waves observed at geostationary orbit

Abstract: Energetic particle data from the 1977-007 and 1979-053 satellites and magnetic field data from the GOES 2 and 3 satellites have been used to study eight compressional Pc 5 wave events observed at geostationary orbit during 1979. All the events occurred on the dayside, and most of them were observed during the recovery phase of a geomagnetic storm. By using the data from two of the satellites which were close to each other, we measured the azimuthal phase velocity V/sub phi/ and azimuthal wave number m for selected intervals. For all these intervals the waves propagated westward in the spacecraft frame, and we obtained Vertical Bar V/sub phi/ Vertical Bar = 4--14 km/s and Vertical Bar m Vertical Bar = 40--120. In addition, harmonics of a local standing Alfven wave were often present simultaneously with a compressional Pc 5 wave. The frequency of the compressional wave was typically 25% of that of the second harmonic of the Alfven wave. These observed features are discussed in the light of existing theories of instabilities in the ring current plasma.

A multiple scattering theory for elastic wave propagation in discrete random media

Abstract: A multiple scattering theory for elastic wave propagation in a discrete random medium is presented. A self‐consistent multiple scattering formalism using the T matrix of a single scatterer in conjunction with the quasicrystalline approximation (QCA) and a self‐consistent pair correlation function is employed to study the phase velocity and coherent attenuation of elastic waves by a random distribution of cavities and elastic inclusions embedded in an elastic matrix. Both uniform and Gaussian size distributions are assumed. The theoretical results obtained in this study are shown to be in excellent agreement with experimental observations.

A SAFARI-EISCAT comparison between the velocity of F region small-scale irregularities and the ion drift

Abstract: Simultaneous data were obtained between the SAFARI HF coherent radars and the EISCAT incoherent scatter experiment in December 1983. The SAFARI experiment (Scandinavian And French Auroral Radar Investigation) is a set of two HF coherent radars located at Lycksele (Sweden) and Oulu (Finland). These radars are able to detect λ = 10 m F region ionospheric irregularities in the polar and auroral zone. The phase velocity of the irregularities is deduced from the Doppler spectra. During the joint measurements, EISCAT was operated in a meridian scan mode. In this mode, the ion drift velocity is measured at 325-km altitude for each different position of the radar beam, and after completion of the scan, a two-dimensional altitude - latitude map of electron density is obtained. This electron density map is used together with a ray tracing program to accurately localize the HF radar echoes. Then, the phase velocity of small-scale F region irregularities is compared with plasma drift velocity from simultaneous observations of the same volume of the ionosphere. For the set of measurements these drifts are found to be approximately equal. Implications in the existing theories for the generation of F region plasma irregularities at high-latitude are presented, as well as the potentialities of HF radars to measure the plasma convection at very high latitude.

Geometric effects of global lateral heterogeneity on long‐period surface wave propagation

Abstract: Long-period Rayleigh waves from Iranian earthquakes have large amplitude asymmetries between minor arc and major arc arrivals (e.g., R_2 and R_3) at digital stations in the azimuth range N20°W to N60°E. These asymmetries are as large as a factor of 2 at a period of 256 s and persist to periods greater than 300 s. In some cases the entire Rayleigh wave group arrival spanning periods from 100 to 300 s is either uniformly enhanced in amplitude or diminished to such a degree that the group arrival appears to be missing. The amplitude anomalies are generally not accompanied by significant phase anomalies. The irregular azimuthal distribution of the amplitude asymmetries and their occurrence for events with different focal mechanisms and epicentral separations of several hundred kilometers preclude an explanation of these observations by source complexity. Events in the Mediterranean and Nepal do not produce similar amplitude asymmetries at the same stations. The anomalies are thus most likely due to focusing and defocusing propagation effects. As a preliminary investigation of the effects of lateral heterogeneity of upper mantle velocity structure on long-period surface wave amplitudes, surface wave ray-tracing calculations are performed using recently proposed global phase velocity distributions. Dramatic deviations from great circle paths are predicted for long propagation paths (e.g., R_3). The particular spatial distribution of lateral velocity gradients around a given source location determines whether substantial amplitude asymmetries will be observed between minor arc and major arc arrivals and whether these will persist for sequential great circle orbits. The 200-s period amplitude asymmetry observed at KIP for the Iranian source region (R_(2,4) ≪ R_3) is well predicted by the ray-tracing results. The absence of this anomaly for the other source regions is also predicted. Other observed anomalies are not all well predicted, but it is clear that geometric effects can contribute significantly to the observed variations of Rayleigh and Love wave amplitudes. This is the probable explanation for the instability of Q estimates made from surface waves. Other source regions producing large surface wave amplitude anomalies include Japan and southeastern Alaska.

Observations of mesospheric wind velocities: 1. Gravity wave horizontal scales and phase velocities determined from spaced wind observations

Abstract: Dual bistatic radar and the Saskatoon MF radar were used to obtain horizontal scales, phase velocities and power spectral density cross sections of upper middle atmosphere gravity waves as determined from spaced wind velocities. The wave scales averaged 60-110 km and varied from 44-210 km during the 10-100 min observation periods. The horizontal length scales varied directly with the length of the observation interval, while the phase speeds decreased as the observation interval increased. The rms velocity perturbations were about 5 m/sec. The associated vertical wavelengths were 30 and 6 km for the 10-100 min intervals. The power spectra densities obtained, when compared with similar data from previous compaigns, were found to vary on an annual basis. The spectral densities were noted to track the zero line of mean zonal velocity closely in the 10 min to 8 hr period bands. This last phenomena strongly indicates the occurrence of gravity wave mean flow interactions. 80 references.

Microwave holographic imaging of underground objects

Abstract: The resolving capability of underground imaging radar employing a multifrequency holographic approach is characterized in terms of controlling parameters such as the synthetic aperture length, soil conductivity and dielectric constant, and antenna beamwidth. The propagation velocity of electromagnetic wave in soil, which varies from soil to soil, is an essential parameter for reconstructing object images using the holographic approach. Hence, a method of estimating the propagation velocity and also the depth of an object from a pulse-echo image based on the minimum squared error is proposed. The result of underground object image reconstruction from real pulse-echo data is reported to demonstrate high estimation accuracy of the propagation velocity and fine resolution of the reconstructed image.

On phase velocity and growth rate of wind-induced gravity-capillary waves

Abstract: The generation and growth of gravity-capillary waves by wind are considered using linear instability theory to describe the process. The growth rate of the initial wavelets, the first waves to be generated by wind, is found to be proportional to the cube of the friction velocity in air. The effect of changes in the shape of the profiles of wind and wind-induced current is also considered; the growth rate is found to be very sensitive to the shape of the wind profile while the influence of changes in the current profile is much smaller. The values of the current and the current shear at the interface are much more important for determining the phase velocity correctly than the shape of either the wind or the current profile.

Wave radiation and wave diffraction from a submerged body in a uniform current

Abstract: Radiation and diffraction of free-surface waves due to a submerged body in a uniform current is considered. The fluid layer is infinitely deep and the motion is two-dimensional. Applying the method of integral equations, the radiation problem and the diffraction problem for a submerged circular cylinder are examined. For small speed U of the current a forced motion of a given frequency will give rise to four waves. It is shown, however, that, for a circular cylinder, an incoming harmonic wave gives rise to two waves only. Depending on the frequency, the new generated wave may be considered as a transmitted or a reflected wave. The mean second-order force is computed. For the radiation problem the first-order damping force is also obtained. It is shown that, for some values of the parameters, the damping force is negative. This result is closely related to the fact that a harmonic wave travelling upstream with a phase velocity less than U conveys negative energy downstream. The forces remain finite as Uσ/g (σ ≡ the frequency, g ≡ the acceleration due to gravity) approaches ¼.

Analysis and computation for nonlinear elastic surface waves of permanent form

Abstract: Linear elastic surface waves are nondispersive. All wavelengths travel at the Rayleigh wave speed c R. This absence of frequency dispersion means that nonlinear waves of permanent form cannot be determined as a small perturbation from a sinusoidal wavetrain. By representing the general Rayleigh wave of the linear theory in terms of a pair of conjugate harmonic functions, waves which propagate without distortion are characterized as those having surface elevation profiles which satisfy a certain nonlinear functional equation. In the small-strain limit, this reduces to a quadratic functional equation. Methods for the analysis of this equation are presented for both periodic and nonperiodic waveforms. For periodic waveforms, the infinite system of quadratic equations for the Fourier coefficients of the profile is solved numerically in the case of a certain ‘harmonic’ elastic material. Two distinct families of profiles having phase speed differing from the linearized Rayleigh wave speed are found. Additionally, two families of exceptional waveforms are found, describing profiles which travel at the Rayleigh wave speed.

Dynamics of space‐charge waves in the laser beat wave accelerator

Abstract: The excitation of plasma waves by two laser beams, whose frequency difference is approximately the plasma frequency, is analyzed. Our nonlinear analysis is fully relativistic in the axial and transverse directions and includes mismatching of the laser beat frequency to the plasma frequency, time dependent laser amplitudes, and an applied transverse magnetic field (surfatron configuration). Our analytical results for the large amplitude plasma waves include an axial constant of motion, accelerating electric field, and its phase velocity. The analytical results in the weak laser power limit are in good agreement with numerical results obtained from the complete equations. The imposed transverse magnetic field is found to increase the effective plasma frequency, but has little effect on the plasma dynamics.

Dynamics of space-charge waves in the laser beat-wave accelerator. Memorandum report

Abstract: The excitation of plasma waves by two laser beams, whose frequency difference is approximately the plasma frequency, is analyzed. This nonlinear analysis is fully relativistic in the axial and transverse directions and includes mismatching of the laser beat frequency to the plasma frequency, time-dependent laser amplitudes, and an applied transverse magnetic field (surfatron configuration). The analytical results for the large-amplitude plasma waves includes an axial constant of motion, accelerating electric field, and its phase velocity. The analytical results in the weak laser power limit are in good agreement with numerical results obtained from the complete equations. The imposed transverse magnetic field is found to increase the effective plasma frequency, but has little effect on the plasma dynamics.

Deep structure of southern Tibet inferred from the dispersion of Rayleigh waves through a long-period seismic network

Abstract: Our understanding of the tectonic framework for the formation of Tibet and the collision of India with Eurasia1 depends on our knowledge of the regional structure of the crust and upper mantle. Such basic information can be derived from seismic studies, but lateral inhomogeneities cause problems with interpretation of external observations, owing to the lack of stations inside a hardly accessible landmass. In 1982, as part of the French–Chinese cooperation programme, a network of long-period seismic stations was installed for the first time in southern Tibet itself with the object of obtaining local pure-path seismic data. Previously (with the exception of ref. 2) pure-path Tibet dispersion curves were extracted from mixed-path observations3–9, which required assumptions about neighbouring regions and focal mechanisms. In this study, local Rayleigh phase-velocity dispersions from the network were inverted to yield S-wave velocity models. As the period range of the data extends beyond 120 s, the information so obtained constrains deep-seated structures down to 200 km. The crust is shown to be very thick (65–70 km), in accordance with previous estimates2–9, and is divided into an upper part with a velocity of 3.2 km s−1 and a lower part with a steep velocity gradient. The underlying mantle has a high velocity lid (Vs = 4.7 km s−1), beneath which the structure resembles that of western Europe, with a relatively weak velocity minimum (compared with active tectonic regions) of 4.36 km s−1 at a depth of 150 km.

The Backus—Gilbert approach to the three-dimensional structure in the upper mantle — I. Lateral variation of surface wave phase velocity with its error and resolution

Abstract: Summary. The Backus–Gilbert method is applied to obtain the phase velocity variations on a sphere from the measured phase velocity. Narrow peak kernels, with radii of about 2000 km, are obtained for almost everywhere on the sphere. The phase velocity results are thus interpreted as an average within such regions. The most trouble comes from the antipodal peak in the resolution kernel. This is evaluated as contamination and is incorporated in the error estimation. The total error, which is a root mean square of contamination from the antipodal peak and statistical error estimated from the data covariance matrix, is about 1 per cent of the phase velocity in the average earth model, which is the Preliminary Reference Earth Model (PREM). However, there is about a factor of 2 variation of errors on the sphere. Maximum variations of phase velocity are about 3–4 per cent of the phase velocity in the average earth model, and thus there still remain anomalies which exceed estimated errors. The estimated errors correspond to one standard deviation under the assumptions of uncorrelated Gaussian distribution. For high confidence interval, they show that statistically significant anomalies are scarce for the current data set. Generally, Love-wave phase velocity maps show more resolved features than Rayleigh-wave maps and we can see, in high confidence maps, fast velocities in old oceans and old continents and slow velocities in tectonically active regions like the East Pacific Rise and various back-arc regions.

Effect of rotation and relaxation times on plane waves in generalised thermo-elasticity

Abstract: The propagation of harmonically time-dependent thermo-elastic plane waves of assigned frequency in infinite rotating media is studied using the theory of thermo-elasticity recently proposed by Green and Lindsay. A more general dispersion equation is deduced to determine the effect of rotation and relaxation times on the phase velocity of the coupled waves. The solutions for the phase velocity and the attenuation coefficient are obtained for small thermo-elastic coupling by a perturbation technique. Cases of low and high frequencies are also studied to determine the effect of rotation, the relaxation parameters and thermo-elastic coupling on the phase velocity and the attenuation coefficient of the waves.

A model for Doppler peak spectral shift for low grazing angle sea scatter

Abstract: A model is formulated for Doppler spectral characteristics of radar sea scatter for low grazing angles, and is compared with previous radar measurements reported in the literature. The Doppler model is based upon the two-scale model for radar scatter, with scatterer motions hypothesized as due to the orbital wave velocity of the large-scale waves, Stokes and wind drift currents, and the phase velocity of the small-scale Bragg scatterers. Expressions for Doppler shifts due to these motions are derived, and are given as a function of wave height, wave period, and wind speed. Although this model appears to account for the peak Doppler shift of the sea-scatter Doppler spectrum for vertical polarization, it is insufficient to describe horizontally and cross-polarized data, which have larger mean Doppler shifts. However, these two cases are found to scale very closely with the nearly simultaneous vertically polarized data for the variety of environmental conditions reported. Implications of the extension of these results to higher-angle remote-sensing applications are discussed.

Wavelength-independent polarization converter

Abstract: An electrooptical polarization mode converter that operates independently of the wavelength of the light being converted. The converter includes a titanium in-diffused waveguide formed in a lithium niobate substrate, but light is propagated in the direction of the optic axis, rather than perpendicular to it as in prior devices. Both transverse-electric (TE) and transverse magnetic (TM) modes experience the same material refractive index, and mode switching can be effected with only minimal phase velocity mismatch, by applying a bias voltage across the waveguide. The phase velocity mismatch is corrected electrooptically by applying an orthogonal electric field to the waveguide, and mode switching and phase velocity correction effects can be controlled independently. The resulting device is not only wavelength independent, but is insensitive to temperature changes, immune to optical damage due to the photorefractive effect and immune to problems often caused by out-diffusion of lithium oxide from lithium niobate.

Partial derivatives of surface wave phase velocities for flat anisotropic models

Abstract: Summary. Surface wave behaviour in flat anisotropic structures is first illustrated by performing an exact computation on a simple two-layer model. The variational procedure of Smith & Dahlen is then used to compute the partial derivatives of surface wave phase velocities with respect to the elastic parameters in more realistic earth models. Linear relationships between the partial derivatives for a general anisotropic structure and those for a transversely isotropic structure are derived. When considering waves propagating in a fixed direction, there are only four independent derivatives for Rayleigh waves, and two for Love waves. To avoid the lack of resolution in an inverse method, we propose to use physically constrained models. These results are illustrated by using a model with hexagonal symmetry and a symmetry axis oriented either vertically or horizontally. Quasi-Love- and quasi-Rayleigh-wave partial derivatives are computed for both axis orientations. Modes up to the second overtone and periods ranging between 45 and 130 s have been considered. Finally, anomalies of phase velocity are computed in an oceanic model made of 1/6 oriented olivine crystals with horizontal or vertical preferred orientations of the a-axis.

The dispersion of sound in sediment

Abstract: The attenuation of sound through a wide variety of sediments is proportional to the first power of frequency. In order that a plane wave remain causal after suffering such an attenuation, it must also be dispersed. The dispersion necessary to maintain causality in typical sediment is shown to have a logarithmic dependence on frequency and to be measurably large. A truncated parametric array is used to provide a wideband pulse whose travel through a typical medium sand is observed. The measured dispersion is in agreement with the theoretical prediction, exhibiting a variation in phase velocity of 0.5% across a frequency range of 50–350 kHz.

An Analysis of Wave Propagation in Bubbly Two-Component, Two-Phase Flow

Abstract: Wave propagation in bubbly two-phase, two-component flow was analyzed to assess the validity of some interfacial transfer laws for two-fluid models of two-phase flow. A dispersion relation was derived from the linearized conservation equations and the Rayleigh equation. The phase velocity and wave attenuation calculated from the dispersion relation, compared well with existing high- and low-frequency data. The virtual mass term was found to have a significant effect on wave dispersion in the bubbly flow regime. Thermal effects were found to be important in determining the resonance phenomenon and wave scattering was a major source of damping at frequencies higher than the resonance frequency.

Equatorial Solitary Waves. Part 3: Westward-Traveling Modons

Abstract: Boyd's previous work on equatorial Rossby solitary waves which derived the Korteweg-deVries equation using the method of multiple scales is here extended in several ways. First, the perturbation theory is carried, to the next highest order to (i) assess the accuracy and limitations of the zeroth-order theory and (ii) analytically explore solitons of moderate amplitude. Second, using the refined theory, it is shown that Rossby solitary waves will carry a region of closed recirculating fluid along with the wave as it propagates provided that the amplitude of the wave is greater than some (moderate) threshold. The presence of such closed “streaklines”, i.e., closed streamlines in a coordinate system moving with the wave, is an important property of modons in the theory of Flieri, McWilliams and others. The “closed-streakline” Rossby waves have many other properties in common with modons including (i) phase speed outside the linear range, (ii) two vortex centers of equal magnitude and opposite sign, ...

Self‐consistent analysis of electron drift velocity measurements with the STARE/SABRE System

Abstract: Recent work with the STARE (Scandinavian Twin Auroral Radar Experiment) and SABRE (Sweden and Britain Radar Experiment) data sets has shown some inconsistency with existing theories (fluid and kinetic theory) of radar aurora. A new technique, which we call the superimposed grid point method, has proven to be a very valuable tool in the study of this inconsistency. This technique can be used under conditions where the electron drift velocity is approximately constant over an entire STARE (or SABRE) latitude interval and consists of superimposing all of the observed radial Doppler velocity components for the entire latitude interval together into one grid point. This yields, for a given electron drift velocity, a set of Doppler velocity vectors for typically more than 30 different flow angles. Thus this technique allows the study of the angular variation of the Doppler velocities observed with the radars, for a given electron drift velocity. One of the main results of using this technique has been strong evidence that very often the radar Doppler velocities are limited to near the ion acoustic velocity in a manner very similar to the equatorial electrojet. Doppler velocities at flow angles greater than some critical flow angle appear to follow a cosine law, as is usually assumed in the fluid and kinetic theory, while velocities at flow angles less than this critical flow angle seem to deviate greatly from the cosine law and are often limited to the ion acoustic velocity. We have reinterpreted the radar Doppler velocity measurements in the ion acoustic approach (Nielsen and Schlegel, 1985) and find consistency between the results of the superimposed grid point analysis and this new approach.

Tomographic inversion and resolution for rayleigh wave phase velocities in the pacific ocean

Abstract: Phase velocities of Rayleigh waves at periods between 60 and 200 s are measured by using IDA network data, and are inverted to the phase velocity distribution in the Pacific. We apply ART (Algebraic Reconstruction Technique) for the inversion without any a priori regionalizations. In order to estimate the resolving power of our data for the lateral heterogeneity, we use the Backus-Gilbert method. At 60-120 s the lateral variations of the velocities are strongly correlated with the sea floor age or surface tectonics, while such a correlation is weak at 150-200 s. As the period increases, the amplitude of the heterogeneity decreases in most parts of the Pacific. The marginal sea regions have more complicated features than the normal Pacific Ocean. In the Philippine Sea region, the velocities are lower at short periods than the average of the Pacific, but the sign of the heterogeneity is reversed at long periods. This feature may suggest that a cold slab descending beneath this region shows up at long periods. The Aleutian Sea and the Tasman Sea are slow, at 60-200 s. This regional difference in velocities may be due to the difference in geometries of the descending slabs.

Characteristic time constants and velocities of high-latitude Pi 2's

Abstract: Ground-based measurements of the phase velocities, group velocities, and rise times of the magnetic fields of high-latitude (60°–68°N corrected geomagnetic latitude), substorm associated Pi 2's indicate that these pulsations may be caused by the transient reflection of an Alfven wave from the auroral ionosphere. Individual pulsation wave packets can be very short, typically one cycle, with a duration of 100–150 s. The phase velocities are eastward to the east of the region of the onset of the field-aligned currents, and westward to the west of the region of the onset. The group velocities follow a pattern similar to that of the phase velocities but tend to have values somewhat lower than the phase velocities. The longitudinal phase velocities are very high, typically 20 km/s or greater, suggesting that the Pi 2's are not connected with auroral forms such as the westward traveling surge but are more likely connected with the initial brightening of the arc associated with the breakup. Consequently, the longitudinal expansion of the field-aligned currents and Alfven waves causing the Pi 2's may be a direct result of the mechanism leading to the onset of the substorm expansive phase in the magnetotail.