Showing papers on "Phase velocity published in 1993"

Semiautomated method for noise reduction and background phase error correction in MR phase velocity data.

Abstract: Background phase distortion and random noise can adversely affect the quality of magnetic resonance (MR) phase velocity measurements. A semiauto-mated method has been developed that substantially reduces both effects. To remove the background phase distortion, the following steps were taken: The time standard deviations of the phase velocity images over a cardiac cycle were calculated. Static regions were identified as those in which the standard deviation was low. A flat surface representing an approximation to the background distortion was fitted to the static regions and subtracted from the phase velocity images to give corrected phase images. Random noise was removed by setting to zero those regions in which the standard deviation was high. The technique is demonstrated with a sample set of data in which the in-plane velocities have been measured in an imaging section showing the left ventricular outflow tract of a human left ventricle. The results are presented in vector and contour form, superimposed on the conventional MR angiographic images.

Properties of photon density waves in multiple-scattering media

Abstract: Amplitude-modulated light launched into multiple-scattering media, e.g., tissue, results in the propagation of density waves of diffuse photons. Photon density wave characteristics in turn depend on modulation frequency (ω) and media optical properties. The damped spherical wave solutions to the homogeneous form of the diffusion equation suggest two distinct regimes of behavior: (1) a high-frequency dispersion regime where density wave phase velocity Vp has a ω dependence and (2) a low-frequency domain where Vp is frequency independent. Optical properties are determined for various tissue phantoms by fitting the recorded phase (ϕ) and modulation (m) response to simple relations for the appropriate regime. Our results indicate that reliable estimates of tissuelike optical properties can be obtained, particularly when multiple modulation frequencies are employed.

Automated Surface Wave Method: Field Testing

Abstract: The spectral analysis of surface waves (SASW) method is a nondestructive in situ seismic testing method for determining shear wave velocity profiles of soil sites and stiffness profiles of pavement systems. The key steps involved are construction of an experimental dispersion curve from data collected in situ, and inversion of the dispersion curve to determine the stiffness profile. In this paper, an automated method for the construction of dispersion curves is discussed. Weighted least-squares best-fit solution is used to estimate the phase at each frequency with coherence as weighted function. By knowing the distance between the receivers and the phase at each frequency, phase velocity and wavelength associated with that frequency are calculated. These raw data are then combined using the least-absolute-value best-fit criterion to construct a dispersion curve. The inversion process for determination of stiffness profile from the dispersion curve is described in a companion paper.

Two theorems for the group velocity in dispersive media

Abstract: Two theorems on the group velocity are presented in this paper. First a simple proof is given that for any dispersive dielectric, there must be a frequency at which the group velocity of an electromagnetic pulse becomes abnormal, i.e., greater than the vacuum speed of light, infinite, or negative. Second, at the frequency at which the attenuation (or gain) is a maximum, the group velocity must be abnormal (or normal). This second theorem is more widely applicable, e.g., to propagation in waveguides or through multilayer dielectrics. To illustrate these theorems we discuss dispersion in a medium with two resonance lines, one absorption and the other gain. We find that the group velocity is abnormal within the absorption line and in a transparent region outside the gain line.

Wave and vortex dynamics on the surface of a sphere

Abstract: Motivated by the observed potential vorticity structure of the stratospheric polar vortex, we study the dynamics of linear and nonlinear waves on a zonal vorticity interface in a two-dimensional barotropic flow on the surface of a sphere (interfacial Rossby waves). After reviewing the linear problem, we determine, with the help of an iterative scheme, the shapes of steadily propagating nonlinear waves; a stability analysis reveals that they are (nonlinearly) stable up to very large amplitude. We also consider multi-vortex equilibria on a sphere: we extend the results of Thompson (1883) and show that a (latitudinal) ring of point vortices is more unstable on the sphere than in the plane; notably, no more than three point vortices on the equator can be stable. We also determine the shapes of finite-area multi-vortex equilibria, and reveal additional modes of instability feeding off shape deformations which ultimately result in the complex merger of some or all of the vortices. We discuss two specific applications to geophysical flows: for conditions similar to those of the wintertime terrestrial stratosphere, we show that perturbations to a polar vortex with azimuthal wavenumber 3 are close to being stationary, and hence are likely to be resonant with the tropospheric wave forcing; this is often observed in highresolution numerical simulations as well as in the ozone data. Secondly, we show that the linear dispersion relation for interfacial Rossby waves yields a good fit to the phase velocity of the waves observed on Saturn’s ‘ribbon’.

Ion Bernstein wave heating research

Abstract: Ion Bernstein wave heating (IBWH) utilizes the ion Bernstein wave (IBW), a hot plasma wave, to carry the radio frequency (rf) power to heat the tokamak reactor core. Earlier wave accessibility studies have shown that this finite‐Larmor‐radius (FLR) mode should penetrate into a hot dense reactor plasma core without significant attenuation. Moreover, the IBW’s low perpendicular phase velocity (ω/k⊥≊VTi≪Vα) greatly reduces the otherwise serious wave absorption by the 3.5 MeV fusion α particles. In addition, the property of IBW’s that k⊥ρi≊1 makes localized bulk ion heating possible at the ion cyclotron harmonic layers. Such bulk ion heating can prove useful in optimizing fusion reactivity.In another vein, with proper selection of parameters, IBW’s can be made subject to strong localized electron Landau damping near the major ion cyclotron harmonic resonance layers. This property can be useful, for example, for rf current drive in the reactor plasma core. IBW’s can be excited with loop antennas or with a lowe...

Displacement phase differences in a harmonically oscillating pile

Abstract: Analytical solutions are developed for harmonic wave propagation in an axially or laterally oscillating pile embedded in homogeneous soil and excited at the top. Pilesoil interaction is realistically represented through a dynamic Winkler model, the springs and dashpots of which are given values based on results of finite element analyses with the soil treated as a linear hysteretic continuum. Closed form expressions are derived for the phase velocities of the generated waves; these are compared with characteristic phase velocities in rods and beams subjected to compressionextension (axial) and flexural (lateral) vibrations. The role of radiation and material damping is elucidated; it is shown that the presence of such damping radically changes the nature of wave propagation, especially in lateral oscillations where an upward propagating (reflected) wave is generated even in a semi-infinite head-loaded pile. Solutions are then developed for the phase differences between pile displacements at various depths. For most piles such differences are not significant and waves emanate nearly simultaneously from the periphery of an oscillating pile. This conclusion is useful in analysing dynamic pile to pile interaction, the consequences of which are shown in this Paper.

Femtosecond pulse front tilt caused by angular dispersion

Abstract: Femtosecond pulse fronts suffer a time delay across the beam when propagating through diffraction gratings or dispersive prisms. A general relation was found describing the tilt angle γ of the pulse front as, tanγ=λde/dλ where de/dλ is the angular dispersion of the grating or prism and λ is the central wavelength of the pulse. The expression is valid for any spectral device having angular dispersion (e.g., Fabry-Perot interferometer, Lummer-Gehrcke plate, and Michelson echelon). The tilt angle is shown to have a close relation to the classical uncertainty principle.

Wave-turbulence dynamics in the stably stratified boundary layer

Abstract: New data obtained at the Boulder Atmospheric Observatory are analyzed to obtain separation of wave, turbulence, and mean field necessary for a complete treatment of wave-turbulence interaction. The data were compared with a linear stability analysis of the background atmospheric state, showing good agreement between measured wave parameters (such as wavelength, period, and vector phase velocity) and the eigenvalues of the linear solution. The analysis of the budgets of wave heat flux and temperature variance revealed the essential role of wave-turbulence interaction in maintaining a large amplitude temperature wave and countergradient heat flux. A mechanism for the maintenance of turbulence by waves in strongly stratified boundary layers is described, which emphasizes that the time-mean Richardson number is an irrelevant parameter at such times.

Electromagnetic ion‐cyclotron instability in space plasmas

Abstract: Natural space plasmas generally exhibit a pronounced high-energy tail distribution that can best be modeled by a generalized Lorentzian (kappa) distribution. We employ the recently introduced modified plasma dispersion function [Summers and Thorne, 1991] to obtain the dispersion relation for field-aligned electromagnetic waves in such a plasma, and use this to study the instability properties of R mode and L mode waves in the solar wind and in planetary magnetospheres. We demonstrate for a wide range of plasma parameters that the growth of R mode waves in the solar wind can be significantly enhanced by the presence of a pronounced high-energy tail; previous studies based on a Maxwellian distribution could therefore be seriously in error. The corresponding enhancement in the growth rate of L mode waves in planetary magnetospheres is less dramatic, but the kappa distribution tends to produce significant wave amplification over a broader range of frequency than a Maxwellian distribution with comparable bulk properties. At frequencies comparable to the ion gyrofrequency wave growth is primarily caused by cyclotron resonance with ions. Hot anisotropic electrons can nevertheless influence the instability as a result of changes in the wave phase velocity. This modulating effect is most important for a Maxwellian plasma and becomes less significant as the spectral index of the kappa distribution is reduced.

Transient Wave Propagation Methods for Determining the Viscoelastic Properties of Solids

Abstract: The following two solutions are proposed for deducing the viscoelastic properties of a solid from the change in the shape of a one dimensional transient mechanical wave as it propagates through the medium: the general solution (the phase velocity and the attenuation coefficient are expressed in terms of the Fourier transfors of the pulse after two distances of travel), and a filter method. This method fills a gap between the existing vibratory and ultrasonic methods

On parasitic capillary waves generated by steep gravity waves: an experimental investigation with spatial and temporal measurements

Abstract: An experimental investigation of steep, high-frequency gravity waves (∼ 4 to 5 Hz) and the parasitic capillary waves they generate is reported. Spatial, as well as temporal, non-intrusive surface measurements are made using a new technique. This technique employs cylindrical lenses to magnify the vertical dimension in conjunction with an intensified, high-speed imaging system, facilitating the measurement of the disparate scales with a vertical surface-elevation resolution on the order of 10 μm. Thus, high-frequency parasitic capillary waves and the underlying gravity wave are measured simultaneously and accurately in space and time. Time series of spatial surface-elevation measurements are presented. It is shown that the location of the capillary waves is quasi-stationary in a coordinate system moving with the phase speed of the underlying gravity wave. Amplitudes and wavenumbers of the capillaries are modulated in space; however, they do not propagate with respect to the gravity wave. As capillary amplitudes are seen to decrease significantly and then increase again in a recurrence-like phenomenon, it is conjectured that resonance mechanisms are present. Measured surface profiles are compared to the theories of Longuet-Higgins (1963) and Crapper (1970) and the exact, two-dimensional numerical formulation of Schwartz & Vanden-Broeck (1979). Significant discrepancies are found between experimental and theoretical wavetrains in both amplitude and wavenumber. The theoretical predictions of the capillary wave amplitudes are much smaller than the measured amplitudes when the measured phase speed, amplitude, and wavelength of the gravity wave are used in the Longuet-Higgins model. In addition, this theory predicts larger wavenumbers of the capillaries as compared to experiments. The Crapper model predicts the correct order-of-magnitude capillary wave amplitude on the forward face of the gravity wave, but predicts larger amplitudes on the leeward face in comparison to the experiments. Also, it predicts larger capillary wavenumbers than are experimentally determined. Comparison of the measured profiles to multiple solutions of the stationary, symmetric, periodic solutions determined using the Schwartz & Vanden-Broeck numerical formulation show similar discrepancies. In particular, the assumed symmetry of the waveform about crest and trough in the numerical model precludes a positive comparison with the experiments, whose underlying waves exhibit significantly larger capillaries on their forward face than on their leeward face. Also, the a priori unknown multiplicity of numerical solutions for the same dimensionless surface tension and steepness parameters complicates comparison. Finally, using the temporal periodicity of the wave field, composite images of several successive wavelengths are constructed from which potential energy and surface energy are calculated as a function of distance downstream.

Kadomtsev–Petviashivili equation for an ion‐acoustic soliton in a collisionless weakly relativistic plasma with finite ion temperature

Abstract: A Kadomtsev–Petviashivili equation is derived for a two‐dimensional ion‐acoustic soliton propagating in a collisionless weakly relativistic plasma containing the finite temperature ions. This equation is solved in a stationary frame to obtain expressions for the phase velocity, amplitude, width, peak ion density, peak pressure, and energy of the soliton. It is shown that both the relativistic effect and the ion temperature greatly influence the phase velocity, amplitude, and the width. The soliton behavior is described in detail, and a comparison is made between the present results and the previous theories.

Tissue characterization and imaging using photon density waves

Abstract: The optical properties of brain tissues have been evaluated by measuring the phase velocity and attenuation of harmonically modulated light. The phase velocity for photon density waves at 650-nm wavelength has been found to be in the range of 5 to 12% of the corresponding velocity in a nonscattering medium, and the optical penetration depth was in the range 2.9 to 5.2 mm. These results are used to predictthe resolution of optical imaging of deep tissue structures by diffusely propagating incoherent photons. The results indicate that structures of a few millimeters in linear dimension can be identified at 10 mm depth provided that proper wavelength and time resolution are selected. This depth can possibly be enlarged to 30 mm in the case of tissues with very low scattering such as in the case of the neonatal human brain.

Constraining Upper Mantle Anelasticity Using Surface Wave Amplitude Anomalies

Abstract: SUMMARY We present an iterative method to constrain lateral variations in surface wave attenuation using long-period surface wave amplitude anomalies. the method acts to isolate the anelastic signal from elastic focusing effects, yielding largely unbiased estimates of lateral variations in the inverse seismic quality factor, q(ω) =Q=−1(ω) of the surface wave. In the zeroth iteration, linearized ray theory motivates the construction of a reduced datum, using measurements from four consecutive surface wave orbits, which is insensitive to elastic heterogeneity, an operation which requires no a priori knowledge of elastic structure. Synthetic experiments using both ray theoretic formalisms and normal-mode calculations reveal that significant levels of elastic bias remain in the reduced data due to deviations from linearized ray theory. In further efforts to eliminate elastic bias, the remaining elastic signal in each reduced datum is predicted and subtracted using accurate forward theory and existing aspherical elastic mantle models. This operation is the first iteration of a non-linear inversion in which the data at each iteration are the residuals between the observed anomalies and the anomalies predicted for a fixed phase velocity model and updated attenuation model. The zeroth and first iterations are performed with 1610 vertical and 790 longitudinal component seismograms from 144 events. Heterogeneity maps of Rayleigh wave attenuation δq(ω, θ, φ) are retrieved for the even degrees 2, 4 and 6 of a spherical harmonic expansion in the period range of 150–300s (oS25 - oS60)-These surface wave attenuation maps are analogous to elastic phase velocity in their radial averaging of, and linear relationship to, intrinsic heterogeneity and are inverted for upper mantle anelastic structure. Under the physically plausible assumption that intrinsic elastic and anelastic structure are correlated at every depth, the surface wave attenuation maps are well explained by a source region of anelastic heterogeneity that is radially localized in the shallow mantle (100-300 km) in a region we infer to be near the solidus temperature.

Repulsion of phase‐velocity dispersion curves and the nature of plate vibrations

Abstract: The Lamb waves propagating in an elastic plate in vacuo generate compressional (L) and shear type (T) plate vibrations that are coupled due to the boundary conditions. Without such coupling, their phase‐velocity dispersion curves would form two intersecting families, which at high frequency tend towards the elastic‐wave speeds CL and CT, respectively. It is shown that the coupling causes a repulsion of the dispersion curves, similar to that encountered in atomic physics for the energy levels of atoms combining into molecules, which prevents their intersection and at the same time exchanges the nature (L↔T) of the underlying vibrations. However, in the repulsion regions a succession of dispersion curves combines to asymptotically approach the uncoupled L or T dispersion curves, respectively. For the case of a plate bounded by fluid on one side, and vacuum on the other, the dispersion curves of the fluid‐borne (Stoneley–Scholte type) wave, which is known from the studies of Grabovska and Talmant to be prese...

Velocity shift in random media

Abstract: SUMMARY Seismic waves in a random medium (with standard deviation E and correlation distance a of the relative slowness fluctuations) prefer fast paths, and therefore the apparent velocity of wave propagation is larger than the velocity which corresponds to the volume average of slowness. This velocity shift can be determined by ray perturbation theory (Snieder & Sambridge 1992), by the Huygens method (Podvin & Lecomte 1991) and by wave theory (Muller, Roth & Korn 1992). We apply all three methods to plane-wave propagation through a 2-D acoustic medium with Gaussian or exponential autocorrelation function of the slowness fluctuations. Ray perturbation theory gives numerical and analytical results, but has path-length (L) limitations. The Huygens method, which also gives the ray-theoretical velocity shift, can be used for Lla ratios of seismological interest. Wave theory shows that the velocity shift also depends on the wavelength A and that for Ala less than about 0.1 the velocity shift agrees with the result of the Huygens method. For Ala = 1 the wave-theoretical (i.e. true) shift is lower than the Huygens-method shift by a factor of 0.25 to 0.5. Simple formulae for the E dependence of the Huygens-method shift at long path lengths (Lla 2 80) are given, and a correction factor is derived which approximately transforms plane-wave 2-D into spherical-wave 3-D velocity shifts; the latter correspond to 3-D two-point ray tracing. For short-period seismic waves, propagating to teleseismic distances, mantle heterogeneity with E = 1 per cent and a = 100 km produces a velocity shift of about 0.2 per cent. Shifts of this order can explain the difference in earth models, derived from free oscillations on the one hand and from short-period body waves on the other. A velocity shift (or velocity dispersion) due t o anelasticity would be

Single-force representation of shallow landslide sources

Abstract: A horizontal thrust fault situated at the Earth9s surface does not excite any seismic radiation. Because of this and because it provides a satisfactory fit to the data, Kanamori and his co-workers have used a point force rather than a conventional moment tensor to represent the long-period Love- and Rayleigh-wave radiation from a number of shallow landslide sources. The force is supposed by Newton9s third law to be ω 2 MD , where ω is the angular frequency, M is the slide mass, and D is the displacement. Day and McLaughlin (1991) have recently shown that the spall accompanying an underground explosion can be represented either by a shallow horizontal tension crack or by a vertical surface point force ω 2 MD , where M is the spall mass and D is the crack separation. Using their method, we show that a landslide can be represented in the JWKB approximation either by a shallow double couple or by a horizontal surface point force; for a Love wave the force is F L = ω 2 MD (1 − β 2 0 / c 2 0 ), whereas for a Rayleigh wave it is F R = ω 2 MD (1 − 8β 2 0 /3 c 2 0 ), where β 0 is the shear-wave velocity within the slide mass and c 0 is the phase velocity of the surface wave in the vicinity of the source. The sliding block appears to be mechanically decoupled from the rest of the Earth, so that F L ≈ F R ≈ ω 2 MD , because of the reduced shear velocity β 0 within the brecciated rockmass.

Excitation of high frequency surface acoustic waves by phase velocity scanning of a laser interference fringe

Abstract: We present a novel method for generating 100 MHz band surface acoustic wave (SAW) by using a scanning interference fringe at the phase velocity of the SAW. The scanning interference fringe is obtained by intersecting two laser beams with different frequencies, and used as a thermoelastic source. The principle of this method is described, and experimentally demonstrated in the 110 MHz Rayleigh waves on an aluminum specimen generated by a long‐pulse (140 ns) Q‐switched Nd:YAG laser.

Experimental investigation of instability wave propagation in a three-dimensional boundary-layer flow

Abstract: Wave propagation phenomena in three-dimensi onal boundary-layer flows with crossflow instability were investigated experimentally. A 10-element hot-film sensor was flush-mounted on a rotatable insert in a swept flate plate with imposed favorable pressure gradient. By means of cross-spectra l analysis it was possible to obtain direction and magnitude of the phase velocity and the group velocity of the traveling instability waves, thus filling a gap in the knowledge of crossflow instability characteristics. The waves were found to propagate approximately normal to the potential streamline direction, according to linear theory. Phase velocity and the resulting wavelengths also agree satisfactorily, whereas the measured direction and magnitude of the group velocity shows significant differences. Nomenclature c = chord length, 0.5 m cgr = group velocity cph = phase velocity E = voltage F = dimensionless frequency, / • / = dimensional frequency Ga = power spectrum of Xa(t) Gab(f) = cross spectrum of Xa(t) and Xb(t) k - complex wave number vector, k = (kr, &/), IA>l=27r/X

An inverse technique for retrieving higher mode phase velocity and mantle structure

Abstract: SUMMARY We present a new inverse method for retrieving the mantle structure, using the fundamental and higher modes surface waves. The fundamental mode is only sensitive to structures down to 400-500 km but higher modes have a depth resolution down to 1000-1500 km. So, they are well suited to the study of the transition zone between 400 and 1000 km depth. A data set of seismograms corresponding to events all located in a small area and recorded at a single station is selected. The inversion of the seismograms is divided into two steps. First, the difference between the real spectra and the sum of the higher modes synthetic spectra is inverted for retrieving the phase velocities of the first higher modes. In a second step, these phase velocities are inverted at depth in order to retrieve the average mantle structure between the receiver and the epicentral area. This structure is modelled as a transversely isotropic medium with a vertical symmetry axis. Because of the non-linearity of the problem, it is necessary to iterate the procedure and to recalculate the Earth eigenfunctions and the new synthetic spectra at each iteration. Numerical tests on synthetic data have been performed and they demonstrate that we have a good resolution at depth down to 1500 km. Some results obtained on real data recorded on GEOSCOPE network are also presented. This method can now be applied systematically to real data.

Variational Principles for Surface Wave Propagation on a Laterally Heterogeneous Earth—III. Potential Representation

Abstract: Summary We present a frequency-domain analysis of travelling and standing surface waves on a smooth, laterally heterogeneous Earth model, using a potential representation that is valid everywhere, including in the neighbourhood of surface wave caustics. the Love and Rayleigh wave displacement fields are written in the form uL=k-1LW (-řX▿1)χL and uR=UřχR+k-1RV▿1χR; the quantities U, V and W are the local radial eigenfunctions, kL and kR are the local Love and Rayleigh wavenumbers, and χL and χR are surface wave potentials that vary rapidly on the surface of the unit sphere. the natural normalization condition for the local radial eigenfunctions is cCI1= 1, where c is the local phase velocity, C is the local group velocity and I1 is the local radial kinetic energy integral; with this normalization, the Love and Rayleigh wave potentials satisfy the spherical Helmholtz equations ▿21χL + k2LχL = 0 and ▿21χR + k2RχR = 0. Standing wave eigenfunctions χL and χR can be determined either by solving a truncated matrix eigenvalue problem or by using the EBK semi-classical method; the results incorporate multiplet coupling along a single dispersion branch but ignore cross-branch coupling. the theory allows for slowly varying topography of the Earth's surface and the core-mantle boundary, and incorporates the effect of self-gravitation.

Discrete wave packets at the proton cyclotron frequency at comet P/Halley

Abstract: We present in this letter the first experimental evidence for wave packets near the local proton cyclotron frequency in the plasma environment of a comet. The observations have been made by the GIOTTO magnetometer experiment (MAG) around comet P/Halley on both sides of closest approach. The waves are always left-handed in the spacecraft frame, elliptically or nearly circularly polarized and they propagate at small angles from the ambient magnetic field. Their period in the spacecraft frame always closely fits the local proton cyclotron period. The possible generation mechanisms of these waves are discussed. They can be consistently interpreted as waves generated by a resonant helical beam instability fed by the cometary pick-up protons. These waves are intrinsically right-handed waves in the plasma rest frame and are anomalously Doppler-shifted from the plasma frame to the spacecraft frame because their phase velocity is small compared to the local solar wind speed. A generation by a resonance with heavy (water group) ions introducing a temperature effect is also discussed but is less satisfactory.

Propagation of Hydrodynamic Waves in Optically Thin Plasmas

Abstract: The propagation of thermal and magnetosonic linear waves in a general optically thin plasma is studied. In particular, the plasma with solar abundances in the temperature range 10 4 -10 8 K is analyzed. The above plasma is assumed to be cooled by the corresponding standard cooling function, and five different kinds of heating mechanisms are considered. The phase velocity and the scale length for damping (or amplification) of the thermal and magnetosonic wave modes are obtained, and an explicit analytical condition for magnetosonic wave amplification is found. Applications to the different regions of the solar atmosphere are outlined

Nonlinear evolution of a strongly sheared cross‐field plasma flow

Abstract: A study is presented of the nonlinear evolution of a magnetized plasma in which a localized electron cross‐field flow is present. The peak velocity of the flow is denoted by V0; LE represents the flow’s shear scale length; and the regime ρe

Statistical and dynamical analysis of internal waves on the continental shelf of the Middle Atlantic Bight from space shuttle photographs

Abstract: The internal waves on the continental shelf on the Middle Atlantic Bight seen on Space Shuttle photographs taken during the STS-40 mission in June 1991 are measured and analyzed. The internal wave field in the sample area has a three-level structure which consists of packet groups, packets, and solitons. An average packet group wavelength of 17.5 km and an average soliton wavelength of 0.6 km are measured. Finite-depth theory is used to derive the dynamic parameters of the internal solitons: the maximum amplitude of 5.6 m, the characteristic phase speed of 0.42 m/s, the characteristic period of 23.8 min, the velocity amplitude of the water particles in the upper and lower layers of 0.13 m/s and 0.030 m/s respectively, and the theoretical energy per unit crest line of 6.8 x 10 exp 4 J/m. The frequency distribution of solitons is triple-peaked rather than continuous. The major generation source is at 160 m water depth, and a second is at 1800 m depth, corresponding to the upper and lower edges of the shelf break.

Ultrasonic nondestructive evaluation of thin (sub-wavelength) coatings

Abstract: This paper describes a technique for ultrasonic nondestructive evaluation of a thin coating (subwavelength) on a thick substrate. A plane longitudinal wave which is normally incident upon the coating is considered. Transfer functions have been derived for both the coating‐side and the substrate‐side insonification. A systematic analysis of the sensitivity of the transfer functions to the thickness and wavespeed has been carried out. An inverse algorithm has been developed to reconstruct the thickness and the phase velocity through a comparison of the theoretical and the measured transfer functions. Using this technique both the thickness and the wave speed of the coating can be extracted from the same measurement, without knowing either. The technique was used to measure the thickness and wave speed of epoxy and Plexiglas coatings (50–100 μm) on an aluminum substrate using low‐frequency (10 and 20 MHz) transducers; the ratio of thickness/wavelength was about 1/3. The precision in the measurement of the th...