Showing papers on "Wave propagation published in 1982"

Wave propagation and sampling theory—Part I: Complex signal and scattering in multilayered media

Abstract: From experimental studies in digital processing of seismic reflection data, geophysicists know that a seismic signal does vary in amplitude, shape, frequency and phase, versus propagation time To enhance the resolution of the seismic reflection method, we must investigate these variations in more detail. We present quantitative results of theoretical studies on propagation of plane waves for normal incidence, through perfectly elastic multilayered media. As wavelet shapes, we use zero-phase cosine wavelets modulated by a Gaussian envelope and the corresponding complex wavelets. A finite set of such wavelets, for an appropriate sampling of the frequency domain, may be taken as the basic wavelets for a Gabor expansion of any signal or trace in a two-dimensional (2-D) domain (time and frequency). We can then compute the wave propagation using complex functions and thereby obtain quantitative results including energy and phase of the propagating signals. These results appear as complex 2-D functions of time and frequency, i.e., as “instantaneous frequency spectra. ’ ’ Choosing a constant sampling rate on the logarithmic scale in the frequency domain leads to an appropriate sampling method for phase preservation of the complex signals or traces. For this purpose, we developed a Gabor expansion involving basic wavelets with a constant time duration/mean period ratio. For layered media, as found in sedimentary basins,

Wave propagation and sampling theory—Part II: Sampling theory and complex waves

Abstract: Morlet et al (1982, this issue) showed the advantages of using complex values for both waves and characteristics of the media. We simulated the theoretical tools we present here, using the Goupillaud-Kunetz algorithm. Now we present sampling methods for complex signals or traces corresponding to received waves, and sampling methods for complex characterization of multilayered or heterogeneous media. Regarding the complex signals, we present a twodimecsional(2-D) method of sampling in the time-frequency domain using a special or “extended” Gabor expansion on a set of basic wavelets adapted to phase preservation. Such a 2-D expansion permits us to handle in a proper manner instantaneous frequency spectra. We show the differences between “wavelet resolution” and “sampling grid resolution.” We also show the importance of phase preservation in high-resolution seismic. Regarding the media, we show how analytical studies of wave propagation in periodic structured layers could help when trying to characterize the physical properties of the layers and their large scale granularity as a result of complex deconvolution. Analytical studies of wave propagation in periodic structures are well known in solid state physics, and lead to the so-called “Bloch waves.” The introduction of complex waves leads to replacing the classical wave equation by a Schriidinger equation. Finally, we show that complex wave equations, Gabor expansion, and Bloch waves are three different ways of ‘introducing the tools of quantum mechanics in highresolution seismic (Gabor, 1946; Kittel, 1976, Morlet, 1975). And conversely, the Goupillaud-Kunetz algorithm and an extended Gabor expansion may be of some use in solid state physics.

Long Wave Generation by a Time-Varying Breakpoint

Abstract: A two-dimensional parametrization of a surf zone with a time-dependent breakpoint due to groupiness in the incident wave field is developed. The breakpoint is defined in terms of a mean position X plus a modulation Aa. Free wave solutions are obtained on a plane beach at the group frequency and its har- monics. Shoreward of the breakpoint, standing waves are found, while seaward an outgoing progressive wave exists. The amplitude of the standing wave is relatively insensitive to the incident wave field. The amplitude of the outgoing wave depends on X, the group frequency o, and the beach slope tan . For certain values of X -- (o2X?g tan ) the amplitude of the outgoing wave goes to zero. It appears that any 'resonant' response of the standing wave shoreward of the breakpoint is suppressed by seaward radiation of energy by the outgoing wave. As waves propagate onshore and through the surf zone, en- ergy is transferred away from the primary incident wave fre- quencies. Within the surf zone, a mean pressure gradient is es- tablished resulting in wave setup (Longuet-Higgins and Stewart, 1964) and obliquely incident waves drive longshore currents (Bowen, 1969; Longuet-Higgins, 1970a, b). The first reports of low frequency motions in the nearshore zone were made by Munk (1949) and Tucker (1950). Since then, rela- tively high levels of low frequency energy in the nearshore have been widely reported in the literature. The resonant excitation of free edge waves can account for a significant part of this low frequency energy (Huntley, 1976; Holman et al., 1978; Holman, 1979). Theoretically, obliquely incident wave groups may transfer energy to free waves satis- fying the edge wave dispersion relation (Gallagher, 1971; Bowen and Cruza, 1978), and this resonant process can result in large amplitude waves trapped to the shoreline. There is, however, evidence that other motion not associ- ated with free edge waves also contributes significantly to the low frequency energy (Tucker, 1950; Huntley et al., 1981). Tucker observed a correlation between a long wave and the envelope of the incoming swell, with a lag approximately equal to the time required for the swell to propagate into the surf zone and for the associated long wave to be reflected back as a free wave. Longuet-Higgins and Stewart (1964), using the concept of radiation stress, were able to show the existence of a long period forced wave associated with incident wave groups. This forced wave is 180 o out of phase with the in- cident wave group and travels at the group velocity. In view of Tucker's observations, Longuet-Higgins and Stewart suggest that this forced wave is released at the breakpoint and travels seaward as a free wave; but the mechanism by which this oc- curs is not discussed. Huntley et al. (1981) describe data from an extensive array of two component electromagnetic current meters that consistently show energy levels in the onshore- offshore component of flows to be substantially larger than predicted from measured longshore flows by using edge wave theory. Forced wave motion is a possible source of energy that, for near-normally incident waves, may be predominantly in the onshore-offshore direction. None of the published models of long wave forcing account

The interaction between waves and a turbulent current: waves propagating with the current

Abstract: This paper describes an experimental programme carried out in a laboratory channel with rough and smooth beds, to investigate the interaction between gravity waves and a turbulent current. In particular, changes induced in the mean-velocity profiles, turbulent fluctuations, bed shear stresses and wave attenuation rates are considered for a range of wave heights, keeping the wave period constant. The smooth-boundary tests were carried out as a necessary preliminary to the more-realistic rough-boundary condition. A directionally sensitive laser anemometer was used to measure horizontal, vertical, and 45° velocity components in the oscillating fluid, and an on-line minicomputer was programmed to produce ensemble averages of velocities, Reynolds stresses and wave-elevation data. The cycle was sampled at 200 separate phase positions, with 180 observations at each position. Measurements were made at up to 30 points in the vertical. Preliminary tests were carried out on the unidirectional current and on the waves alone. These show that mean-velocity profiles and turbulence parameters of the current agree satisfactorily with previous experiments, and that the waves are approximated closely by Stokes’ second-order theory. For combined wave and current tests, mean-velocity profiles are generally found to differ from those suggested by a linear superposition of wave and current velocities, a change in boundary-layer thickness being indicated. However, shear stresses at the smooth boundary are found to be described by such a linear addition.

Propagation Speeds and Acoustic Damping of Waves in Magnetic Flux Tubes

Abstract: Propagation speeds are derived for the wave modes of a thin magnetic tube in an otherwise homogeneous magnetized or unmagnetized fluid. These results generalize results obtained by previous authors. There are three types of wave, a (torsional) Alfven wave and two waves which are specific for the thin tube. These are named the longitudinal and transversal tube waves, according to their polarization properties. They can be camped by radiating an MHD or acoustic wave into the surroundings of the tube. Conditions for occurrence of this acoustic damping, and the damping rates, are derived. The behavior of the waves in the solar convection zone and corona is discussed.

Exact time-dependent wave packet propagation: Application to the photodissociation of methyl iodide

Abstract: We propose a technique for exact wave packet propagation by a straightforward extension of the semiclassical wave packet propagation procedure. This is an efficient method to calculate photodissociation, Raman, and resonance Raman scattering cross sections. It is applied to the photodissociation of CH3I. The potential surfaces for CH3I are those suggested by Shapiro and Bersohn [J. Chem. Phys. 73, 3810 (1980)]. The results that we obtained by this time‐dependent approach differs significantly from those of Shapiro and Bersohn, where a time‐independent technique is used to calculate the cross sections.

Observations of internal wave reflection off sloping bottoms

Abstract: Current and temperature spectra exhibit intensification and polarization near sloping bottoms over a band of frequencies centered at the local internal wave critical frequency. Examples are drawn from a variety of island, seamount, and continental slope observations. Waves propagating down from mid-depth change energy density, wave number, and azimuth when they reflect off the bottom, providing a natural perturbation to the deep ocean interior internal wave spectrum. Deviations from linear theory are interpreted as evidence for dissipation through subsequent shear instability and/or nonlinear interaction. Topographic features appear likely to be energy sinks for internal wave energy.

Experimental investigations of the propagation of surface waves along a plasma column

Abstract: Plasma surface waves were discovered in 1958. The experiments done since then on these waves are critically reviewed and analysed in terms of appropriate models and corresponding dispersion relations. Discrepancies and unresolved issues are identified and discussed. Wave damping experiments and analysis, and results of more recent works on nonlinear aspects of these waves, are also reported.

Energy saturation and phase speeds measured on a natural beach

Abstract: Field measurements of wave height and speed from 7-m depth shoreward are described. The experiment plan consisted of a shore-normal transect of closely spaced (compared to a dominant wave length) velocity, pressure, and elevation sensors on an almost plane profile having an inshore slope of 1:50. As the waves shoal and begin to break, the dominant dissipative mechanism is due to turbulence generated at the crest, and wave heights become increasingly depth controlled as they progress across the surf zone. Wave heights in the inner surf zone are strongly depth independent: the envelope of the wave heights is described by H/sub rms/ = 0.42 h. The depth dependence of the breaking wave height is shown to be related to the kinematic instability criterion. Celerity spectra were measured by using phase spectra calculated between pairs of adjacent sensors. Inshore of 4-m depth, the celerity was found distant over the energetic region of the spectrum. A 'mean' celerity was compared with linear theory and was within +20% and -10%, showing good agreement for such a nonlinear, dissipative region.

Wave propagation in a magnetically structured atmosphere: III: The slab in a magnetic environment

Abstract: The propagation of waves in a magnetic slab embedded in a magnetic environment is investigated. The possible modes of propagation are examined from the general dispersion relation, both analytically and numerically, for disturbances which are evanescent in the environment. Approximate dispersion relations governing propagation in a slender slab of field are derived both from the general dispersion relation and from an application of the slender flux tube approximation.Several different situations, representative of both photospheric and coronal conditions, are considered. In general, the structures are found to support both fast and slow, body and surface, waves. Under coronal conditions, for two dimensional propagation, disturbances propagate as fast and slow body waves. The fast body waves are analogous to the ducted shear waves of seismology (Love waves).

Instabilities of finite-amplitude water waves

Abstract: A numerical investigation of normal-mode perturbations of a finite-amplitude Stokes wave has revealed regions of instability lying near resonance curves given by the linear-dispersion relation. It is found that, for small amplitude, the dominant instability is two-dimensional (of Benjamin-Fier type) but, for larger amplitudes, the dominant instability becomes a three-dimensional perturbation. Results are compared with recent experimental observations of steep wave trains.

Alfven waves in the solar atmosphere. III - Nonlinear waves on open flux tubes

Abstract: Consideration is given the nonlinear propagation of Alfven waves on solar magnetic flux tubes, where the tubes are taken to be vertical, axisymmetric and initially untwisted and the Alfven waves are time-dependent axisymmetric twists. The propagation of the waves into the chromosphere and corona is investigated through the numerical solution of a set of nonlinear, time-dependent equations coupling the Alfven waves into motions that are parallel to the initial magnetic field. It is concluded that Alfven waves can steepen into fast shocks in the chromosphere, pass through the transition region to produce high-velocity pulses, and then enter the corona, which they heat. The transition region pulses have amplitudes of about 60 km/sec, and durations of a few tens of seconds. In addition, the Alfven waves exhibit a tendency to drive upward flows, with many of the properties of spicules.

Acoustic slow waves and the consolidation transition

Abstract: We have investigated the ultrasonic properties of unconsolidated (loose) glass beads and of lightly fused (consolidated) glass beads when the pore space is saturated with water. At a frequency of 500 kHz we have observed a single compressional wave in the former whose speed is 1.79 km/s and two distinct compressional waves with speeds 2.81 km/s and 0.96 km/s in the latter. The Biot theory is shown to give an accurate description of this phenomenon. We also analyze the acoustics of low temperature He ii in packed powder superleaks; either the fast wave for unconsolidated systems or the slow wave in a highly consolidated (fused) frame may be considered to be the 4th sound mode. In all such systems, the acoustic properties can be very simply understood by considering the velocities of propagation as continuous functions of the elastic moduli of the solid skeletal frames.

Observations of Stimulated Scattering of a Strong High-Frequency Radio Wave in the Ionosphere

Abstract: Electromagnetic sideband spectra induced by a strong monochromatic high-frequency radio wave in an overdense ionosphere have been observed for the first time by means of a new direct observational technique. The observed asymmetry of the spectra, a characteristic feature of stimulated scattering, is tentatively attributed to parametric and linear-mode-conversion processes occurring in the irradiated ionospheric-plasma volume.

Optical generation of tunable ultrasonic waves

Abstract: A convenient method of optically exciting and monitoring coherent acoustic waves in transparent or light‐absorbing liquids and solids is described. The acoustic frequency is easily and continuously tunable from ≊3 MHz to at least 30 GHz with our experimental apparatus and in principle over a considerably wider range. In anisotropic materials any propagation direction can be selected. The optically generated acoustic waves can be optically amplified, cancelled, or phase shifted.

Effect of surface topography on the diffraction of P, SV, and Rayleigh waves

Abstract: A generalized inverse method for approximate boundary conditions is adapted for boundary value problems in elastic wave propagation. The diffraction of P, SV , and Rayleigh waves at the vicinity of a semi-elliptical canyon is considered. The effects of mode conversion from compressional to shear waves, or vice versa, are examined in detail. The maximum amplification for each plane wave is also studied.

Determination of in situ shear wave velocities from spectral analysis of surface waves

Abstract: A method for determining elastic moduli at soil and pavement sites was proposed and tested. Surface receivers were utilized to evaluate the Rayleigh wave motion created by a vertical, impulsive source that could excite a wide range of frequencies with a single impact. Analysis was facilitated by using a portable spectral analyzer to study the magnitude and phase of the frequency content of the recorded wave pulse. Results from field testing at two flexible pavement sites and two soil sites indicate that the spectral analysis of surface waves provides an accurate estimation of the velocity (and hence modulus) profile at a site. Moduli calculated from wave propagation velocities were generally comparable to moduli calculated by deflection measurements from Dynaflect testing. (FHWA)

A unified model for the evolution of nonlinear water waves

Abstract: Details of a new model of water waves that describes wave propagation over long distances accurately, at low cost, and for a wide variety of physical situations are given. The analysis and numerical methods selected for computer solution are given in some detail. The model uses exact prognostic equations, and a high-order expansion to relate variables at each time step. The accuracy of the model is demonstrated most completely for solitary wave propagation, where model results are compared to exact results. It is found that the model results are much more accurate for high solitary waves than are earlier, Boussinesq-type theories, and give good results for waves so high that they are almost breaking. The capability of the model to treat a variety of situations is demonstrated for colliding solitary waves, nonlinear dispersive wave trains, waves in channels of varying breadth, and undular bores. Formally, the model incorporates nonlinear long wave theory exactly, incorporates enough dispersion to describe linear waves with fourth-order precision, so that both shallow water waves and deep water waves are included, and describes accurately waves for which dispersive and nonlinear effects are both important.

The scattering of ultrasonic waves by polycrystals

Abstract: An ultrasonic scattering theory is presented which allows one to calculate the scattering coefficients and velocities of plane longitudinal and transverse waves in polycrystals as a function of the wavenumber k times grain radius a without limitation to the Rayleigh region. The theory includes mode conversion and multiple scattering and can be used to describe ultrasonic propagation in polycrystals with randomly orientated grains as well as in those with preferred grain orientation. The calculation was done for compressional waves in polycrystals of cubic symmetry with randomly orientated grains in second‐order perturbation theory using the assumption that the changes in the elastic constants and in the density of the materials from grain to grain are small. The asymptotic values at low ka (Rayleigh scattering) are exactly the same as the well‐known results from Bhatia and Moore. Numerical calculations are carried out for some examples.

Upper mantle anisotropy - Evidence from free oscillations

Abstract: Isotropic earth models are unable to provide uniform fits to the gross Earth normal mode data set or, in many cases, to regional Love-and Rayleigh-wave data. Anisotropic inversion provides a good fit to the data and indicates that the upper 200km of the mantle is anisotropic. The nature and magnitude of the required anisotropy, moreover, is similar to that found in body wave studies and in studies of ultramafic samples from the upper mantle. Pronounced upper mantle low-velocity zones are characteristic of models resulting from isotropic inversion of global or regional data sets. Anisotropic models have more nearly constant velocities in the upper mantle. Normal mode partial (Frediet) derivatives are calculated for a transversely isotropic earth model with a radial axis of symmetry. For this type of anisotropy there are five elastic constant. The two shear-type moduli can be determined from the toroidal modes. Spheroidal and Rayleigh modes are sensitive to all five elastic constants but are mainly controlled by the two compressional-type moduli, one of the shear-type moduli and the remaining, mixed-mode, modulus. The lack of sensitivity of Rayleigh waves to compressional wave velocities is a characteristic only of the isotropic case. The partial derivatives of the horizontal and vertical components of the compressional velocity are nearly equal and opposite in the region of the mantle where the shear velocity sensitivity is the greatest. The net compressional wave partial derivative, at depth, is therefore very small for isotropic perturbations. Compressional wave anisotropy, however, has a significant effect on Rayleigh-wave dispersion. Once it has been established that transverse anisotropy is important it is necessary to invert for all five elastic constants. If the azimuthal effect has not been averaged out a more general anisotropy may have to be allowed for.

Determination of in situ attenuation from full waveform acoustic logs

Abstract: Method for the determination of in situ P and S wave attenuation from full waveform acoustic logs are developed. For P waves, the peak amplitude ratios of the refracted P waves from two different receivers can be used with geometrical spreading taken into account. For S waves, owing to the contamination by the guided waves, its attenuation cannot be determined directly. Instead, S wave attenuation is determined from the attenuation of the guided waves using the partition coefficients (normalized partial derivatives of the phase velocity with respect to the body wave velocities). Analytical forms of these partition coefficients are presented here, along with examples for a number of different rock formations (granite, limestone, sandstone and soft sediments). The results show that in high velocity rocks, the fluid attenuation controls the guided wave attenuation except near the cut-off frequency of the pseudo-Rayleigh wave. For low velocity rock formations, especially in the case where the S wave velocity is lower than the fluid velocity, the S wave attenuation is the main contributor to the guided wave attenuation. Synthetic microseisgmogram calculated with the measured body wave attenuation agrees well with the actual microseismograms.

Long wavelength irregularities in the equatorial electrojet

Abstract: We have used the radar interferometer technique at Jicamarca to study in detail irregularities with wavelengths of a few kilometers generated in the unstable equatorial electrojet plasma during strong type 1 conditions. In-situ rocket observations of the same instability process are discussed in a companion paper. These large scale primary waves travel essentially horizontally and have large amplitudes. The vertical electron drift velocities driven by the horizontal wave electric fields reach or exceed the ion-acoustic velocity even though the horizontal phase velocity of the wave is considerably smaller. A straightforward extension to the long wavelength regime of the usual linear theory of the electrojet instability explains this and several other observed features of these dominant primary waves.

Pulse propagation in a magnetic flux tube

Abstract: The linear development of a pulse as it propagates adiabatically along an isothermal magnetic flux tube embedded in a gravitationally stratified atmosphere is studied. It is shown that, for a quiescent environment, longitudinal disturbances in the tube are governed by an equation of the Klein-Gordon type. An impulsively generated disturbance results in a wave front propagating at the subsonic and subAlfvenic tube speed; the wave front trails a wake oscillating at the tube frequency. The results are illustrated for solar photospheric conditiions.

Effective propagation constants for coherent electromagnetic wave propagation in media embedded with dielectric scatters

Abstract: In studying the multiple scattering of electromagnetic waves by random distributions of scatterers with appreciable fractional volume, the approach of quasicrystalline approximation together with the hole correction approximation has been a common method. In this paper, it is shown that such an approach will give rise to negative attenuation rate indicating a growth of the coherent wave in space which is a nonphysical solution. The result of the Percus–Yevick equation is a better representation of the pair distribution function for appreciable concentration. We use it together with the quasicrystalline approximation to study multiple scattering of electromagnetic waves by discrete spherical scatters. Waterman’s T matrix formalism is used in formulating the multiple scattering problem. Closed from solutions are obtained for the effective propagation constants in the low frequency limit and agree with Twersky’s results. Effective propagation constants at higher frequencies are calculated by numerical methods.

Strongly nonlinear waves

Abstract: As steep waves have recently come to be described with increasing accuracy, a number of unexpected physical and mathematical phenomena have been revealed. Until ten years ago it had been assumed that accurate solutions for high waves would hold few surprises. Examples of such suppositions are that deep-water solutions would converge for all waves short of the highest, that important integral quantities such as speed, energy, and momentum would increase with wave height until the highest is reached, that the solutions for periodic waves would be unique, and that if one solitary wave overtakes another any change of wave height would be a decrease. It is now known that all these suppositions are false, having been disproved in the last decade. The nonlinearity of the describing equations produces a complexity of solution structure that is only now beginning to be appreciated. This review will deal with effectively exact solutions for nonlinear waves and the phenomena revealed by such solutions. The governing equation within the fluid is taken to be Laplace’s equation, corresponding to irrotational flow of an incompressible fluid. Excluded are the physical effects of viscosity, density gradients, compressibility, and rotation. This model of the flow is the simplest, but one which is an excellent approximation in many cases of wave motion, and is the traditional avenue of approach to most problems of fluid flow. Throughout his review, however, the problems and solutions described are those where the complete nonlinear boundary conditions have been included. It has been the nonlinearity of these conditions which has made the accurate solution of water-wave problems so difficult.

Characteristics of the ULF waves associated with upstream ion beams

Abstract: A new class of upstream wave is reported with relatively high frequencies of about 1 Hz and small amplitudes compared to the more common larger amplitude, low-frequency (0.03 Hz) upstream wave. The waves were first noted in association with beams of ions reflected back upstream at the bowshock, and although beam presence appears to be a necessary condition for the observation of the waves, it is not a sufficient condition for the existence of the waves. Magnetometer measurements are used to determine intrinsic properties of the waves, and simultaneous two point measurements are used to calculate and eliminate Doppler shifting effects. Results indicate that the waves are right-hand elliptically polarized whistler mode waves with plasma rest frame frequencies of about 20-100 times the proton gyrofrequency and wavelengths of about 100 km.

Finite amplitude Alfvén waves in a multi-ion plasma: Propagation, acceleration, and heating

Abstract: An expression is derived for the wave action flux of finite-amplitude Alfven waves in a multi-ion plasma. The expression is valid in the presence of dissipative forces and permits an arbitrary angle between the average magnetic field and the wave vector. Applying the conservation of wave action and the first law of thermodynamics yields, for a multi-ion plasma, an expression for the spatial evolution of Alfven wave amplitude in the absence of dissipation. It also gives the relationship between the wave amplitude and the dissipative heating, as well as an expression for the acceleration of an ion species by finite-amplitude Alfven waves. It is pointed out that the acceleration comprises a nondissipative wave pressure that is identical to that derived previously under more restrictive conditions and a new term giving the acceleration that must accompany dissipative heating. The results are discussed in the context of the observations of heavy ions in the solar wind.

Measurement of velocities in solitary waves

Abstract: The water surface profiles and corresponding water particle velocities of several solitary waves have been obtained. The measurements of the horizontal and vertical velocity components are conducted using a two-dimensional laser-Doppler velocimeter (LDV). Results are presented for three different wave height-to-depth ratios: ϵ = 0.11, 0.19 and 0.29. The experimental results are compared with existing theories which follow different orders of approximation, and the theories are found to agree well with the experiments. It has been convincingly demonstrated that the LDV measurement technique offers an unmatched advantage to determine the water particle velocities under water waves, especially in the region above the still water level.