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Work to detect and locate distributed subsurface cracks in concrete by extracting non-propagating oscillatory fields is presented. The medium of interest is concrete, but the approach also applies to other types of inhomogeneous media. The theoretical basis of the work is first presented through a one-dimensional point-scatterer model that considers the wavefield set up by multiple distinct scatterers. More complex scattering scenarios are then investigated using numerical simulation. The numerical models consider two types of scatterers: elliptic large-scale particles distributed throughout a medium, and small-sized cracks localized within a damage zone. The theoretical and numerical analyses show that forward propagating waves undergo distinct scattering behavior within the crack damaged zone: non-propagating resonance-like oscillatory fields are set up within the cracked zone, and are distinct from the scatter caused by the large-scale particles. Frequency-wavenumber (f-k) domain analyses to extract the energy of non-propagating oscillatory fields and thus to detect and locate zones of distributed cracking are employed. The proposed approach is evaluated using numerical simulation and experimental data collected from concrete specimens that contain simulated distributed cracks. The results demonstrate that the location of distributed crack zones in discrete random media, such as concrete, can be successfully detected.

As an essential necessity for fundamental study and a broad variety of technological applications, it is important to control the propagation of acoustic waves and select their particular wavefronts. This work is to achieve effective wavefront shaping of acoustic waves along specific paths in strongly scattering media including phononic periodic structures and random media. In the phononic crystal, a kind of artificial phononic structures, wavefront shaping, and super-resolution imaging have been achieved by designing the geometry and material parameters. Furthermore, the confocal technique of the optical beam and acoustic beam has been improved to achieve sub-wavelength imaging in random media with strongly scattering. The presented results of wavefront shaping have implications for tailoring phonon dynamics in scattering media, which offers further possibilities of controllable acoustic waves in complex materials and enlightens the interaction of multi-physics fields.

Pulse propagation in a weakly and randomly inhomogeneous medium is studied using a time-domain progressive wave equation. An eikonal-like approximated solution to the wave equation derived from the path integral representation is used to obtain the time-dependent statistics of pulses propagating through this random medium. This approach yields both a simple way of producing simulations of time series as well as their statistical properties.

This paper deals with line-of-sight sound propagation in a medium with the von Karman spectra of temperature and medium velocity fluctuations. The mean sound field, the coherence functions of plane and spherical waves and their coherence radii in such a medium are calculated analytically and numerically. It is found that the temperature and medium velocity contributions to these statistical moments of a sound field may differ significantly. The coherence functions of plane and spherical waves for the von Karman spectrum of medium inhomogeneities have been compared with those for the Kolmogorov and Gaussian spectra. The latter two spectra have been used widely in theories of sound propagation in random media. It is shown that, in limiting cases, the coherence functions calculated for the von Karman spectrum coincide with those calculated for the Kolmogorov and Gaussian spectra. This result supports the use of the Gaussian spectrum in theories of sound propagation in random media.

In this paper the spatial coherence properties of the speckle noise backscattered from random media insonified by a broadband pulse are studied. The approach presented is an adaptation of the optical notion of coherence introduced by Zernike. How the statistical parameters (particularly the second-order moment) of the medium determine those of the speckle noise is studied. This is applied to fully or partially incoherent media, and media with anisotropic scatterer distribution such as unidirectional and cross-ply composites; also investigated is the possibility of detecting a coherent reflector among speckle noise through measurements of coherence length. Experimental as well as theoretical results are presented. Measurements were carried out with a linear array of 128 programmable transmitters/receivers.

Shallow water (coastal) acoustics has been a topic of great interest over quarter century, both from the point of view of learning coastal oceanography and of learning coastal acoustics. Indeed, the two are difficult to separate. In this talk, the research done at the Woods Hole Oceanographic Institution (very often in collaboration with other institutions) over the past 25 years will be discussed, with an emphasis on the major experimental efforts that have been fielded, but also including theoretical and computational efforts. The Barents Sea Polar Front experiment, the Shallow Water Acoustic Random Medium experiment, the Shelfbreak PRIMER experiment, the Asian Seas International Acoustics Experiment, the Shallow Water 2006 experiment, and the Quantifying, Predicting and Exploiting Uncertainty program are some of the at-sea efforts to be discussed. Theoretical advances in shallow water acoustics, as well as computational efforts, such as the Integrated Ocean Dynamics and Acoustics project, will also be ...

In many acoustical ray inversion methods, if the wave ray is nonlinear in a random medium, the distribution of the incident angles of the discrete projections is uneven, and this brings forth the distortion in the inversion result. Moreover, the far‐field condition is broken down while the inversion region is large. In order to overcome these drawbacks, a new t‐x (time‐space) domain backprojection method compensating the density of the distribution of incident angles is developed. This paper provides the theory of the incident angle compensation, discusses the efficiency with several point defect examples in the layered medium, and describes the ray tracing method for defect inversion in a layered medium. Finally, it presents a simulation inversion result of a crack defect.

A general solution to the Lighthill-Westervelt equation of nonlinear acoustics, previously developed and successfully applied to model the scattering of sound by sound and to the parametric array, has been generalized further for use in the cases of inhomogeneous and random media. The form of the solution makes use of an exact inverse differential operator in combination with a sequence of perturbation terms that comprise the multiple orders of nonlinear acoustic scattering to arbitrary order. Integration techniques have been developed which allow accurate, approximate, analytical solutions under particular circumstances. These solutions are shown to reduce to other previously known solutions in the appropriate limits.

Acoustical imaging is based on the ability to focus an acoustic beam inside the zone of interest. This remains an issue through a high-order multiple scattering medium because the electronic delay lines that enable one to focus through a multiple scattering medium are a priori unknown. Using time-reversal principles, we show that images can be obtained through a very disordered medium. Surprisingly, the images are better than those obtained in a homogeneous medium with a classical imaging device.

Due to the limitation of sparse seismic observations on the earth’s surface, the deterministic picture of small‐scale heterogeneities in the earth is difficult to obtain in general. Statistical characterization is a viable alternative to study the distribution and properties of the small‐scale heterogeneities. The pioneering work of Aki in 1973 modeled the heterogeneities with a single‐layer uniform random medium having only three parameters: scale, perturbation strength, and layer thickness. This simple model is consistent with the observations which are limited to only the transversal coherence functions of seismic wave (phase and amplitude) across an array and it has no depth resolution. The following work in 1970s and early 1980s were based on similar models. Flatte introduced the key idea of angular coherence functions using different earthquakes at large epicentral distances in the late 1980s (Flatte and Wu, 1988), which opened a new area of earth heterogeneity characterization by extending the single, uniform layer model to a depth‐dependence model. Later, the angular coherence function was extended to the joint transverse‐angular coherence function, which significantly increases the depth resolution of the heterogeneity spectra. In this talk, we summarize the research results along this direction conducted by a group of scientists in the earth science at University of California, Santa Cruz, collaborated with Flatte in different stages.

Flatte had a significant impact on my dissertation and early education in the field of ocean acoustic propagation. In particular, Flatte’s work on the impact of internal wave scattering on deep ocean propagation was central to my early work in adiabatic mode scattering in the presence of deep water internal waves. In this paper, we will revisit some of Flatte’s wave propagation in a random media theory and show its phenomenological impact on deep water propagation, primarily within his explanation of the Slice89 experiment. In this experiment the axial finale (latest arriving energy) is broadened in depth. Flatte correctly asserted that this was due to internal wave scattering to higher modes (with larger depth extents) and used this as a method for heuristically determining the internal wave strength. Results from Heaney [Ph.D. thesis, SIO‐UCSD (1997)] will be presented using the ATOC experiment. More recent results using NPAL data as well as more recent modeling will be presented. The impact of these re...

We consider the estimation of Green’s functions, or travel times, from noisy data when the medium is not homogeneous. In the homogeneous case travel times can be estimated from cross correlations of noisy traces at the two points between which the travel time is to be estimated, given information about the nature and extent of the noise sources. In a randomly inhomogeneous medium the noisy traces contain information not only about the homogeneous background but also about the inhomogeneities. It is shown how to assess this effect and the limits it puts on travel time estimation.

An angle‐of‐arrival estimator is derived for acoustic waves that propagate in atmospheric turbulence. The estimator directly accounts for the effects of random fluctuations in the propagation environment. The first and second moments of the sound field, as derived from the theory of wave propagation in a random medium, and realistic atmospheric turbulence models are utilized. Results using this estimator are compared to results using conventional beamformers that do not account for the effects of atmospheric turbulence.

The presence of internal structure can greatly alter the acoustic behavior of elastic structures. Even in relatively simple systems, it is necessary to employ approximate models, effectively averaging out unwanted detail. Some phenomenological aspects can be easily obtained in this way provided the ‘‘base’’ structure is not too complicated. For example, the locus of peaks in the scattering cross section as a function of frequency and angle can often be predicted in a deterministic manner, but estimating the actual scattering levels requires more sophisticated modeling. One approach to this modeling problem is to employ a ‘‘fuzzy’’ structures paradigm in which a Neumann series involving the random aspects of the internal structure is averaged. A more sophisticated approach involves directly constructing and approximating equations for the desired averages; employing the Dyson and Bethe‐Salpeter equations of random media theory. These techniques have been applied to predict the scattering cross section from an irregular ribbed structure. The results will be discussed and compared.

Reliable, high‐capacity communications in scattering media can be effectively established with some basic remote sensing techniques involving time reversal. I will formulate these problems and discuss the various mathematical approaches that can be used for analysis. It turns out that stochastic analysis plays an important role and, in some cases, gives very satisfactory results. One such result is the spectacular increase in communications capacity in a richly scattering environment. I will end with a discussion of applications and computational issues that arise in the realistic simulation of communication systems.

In the stratified random medium considered here, the spatially fluctuating wave speed and refractivity vary only in the range direction, which is normal to the planes of stratification. To treat backscattering in such a medium, it is convenient to split the field into forward‐ and backward‐propagating components, and derive coupled equations that govern the range evolution of the statistical moments of these components. The derivation entails an ensemble‐averaging operation, which is here predicated on the key assumption that the two components, which are incident from opposite directions on a differential range slab, are statistically independent of the refractivity fluctuations within that slab. The assumption is justifiable when the fluctuations exhibit a sufficiently rapid time dependence. This procedure is used to derive equations for the bichromatic coherence of the two field components, which are then solved to determine the evolution of the power flux associated with the propagation of a signal due to a planar narrow‐band pulse incident on a semi‐infinite scattering slab. It is shown that the pulse signal is attenuated exponentially in the range direction, on the so‐called ‘‘localization’’ scale, while the scattered power forms echo pulses which are gradually attenuated until all the incident pulse energy is reflected back out of the slab.

Radiative transport equations for elastic waves in random media can be derived from first principles in a certain regime of physical parameters. They account for both longitudinal and transverse waves, as well as polarization. Transport boundary conditions can also be derived from first principles. An important application of transport theory is to the analysis of the deep coda of elastic waves, where some rather interesting phenomena of energy distribution emerge. A reference to work in this area is by Ryzhik et al. [Wave Motion 24, 327–370 (1996)]. Another reference, more directly related to seismics, is Ryzhik et al. [Bull. Seismol. Soc. Am. 86, 1107–1115 (1996)].

We have conducted a careful time reversal and imaging study for long distance wave propagation in random media in the underwater acoustics regime. In this talk we briefly describe the computational technology, which is based on a phase‐screen propagation code for the paraxial wave equation. The advantages and limitations of the code are discussed. We show some time reversal results which demonstrate the super‐resolution phenomenon and its statistical stability in the time domain. We also show results of imaging in random media using an array of active transducers.

Time reversal in random media can result in refocusing on the source with a resolution that is better than the diffraction limit. This is because of the multipathing that occurs in the random medium, making the time reversal array appear to be wider than it is. What is not clear, however, is why this phenomenon is statistically stable. That is, why the refocused spot size does not fluctuate in the random medium. The reason for this statistical stability is that it is a time domain phenomenon and does not occur with narrow band signals. I will explain this effect analytically and will also show how it can be used for imaging in random media.

Bradford Sturtevant (1933–2000) spent his entire academic career in the Graduate Aeronautical Labs at Caltech (GALCIT). He was a distinguished and internationally respected member of the fluid mechanics community, known particularly for his research on shock waves. Although a member of the Acoustical Society since 1974, he rarely if ever published in JASA. Nevertheless, his contributions to acoustics, mainly in what we think of as nonlinear acoustics although he probably saw them simply as part of fluid mechanics, are significant. Examples are: shock focusing, nonlinear resonance in closed‐ and open‐end tubes, sonic booms, and propagation of weak shocks through a random medium. In the late 1980s he became interested in lithotripsy. When Andrew Evan (Indiana University School of Medicine) organized a multidisciplinary consortium to solve many of the mysteries of lithotripsy, it is not surprising that Brad was picked for his expertise on shock waves and his interest in shock waves in the body. The research effort that ensued, now in its eighth year, owes much to the work of Brad and his students and to his counsel. Brad was especially concerned about the mechanism(s) by which stone breakup occurs.

The feasibility of acoustic monitoring of generation and evolution of shallow‐water solitary internal waves is investigated by using the acoustic and environmental data collected during the 1995 Shallow Water Acoustics in a Random Medium (SWARM) experiment. Spatial and temporal variability of acoustic signals (60 to 450 Hz) were measured by using two well‐populated vertical receiving arrays at 30‐ and 40‐km ranges from two moored sources and at 20‐km cross‐range from two ship‐deployed sources. Environmental data were collected by using CTDs, thermistor strings, a high‐frequency acoustic backscattering imaging system, and a chirp sonar system. Correlation between cross‐range propagation and oceanographic measurements during the generation and evolution of a solitary internal wave packet indicates the possibility of acoustic monitoring of this oceanographic process. Results of a parametric study using broadband numerical simulations are also presented to develop the best monitoring strategies for future exp...

Three years ago, the first experiments showing the reversibility of acoustic waves propagating through high‐order multiple scattering media were reported [A. Derode, P. Roux, and M. Fink, Phys. Rev. Lett. 75, 4206 (1995)]. These experiments were performed in a transmission mode by means of a time reversal mirror (TRM). Here, new time‐dependent experimental results obtained in a backscattering mode are reported. The experiment can be described as follows: the TRM used is a linear array of 128 transducers. One of the elements transmits a pulsed wave into the sample which is a random set of 2400 steel rods. In the 128 recorded backscattered signals, short windows are selected which are time‐reversed and retransmitted. Surprisingly, it is found that the synthesized time‐reversed waves revive their past and converge onto the initial emitting element, despite disorder. Thus the image of the source is recreated, what is referred to as the mirror effect. The spatial refocusing is found to be improved when selecting windows farther and farther in the backscattered signals. The refocused spot time‐evolution is well explained by a simple model including both single and multiple scattering contributions.

Recent experiments demonstrating the enhanced backscatter of 5‐MHz ultrasound of a random medium are reported. The effect has been observed in a sample composed of a highly concentrated slurry of 250‐μm glass spheres in water, as well as in a sample of polycrystalline brass with randomly oriented grains. The scattered intensity is found to be enhanced within a wide angular cone, thereby indicating a parameter regime that approaches the Ioffe‐Regel criterion for the Anderson localization transition. Prospects for the observation of strong ultrasonic Anderson localization are discussed. [Work supported by NSF.]

Wave propagation in randomly fluctuating media is a problem of continuing interest in ocean acoustics. Usually the work done in this field is carried out in the frequency domain since there are powerful techniques to study wave scattering in the frequency domain, while time‐domain formulations are notoriously more difficult to use and obtain results. Nevertheless, our intuition about wave phenomena is much better when discussing such phenomena in a space‐time formulation than in a space‐frequency formulation. In this presentation wave propagation in a weakly and randomly fluctuating medium is discussed entirely within the space‐time formulation. McDonald and Kuperman derived from the wave equation an approximate time‐domain progressive wave equation which is the equivalent in the space‐time formulation of the well‐known parabolic wave equation in the space‐frequency formulation. A path integral representation for the solution of this equation is used here to study wave propagation in random media. The weakly inhomogeneity assumption yields an approximate evaluation of the path integral for the Green’s function thus allowing an analysis of the time‐dependent statistics of acoustic fields propagating through random media. [Work supported by ONR.]

The effective structure‐function parameter for scattering by atmospheric, turbulent velocity fluctuations has normally been assumed to be Ceff2=4C2V/c20 However, a new derivation by V. E. Ostashev [Waves Random Media 4, 403–428 (1994)], which takes into account the vectorial nature of the wind velocity field, suggests that Ceff2=22C2V/3c20. An experiment was designed to determine the correct value of the coefficient. Amplitude variances were monitored for several discrete frequencies between 380 and 3500 Hz, at distances up to 675 m. Cup and hot‐wire anemometers were used to determine C2V. A theory for scattering by inertial‐subrange turbulence was then used to calculate the Ceff2 coefficient from the amplitude variance and C2V. Although there is some tendency in favor of the 22/3 coefficient, the results cannot be considered conclusive. The main difficulty appears to be obtaining a sufficiently accurate measurement of C2V.

The coherence functions of a spherical sound wave after passing through a turbulent jet were measured for different values of sound frequencies and mean speed of the jet [Ph. Blanc‐Benon, Ext. Rev. Cethedec‐Ondes Signal, No. 79‐1984 (1984)]. In the presentation, the experimental data obtained are compared with the theoretical predictions based on the previous theories of sound propagation in turbulent media with medium velocity fluctuations [e.g., E. H. Brown and F. F. Hall, Rev. Geophys. Space Phys. 16 (1), 47–110 (1978)] and with the predictions of the theory recently developed [V. E. Ostashev, Waves Random Media 4, 403–428 (1994)]. The differences between these theories and their results for the coherence function of a spherical wave are explained. It is also shown that the predictions based on the previous theories do not agree with the experimental data. On the other hand, the predictions of the theory developed by V. Ostashev fit the measured coherence functions fairly well. [This material is based ...

Modeling the effect of a rough air–sea interface on an acoustic signal is of considerable practical importance; for example, it is relevant in the detection of underwater mines, torpedoes, and submarines. Several promising theories have been developed for rough surface scattering. Among the most successful is the small slope approximation (SSA) [A. G. Voronovich, Sov. Phys. JETP 62, 65–70 (1985)]. Recent numerical studies [see S. L. Broschat and E. I. Thorsos, submitted to J. Acoust. Soc. Am. (1996), and references therein] have shown that the higher‐order SSA gives excellent results over a broad range of scattering angles for rms surface slopes up to 1. However, at the lowest forward grazing angles the results become somewhat high. At these angles multiple interactions with the surface at distant points have an appreciable effect on scattering levels. Voronovich recently modified the SSA to extend the nonlocal scattering effects [A. G. Voronovich, Waves in Random Media 6, 151 (1996)]. In this paper, a pr...

The scattering cross section, σ, and the variances of log‐amplitude and phase fluctuations, 〈χ2〉 and 〈φ2〉, of a sound wave propagating in a moving random medium (turbulent atmosphere or ocean, etc.) with the von Karman spectra of temperature and medium velocity fluctuations are calculated. The derived equation for σ differs from that obtained in the paper [Baikalova et al., J. Acoust. Soc. Am. 83, 1332–1335 (1988)]. The difference is due to the fact that in this paper the von Karman spectra of temperature and medium velocity fluctuations are assumed to have the same form, while it is known in the theory of turbulence that these spectra have different forms [J. Hinze, Turbulence (McGraw‐Hill, New York, 1975)]. The derived equations for 〈χ2〉 and 〈φ2〉 are new results. It is shown that 〈χ2〉 and 〈φ2〉 depend on the wave parameter D, widely used in the theory of waves in random media. For D≪1 and D≫1, 〈χ2〉 and 〈φ2〉 coincide with the values previously calculated for the cases of sound propagation in media with th...

In periodic media, frequency regions may exist at which no bounded at infinity solution of the wave equation exists. In random systems frequency regions may appear at which all bounded solutions are localized, i.e., decay exponentially at infinity. Both regions give rise to stop bands. Such stop bands appear easily for acoustic waves in bubbly liquids. They are also predicted to exist for elastic waves in binary composites consisting of gold or lead spherical inclusions periodically placed in a Si, Be, or SiO2 (for gold inclusions only) matrix and occupying about 10% of the volume. The midfrequency ωg of the stop band was found to satisfy the relation ωg=ycil/Ri, where cil is the longitudinal velocity in the inclusion material, Ri is the radius of each inclusion, and y is a number between 1 and 2.

While there has been extensive theoretical work on the effective propagation characteristics of scalar waves in random media, the more complicated case of elastic waves has not yet been treated with a method purported to be valid over a wide parameter range in inclusion concentration and wave frequency. Such a treatment is reported here. The on‐mass‐shell T‐matrix method formulation of the Lax quasicrystalline equations as presented by Varadan, Varadan, and Pao is employed, and this formulation is also adapted to the Roth effective medium equations long hailed as superior in the case of density of state calculations for the electronic properties of liquid and amorphous metals. Effective propagation characteristics and modal densities are exhibited and compared. The effect of various choices for the pair correlation function is also investigated. [Work supported by NSF.]

Using a three‐scale expansion, we solved the equation governing the propagation of the coherence function in a random medium with a mean index of refraction profile. An expression for the intensity distribution near a caustic was obtained including both diffraction and scattering effects. The expression may be readily evaluated in the absence of scattering and in the case of weak or strong scattering. Numerical examples are presented.

This paper is concerned with the correlation between arbitrarily oriented points for a plane wave propagating in a statistically homogeneous and isotropic medium. The bearing response pattern of a line array in such a medium is obtained and numerical results are presented.Subject Classification: 60.20; 30.20; 60.30.

A general formulation of the problem of extracting information about nontransient sources immersed in a randomly fluctuating medium is presented. The formulation is based upon a Green’s function approach in which the medium is treated as a random linear system. It is shown that the problem may be cast into two possible forms, each involving an integral equation the solution of which describes the locations and spectral content of all sources. One of these integral equations is time independent and consists exclusively of deterministic quantities. The other equation is time dependent, consists of stochastic as well as deterministic quantities, and contains considerably more detail. Approximate solutions to the second equation enable one to study image undulations as explicit functions of time. Examples are presented which illustrate some of the difficulties induced by the medium fluctuations when one attempts to solve the basic integral equations.

In a previous article [R. Mazar and L. B. Felsen, J. Acoust. Soc. Am. 81, 925–937 (1987)], it has been shown how the ray trajectories in the refracting background of a weakly fluctuating medium with large scale inhomogeneities can form the basis for propagating and evaluating the high‐frequency two‐point coherence function. Approximate results there, derived by a multiscale expansion technique, account for multiple isolated ray arrivals at observation points far from caustics, and blend smoothly into the transitional behavior due to closely adjacent rays near caustics. In the absence of fluctuations, this assertion has been verified by recovery of the isolated ordinary and uniform deterministic ray theory intensities, respectively, and it is therefore believed that our spectral construction properly describes the high‐frequency two‐point coherence function when randomness is included. The ray‐based approach is now extended to multifrequency higher‐order coherence functions. The new results are shown to re...

Integral equations describing the multiple‐scattering effects of waves propagating in a discrete random medium are solved using Fourier transform techniques. The average intensity in the medium for a given source radiation is expressed in terms of a Green's function which consists of residue contribution at a pole representing diffusion and a branch cut integration pertaining to nearfield. It is shown that for a plane wave, multiple scattering becomes significant when the particles are mostly scattering (albedo, b > 0.5) for all distances greater than a fraction of an optical depth Z. When the particles are mostly absorbing, multiple scattering will not take effect until at least Z > 2. For a spherical wave, the multiple‐scattering influence does not become significant until several optical depths, except when the scatterers are extremely low loss (b → 1).

We apply the two‐scale expansion developed previously to solve the equation governing the propagation of the coherence function in a random medium with a mean speed‐of‐sound profile. We obtain a formula for the vertical intensity distribution, resulting from an acoustic beam propagating in a statistically homogeneous, isotropic random medium with channel velocity profile. We use this formula to calculate the intensity distribution in the vicinity of a caustic in two limiting cases: weak scattering and strong scattering. We present a numerical example.

The formulation of scattering of low‐frequency acoustic radiation in an anisotropic random medium, like the ocean, results in an integro‐differential equation for the coherence function. It was argued, however, that for horizontal scattering a more simplified differential equation is adequate. In this paper we demonstrate, by direct numerical calculation, that for a realistic case, this simplification is indeed appropriate and that the errors introduced are only of the order of a few percent. For vertical scattering in the absence of refraction, it is pointed out that a quasiasymptotic angular distribution results for large propagation distances in contrast to the exact asymptotic state that is predicted by the differential equation.

Extensive studies have been made on the mean or effective properties of waves propagating in a random medium. We present in this paper a set of correlation equations which are useful in the quantitative determination of the covariance properties of the waves. As an example, the problem of a scalar wave propagating in a random medium is considered.

Measurements were made of the random variation produced in the amplitudes of sonic pulses propagated through a water medium in which was induced a nearly homogeneous random perturbation in temperature. The measurements were carried out at frequencies of 480 kHz and 1.42 MHz for transmitter‐to receiver separations ranging from 1638 to 7658 in. The amplitude variations of the received pulses were analyzed to determine their time autocorrelation and variance as functions of range, i.e., transmitter‐to‐receiver separation and frequency. It was found that the time autocorrelation of the sonic‐pulse amplitudes was equivalent to that measured for the temperature microstructure. The variance in sonic‐pulse amplitude was determined as a function of range at both operating frequencies. These findings are compared with the theoretical findings of Mintzer and Bergmann. An equivalence of the time autocorrelation of sonic‐pulse amplitude and temperature microstructure predicted by theoretical considerations is indeed s...

In a previous paper, the author examined the bearing response pattern of a line array to a plane wave in a random medium. It was found that random effects are strongest when the source is broadside to the array. In this paper, the corresponding situation for a cylindrical wave is examined. A comparison is made with the plane‐wave case.Subject Classification: [43]30.20, [43]30.40; [43]45.10; [43]20.15; [43]30.82.

A multiple scattering theory for elastic wave propagation in a discrete random media is presented. A self‐consistent multiple scattering formalism using the quasicrystalline approximation and a self‐consistent paircorrelation 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.

In the subject paper, the match between experiment and the theoretical findings of Mintzner [J. Acoust. Soc. Amer. 25, 922–927, 1107–1111 (1953); 26, 186–190 (1954)] and Bergmann [Phys. Rev. 70, 486–492 1946)] was not particularly good. It is suggested that the theory of Chernov [Wave Propagation in a Random Medium (McGraw‐Hill, New York, 1960)] offers a better fit.

Rytov's approximation has been studied extensively by workers concerned with waves in random media, although this fact appears not to be appreciated by researchers in acoustics. This letter indicates that the approximation is not equivalent to the Born approximation in its domain of validity. A guide to recent literature is given.

A theoretical analysis of the incoherent (or fluctuating) component of the wave field radiated by a point source in a one‐dimensional random medium is presented. The approach is based on a perturbation technique which is similar to the Rytov method, and which is referred to here as the quasi‐Rytov method. The analysis includes both multiple forward‐scatter and multiple backscatter effects. An approximate expression for the second moment of the incoherent wave as a function of propagation range is obtained for the case in which the wavelength is much less than the correlation length of the medium. This expression shows that the fluctuations of the wave increase relatively rapidly with propagation range until a maximum value (the supersaturation value) is reached, after which they decrease relatively slowly with further increase in range. These results are in qualitative agreement with observations of intensity fluctuations of optical waves propagating in the lower atmosphere. [Work sponsored by NORDA.]

Both heating and cooling techniques have been developed for generating random sound speed fields along a ten meter acoustic propagation path in a 14 m tank having a 3.7 × 3.7 m cross section. A 1.5‐MHz cw signal was propagated along this path for the purpose of studying high‐frequency acoustic signal fluctuations in a random medium. Previous investigators of acoustic fluctuations have produced random sound speed distributions by locating heating elements beneath the propagation path. Localized heating of water generates bubbles due to degassification, and it has been suggested that observed fluctuations may be due to resonant scattering by these rising microbubbles [J. A. Neubert and J. L. Lumley, J. Acoust. Soc. Am. 64, 1148–1158 (1978)]. Preliminary qualitative results indicate that statistically similar random sound speed fields generated by heating from below or by cooling from above produce similar acoustic fluctuations.