Multipath correlation at mid-frequency in a convergence zone.

Wave propagation in random media is important in many applications such as sound propagation in a turbulent atmosphere and scattering by bubbles and microparticles in the ocean. Formulations for the statistical moments of the sound pressure field in continuous and discrete random media are usually done independently. In this presentation, it is demonstrated that the equations for the first two statistical moments in a continuous random medium have the same form as those for a discrete random medium if the scattering properties of the media are expressed in terms of the differential scattering cross section and total cross section. This analogy enables us to apply methods developed in wave propagation in continuous random media to discrete media, and vice versa. As an example, the existing theory of the interference of the direct and ground reflected waves in a turbulent atmosphere is used to study the effect of trees on the interference of these waves in a forest. The results obtained are compared with experimental data. The correspondence between wave propagation in discrete and continuous random media can also be used in other fields of physics.

Attenuation of Seismic Waves Due to Wave‐Induced Flow and Scattering in Randomly Heterogeneous Poroelastic Continua

FURTHER APPLICATIONS OF THE SYSTEMATIC THEORY OF MATERIALS WITH DISORDERED CONSTITUTION

This paper considers the theory of the multiple scattering of waves in extensive random media. The classical theory of wave propagation in random media is discussed with reference to its practical limitations, and in particular to the inability of the lowest order approximation to the Bethe-Salpeter equation, which describes the propagation of correlations, to account for conservation of energy. An alternative kinetic theory is formulated, based on the theory of energy transfer processes in random media. The proposed theory satisfies conservation of energy and the Second Law of Thermodynamics. It is illustrated by a consideration of three problems each of which is difficult or impossible to treat by classical scattering theory. These involve the transmission of energy through a slab of random medium; the scattering theory of geometrical optics; and scattering by a randomly inhomogeneous half-space.

Several mathematical methods are used in the studies of ultrasonic wave propagation in random media [1–6]. The length of acoustic waves in comparison to the dimensions of inhomogeneities, as well as the intensity of fluctuations of medium refractive index for acoustic wave, determine the choice of the method actually used. When medium inhomogeneities are large in comparison with the wavelength, the method of optical geometry (or ray theory) can be used [1–3]. In the case of weakly inhomogeneous media the method of small perturbations [1–3] and the so called smooth perturbations method (Rytov’s method) are employed in studies of acoustic wave propagation. If the wavelength is small in comparison with the correlation distance of medium refractive index fluctuations, so that the Fresnel approximation can be used, the method of parabolic equation is preferred [1,3,7]. Recently, progress in the theory of ultrasonic wave propagation in strongly inhomogeneous random media has been achieved by the application of a method elaborated in the quantum field theory [2,4,8].

Measurements of basin-scale acoustic transmissions made during the last four years by the Acoustic Thermometry of Ocean Climate (ATOC) program have allowed for the study of acoustic fluctuations of low-frequency pulse propagation at ranges of 1000 to 5000 km. Analysis of data from the ATOC Acoustic Engineering Test conducted in November 1994 has revealed new and unexpected results for the physics of ocean acoustic wave propagation in random media. In particular, use of traditional /spl Lambda/, /spl Phi/ methods (using the Garrett-Munk (GM) internal wave model) to identify the wave propagation regime for early identifiable wavefronts predict the saturated regime, whereas observations of intensity probability density functions, intensity variance, and pulse time spread and wander suggest that the propagation is more likely near the border between the unsaturated and partially saturated regimes. Calculations of the diffraction parameter /spl Lambda/ are very sensitive to the broad-band nature of the transmitted pulse, with CW calculations differing from a simplistic broad-band calculation by 10/sup 3/. A simple model of pulse propagation using the Born approximation shows that CW and broad-band cases are sensitive to a random medium very differently and a theoretical description of broad-band effects for pulse propagation through a random media remains a fundamental unsolved problem in ocean acoustics. The observations show that, at 75-Hz center frequency, acoustic normal mode propagation is strongly nonadiabatic due to random media effects caused by internal waves. Simulations at a lower frequency of 28 Hz suggest that the first few modes might be treated adiabatically even in a random ocean. This raises the possibility of using modal techniques for ocean acoustic tomography, thereby increasing the vertical resolution of thermometry. Finally, the observation of unsaturated or partially saturated propagation for 75-Hz broad-band transmissions, like those of ATOC, suggests that ray-based tomography will be robust at basin-scales. This opens up the possibility of ray-based internal wave tomography using the observables of travel time variance, and vertical and temporal coherence. Using geometrical optics and the GM internal wave spectrum, internal wave tomography for an assortment of parameters of the chi model can be formulated in terms of a mixed linear/nonlinear inverse. This is a significant improvement upon a Monte Carlo approach presented in this paper which is used to infer average internal wave energies as a function of depth for the SLICE89 experiment. However, this Monte Carlo approach demonstrated, for the SLICE89 experiment, that the GM model failed to render a consistent inverse for acoustic energy which sampled the upper 100 m of the ocean. Until a new theory for the forward problem is advanced, internal wave tomography utilizing the signal from strong mode coupling can only be carried out using time-consuming Monte Carlo methods.

ABSTRACTOn October 13, 2019 is the ninetieth birthday of the renowned physicist Professor Valerian I. Tatarskii. He is one of the founders of the international journal Waves in Random and Complex Media and its Associate Editor from 1991 to 1998. Outstanding seminal works of Professor V. I. Tatarskii made a global impact on physical science. The article describes main milestones of his life in science and his achievements in the theory of wave propagation in random media.

We consider sensor array imaging with the purpose to image reflectors embedded in a medium. Array imaging consists in two steps. In the first step waves emitted by an array of sources probe the medium to be imaged and are recorded by an array of receivers. In the second step the recorded signals are processed to form an image of the medium. Array imaging in a scattering medium is limited because coherent signals recorded at the receiver array and coming from a reflector to be imaged are weak and dominated by incoherent signals coming from multiple scattering by the medium. If, however, an auxiliary passive (receiver) array can be placed between the reflector to be imaged and the scattering medium then the cross correlations of the incoherent signals on this array can also be used to image the reflector. This situation is important in particular in oil reservoir monitoring when auxiliary receivers can be implemented in wells and its study requires a multiscale analysis of wave propagation in random media. In this review we describe the results obtained in two recent papers using multiscale analysis of wave propagation in random media. In [J. Garnier and G. Papanicolaou, Inverse Problems 28 (2012), 075002] we show that if (i) the source array is infinite, (ii) the scattering medium is modeled by either an isotropic random medium in the paraxial regime or a randomly layered medium, and (iii) the medium between the auxiliary array and the object to be imaged is homogeneous, then imaging with cross correlations completely eliminates the effects of the random medium. It is as if we imaged with an active array, instead of a passive one, near the object. In [J. Garnier and G. Papanicolaou, SIAM J. Imaging Sci. 7 (2014), 1210] we analyze the resolution of the image when both the source array and the passive receiver array are finite. We show that for isotropic random media in the paraxial regime, imaging not only is not affected by the inhomogeneities but the resolution can in fact be enhanced. This is because the random medium can increase the diversity of the illumination. We also show analytically that this does not happen in a randomly layered medium, and there may be some loss of resolution in this case.

A theory of wave propagation in random media must actually refer to a suite of predictive models of the effects of a random heterogeneity. This is because a single general formalism, suitable for all stochastic experiments, would be too complicated for realistic scenarios to have any computational capability. Thus predictive models expressed in partial descriptors of a propagating radiation field, intended for specific experiments are acceptable. In this talk, a number of thought experiments for the propagation of waves in random media will be presented. The point of this is to highlight a richness in the observations one might expect to obtain as a result of random heterogeneity, and to provide a discussion of the possible physical bases for these observations. Appropriate descriptors of the radiation field for each of the thought experiments will be considered, as will be the derivation of prediction models expressed in these measures. A number of specific issues to be addressed are: the possibility of ...

Ocean acoustics has been a useful avenue for testing evolving theories for Wave Propagation in Random Media (WPRM). These theories generally assume that the index of refraction statistics are stable in space and time, an assumption proven reasonably true in the deep ocean for acoustic paths away from boundaries. In the present work, results from 60 years of theoretical and experimental WPRM research at the University of Washington's Applied Physics Laboratory (APL) are reviewed. The first experiment was performed in 1959 to test theories for amplitude fluctuations based on the Born approximation. The Rytov approximation (from Russian literature) for calculating the log-amplitude fluctuations was also evaluated. Conclusion: neither applied. Experiments in 1971 and 1977 measured acoustic fluctuation statistics for an 18 km acoustic path at sonar-relevant frequencies, 2–13 kHz. A 1985 experiment under Arctic ice used 2–16 kHz signals over a 6 km path. These experiments are discussed together with theoretical issues based on the Moment Equation method to provide one viewpoint on the history of ocean acoustic WPRM. The following translation of Voltaire is appropriate: “The ancients when reasoning about physics without the enlightenment of experiments are like blind men explaining the nature of colors to other blind men.”

A general discussion is presented of the propagation, attenuation, growth, reflection, scattering, and energy transport of waves in the presence of weak but extensive random media or boundaries. Applications of the theory to various types of long‐period waves in the ocean are given: gravity waves, shear waves, internal and inertial waves, Rossby waves, Kelvin and Poincaré waves, and edge waves. The mathematical methods used in this paper to solve the relevant random differential equations are generally of an asymptotic or approximate nature; however, attempts have been made to assess the validity of these methods. A brief discussion is also given of some recent exact methods which have been developed to study wave propagation in the presence of strong random fluctuations. There has been no attempt to summarize the extensive work done on electromagnetic, optical, and acoustic wave propagation in random media, since a number of reviews and books have already appeared on these topics.

An exact result in the theory of wave propagation in random media is presented. Using the ergodic theory of dynamical systems, it is shown that a semi-infinite, one-dimensional random medium is totally reflecting. A direct numerical study shows that the mean reflection coefficient converges exponentially to one.

In this survey, we fully review almost all potential ionospheric effects on the performance of space-based radar systems (SBRs), which operate in the ambient ionosphere environment; in particular, we review the use of space-based synthetic aperture radar systems (SARs) for imaging. There are two families of effects involved. One is the effects of the background ionosphere (non-turbulent ionosphere), such as dispersion, group delay, refraction, Faraday rotation, and phase shift. The other is the effects due to ionospheric irregularities, such as refractive index fluctuation, phase perturbation, angle-of-arrival fluctuation, pulse broadening, clutter, and amplitude scintillation. These effects adversely affect SAR imaging in several respects, such as by causing image shift in the range, and degradations of the range resolution, azimuthal resolution, and/or the resolution in height (elevation). We also review ionospheric irregularity characteristics and descriptions, propagation channel statistics, received signal statistics, and detection performance of SBRs in ionospheric scintillation situations. First, a brief outline of SBR systems and principles, and theories of wave propagation in random media, especially some effects caused by two-way propagation, is given. Finally, several of the most probable directions of future research are pointed out.

We have developed a model for light propagation in porous silicon (PS) based on the theory of wave propagation in random media. The low porosity case is considered, with silicon being the host material assuming randomly distributed spherical voids as scattering particles. The specular and the diffuse part of the light could be determined and treated separately. The model is applied to the case in which porous silicon would be used as a diffuse back reflector in a thin‐film crystalline silicon solar cell realized in an ultrathin (1–3 μm) epitaxially grown Si layer on PS. Three layer structures (epi/PS/Si) have been fabricated by atmospheric pressure chemical vapor deposition (APCVD) of 150–1000 nm epitaxial silicon layers on silicon wafers of which 150–450 nm of the surface has been electrochemically etched. An excellent agreement is found between the experimentally measured reflection data in the 400–1000 nm wavelength range and those calculated using the proposed model. The values of the layer thickness agree, within a reasonable experimental error, with those obtained independently by cross sectional transmission electron microscopy (XTEM) analysis. This provides an experimental verification of the random medium approach to porous silicon in the low porosity case. The analysis shows that the epitaxial growth process has led to appreciable porosity decrease of an initially high porosity layer from about 60% to 20–30%. Copyright © 2001 John Wiley & Sons, Ltd.

Theory of wave propagation in random media