Measurements have been made of sound scattered in the specular direction by fixed rough surfaces. The surfaces used were physical realizations of computer generated topographies which corresponded to Gaussian distributions in height to within specified limits. Measurements were made in water using 0.5-, 1.0-, and 2.25-MHz transducers. Transient pulse analysis techniques were used to provide information about the scattered pulse over a wide range of frequencies. Comparisons are made with several theoretical models including a multiple scattering model. The scattered field is also illustrated by means of schlieren visualization. (Author).
Wave Scattering from Statistically Rough Surfaces discusses the complications in radio physics and hydro-acoustics in relation to wave transmission under settings seen in nature. Some of the topics that are covered include radar and sonar, the effect of variations in topographic relief or ocean waves on the transmission of radio and sound waves, the reproduction of radio waves from the lower layers of the ionosphere, and the oscillations of signals within the earth-ionosphere waveguide. The book begins with some fundamental idea of wave transmission theory and the theory of random processes as used to rough surfaces and to wave fields. This discussion is followed by an analysis of the average fields of sound and electromagnetic waves. A section on spatial correlation characteristics in the approximation of small perturbations is then given. Another chapter of the text explains the Kirchhoff method. The book will provide useful information to physicists, mechanical engineer, students, and researchers in the field of acoustics.
A review of theories developed for the study of acoustic, elastic and electromagnetic wave scattering from randomly rough surfaces, and a comprehensive summary of the latest techniques. Different theories are illustrated by experimental data.With applications in radar, sonar, ultrasonics and optics this book will be invaluable to graduate students, researchers and engineers.
Diverse areas of physics and its applications deal with wave scattering at rough surfaces: optics, acoustics, remote sensing, radio astronomy, physics of solids, diffraction theory, radio and wave-propagation techniques, etc. The mathe matical description of relevant problems is rather universal and theoretical methods analysing this phenomenon form a definite area of mathematical physics. It was founded by Lord Rayleigh at the beginning of the 20th century and has been intensively developed since 1950 in response to practical needs. Modern theory involves, along with the classical methods, some new ap proaches with much more extensive possibilities. The theoretical methods describing wave scattering at rough surfaces repre sent the subject of this book. Having studied this area over many years, the author came to the conclusion that most of the results found in this theory can easily be obtained and comprehended in the framework of a rather universal scheme and this became the motive for writing the present monograph. The first half of the book deals with the classical results. However, several new problems are considered in connection with the methods used here (for example, some applications of the Rayleigh hypothesis and its relation to the Lippman argument). The second half is fully devoted to recent results presented in papers but not yet in books. For this reason the author hopes that the present book will be of interest to both newcomers and experts in this area.
The three main types of approximations used for the scattering of acoustic waves from rough surfaces are discussed: Rayleigh's Ansatz, the Kirchhoff geometrical-interference approach and the perturbation technique as used by Meecham. In order to compare them they are given in a uniform wave-number representation. They are justified with aid of the Helmholtz integral, which is completely Fourier-transformed. In each approximation the scattering formulae consist of the product of two parts: one that is represented by a spectrum of the phase modulations induced by the surface irregularities and another that is a geometrical factor. The corresponding first steps in each approximation are shown to be quite close to each other. The limits of validity are estimated. An interpolation formula unifying the different types of approximations is proposed. (Author).
The Helmholtz integral is often used as the basis for theories on scattering of acoustic signals from rough surfaces, but several approximations must be made to obtain analytical solutions. Many of the mathematical difficulties in analytical computations can be avoided by numerically evaluating the Helmholtz integral. A numerical technique is described which uses measured values of the acoustic pressure of the incident beam, including the side lobes, thereby removing the uncertainty which normally results from approximating the form of the incident beam. A comparison of numerical, analytical, and experimental results is made for the case of a vertically incident beam and a moderately rough surface. The numerical computations are shown to yield values of the scattered pressure which agree well with experimental data for both rough and smooth surfaces. (Modified author abstract).
The topic of surface waves lies at the interface between a number of disci plines - physics, theoretical and applied mechanics, electroacoustics, ap plied mathematics, surface science and seismology. This volume, based on papers delivered at European Mechanics Colloquium 226, reflects this diversity in approach and background, while showing strong links between phenomena arising from different fields. The emphasis is on recent de velopments such as nonlinear and other nonclassical effects,which have great importance for both pure science and for applications such as signal processing, nondestructive evaluation and seismic studies. In recent years there has been considerable progress in the mathe matical treatment of nonlinear effects, of viscoelastic and of more novel constitutive effects which modify the predictions of linear elastic and piezo electric theory for surface acoustic wave (SAW) propagation. A number of these themes serve to group the contents of this volume. Part I contains recent advances in the rigorous mathematical treatment of nonlinearity, together with a paper giving experimental results showing the need for further theoretical development. Part II deals with anisotropic elasticity, showing that even the linear theory presents many possible behaviours, which are still not fully categorized.
