Guillermo C. Gaunaurd

Signal analysis by means of time-frequency (Wigner-type) distributions-applications to sonar and radar echoes

Time series data have been traditionally analyzed in either the time or the frequency domains. For signals with a time-varying frequency content, the combined time-frequency (TF) representations, based on the Cohen class of (generalized) Wigner distributions (WDs) offer a powerful analysis tool. Using them, it is possible to: (1) trace the time-evolution of the resonance features usually present in a standard sonar cross section (SCS), or in a radar cross section (RCS) and (2) extract target information that may be difficult to even notice in an ordinary SCS or RCS. After a brief review of the fundamental properties of the WD, we discuss ways to reduce or suppress the cross term interference that appears in the WD of multicomponent systems. These points are illustrated with a variety of three-dimensional (3-D) plots of Wigner and pseudo-Wigner distributions (PWD). The plots are all obtained from an extensive analysis we have made over the years of the resonance acoustic echoes backscattered by a variety of elastic shells submerged in water, when they are excited by various types of incident pressure waves, including the short pulses generated by explosive charges. We also review studies we have made of the echoes returned by conducting or dielectric targets in the atmosphere, when they are illuminated by broadband radar pings. These short incident pulses are used to analytically model the performance of ultrawide band (UWB) radars, often called impulse radars. A TF domain analysis of these impulse radar returns demonstrates their superior information content.

Acoustic scattering by a pair of spheres

If acoustic scattering by a single sphere is the most basic problem of scalar scattering, then sound scattering by a pair of spheres is next in the hierarchy of complexity. The problem has been formulated by several approaches in the past, but no actual detailed studies have been openly published so far. Two spheres insonified by plane waves at arbitrary angles of incidence are considered. The solution of this simplest of multiple‐scattering problems is generated by exactly accounting for the interaction between the two spheres, which can be strong or weak depending on their separation, compositions, frequency, and directions of observation. The tools to attack this type of problem are the (forward/backward) addition theorems for the spherical wave functions, which permit the field expansions—all referred to the center of one of the spheres—by means of Wigner (3‐j) symbols. The fields scattered by each sphere are obtained as pairs of (double) sums in the spherical wave functions, with coefficients that are coupled through an infinite set of two linear, complex, algebraic equations. These are then solved (by truncation) and used to obtain (i) the scattered fields and (ii) the scattering cross section of the pair of spheres. These exact results are illustrated with many plots of the form functions at various relevant incidence angles, separations, frequencies, etc. Finally, some asymptotic approximations for this problem that are analytically simple are obtained. They are displayed and compared to the exact solutions found above, with quite satisfactory results, even for the simple approximations used here. Thus the phenomenon is described, explained, graphically displayed, physically interpreted, and reduced to a simple accurate approximation in some important cases.

Sonar cross sections of bodies partially insonified by finite sound beams

An object that is partially insonified by a collimated sound beam may have a scattering cross section sometimes much larger than when the object is totally covered by the incident beam. We quantitatively study this partial insonification problem here, under the classical method of physical optics. The importance of this study stems from the fact that partial coverage of the target by the beam is the situation most likely to occur in many cases of practical importance. We consider several basic target shapes partially insonified by finite beams. These shapes include the spherical, the infinite and finite cylinder, the flat plate, and the capped sphere. High-frequency approximations of the resulting integrals, obtained by means of the saddle-point method, show the relative importance of the scattering centers located at the beams specular reflection points, or at the edges of the spots that the beam shines on the scatterers. The physical-optics method is extended to obtain formulas for the bistatic cross sections of partially insonified objects. The results are numerically evaluated and graphically displayed in many pertinent instances and compared to the predictions of approaches, such as the Fresnel-zones method and the Geometrical Theory of Diffraction (GTD). The predictions of the physical-optics method have all the advantages and deficiencies of this method and, with very minor modifications, hold equally well for the partial illumination of objects by beams of electromagnetic radiation.

Sound scattering by a spherical object near a hard flat bottom

We consider the scattering of plane acoustic waves by spherical objects near a plane hard surface. The angles of incidence are arbitrary and so are the distances of the objects from the hard boundary. We use the method of images. The final result for the sound field consists of four parts: the incident field and its reflection from the boundary, which are shown combined; the scattered field from the sphere, and that scattered by its image. These last two appear coupled since both sphere and image are repeatedly interacting with each other. The entire solution is referred to the center of the real sphere. This can be accomplished in an exact fashion by means of the addition theorems for spherical wave-functions. These theorems are taken from the atomic physics literature, where they are more frequently used. The required coupling coefficients, b/sub mn/, are obtained from the solution of an infinite linear complex system of transcendental equations with coefficients given by series. The system is suitably truncated to obtain numerical predictions for the form-functions by means of the Gauss-Seidel iteration method. Many calculations are displayed exhibiting the distortion that the proximity of the hard boundary causes on the free-space solution. The form-functions are graphed versus ka, for various values of the normalized separation D/spl equiv/d/a of the sphere from its image. They are also plotted versus the angle of observation, for fixed values of /spl Omega/=La and D. These plots are the exact benchmark curves against which the accuracy of approximate solutions, found by other methods, could be assessed. They could also serve to determine the distances above the bottom, beyond which the bottom effect could be neglected. This is an idealized model to predict the distorted sonar cross section of a hard spherical object near a hard flat bottom.

Acoustic scattering by an air-bubble near the sea surface

High data rate acoustic transmission is required for diverse underwater operations such as the retrieval of large amounts of data from bottom packages and real time transmission of signals from underwater sensors. The major obstacle to underwater acoustic communication is the interference of multipath signals due to surface and bottom reflections. High speed acoustic transmission over a shallow water channel characterized by small grazing angles presents formidable difficulties. The reflection losses associated with such small angles are low, causing large amplitudes in multi-path signals. In this paper we propose a simple but effective model for multipath interference, which is then used to assess the performance of a digital communication system operating in a shallow water channel. The results indicate that transmission rates in excess of 8 k-bits/s are possible over a distance of 13 km and channel depth of only 20 meters. Such a system offers improved performance in applications such as data collection from underwater sensors.

Scattering of a plane acoustic wave by a spherical elastic shell near a free surface

Abstract The acoustic scattering by a submerged spherical elastic shell near a free surface, which is insonified by plane waves at arbitrary angles of incidence is analyzed in an exact fashion using the classical separation of variables technique. To satisfy the boundary conditions at the free surface as well as on the surface of the spherical elastic shell, the mathematical problem is formulated using the image method. The scattered wave fields are expanded in terms of the classical modal series of spherical wave functions utilizing the translational addition theorem. Quite similar to the problem of scattering by multiple spheres, numerical computation of the scattered wave pressure involves the solution of an ill-conditioned complex matrix system the size of which depends on how many terms of the modal series are required for convergence. This in turn depends on the value of the frequency, and on the proximity of the spherical elastic shell to the free surface. The ill-conditioned matrix equation is solved using the Gauss-Seidel iteration method and Twerskys method of successive iteration cross checking each other. Backscattered echoes from the spherical elastic shell are extensively calculated and displayed. The result also demonstrates that the large amplitude low frequency resonances of the echoes of the submerged elastic shell shift upward with proximity to the free surface. This can be attributed to the decrease of added mass for the shell vibration. The present benchmark solution could eventually be used to validate those found by numerical schemes.

Frequency- and time-domain analysis of the transient resonance scattering resulting from the interaction of a sound pulse with submerged elastic shells

The authors present a resonance scattering analysis of the echoes returned by a submerged, air-filled, elastic spherical shell, and also from a rigid sphere, when they are insonified by sound pulses. They consider arbitrary pulsed incidences of any duration, carrier frequency, envelope and shape. The approach is equally effective in the frequency and the time domains. They compare backscattered echoes returned by the structures under study in various instances, which are predicted by exact modal approaches, and by the approximate Kirchhoff method. The effects of pulse duration are examined, and so are the various kinds of resonances that develop when a shell is insonified by extremely narrowband pulses. Also examined is the concept of an impulse sonar, for incident pulses that are short- and broadbanded. An inverse scattering analysis shows how and how well physical target characteristics extracted in situ from the remotely sensed echoes can be used for target identification. Various sample cases are constructed and solved and the results interpreted.<<ETX>>

Transient acoustic scattering by fluid-loaded elastic shells

Abstract We study the general scattering interaction of acoustic pulses of arbitrary shape and duration with a submerged elastic spherical shell. We first obtain the backscattering or sonar crosssection (SCS) of such a target and analyze the resonance features that are present within its resonance region. The elastic composition of the shell makes the resonance features become very prominent in a very wide band. Transient echoes from submerged shells are related to poles of the scattering amplitude and to their associated residues in the complex frequency plane. We show by exact Fourier synthesis that the individual resonances associated with each pole (i.e., eigenfrequencies) can be obtained and studied one at a time, provided we use long illuminating pulses, since these excite transients at their carrier frequencies that ring and decay. Of greater practical importance is the use of short pulses, not only because these are the most frequently used by sonars, but because they are shown here to produce backscattered pulses with spectra that replicate the entire set of features in the SCS of the shell. This replication of the SCS occurs in bands that have widths directly proportional to their energy and their carrier frequency, xn. Our computational methodology can handle pulses of any duration, shape, and any conceivable spectra, as well as lossless or lossy fluidloaded shells, either single or multi-layered. We can predict the returns in all instances. For long insonifying pulses, the backscattered echoes exhibit a double transient nature when xn coincides with any shell resonance. The successive tail bursts that follow the specular part of the return in the time domain not only are seen to decrease in amplitude, but the decrease occurs in distinct discrete jumps. We predict the backscattered echoes for various types of pulses, carrier frequencies, bands, shapes and durations and we display the results in the (non-dimensional) time and frequency domains, while giving the appropriate physical interpretations of the results in all instances.

Multipole character of the large-amplitude, low frequency resonances in the sonar echoes of submerged spherical shells

Abstract We analyze the large-amplitude resonance features, which arc present at low frequencies in the backscattering cross-sections (BSCS) of air-fillcd, spherical, elastic shells submerged in water. By means of partial-wave expansions we demonstrate the multipole character of those features. For the materials and thicknesses investigated, it is confirmed that about half-a-dozen modes contribute to their formation. As the shell thickness decreases we note that : (i) fewer modes are seen to contribute to the BSCS. Ultimately, as the shell thickness approaches zero, only the monopole,n = 0. mode has an effect, just as for an air-bubble in water. (ii) In the bubble case, the large amplitude becomesgiant. the various peaks coalesce into one. and its spectral location shifts down tok1a ∼ 10−2. (iii) The narrow, low-amplitude set of overtones caused by the internal air remains present at all thicknesses, as the shell thickness decreases. Finally, we give a physical interpretation for these large features. They seem to he caused by a pseudo-Lamb wave denoted here bya01, investigated earlier by Junger (1967), by means of Donnells shell theory. This wave is slower than the generalized zeroth-order antisymmetrica0, lamb wave for a shell. Its dispersion plot—which we display—exists only in the same narrow, low-frequency spectral band where the large echo features in question also occur. We investigate here its cause and effect by means of an exact, threedimensional elasticity description of the shell motions, which was derived earlier by Ayreset al (1987). We emphasize that what we have called, here and in the referenced paper, thea0-wave, is really a “generalized” antisymmetric zeroth-order Lamb wave for ashell, fluid-loaded on both sides by dissimilar fluids (and not for aplate in vacuum, as is often done). Thea01 is a companion type of generalizeda0-wave for shells that emerges from the roots of the same characteristic equation, and which has no counterpart for Hat plates.

Transient effects in the scattering of arbitrary EM pulses by dielectric spherical targets

We study the general scattering interaction of electromagnetic (EM) pulses of arbitrary shape and duration with a spherical target. The target is assumed penetrable and we model it either as totally dielectric, or as perfectly conducting but covered with a thin outer masking coating of a dielectric material. We obtain the radar cross-sections (RCS) of such targets and analyze the many resonance features that are present within their resonance region. The dielectric composition makes the resonance features become very prominent and it relates them to the eigenfrequencies in ways analogous to those of the Singularity Expansion Method (SEM), originally developed for perfectly conducting scatterers. Transient echoes from these targets are linked to poles and residues in the complex-frequency plane. The individual resonances associated with each pole (i.e., eigenfrequencies) can be studied one at a time, provided we use long illuminating pulses since these excite transients at their carrier frequencies that ri...