CiteULike: norris's scattering

Multiple Scattering of Waves. II. “Hole Corrections” in the Scalar Case

JG Fikioris — 2008-07-15T19:41:43-00:00

Journal of Mathematical Physics, Vol. 5, No. 10. (1964), pp. 1413-1420.

Reflection and transmission by randomly spaced elastic cylinders in a fluid slab-like region

Pierre Le Bas — 2008-07-15T19:14:19-00:00

The Journal of the Acoustical Society of America, Vol. 117, No. 3. (2005), pp. 1088-1097.

An extension of Fikioris and Waterman's formalism is developed in order to describe both the reflection and transmission from a slab-like fluid region in which elastic cylindrical scatterers are randomly placed. The dispersion equation of the coherent wave inside the slab must be solved numerically. For solid cylinders, there is only one solution corresponding to a mean free path of the coherent wave larger than one wavelength. In that case, the slab region may be described as an effective dissipative fluid medium, and its reflection and transmission coefficients may be formally written as those of a fluid plate. For thin hollow shells, a second solution of the dispersion equation is found, at concentrations large enough for the shells to be coupled via the radiation of a circumferential Scholte–Stoneley A wave on each shell. This occurs at a few resonance frequencies of the shells. At those frequencies, then, two different coherent waves propagate in the slab, and it can no longer be considered a dissipating fluid slab. ©2005 Acoustical Society of America.

Multiple scattering by random configurations of circular cylinders: Second-order corrections for the effective wavenumber

CM Linton — 2008-05-28T13:38:43-00:00

The Journal of the Acoustical Society of America, Vol. 117, No. 6. (2005), pp. 3413-3423.

A formula for the effective wavenumber in a dilute random array of identical scatterers in two dimensions is derived, based on Lax's quasicrystalline approximation. This formula replaces a widely-used expression due to Twersky, which is shown to be based on an inappropriate choice of pair-correlation function. ©2005 Acoustical Society of America.

Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter II. The full Maxwell equations

Habib Ammari — 2008-01-20T20:20:07-00:00

Journal des Mathematiques Pures et Appliques, Vol. 80, No. 8. (October 2001), pp. 769-814.

We consider solutions to the time-harmonic Maxwell Equations. For such solutions we provide a rigorous derivation of the the leading order boundary perturbations resulting from the presence of a finite number of interior inhomogeneities of small diameter. These formulas generalize those by Vogelius and Volkov, where only solutions with "transverse electric" and "transverse magnetic" symmetries were considered. Our formulas may be expected to lead to very effective computational identification algorithms, aimed at determining specific internal features of an object based on electromagnetic boundary measurements.

Diffraction by a wedge with a face of variable impedance

Bair Budaev — 2007-09-08T14:03:30-00:00

Radio Science (2007)

Simplified representation of the generalized Green's equations for the constant motion of translation of a rigid body in a viscous fluid

H Faxen — 2007-04-09T18:43:51-00:00

Arkiv för Matematik, Astronomi och Fysik, Vol. 20, No. 8. (1927)

Multiple scattering of light and some of its observable consequences

Craig Bohren — 2007-04-02T14:40:54-00:00

American Journal of Physics, Vol. 55, No. 6. (1987), pp. 524-533.

Many common observations are inexplicable by single-scattering arguments: the variation of brightness and color of the clear sky; the brightness of clouds; the whiteness of a glass of milk; the appearance of distant objects; the blueness of light transmitted in snow and other natural ice bodies; the darkening of sand upon wetting. Yet multiple scattering is seldom mentioned in optics textbooks. It is possible to understand many observable phenomena without invoking the complete theory of multiple (incoherent) scattering. A simple two-stream theory, in which photons are constrained to be scattered in only two directions, forward and backward, is adequate for interpreting many observations, even quantitatively, and it paves the way for advanced study. ©1987 American Association of Physics Teachers

SCATTERING OF SHEAR WAVES BY SPHERICAL OBSTACLES

Leon Knopoff — 2007-03-29T16:56:10-00:00

Geophysics, Vol. 24, No. 2. (1959), pp. 209-219.

The problem of the scattering of plane S waves by a perfectly rigid, infinitely dense sphere is formulated. Calculations are made for the case in which the medium outside the sphere has a Poisson's ratio of . The range of sizes of obstacles used in the calculations includes radii very small compared with the wave length and radii comparable to the wave length. The scattered wave motions include a P mode and two S modes. One of the S modes has a formal correspondence to the SH mode of plane seismology; the other corresponds to the SV mode. At large distances from the obstacle the scattered P and S fields are computed together with the phase shifts in time occurring in all the components. For small obstacles, the scattered azimuthal S component is circularly symmetric; the scattered meridional S component diffraction pattern is generally elongated in the direction of propagation; the scattered P component is generally broadside to the direction of propagation.

Survey of some early studies of the scattering of plane waves by a sphere

NA Logan — 2007-03-29T16:42:09-00:00

Proceedings of the IEEE, Vol. 53, No. 8. (1965), pp. 773-785.

This survey of the literature prior to World War II shows that the study of the scattering of plane waves by a sphere has a history in which the list of contributors includes some of the greatest names in mathematical physics from the late nineteenth and early twentieth centuries. When viewed in retrospect, this literature appears to be characterized by the appearance of papers by writers who apparently failed to appreciate the significance of the contributions made by their contemporaries and predecessors. Emphasis is placed upon the relatively unknown contributions of Clebsch, Lorenz, Nicholson, Bromwich, Proudman, Doodson, Kennedy, and White. The uncovering of the "lost" contributions of these writers serves to enrich the historical perspective against which one should view the voluminous literature which has accrued since World War II.

The Born approximation in the theory of the scattering of elastic waves by flaws

JE Gubernatis — 2007-03-27T17:16:52-00:00

Journal of Applied Physics, Vol. 48, No. 7. (1977), pp. 2812-2819.

We used the integral equation formulation of the scattering of elastic waves to generate an approximate solution analogous to the Born approximation in quantum mechanics. This solution is attractive because of the ease with which it may be applied to scatterers of complicated shapes. We investigated the validity of the approximation by comparing it with exact results for spherical scatterers. Our conclusion for voids in elastic media is that the approximation describes well the scattering when the wavelength of the incident wave is approximately an order of magnitude larger than the scatterer and when the scattering is viewed in the backscattered directions. For many applications this range of validity is experimentally accessible. For elastic inclusions, however, where the properties of defect and host differed by 20–40%, the Born approximation is surprisingly good for all angles and even at short wavelengths. Journal of Applied Physics is copyrighted by The American Institute of Physics. doi:10.1063/1.324142 PACS: 62.30.+d, 03.40.Kf, 81.70.+r, 91.30.-f Additional Information Full Text: [ PDF (889 kB)

Scattering of a Plane Transverse Wave by a Spherical Obstacle in an Elastic Medium

Norman Einspruch — 2007-03-27T17:12:58-00:00

Journal of Applied Physics, Vol. 31, No. 5. (1960), pp. 806-818.

An analysis of the scattering of transverse elastic waves by spherical obstacles is presented. The scatterer is taken to be (a) a cavity, (b) a rigid sphere, (c) a fluid-filled cavity, and (d) to consist of an elastic material with properties different from those of the surrounding material. The problems are carried as far as possible analytically without approximations and are reported as matrix equations. The solution of these equations yields the expansion coefficients that describe the waves which are scattered outward from the obstacle and which are excited within the scatterer. A general expression for the scattering cross section offered to a transverse wave has been derived. The Rayleigh approximation is then considered in detail for three of the cases. ©1960 The American Institute of Physics

Scattering of a Plane Longitudinal Wave by a Spherical Obstacle in an Isotropically Elastic Solid

CF Ying — 2007-03-27T17:10:55-00:00

Journal of Applied Physics, Vol. 27, No. 9. (1956), pp. 1086-1097.

Scattering by a spherical obstacle of a plane longitudinal wave propagating in an isotropically elastic solid is computed. Expressions for the scattered wave and the total scattered energy are given. Three special types of obstacle—an isotropically elastic sphere, a spherical cavity, and a rigid sphere—are discussed in detail, especially for Rayleigh scattering. The result for the isotropically elastic sphere is compared with the well-known result of scattering of a plane wave propagating in an ideal fluid by a sphere of another ideal fluid. Journal of Applied Physics is copyrighted by The American Institute of Physics.

Response of a Rigid Spheroidal Inclusion to an Incident Plane Compressional Elastic Wave

SK Datta — 2007-03-26T16:59:08-00:00

SIAM Journal on Applied Mathematics, Vol. 26, No. 2. (1974), pp. 350-369.

Dyadic Scattering by Small Obstacles. The Rigid Sphere

George Dassios — 2007-03-26T13:51:22-00:00

Q J Mechanics Appl Math, Vol. 54, No. 3. (1 September 2001), pp. 341-374.

The general theory of low-frequency dyadic scattering is developed for the near fields, the far fields and all the energy functionals associated with scattering problems. The incident field could be any complete dyadic field generated either in the exterior medium of propagation (point source) or at infinity (plane waves). The case of a small rigid sphere, which is illuminated by a plane dyadic field, is solved and the corresponding results for acoustic and elastic scattering are recovered as special cases. In order to solve analytically the sphere problem a special technique had to be developed, which generates Papkovich-type differential representations of dyadic elastostatic displacements. Comparison of numerical results, obtained via the boundary element method, show an amazing accuracy with our analytical results. 10.1093/qjmam/54.3.341

Curle's equation and acoustic scattering by a sphere.

AM Davis — 2007-03-26T13:34:12-00:00

J Acoust Soc Am, Vol. 119, No. 4. (April 2006), pp. 2018-2026.

Recent papers have initiated interesting comparisons between aeroacoustic theory and the results of acoustic scattering problems. In this paper, we consider some aspects of these comparisons for acoustic scattering by a sphere. We give a derivation of Curle's equation for a specific class of linear acoustic scattering problems, and, in response to previous claims to the contrary, give an explicit confirmation of Curle's equation for plane wave scattering by a stationary rigid sphere of arbitrary size in an inviscid fluid. We construct the complete solution for scattering by a rigid sphere in a viscous fluid, and show that the neglect of viscous terms in Curie's equation yields an incomplete prediction of the far field dipole pressure. We also consider the null field solution of the sphere scattering problem, and give its extension to the vorticity modes associated with viscosity. Finally, we construct a solution for an elastic sphere in a viscous fluid, and show that the rigid sphere/null field solution is recovered from the limit of infinite longitudinal and shear wave speeds in the elastic solid.

Anderson (1950) revisited

C Feuillade — 2007-03-26T13:24:44-00:00

The Journal of the Acoustical Society of America, Vol. 106, No. 2. (1999), pp. 553-564.

The Anderson fluid sphere scattering model [J. Acoust. Soc. Am. 22, 426–431 (1950)] is reexamined to clarify three issues which have been the source of misunderstanding among underwater acousticians. First, the accuracy of the Morse large range approximation for the spherical Hankel functions is investigated. It is shown that the minimum range for use of the approximation is strongly mode number dependent, and should be carefully evaluated in short range and/or high frequency applications. Second, the precise characterization of the forward scatter region is studied. When the scattered field and the incident plane wave are combined, it is shown that little advantage is obtained in detection and localization applications by using forward scattering, rather than backscattering. Third, the translational response, or "rebound," of the sphere under the action of the incident field is examined. By demonstrating that Anderson's theory is a limiting case of Faran's scattering model [J. Acoust. Soc. Am. 23, 405–418 (1951)] for an elastic sphere, which contains the rebound response, it is shown that the response is completely explainable within Anderson's theory, and is consistent with a description which uses a normal mode expansion around a fixed origin. ©1999 Acoustical Society of America.

Sound Scattering by Solid Cylinders and Spheres

James Faran — 2007-03-26T13:20:20-00:00

The Journal of the Acoustical Society of America, Vol. 23, No. 4. (1951), pp. 405-418.

The theory of the scattering of plane waves of sound by isotropic circular cylinders and spheres is extended to take into account the shear waves which can exist (in addition to compressional waves) in scatterers of solid material. The results can be expressed in terms of scattering functions already tabulated. Scattering patterns computed on the basis of the theory are shown to be in good agreement with experimental measurements of the distribution-in-angle of sound scattered in water by metal cylinders. Rapid changes with frequency in the distribution-in-angle of the scattered sound and in the total scattered energy are found to occur near frequencies of normal modes of free vibration of the scattering body. ©1951 Acoustical Society of America

Scattering of Sound by a Rigid Movable Sphere

Robert Hickling — 2007-03-26T13:15:10-00:00

The Journal of the Acoustical Society of America, Vol. 39, No. 2. (1966), pp. 276-279.

The echoes from a rigid, freely movable sphere, due to an incident train of plane waves, are computed, together with the associated rigid-body motions of the sphere. These results are compared with those for a rigid, immovable sphere and it is shown that they differ significantly only for values of ka below about 5. The significance of the results in relation to previous work on sonar echoes from solid, elastic spheres in water is discussed. A particular case of forced motion of the rigid sphere, where the echoes diminish to zero at high frequencies, is also investigated. ©1966 Acoustical Society of America

The disturbance of a plane dyadic wave by a small spherical cavity

George Dassios — 2007-03-26T13:07:17-00:00

International Journal of Engineering Science, Vol. 40, No. 17. (October 2002), pp. 1975-2000.

Scattering of a Spherical Dyadic Field by a Small Rigid Sphere

George Dassios — 2007-03-26T12:59:45-00:00

Mathematics and Mechanics of Solids, Vol. 7, No. 1. (1 February 2002), pp. 3-40.

A complete dyadic field, which is generated at a point and propagates within a homogeneous and isotropic elastic medium, is disturbed by a small rigid sphere. Analytic solutions for this complicated dyadic scattering problem are provided with the help of an extended theory of the Papkovich representation for elastostatic dyadic fields. Relative results obtained numerically show an amazing coincidence as long as we stay in the low-frequency regime. In contrast to the plane wave excitation case, where only a few multipole terms are needed to express the leading low-frequency approximations, the case of point source excitation provides low-frequency solutions where an infinite number of multipoles are present. An exception is offered by the first-order approximation, which enjoys a closed-form expression. 10.1177/1081286502007001219

Scattering of elastic waves by a movable rigid sphere embedded in an infinite elastic solid

Y Iwashimizu — 2007-03-26T12:53:07-00:00

Journal of Sound and Vibration, Vol. 21, No. 4. (22 April 1972), pp. 463-469.

Scattering of an elastic wave by a rigid but movable spherical obstacle is studied, its oscillation being taken into account. The scattered wave, the oscillation of the rigid sphere and the scattering cross section are calculated for an incident longitudinal or shear wave. These calculations reveal the differences between the scattering by a movable rigid sphere and that by an immovable one, especially in the Rayleigh limit. The scattering cross section in this limit is shown to depend on the inverse of the fourth power of the wavelength, while it was reported to be independent of the wavelength for an immovable rigid sphere.

Multiple scattering by multiple spheres: a new proof of the Lloyd-Berry formula for the effective wavenumber

CM Linton — 2007-03-25T21:55:24-00:00

(2005)

The One-Dimensional Inverse Problem of Reflection Seismology

Kenneth Bube — 2006-10-28T12:59:12-00:00

SIAM Review, Vol. 25, No. 4. (1983), pp. 497-559.

An impulsive normal traction is applied uniformly over the surface of a perfectly stratified plane layered earth. The ensuing particle velocity at the surface is assumed to be measured. The problem of calculating the subsurface characteristic impedance from knowledge of the input pulse and the measured data is the one-dimensional inverse problem of reflection seismology. The problem is set up mathematically as an inverse problem for a first order 2 × 2 hyperbolic system. The role of propagation of singularities is explained and the relation between the solution of the inverse problem and the Cholesky factorization of certain matrices constructed from the data is elaborated for both the continuum problem and the related discrete problem. It is found that recursive numerical techniques such as the Levinson algorithm and certain other fast methods for Cholesky factorization are intimately related to explicit finite-difference schemes for solving hyperbolic systems. The order of approximation between the solutions of the discrete schemes and of the differential equations is discussed. Finally the favored discrete downward continuation (DC) algorithm is demonstrated by means of numerical examples, which are illustrated graphically.

Retrieving the Elastodynamic Green's Function of an Arbitrary Inhomogeneous Medium by Cross Correlation

Kees Wapenaar — 2006-10-15T14:30:16-00:00

Physical Review Letters, Vol. 93, No. 25. (2004)

A correlation-type reciprocity theorem is used to show that the elastodynamic Green's function of any inhomogeneous medium (random or deterministic) can be retrieved from the cross correlation of two recordings of a wave field at different receiver locations at the free surface. Unlike in other derivations, which apply to diffuse wave fields in random media or irregular finite bodies, no assumptions are made about the diffusivity of the wave field. In a second version, it is assumed that the wave field is diffuse due to many uncorrelated sources inside the medium.

Quantum multiple scattering: Eigenmode expansion and its applications to proximity resonance

Sheng Li — 2006-10-09T16:37:53-00:00

Physical Review A (Atomic, Molecular, and Optical Physics), Vol. 67, No. 3. (2003)

We show that for a general system of N s-wave point scatterers, there are always N eigenmodes. These eigenmodes or eigenchannels play the same role as spherical harmonics for a spherically symmetric target—they give a phase shift only. In other words, the T matrix of the system is of rank N, and the eigenmodes are eigenvectors corresponding to nonzero eigenvalues of the T matrix. The eigenmode expansion approach can give insight to the total scattering cross section; the position, width, and superradiant or subradiant nature of resonance peaks; the unsymmetric Fano line shape of sharp proximity resonance peaks based on the high-energy tail of a broadband; and other properties. Off-resonant eigenmodes for identical proximate scatterers are approximately angular-momentum eigenstates.

Multiple scattering: The key to unravel the subwavelength world from the far-field pattern of a scattered wave

F Simonetti — 2006-10-09T16:24:09-00:00

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol. 73, No. 3. (2006)

For more than a century the possibility of imaging the structure of a medium with diffracting wave fields has been limited by the tradeoff between resolution and imaging depth. While long wavelengths can penetrate deep into a medium, the resolution limit precludes the possibility of observing subwavelength structures. Near-field microscopy has recently demonstrated that the resolution limit can be overcome by bringing a probing sensor within one wavelength distance from the surface to be imaged. This paper extends the scope of near-field microscopy to the reconstruction of subwavelength structures from measurements performed in the far-field. It is shown that the distortion undergone by a wave field as it travels through an inhomogeneous medium and the subsequent generation of local evanescent fields encode subwavelength information in the far-field due to multiple scattering within the medium. This argument is proved theoretically and supported by a limited view experiment performed with elastic waves in which an image with a resolution better than a third of the wavelength is achieved.

Scattering relations for point sources: Acoustic and electromagnetic waves

C Athanasiadis — 2006-09-16T16:57:05-00:00

Journal of Mathematical Physics, Vol. 43, No. 11. (2002), pp. 5683-5697.

The problem of scattering of spherical waves by a bounded obstacle is considered. General scattering theorems are proved. These relate the far-field patterns due to scattering of waves from a point source put in any two different locations. The scatterer can have any of the usual properties, penetrable or impenetrable. The optical theorem is recovered as a corollary. Mixed scattering relations are also established, relating the scattered fields due to a point source and a plane wave. ©2002 American Institute of Physics.

Effect of Defects on Lattice Vibrations

Elliott Montroll — 2006-08-19T18:38:57-00:00

Physical Review, Vol. 100, No. 2. (15 October 1955), 525.

The theory of the effect of localized defects such as impurities; holes; and interstitials on the vibrations of crystal lattices is developed. Although most of the analysis is concerned with one-dimensional chains; the general approach to defects in three-dimensional lattices is outlined through the example of a simple cubic lattice with nearest-neighbor interactions. Many types of defects cause localized normal modes whose effect dies out rapidly with distance from the defect. Mathematical techniques; which involve the use of Green's functions; are discussed for the theory of these localized modes. The vibrational frequencies of these modes are displaced out of the band of frequencies of a perfect lattice. The theory of interaction of two defects as a function of their distance of separation is developed for the range of very low temperatures through the calculation of the change of zero-point energy of a lattice as a result of the introduction of a defect pair. Defects attract each other in a monatomic lattice. The attraction between two mass defects in a linear chain is inversely proportional to the cube of their distance of separation. The effect of a localized defect mode in a simple cubic lattice diminishes as with the distance r as r -1 exp(- A r ).

Scattering theory for crystal dislocations

RA Brown — 2006-08-08T14:53:19-00:00

Journal of Physics F: Metal Physics, Vol. 7, No. 7. (1977), pp. 1269-1281.

Standard techniques for point scattering centres are extended to the case of scattering by a straight line defect of arbitrary type in a crystal of arbitrary bandstructure. The formulation takes explicit account of point symmetry elements of the defect and utilizes a nonperturbative phaseshift approach. The main aim is to facilitate the study of resonance scattering phenomena associated with dislocations. The qualitative effect of interband scattering on the resonance cross section is clarified as is the effect of the long-range strain field.

Interaction between an elastic wave and a single pinned dislocation

Agnes Maurel — 2006-08-08T14:23:28-00:00

Physical Review B (Condensed Matter and Materials Physics), Vol. 72, No. 17. (2005)

Acoustic, and more generally elastic, waves in solids are damped by several mechanisms, among which dislocation motion is believed to play an important role. This is because an elastic wave interacts with a dislocation causing it to oscillate in response, and the resulting transfer of energy from wave to dislocation damps the acoustic vibrations. Recently, improved experimental techniques as well as improved numerical methods have been able to probe in some detail this interaction, isolating the effect of a single dislocation, and at this stage the theory, in its analytic form, is not sufficiently developed to provide quantitative comparison with experimental data and computer simulations. There is thus a need for an improved theoretical study of this issue. In this paper, we consider the interaction of transverse (T) and longitudinal (L) polarized waves in a homogeneous and isotropic, three dimensional, continuum linear elastic medium interacting with a dislocation segment pinned at both ends. An elastic wave incident upon such a dislocation segment is scattered, and the resulting scattered wave is characterized by its scattering amplitudes, that account for possible T-L mode conversions. Such scattering amplitudes are explicitly calculated. As a consequence, it is possible to calculate the resulting interference patterns of incident with scattered wave, such as have been observed in recent experiments [Shilo and Zolotoyabko, Phys. Rev. Lett. 91, 115506 (2003)]. The energy loss per cycle is also calculated using the optical theorem and results are shown to be in qualitative agreement with the results of numerical experiments [Greaney et al., Comput. Mater. Sci. 25, 387 (2002)].

Scattering of an elastic wave by a single dislocation

Agnes Maurel — 2006-08-08T14:13:42-00:00

The Journal of the Acoustical Society of America, Vol. 115, No. 6. (2004), pp. 2773-2780.

The scattering amplitude for the scattering of anti-plane shear waves by screw dislocations, and of in-plane shear and acoustic waves by edge dislocations are computed within the framework of elasticity theory. The former case reproduces well-known results obtained on the basis of an electromagnetic analogy. The latter case involves four scattering amplitudes in order to fully take into account mode conversion, and an adequately generalized optical theorem for vector waves is provided. In contrast to what happens for scattering by obstacles, the scattering amplitude increases with wavelength, and, in general, mode conversion in the forward direction does not vanish. ©2004 Acoustical Society of America.

On the factorization of n × n matrix Wiener-Hopf kernels with distinct eigenvalues

Benjamin Veitch — 2006-07-30T14:52:31-00:00

(2006)

Microlocal analysis of seismic inverse scattering in anisotropic elastic media

Christiaan Stolk — 2006-06-19T14:52:00-00:00

Communications on Pure and Applied Mathematics, Vol. 55, No. 3. (2002), pp. 261-301.

Seismic data is modeled in the high-frequency approximation, using the techniques of microlocal analysis. We consider general, anisotropic elastic media. Our methods are designed to allow for the formation of caustics. The data is modeled in two ways. First, we give a microlocal treatment of the Kirchhoff approximation, where the medium is assumed to be piecewise smooth, and reflection and transmission occur at interfaces. Second, we give a refined view on the Born approximation based upon a linearization of the scattering process in the medium parameters around a smooth background medium. The joint formulation of Born and Kirchhoff scattering allows us to take into account general scatterers as well as the nonlinear dependence of reflection coefficients on the medium parameters. The latter allows the treatment of scattering up to grazing angles.The outcome of the analysis is a characterization of the singular part of seismic data. We obtain a set of pseudodifferential operators that annihilate the data. In the process we construct a Fourier integral operator and a reflectivity function such that the data can be represented by this operator acting on the reflectivity function. In our construction this Fourier integral operator becomes invertible. We give the conditions for invertibility for general acquisition geometry. The result is also of interest for inverse scattering in acoustic media. © 2002 John Wiley & Sons, Inc.

Inverse potential scattering in duct acoustics

Barbara Forbes — 2006-06-15T17:18:17-00:00

The Journal of the Acoustical Society of America, Vol. 119, No. 1. (2006), pp. 65-73.

The inverse problem of the noninvasive measurement of the shape of an acoustical duct in which one-dimensional wave propagation can be assumed is examined within the theoretical framework of the governing Klein–Gordon equation. Previous deterministic methods developed over the last 40 years have all required direct measurement of the reflectance or input impedance but now, by application of the methods of inverse quantum scattering to the acoustical system, it is shown that the reflectance can be algorithmically derived from the radiated wave. The potential and area functions of the duct can subsequently be reconstructed. The results are discussed with particular reference to acoustic pulse reflectometry. ©2006 Acoustical Society of America