V. A. Burov

Multifrequency generalization of the Novikov algorithm for the two-dimensional inverse scattering problem

The process of reconstruction of two-dimensional refractive-absorbing scatterers by the modified Novikov algorithm is considered. A generalization of this algorithm to the multifrequency mode is proposed. The scattering data obtained at different frequencies are combined in the process of the solution using the a priori known frequency dependence of the scatterer function, which yields the constraint equations that are absent in the single-frequency version. It is shown that the problem of reconstruction instability observed in strong scatterers in the single-frequency mode can be removed by the multifrequency mode. The quality of the scatterer estimate in the multifrequency mode is significantly higher than that of the estimate obtained by straightforwardly averaging the single-frequency solutions. Interference resistance of the algorithm is sufficiently high to allow its application in practice.

Acoustic double-negative media

We consider the possibility of the existence of media in acoustics that are similar in several effects to the widely discussed electrodynamic left-handed media. The density and compressibility of a medium are shown to be the mechanical analogues of negative permittivity and permeability. We discuss the physical meaning of their negativity and mechanical models with such properties. To identify the effects related to the sign of the density and compressibility, we have performed our analysis based on linearized hydrodynamic equations instead of the wave equation or the Helmholtz equation. We have obtained an analogue of the Lippmann—Schwinger equation and constructed a theory of wave scattering by inhomogeneities in a medium with arbitrary values and signs of the density and compressibility. Our numerical simulations have revealed all of the expected effects. We consider the questions concerning the fulfillment of the causality principle and its consequences generalized to the case of negative media in the form of a connection between the damping and dispersion of waves.

Reconstruction of Fine-Scale Structure of Acoustical Scatterer on Large-Scale Contrast Background

One of the most actual medical problems is a diagnostics of different pathologies of biological tissues. It is very important to reveal a malignant pathology at the earliest stage of its growth, when the size of a disease area is a part of a millimeter. Then strict mathematical methods of the solution of inverse problems are necessary for revealing this area on the basis of experimental acoustical scattering data.

Solution of the three-dimensional acoustic inverse scattering problem. The modified Novikov algorithm

For the first time, three-dimensional model scatterers of various strengths and size are numerically reconstructed on the basis of the monochromatic functional-analytical Novikov algorithm. The algorithm allows for the multiple scattering processes and does not impose stringent constraints on the scatterer strength. The resulting scatterer estimate approaches the true value after the width of the scatterer’s spatial spectrum is restricted to a region with a radius of about 2k0. The noise robustness of the algorithm, i.e., the robustness to random errors in experimental data, is sufficiently high for diagnostic applications. However, the amount of numerical operations required by the algorithm is great.

Simulation of a functional solution to the acoustic tomography problem for data from quasi-point transducers

Two variants of a functional-analytical algorithm intended for solving inverse tomography problems are discussed and numerically carried out. The acoustic fields that are transmitted and received by transducers, which are equivalent to point ones, serve as experimental data. These data are used to calculate the classical or generalized scattering amplitude, and the scatterer characteristics are then reconstructed. The algorithm requires neither model linearization, no iterations for refining the estimates of scatterers, thus making it attractive for solving acoustic-tomography problems in different applications. The results of the numerical reconstruction of inhomogeneities in the sound velocity and absorption in a medium are presented.

The use of low-frequency noise in passive tomography of the ocean

A possible design of the mode tomography of the ocean with the use of a scheme requiring no expensive low-frequency radiators is considered. The design is based on the widely discussed method of estimating the Green’s function from the cross-coherence function of noise field received in a great number of observation points. The relationship between the Green’s function and the noise coherence function is derived from the Helmholtz-Kirchhoff integral. The use of the vertical multielement arrays composed of vector receivers is suggested to decrease the duration of noise signal accumulation required for a reliable determination of the Green’s function. The solution of the tomographic problem is based on the determination of the mode structure of acoustic field from the eigenvectors and eigenvalues of the cross-coherence matrix of the received noise field.

Experimental modeling of the processes of active-passive thermoacoustic tomography

Experiments confirming the major results of the theoretical study of an active-passive mode of acoustic thermotomography are described. Experimental results are obtained with a setup intended for physical modeling of the processes of correlation reconstruction of the temperature, absorption, and phase velocity of sound in the object under investigation in the presence of an additionally introduced “illuminating” acoustic noise field. A possibility of reconstructing the local values of absorption and inhomogeneity of sound velocity from analyzing the correlation dependences based on difference and summary delays and also with the help of a controlled anisotropic acoustic irradiation is demonstrated.

Selection of modes from a shallow-water noise field by single bottom hydrophones for passive tomography purposes

The possibility of selecting modes that propagate between two spaced observation points without the use of vertical arrays and low-frequency emitters is considered. Modes are selected from the cross-correlation function of noise received by single hydrophones. It is shown that modes at frequencies near the minima of the dispersion dependences of their group velocities, where stationary phase regions are observed, make the main contribution to the noise cross-correlation function. This makes it possible to identify modes of different numbers and estimate their propagation times between hydrophones, which can be the basis for shallow-water passive mode tomography using data from single bottom hydrophones. The modes were selected based on data from a experiment carried out in the Barents Sea.

Numerical and physical modeling of the tomography process based on third-order nonlinear acoustic effects

The possibility of employing the nonlinear effect of generation of third-order combination waves for the purposes of medical diagnostics is analyzed. This effect can be used to reconstruct the spatial distribution of acoustic nonlinear parameters in the framework of the wave approach. Contributions of third-order nonlinear scattering itself and of the double second-order scattering are evaluated. These two competing processes evolve simultaneously and produce similar observed effects, which can nevertheless be separated. A two-dimensional experimental scheme that contains only three transmitters and one receiver, uses two primary wideband modulated waves and an introduced third monochromatic wave, is proposed. Results of the numerical and physical model experiments are provided.

The significance of the choice of basis functions in the problems of acoustic tomography of the ocean

Different approaches to the parametric description of the ocean inhomogeneities of both refraction and kinetic types are discussed in the context of the inhomogeneity reconstruction with the use of tomographic techniques. In addition to bases commonly known and widely used in oceanological problems (such as specification of the inhomogeneity parameters at the grid nodes or in nonoverlapping shapes compactly covering the region of interest), a new nonorthogonal and redundant basis consisting of a set of overlapping bands (and, presumably, more convenient for solving tomographic problems) is considered. The abilities of different bases to reconstruct the ocean inhomogeneities are compared with the use of special theoretical approach. The quality of reconstruction on the band and cell bases is investigated against the relationship between the number and composition of the basis elements. Examples of the reconstruction of ocean inhomogeneities with the use of the aforementioned basis functions are given together with the results of comparison.