Аннотация: Acoustic tomography is the unique approach for studying natural media that are transparent to acoustic waves when direct measurement of medium properties is difficult or impossible. The main characteristics, which influence on propagation of acoustic waves and, as result, which can be reconstructed by acoustic tomography methods, are spatial distributions of sound speed, medium density, absorption coefficient, and vector field of flows. To use algorithms, which allow reconstruction of all mentioned medium characteristics for a wide class of scatterers in a joint tomography scheme, is perspective for solution of the inverse scattering problems in acoustic applications.
Most of the known methods for the solution of acoustic tomography problems are approximate. The linear approximation is generally applied with iteration procedures and regularizations. The general perturbation theory is also considered. On the other hand, there are quite mathematically rigorous (at least, for a rather wide class of scatterers) functional-analytical methods for solving the inverse problems; these methods were initially developed in quantum mechanics. Nowadays, detail investigations based on numerical modeling are required to understand applicability of these methods for acoustics inverse problems.
Possibilities of the functional algorithms for the purposes of 2D and 3D acoustic tomography are discussed in the present report. These algorithms take into account the multiple scattering processes and do not require either linearization of the model with iterations or an additional regularization. The joint reconstruction of sound speed, absorption coefficient, medium density and vector field of flows is considered in 2D problem. In comparison with previously reported results, reconstruction of frequency dependence of the absorption coefficient is regarded. The frequency dependence of the absorption coefficient is an additional informative parameter, which can be used in medical applications for early diagnostics of breast cancer.
Results of 3D tomography reconstruction which takes into account multichannel scattering effects are also presented. These results are perspective for the ocean acoustic tomography which takes into account nonadiabatic propagation of acoustic modes in ocean waveguides. Results of the numerical simulation which show high resolution and good interference resistance of the considered functional algorithms are presented. Thus, the algorithm can be acceptable for practical purposes.