ИСТИНА

We consider a moving fluid in a bounded two-dimensional domain D with variable sound speed c, fluid velocity v, density ρ and absorption α. There are acoustic transducers on the boundary of the domain D which can emit and record time-harmonic acoustic waves. In the acoustic tomography experiment one fixes an emitting transducer, which produces a time-harmonic wave at some fixed frequency ω. This wave propagates through the fluid, and the scattered wave is recorded by the receiving transducers. Next, we change the emitting transducer and, possibly, the frequency, and repeat the experiment. The acoustic tomography problem consists in recovering the fluid parameters from the described measurements of the scattered acoustic waves. This problem is motivated by the applications in medical tomography, where one is interested in recovering the parameters of a body including the blood flows, and by the applications in the ocean tomography, where one is interested in recovering the temperature distribution as well as the currents performing the heat transfer. The proposed algorithm is based, in particular, on the papers [1], [2], [3]. The main ingredient is the solution of a non-local Riemann-Hilbert problem. The algorithm was numerically implemented and studied in some particular cases by Andrey Shurup and Olga Rumyantseva from the acoustics department of Moscow State University. The performed simulations give evidences of a relatively good noise stability and, as a corollary, of a good applicative potential of this approach. Literature: 1. Agaltsov, A. D. and Novikov, R. G., Riemann-Hilbert problem approach for two-dimensional flow inverse scattering, Journal of Mathematical Physics 55 (10), 2014, id103502 2. Agaltsov, A. D., Finding scatteromg data for a time-harmonic wave equation with first-order perturbation from the Dirichlet-to-Neumann map, Journal of Inverse and Ill-Posed Problems 23 (6), 2015, 627-645 3. Agaltsov A. D., On the reconstruction of parameters of a moving fluid from the Dirichlet-to-Neumann map, Eurasian Journal of Mathematical and Computer Applications 4 (1), 2016, 4-11