Mode tomography of inhomogeneous media with applications to hydro- and seismoacoustics

Acoustic waves have a unique penetrating ability, which makes them an indispensable source of information about the characteristics of natural environments that are "transparent" to sound. In hydroacoustic applications, this opens up the possibility of monitoring the spatial and temporal variability of vast water areas in a mode close to real time. In geophysical applications, tomographic methods are the main source of information about the deep structure of the Earth. The information obtained with the help of acoustic tomography is important both for global monitoring (for example, for predicting climate changes on Earth, studying the structure of the lithosphere) and for solving local remote sensing problems (such as illumination of the underwater environment of the marginal seas, search for hydrocarbons on the Arctic shelf). From a mathematical point of view, the acoustic tomography problem is a special case of a more general class of inverse scattering problems. The report discusses some methods of acoustic tomography, taking into account the specifics of hydro- and seismoacoustic tasks. The results of numerical modeling and processing of experimental data are presented. The issues of passive mode tomography of the ocean, based on the evaluation of the Green function from the noise cross-correlation function, are touched upon. Examples of the use of linear approximation in the reconstruction of three–dimensional oceanic inhomogeneities, as well as the characteristics of the geophysical medium "elastic half–space - water layer - ice cover" are given. The results of a numerical study of functional-analytical algorithms for solving two-dimensional and three-dimensional problems of acoustic tomography of scalar-vector inhomogeneities taking into account multichannel mode scattering are discussed.