On constructing the Riemannian metrics in refraction tomography problems

A problem of the refraction tomography consists in reconstructing a function or tensor field by their attenuated ray transforms. Usually an absorption coefficient and refraction in the medium are assumed to be known. A solution to the refraction tomography problems can be obtained by approximate methods within the corresponding mathematical models, and the modeling of refraction is one of important elements of the model. We adduce summary data on the Riemannian metrics, suitable for the implementation in numerical tests, methods of their construction and main characteristics. (paper)