In this paper, we describe an iteration approach to the solution of the inverse kinematic problem (IKP) in a linearized formulation based on the algebraic reconstruction of velocity distribution in a medium of a tomographic observation system. Linearization of the problem initially occurs at the velocity depending on the depth. In numerical investigations of the media used in works of this class, the applicability of linearization was about 15 with respect to the size of the restored function from the known linear function. It was noted that useful information about the solution is retained in 25 of the cases. Modern computational technologies created new opportunities for the construction of the algorithm, which allows us to widen significantly the class of restored velocities and increase the accuracy of the solution.
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