An iterative algorithm for determining a layered model of a medium from CDP method data, named R-algorithm by S.V. Gol'din, is considered. The algorithm serves to overcome an aberration of the estimated CDP travel-time differential parameters within travel-time inversion. We have investigated how aberrations of the estimations obtained by hyperbolic velocity analysis and least-squares approximation depend on a deviation of the travel-time curve from a hyperbola. An explicit formula is obtained for the Frechet derivative of the main operator of the iterative algorithm, which allows one to prove the algorithm convergence and to estimate rate of convergence. As examples, cases of the determination of parameters of horizontally layered medium, vertically heterogeneous medium and homogeneous medium with a curvilinear reflector are considered.
