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The paper presents the results of a stability research of estimates of model parameters and static corrections, obtained from reflected wave traveltime curves by means of the adaptive method. The method consists of two main procedures, applied iteratively to the initial estimates. First, current values of parameters are updated according to the difference between actual and estimated traveltime curves. Then the updated values are evened out by using gradient-based local approximation. The adaptive method is used to obtain a stable solution for the inverse traveltime problem of the seismic reflection method. It takes about 6 seconds of machine time to estimate 959 model parameters based on 14767 non-linear equations.