The paper presents the problem of determination of one- and multi-stage prognosis of post-mining surface dislocations. The finite and chronologically ordered vector of geodetic surveys is the describing variable herein. Completed surveys show that the analyzed process can be written as a composition of both deterministic process and singular one. Hence the quantitative description of the kinetics of the process of dislocation forming has been assigned to the class of the stochastic model. An adequate series sum in which time is the argument and random variables are the values makes up the formal definition of the model. The optimization of one-stage prognosis has been carried out for utility purposes. The Durbin-Levinson algorithm is the applied numerical procedure. The utility fragment of this is based on verification of the defined model for certain mining-geological conditions and surveying results. The obtained analytical representation and optimal prognosis of the kinetics of vertical dislocations correspondend to surveying results, which can be testified by adequate measures of the quality of description of the process.

The paper concerns the analysis of the kinematics of the dislocation process that affects surface points within the area of underground exploitation. The problem discussed in the paper is the estimation of the changes concerning spatial configuration of a body, forced by underground influence, Observations of the real process show that the trajectories indicating the dislocations of the medium points are irregular. The deterministic description of the examined process, as a rule, generates smooth trajectories of point dislocation. Therefore, as is natural, the analytical representation of the process cannot be approximated to measurement results with arbitrary accuracy. The entropy has been assumed as the measure of the randomness of a given process. It has been shown then that the entropy is not constant. Hence the description of the post-mining dislocation process has been presented as a stochastic model. The quantitative results of the description have been put to a statistical estimation.

The paper presents an attempt at building an optimum rnathematical model making it possible to prognose the values of missing geodetic surveys of a non-stationary dislocations process within the area of underground exploitation influence. It has been shown thai the analysed process can be assigned 10 the group of stochastic processes. A model (IO) has been determined as the formal definition of the discussed problem, whereas two algorithmic procedures appear to be the real solution. Utility aspect of the paper comprises the modelling of the formation process of actual dislocations. Estimated values of one-stage prognosis are shown in table I and in Fig. 4. Model quality indicator - error distribution - appears to be the confirmation that a quantitative description is adequate to the survey results. It has been shown from the point of view of descriptive statistics, using correlation coefficient, that the results of the dislocations survey of the field points - significantly distant included - are highly correlated.