## 1 Introduction  
The forecasting of continuous deformations of a land surface (i.e., a type of terrain deformation that does not cause a break in the terrain surface, occupies large areas, and occurs slowly, from several to several dozen years [1], e.g., subsidence--W, inclinations--_T_, curvatures--_K_, horizontal strains--_e\({}_{x}\)_, and horizontal displacements--_U\({}_{x}\)_) caused by underground operations on hard coal deposits is a very important issue for many reasons. The results of predictions provide information about the expected condition of the subsoil and buildings during and after a deposit's extraction, and they are useful for urban planners, architects, builders, constructors of engineering structures, surveyors, and many others. For example, urban planners decide on land use based on the categories of a mining terrain that are separated based on inclinations, curvatures, and horizontal strain values [2, 3]; buildings constructors choose the proper load-bearing structure for an object and the building's reinforcement against mining impacts based on the categories of a building's resistance connected with a land category [4, 5]. Similar issues in predicting ground behavior and problems related to the occurrence of land surface deformations may occur during the construction and operation of large diameter underground pipelines, as well as tunnels, which may resemble mining corridors located at relatively shallow depths [6; 7; 8]. Scientists around the world and especially in countries where the underground mining of hard coal deposits is carried out (Ukraine, Poland, Germany, France, Spain, Great Britain, Brazil, Chile, Columbia, the United States of America, Canada, North and South Korea, Russian Federation, China, Malaysia, Indonesia, Australia, India, the Republic of South Africa, and Turkey) have been conducting research for several decades on creating and improving models describing the impact of underground mining on the land surfaces. The first attempts to describe the vertical movement of the ground toward voids created in rock masses due to the mining of hard coal seams were made at the University of Science and Technology in Cracow (Poland) by [PERSON] in the 1950s. This researcher described the profile of a subsidence basin that formed on the land surface after the end of exploitation using the Gaussian function [9]. The profile of the subsidence trough was symmetrical to the point located above the center of the exploitation field, and the \(W\) subsidence reached its maximum value there (\(W_{max}\)). At points located above the edges of the exploitation, the subsidence was half of the maximum value. Then, the scientist developed a possible method for calculating the value of the subsidence at any time during exploitation and after its completion [10]. The model proposed calculating the subsidence values as linear and dependent on the values of the parameters of operation (exploitation coefficient--_a_) and the main influence's ranges (tangent of the \(\beta\) angle of the main influences range--tan \(\beta\)). The value of the coefficient depends on the method of mining concerning the goal's liquidation, the \(\beta\) tangent of the geological-mining conditions of an operation, and the mechanical properties of the rocks constituting the rock mass. [PERSON]'s research was continued by [PERSON], who assumed that the rock mass was a stochastic medium [11; 12; 13; 14; 15]. He used probability theory to determine the vertical displacements of the rock mass [16]. The issue of the horizontal displacement of rock masses as a result of underground mining was dealt with by [PERSON] [17] and [PERSON] [18]. Subsequent researchers refined the [PERSON] model, determined the values of its parameters, and examined the influence of time on the development of the subsidence basin and the exploitation speed on the values of deformation indicators [19; 20; 21].