## 1 Introduction
However, [PERSON]'s model proved to be suitable only for simple mining operations carried out in horizontal seams, the impacts of which are added up and calculated linearly. Therefore, subsequent scientists from the Silesian University of Technology in Gliwice (Poland) developed this model which has the ability to evaluate the impacts of the exploitation of multiple inclined seams. Desymmetrization of the vertical profiles of subsidence troughs along the edges of exploitations was introduced by [PERSON] [22] and [PERSON] [23; 24], and the delinearization of influence values was introduced by [PERSON] [25] and [PERSON] [26]. In addition, the introduced mining margin involved shifting the actual exploitation edge toward the goaves due to the octahedral strain occurring in the roof directly above the workings [27]. After many years of improving [PERSON]'s formula for subsidence, [PERSON] obtained a form of this formula that takes the following into account: nonlinear summation of influences resulting from the exploitation of an unlimited number of inclined seams, desymmetrization of the profile of the subsidence trough with the edges of the exploitation field, which has a complicated shape due to the existence of the \(d\) mining margin, distant influences [28], reactivation of old goaves [29], and the time factor [30; 31]. [PERSON]'s formula for the subsidence of a mining area, as well as the inclination and curvature (sequentially calculated as the first and second derivatives of the subsidence) together with [PERSON]'s hypothesis [32] (which allows for the calculation of the values of the horizontal displacement and horizontal strain), because of their universality and the possibility of being implemented in computer software, are commonly used to forecast continuous deformations of land surfaces caused by underground mining of hard coal carried out in Central and Eastern Europe, the south of Poland, and the Upper Silesian Coal Basin by Jastrzebie Coal Company. [PERSON]'s formula was implemented in the EDN-OPN computer program [33]. It allows for calculating the values of deformation indicators at a specific point (EDBJ1 program) and the creation of maps of the distribution of deformation indicators for the whole surface of the mining area (EDBJ2 program) [34]. There are also other computer programs enabling deformation forecasts based on [PERSON]'s geometric integral theory of mining influences, e.g., MODEZ [35; 36; 37], DEFK [38; 39; 40; 41], and on the finite element method [42; 43; 44; 45; 46; 47] or neural networks [48], but in commercial activity in Poland the most common is the EDN-OPN. The effectiveness and accuracy of this program have been repeatedly checked for various geological-mining conditions [49; 50; 51; 52; 53]. This program is characterized by very good reproductions of actual values of deformation indicators by their predicted values but after determining the appropriate values of the parameters of [PERSON]'s formula [54]. However, this program may not work properly when, in addition to continuous deformations, discontinuous deformations [55; 56; 57; 58; 59; 60] also unexpectedly appear on the terrain's surface (terrain surface deformations that consist of a break in the continuity and relative, macroscopically visible displacement of the subsurface layers of the ground, and the clear destruction of the terrain's surface. Deformations of this type occupy relatively small areas and have clear boundaries. They occur quickly within a few hours or days, or even suddenly--within a few minutes [1]). Incorrect operation of the program was shown in this article on examples of inclination values, as follows: theoretical, calculated in the program and real, observed in the terrain using geodetic measurements made on 51 observation points located around nine objects. The influence of discontinuous linear deformations on buildings and their deflection values [61], as well as on the values of continuous deformations of the terrain surface [56], has already been investigated.