Analysis of tectonic deformations dynamics on the example of the area of the south-west wing of Kalmius-Toretsk kettle hole

The article presents analysis results in the reconstruction of the tectonic conditions dynamics for the formation of local plicative deformations and rupturing under conditions of the research both the macrostructure and its local separation using the example of the southwestern area of Kalmius-Toretska kettle-hole in the Donetsk basin. Authors applied the scientific cognition method, representing a sequence of actions to establish structural links between variables and constant elements of the Investigational tectonic system, based on statistical and mathematical methods of analysis. The characteristics of the anticlinal structure formation in the studied area - fields of the “Butivska” mine were obtained. It was revealed that the initial horizontal attitude of rocks of the studied area was changed by a monoclinal attitude with a north-western dip and a north-east strike. Afterwards, under the conditions of tectonic near latitudinal compression and near meridional tension, anticlinal folding was formed. Then, under the influence of shear fields when the deformation mode was enhanced, a compression duplex was formed within which local echelon folding and fracture was formed - Oktiabrskyi fault #1.


Introduction
The most important task of modern tectonics from the point of view of applied geological research (gas generation, oil generation, ore formation, etc.) is to study the dynamics of the deformation process in the rock strata, which lead to the formation of tectonic structures. The nature of the deformations of any genesis and the conditions for their occurrence are investigated by structural analysis methods -one of the major methods of tectonic research, which is based on the studying the morphology of structures. However, morphological classification without identifying the causes and conditions of structural forms is only a formal description. Any method can be applied both to local areas of the mountain massif and to a large area of the whole region. The major and most difficult task is the right dividing of the studied geological volume (macrostructure) for the researching the location regularities of its individual tectonic elements in space and chronology of their formation.
The choice of the scale in tectonic block dividing is important especially when solving the tasks of specifying the local sections of the rocks in order to search, for example, coal methane accumulation zones. In the current negative situation in the energy sector in Ukraine, this problem has become the greatest relevance. Meanwhile, it is quite obvious that a local area of methane accumulation can be identified only based on knowledge of the causes and mechanism of tectogenesis of the tectonic unit being analyzed, ideas about the genesis and the nature of mining processes occurring in the massif and using modern methods of computer analysis of field data on the base of their mathematical processing.
The most important task of modern tectonics from the point of view of applied geological research (gas generation, oil generation, ore formation, etc.) is to study the dynamics of the deformation process in the rock strata, which lead to the formation of tectonic structures. The nature of the deformations of any genesis and the conditions for their occurrence are investigated by structural analysis methods -one of the major methods of tectonic research, which is based on the studying the morphology of structures. However, morphological classification without identifying the causes and conditions of structural forms is only a formal description. Any method can be applied both to local areas of the mountain massif and to a large area of the whole region. The major and most difficult task is the right dividing of the studied geological volume (macrostructure) for the researching the location regularities of its individual tectonic elements in space and chronology of their formation. The choice of the scale in tectonic block dividing is important especially when solving the tasks of specifying the local sections of the rocks in order to search, for example, coal methane accumulation zones. In the current negative situation in the energy sector in Ukraine, this problem has become the greatest relevance. Meanwhile, it is quite obvious that a local area of methane accumulation can be identified only based on knowledge of the causes and mechanism of tectogenesis of the tectonic unit being analyzed, ideas about the genesis and the nature of mining processes occurring in the massif and using modern methods of computer analysis of field data on the base of their mathematical processing.
Cumulative numerous research results of structural forms of the Earth crust in various scales enable to affirm that there is a close relationship between the formation of various structural forms. Any studied structure can be considered as homogeneous one in relation to a certain structural element, providing that within its boundaries the mutual movement of individual sections (parts) does not cause a change in the entire structure. But if the dimension of the smallest movable segment is more than half of the entire part of the structure under consideration, then this part is already heterogeneous [1]. The issue remains open about what can be as dimension indicator of a tectonic surface when identifying the relationship between the formation of various structural forms of a homogeneous and heterogeneous structure in a rock massif. In 1965 year R. Adler et al. [2] suggested introducing a "scale of significance" that depends on the sizes of the tectonic surface, whether they are a local fracture, a tectonic block, or a tectonic plate. Consequently, depending on the nature of tectonic surfaces, it is possible to make both more fractional and less fractional dissection of them. In this case, the most important requirement for the research is the combined use in statistics of directions and attributes in the "volume" of space, i.e. not only in horizontal planes but also in vertical ones. The precondition is the system analysis [3] of statistical observations of homogeneous, i.e. structurally homogeneous zones, and heterogeneous ones in the course of the study of the possible emergence of the tectonic system. Interest in system representations is manifested not only as a convenient generalizing concept, but also as a means of problem statement with great uncertainty.

Purpose
Analysis of the reconstruction of the tectonic conditions dynamics for the formation of local plicative deformations and rupturing in the conditions of the research of both the macrostructure and its local division into components using the example of the area in the south-western Kalmius-Toretsk kettle hole, the Donetsk Basin.

Methods
To solve the posed task when studying the emergence of a tectonic system (macrostructure), methods of structural and system analysis and mathematical processing of statistically grounded geological data were used. In particular, the methods of trendanalysis and gradient descent were used, which allow using mathematical methods, by removing the regional background, to identify local inhomogeneities of the hypsometric surfaces of the layers. For the construction of cartograms, polynomials of the first degree and higher orders (up to the 5th inclusive) were calculated, allowing to dynamically isolate secondary structures that complicate the monoclinal slopes of the more significant structures. When applying software tools for mathematical processing of operational field data both local areas of a tectonic unit (the coal bed in a hanging and lying wings of a tectonic fracture) and macrostructure (mining allotment as a whole) were taken for analysis. In the research authors uses a scientific method of knowledge, representing a sequence of actions upon the ascertaining of structural links between variables and permanent elements of the tectonic system under study, based on statistical and mathematical methods of analysis.

Results and discussion
Let us consider the problem under study using the example of the section of the southwestern wing in the Kalmius-Toretsk kettle hole, in particular, the northern part of the Donetsk-Makiivka geological industrial region (DMR) on the area of the "Butivska" mine field. The extensive geological and tectonic analysis of this area, as well as a prognosis of local zones of methane concentration of the coal bed n 1 , is presented in papers [4,5]. The authors carried out a structural analysis within the mine field, during which they considered the latter as a combination of several tectonic elements -the block of the hanging wing of the Oktiabrskyi fault No. 1 and, accordingly, the lying one, thus having divided the original tectonic structure into two blocks ( Fig. 1, a ) The boundary of the selected blocks, in this case, is the Oktiabrskyi fault No. 1. Regarding to the proposed approach, the structural analysis of the bed hypsometry (the construction of the approximate mathematical surface (trend) of the bed hypsometry, the construction of residual surfaces (local structures, as a result of the difference between the approximating and the original real surface) was carried out separately for each block (Fig. 1, b). Based on the obtained results on the deviation of the bed hypsometry n1 from the approximating surface (a map of local coal bed structures) within the mine field, two tectonic structures (eastern and western) like structural nose were identified [6]. The first is located in the eastern part of the mine field (to the East of the Oktiabrskyi fault No. 1) between the Oktiabrskyi fault No. 1 and the Panteleimonivskyi fault, the second is to the West of the Oktiabrskyi fault No. 1 (Fig. 2, b). At the same time, their long axes are elongated along Oktiabrskyi fault No. 1 and oriented along the strike of rocks for the western structure and at an angle of approximately 45° to the strike of rocks for the eastern. Short axes of the marked structures, respectively, are perpendicular to the Oktiabrskyi fault. Using the indicated approach, there is no possibility: a phased Fig. 1. The hypsometric plan of the coal bed n 1 within the "Butivska" mine (a); trend of the 1st order (b) for the hanging and lying wings [5]; the trend of the 1-2-5th orders for the whole structure of the coal bed n1 within the mine (c, d, e), respectively. reconstruction at the formation process dynamics of the identified two structural noses, determination of their homo-or heterogeneity, and, accordingly, the identification of causal relationships between the identified and confirmed as a result of operational work in the mine, local zones of methane accumulation. To achieve the purpose in the work, the scale of statistical generalization was changed, i.e. the area of the analyzed surface, increased the degree of the polynomial (Fig. 1, d) and the methods of gradient analysis of structured surfaces was involved (Fig. 2, c, d). rocks for the western structure and at an angle of approximately 45° to the strike of rocks for the eastern. Short axes of the marked structures, respectively, are perpendicular to the Oktiabrskyi fault. Using the indicated approach, there is no possibility: a phased reconstruction at the formation process dynamics of the identified two structural noses, determination of their homo-or heterogeneity, and, accordingly, the identification of causal relationships between the identified and confirmed as a result of operational work in the mine, local zones of methane accumulation. To achieve the purpose in the work, the scale of statistical generalization was changed, i.e. the area of the analyzed surface, increased the degree of the polynomial (Fig. 1, d) and the methods of gradient analysis of structured surfaces was involved (Fig. 2, c, d). The final (sought-for) result -is a cartogram of the surface residue (Fig. 2, a) between the actual surface (hypsometry) of the coal bed n1 (Fig. 1, a) and the mathematical trend of the 5th order (Fig. 1, e) suggests that the accumulation of the original material and forming the attitude surface of the coal bed n1 within the mine field, which took place under horizontal attitude, was changed by a monoclinal attitude with a northwest dip and a northeast strike. Subsequently, under the conditions of tectonic near-latitudinal compression (σ 3 = 290-300º) and near-meridian tension (σ 1 = 20-30º), an anticlinal fold is formed, the axis of which is coaxial with the strike of the current position of the Oktiabrskyi fault No. 1.
Then, at bending in the layer, the substance is redistributed in such a way that it moves from bendings with a relatively small radius of curvature to bendings with a bigger radius of curvature, forming local warping structures (Fig. 2, a) -an area of the increased values of the surface residue. Subsequently, during the shear, under the impact of oppositely directed forces, the echelon folding is formed, which is tilted in the direction of the active forces action and adjoined to the shear surface at an angle close to 45º. On the southern wing of the anticline is formed the fracture of the Oktiabrskyi fault #1.
Most often, it is safe to say how the fold was formed, only on the basis of the researcher's ideas about its formation and must usually use by different models based on theoretical constructions and the results of physical modeling. That is why the same fold can be classified in different ways. If we consider the folds from the point of view of the applied forces orientation with respect to the layer, they can be divided into folds of longitudinal bending and the transverse one. Folds of the 1st class emergence as a result of tangential squeeze of the layers, the forces acting in the folding of the longitudinal bending are compression, and the deformations undergone by the body is deformations of compression, and each layer in separate parts undergoes deformations of tension and compression -in others. The mechanism of the formation of the formed paragenesis in the tectonic structures is apparently due to shear displacements along the deep shear with the formation of a compression fracture anticline on the southern wing. Especially in contrast, tectonic structures are fixed on the cartograms of the surface residue gradient module of the fifth order (Fig. 2, c, d).
The obtained characteristics of the formation conditions of the anticlinal structure are fully matche with the results of work regarding the conditions and features of the DMR tectonics formation [7,8,9]. It is proved that in the region the main tectonic structure, controlling the accumulations of free gas, is the zone of shear dislocations development and have the completely regular orientation (Fig. 3): fractures, presented by faults С* and folding F* (strike azimuth 27º±4º), being formed perpendicular to the axis of shortening (σ 1 * : 297º± 4º) and parallel to the axis of elongation (σ 3 * : 27º±4º).
The obtained results indicate on the formation of the tectonic structures of the "Butivska" mine in the shear dislocation mode and closely match the development interpretation of the regional right shear zone of the north-east strike (strike azimuth 245º± 5º) and its peripheral areas in (DMR) [7,10], The indicated zone was a precondition of a "starter mechanism" in the formation of shears. R 1 *, R 2 *, P*, tension cracks and throws Т*, faults С* and folds F* (on the peripheral adjacent areas) when the deformation mode is strengthened in the central part of the zone in the block, bounded from the northwest by Kalininskyi fault, from the East -by Sofiivskyi one and from the South by the Providance system. The effect of Z-shaped refraction entered into force in the changing the orientations of the main violations within the central part of the shear zone and its peripheral boundary sections (see Fig. 3, b). For the boundary sections of the deformable strip due to the edge effect, with increasing strip dimensions in the direction of the shear axis, the role and impact of normal shear stresses σ 1 *-σ 3 * on the axial zone decreases.
In fact, within the "Butivska" mine, a specific compression duplex was formed [8] -the fault "scaly" plate, within which local folds F and fractures of the"fault" type C are formed, and which practically disappear or flatten out of the coal beds boundaries. Compression duplexes occur due to a local change in the position of the tension axis from subhorizontal to subvertical ones while maintaining the subhorizontal position of the compression axis. Localization of compression duplexes in coal beds significantly affects the formation of prerequisites for gas accumulation manifestations in coal beds, because they are as gathering barriers on the migration way of gaseous hydrocarbons from deep horizons [8]. The objectivity of the obtained results and conclusions confirms the fact that when nalyzing the above papers [7][8][9][10], the block of "Butivska" mine was not included as an object of the research and not considered at all.  [7]. On the inset map a -strike interpretation of small-amplitude tectonic disturbances (synthetic, antithetic shears, stretch cracks, folds and faults) on the total rose-diagram; b -model of development of the main diagonal shear zone.

Conclusions
1. Analysis of the reconstruction of the tectonic conditions dynamics for the formation of local tectonic deformations allowed us tracing the history of the geological development of the area under study, in the part of its tectonic evolution. The initial horizontal rocks attitude of the area under study -the "Butivska" mine field on the section of the southwestern wing at the Kalmius-Toretsk kettle hole of the Donetsk basin, was changed by a monoclinal attitude with a north-western dip and a north-east strike. Subsequently, under conditions of tectonic near latitudinal compression and near meridional tension, the anticlinal fold is formed, the axis of which extends from the south-south-west to the northnorth-east. Then, under the influence of shear fields of stresses, when the deformation mode is strengthened due to a local change in the position of the tension axis from subhorizontal to subvertical while maintaining the subhorizontal position of the compression axis within the "Butivska" mine boundaries, a compression duplex is formed -a fault "scaly" plate, within which a local echelon folding, which is inclined towards the action of active forces and approaches the shear surface at an angle close to 45º and on the southern wing of the anticline fracture of the "fault" type -Oktyabrskyi fault No. 1.
2. Maps of local structures from the polynomial of the 1st order to the highest orders with a fairly large degree of generalization, as the trend surface approaches the real geological surface, show the stages of formation and development of tectonics of the region and essentially they are a phased reconstruction of the tectonic deformations dynamics.
3. The proposed method of consistently studying the trend surfaces of polynomials of various degrees (from the 1st and above) can be successfully applied to the reconstruction of the tectonic development of various regions. Moreover, in each individual case, the size of the area being analyzed and the degree of generalization should be chosen depending on the characteristics and complexity of the tectonic structure of a particular region and the operating objectives.