To the study of block lithospheric structures of seismically vulnerable zones in the region

. The paper describes a method for using regional seismic data based on processing the results of experiments carried out using a tiltmeter to study dangerous seismic conditions and clarify the structural boundaries of lithospheric units in the region. The use of experimental methods will make it possible to determine the true parameters of the block structure, which are necessary for the practical application of the block element method in the study of regional seismicity.


Introduction
The Krasnodar Krai is an important agricultural region, and part of its territory is located in a zone of increased seismic vulnerability. In this regard, the issues of monitoring and assessing the seismic situation are very important. Such importance of the seismic event prediction methods development is also explained by the necessity to ensure the safety of the population, economic facilities, infrastructure and natural complexes of the region.
Modern methods for studying geodynamic phenomena include a variety of experimental and theoretical approaches. The Kuban State University and the Southern Scientific Center of the Russian Academy of Sciences are developing mechanical-mathematical approaches to forecast seismic activity [1][2], based on the analysis of possible destruction mechanisms of lithospheric plates in contact zones or near fault boundaries. The main idea of the approach is to study stress concentrations in lithospheric plates as deformable physical and mechanical objects of complex structure.
To date, there are numerous maps of the geological structure for the Northwest Caucasus including the coastal and mountainous territories of the Krasnodar Krai [3][4]. However, further improvement of the mathematical methods and models for studying the stress-strain state of lithospheric structures requires the development of reliable methods for diagnosing faults of various thicknesses (determining the location and, if possible, the type of contact between lithospheric structures in the areas of their conjugation).
The development of technical means of observational seismology as well as the development of a tool base for measuring the dynamics of geological structures can significantly increase the amount of registered data on ongoing seismic events. Data processing methods oriented towards predicting catastrophic natural phenomena are also being developed. The paper describes a method for using regional seismic data to study dangerous seismic conditions and clarify the structural boundaries of lithospheric units in the region.

Materials and methods
Algorithm of block element method.
As one of the methods for solving boundary value problems for structures of a block nature, we use the block element method (BEM). Generalizing the integral approach widely used for solving problems in layered structures, BEM combines factorization methods with a topological approach. Following the idea of BEM, a set of elements in the block structure is considered as a coating of the topological space. This allows conjugation of the blocks themselves and vector functions on blocks-supports by means of topological gluing [5].
Let the area  occupied by the entire block structure be divided into convex areas  = ∪ l  с with piecewise smooth boundaries . Consider a boundary value problem for a system of partial differential equations (PDEs) of arbitrary order. We can write the problem for PDEs with constant coefficients in the area l  , in operator form: Boundary conditions on l  are as follows: ( The solution l  and given l f , l g , belong to the space of slowly growing functions   s l  H . By applying the three-dimensional Fourier transform 3 V problem (1), (2) in the local coordinate system is reduced to a system of functional equations [5]: is a polynomial matrix-function of the order P in the  -th local coordinate system, In the introduced local coordinate system, the axis The calculation of the Leray residue forms [6] allows us to construct a system of pseudodifferential equations [5]: Which, in turn, is used to construct a system of integral equations (SIE) of the boundary value problem. To solve the latter, we can apply the integral factorization method. The approximate solution of the SIE can be represented as: Where l m  , when   1 2 m x , x    and l n The BEM is one of the effective approaches to the study of mixed dynamic problems. The algorithm does not depend on the type of PDEs.
M.A. Sadovsky in his works gives numerous examples that testify to the block structure of the earth's crust [7]. But for the practical application of the BEM in applications of seismology and geophysics, it is necessary to determine the true parameters of the block structure i.e., the dimensions and boundaries of its components and block interface parameters that affect the propagation of seismic waves. The above information can only be obtained experimentally.
Experimental studies of lithospheric structures.
In accordance with the general objective of the identification of conjugation zones in lithospheric structures, the authors processed the data of experimental methods for diagnosing the structure of the lithospheric units in the region. In [8], we described one of the experimental methods based on the data processed from experiments carried out using a tiltmeter.
The analysis of geophysical data obtained as a result of using this method showed that it can serve to create a model for block structures of the lithospheric plates in the territory of Krasnodar Krai.
The authors processed the measurement data of the slope of the earth's surface and analyzed the spatial and temporal distribution of seismic events. With the help of highprecision GPS receivers, multidirectional horizontal and vertical movements on the surface of both one lithospheric plate and one plate relative to another can be recorded with an accuracy of millimeters per year. The rise or fall of the earth's surface, associated with tectonic deformations of the earth's crust, leads to a change in the slope of the earth's surface. The purpose of the experiments was to discover patterns relating the incline of individual sections of the Earth's surface as well as changes in the structure of the Earth's crust at distances exceeding the dimensions of individual blocks (i.e., in the far zone). According to modern theories, the earthquake source zone is often formed in the contact area of the lithospheric plate blocks and in the area of deconsolidation (dilatancy zone). The contact areas of large lithospheric structures are characterized by the largest number of earthquake locations. In our study, the areas of structure change were determined by the coordinates of the seismic events that took place at the boundaries of the block in the far zone from the place where the tiltmeter was installed. Figure 1 shows  In our work, we used data on earthquakes with indication of their epicenter coordinates, magnitude, depth, obtained at the seismic station of the Kuban State University (broadband digital seismic station SDAS v.3.0, tiltmeter of the Gridnev system). In addition, we used data from the website for the Geophysical Service of the RAS.

Results and Discussion
The vector diagram (Figure 1) shows the following regularity: a slowdown in the rate of change in the incline of the Earth's surface is accompanied by an increase in the probability of an earthquake. In this case, a change in the incline of the Earth's surface, caused by changes in the structure of the source area (an increase in the volume of the dilatancy zone), can be recorded in an area with a radius of about 50 radii of the dilatance inhomogeneity zone [9][10].
We can assume the following scenario for the development of events. The force acting on the system of blocks in the Earth's crust is spent on the destruction of the blocks conjugation area (dilatancy zone). As a result, the incline of the lithospheric plate section in the far zone will change little, and the energy spent on the destruction (decompression) of the crust will eventually lead to a main rupture in the crust destruction zone, that is, to an earthquake. After an earthquake, the strength of the crust is restored, and the rate of change in the incline of the Earth's surface returns to its previous values.
Based on the analysis of the diagram data (Figure 1), the limit of the incline change rate is determined as 0.005 arc seconds/hour. The maximum rate of inclination of the Earth's surface for the periods under consideration is 0.0274 arc seconds/hour.
The vector diagram of the incline for the Earth's surface after its processing by the program for determining the change rate of the incline as well as determining the limiting change rate level is shown in Figures 2 and 3.  The created data processing program, in case of speed deceleration below a certain limit level (0.005 arc seconds/hour), as a predictive warning, changes the color on the vector diagram from blue to red. We can see this in the vector diagrams of 2003 and 2004 ( Figure  2), when the amplitude of the change in the slope of the earth's surface was greater than in other periods.
It should be added that the data of the Earth's surface incline (Figure 1) was averaged when analyzing the incline change rate below the limit level. Averaging was carried out with a sliding window lasting 5 days. But in the case of considering slow deformation waves propagating in the interblock seams of a fractally constructed medium [11], it is necessary to carry out additional studies and the averaging window should not exceed several hours. Therefore, we can talk about the use of data on the Earth's surface incline only in complex use with other prognostic features [12][13][14][15][16][17][18].

Conclusion
In order to develop the mechanical-mathematical concept of regional seismicity prediction and the practical application of the block element method, the paper proposes a method for using experimental data to create a model of block structures of the lithospheric units in the region.
The results of the study led to the conclusion that a slowdown in the change in the Earth's surface incline in the far zone from seismically hazardous areas is accompanied by earthquakes in these areas.
Based on the revealed regularity, we can refine the model of the block structure of the Earth's crust for the territory of Krasnodar Krai, linking the presence of structural boundaries with a change in the rate of incline of the lithospheric plate in the far zone, since the tiltmeter installed in the far zone from the block boundaries is able to respond to changes in the stress-strain state at its boundaries.