3. Using the approaches of the theory of dynamic systems to determine the criteria for changing the regimes of dissipation of real mountain massifs under strong man-made impact

To realize this research, the seismic catalog of the Tashtagol underground mine was used for 2 years from June 2006 to June 2008. As the data, the space–time coordinates of all the dynamic phenomenal responses of the array that occurred during this period inside the mine field, as well as the explosions produced for working out the array, and the value of the energy fixed by the seismic station were used. In our analysis, the entire mine field was divided into two halves: the development of the northwestern section, the areas of the trunks of the western and Novo-Kapital and the outputs from 0 to 14 are designated by us, as the northern section, from 15 to 31 and the southern ventilation and field drifts. The trunk of the southern mine is designated as the southern section. All event responses from horizons �140, �210, �280, and �350 m were taken into account. Explosions were carried out in the southeastern section of mine development at the horizons +70 m, 0 m, ˜70, on the remaining sections—on the above horizons. As the data, the space– time coordinates of all the dynamic phenomena occurring within the minefield and fixed by the seismic station, as well as their energy characteristics were used.

The phase portraits of the state of the arrays of the northern and southern sections are plotted in the coordinates Ev(t) and d(Ev(t))/dt, where t is the time expressed in fractions of the day and Ev is the seismic energy extracted in the array in joules. In this paper, we will first analyze the morphology of the phase trajectories of the seismic response at various successive intervals of time in the southern section of the mine for two reasons: (1) According to the data on the technological and mass explosions produced (Figure 5), most of the energy was pumped into the southern part of the mine. (2) At the end of 2007, the one of the strongest rock shocks occurred in the history of the mine happened in the southern sector. Figure 6 (a)–(h) shows the evolution of the morphology of the phase trajectories of the array response to technogenic impacts from the middle of 2006 to the middle of 2008. Figure 6(c) shows the characteristic morphology of phase trajectories of the response of an array located locally in time in a stable state: there is a local region in the form of a tangle of intertwined trajectories and small outliers from this coil, which do not exceed 105 joules in energy. This same feature is manifested in all the figures presented in Figure 6(d), except that at some intervals this ejection exceeds 105 joules, reaching 106 joules (Figure 6(d) and (e)) and even 109 joules (Figure 6(g)). Since the volume of the array under study is the same and we are studying the process of its activation and decay, obviously, there are two mutually dependent processes: the accumulation of energy in the region attracting the phase trajectories and the resonance discharge of the stored energy (e.g., Figure 6(g)). It is interesting to note that after this reset, the system returns again to the same region attracting the phase trajectories.

Comparison of the phase portraits of the response of the state of the array before and after the mountain impacts of different intensity and at different time intervals indicate that the volume selected by us in the form of the southern section reacts to the effect exerted on it, similarly, by reflecting a coherent or joint mechanism for releasing the accumulated energy Figure 8(a-b). The first results obtained from the analysis of a detailed seismological catalog from the point of view of the

#### Figure 5.

Distribution in time of the absorbed seismic energy as a result of working out of an array by technological and mass explosions.Axis OY: D = Σlg (Ep (N)), where N is time intervals in days (OX axis) and Ep is absorbed energy from explosions. Explosions (1) provided in the southern part of the mine; explosions (2) provided in the northern part of the mine.

Analysis of Seismic Responses of Rock Massif to Explosive Impacts with Using Nonlinear Methods DOI: http://dx.doi.org/10.5772/intechopen.80750

mathematical foundations of synergetics and open dynamical systems possessing the properties of nonlinearity and dissipativity [2, 17, 20, 38] lead us to the necessity of posing a new mathematical modeling problem different from the one previously performed. If in previous productions, the problem of the transition of a system from an ordered state to chaos was investigated; in our case, for our system, the

#### Figure 6

˜ ˜ (a–h) Phase portraits of the array stateresponsein consistent timeintervals: (a) 5-24.09-29.09, 4-01.10-13.10, 3-14.10-12.11 2006; (b) 1-14.10-12.11, 2-12.11-18.11, 3-19.11-25.11 2006; (c) 24.12-29.12 2006; (d) 1-01.01-28.01 2007; (e) 1-29.01-31.03, 2-02.04-25.05 2007; (f) 1-02.04-25.05, 2-25.06-19.07, 3-22.07-27.09, 4-27.09-24.11 2007; (g) 1-30.09-24.11, 2-25.11-29.12 2007; (h) 1-29.12 2007-21.04 2008, 2-01.06-05.08 2008. The axis OXis theenergy allocated by the array in joules at appropriateintervals. The axis OY: <sup>A</sup> <sup>=</sup> aLgf, <sup>f</sup> <sup>¼</sup> , <sup>a</sup> <sup>=</sup> sign <sup>∂</sup>E, where<sup>t</sup> is timein fractions of <sup>a</sup> day. It is of interest to analyzein more detail the phase ˜ <sup>∂</sup><sup>E</sup>˜ <sup>∂</sup><sup>t</sup> trajectories of theseismicresponse of the array before and afterthestrongest impact (Figure 7(a)–(c)). Theentire process is described by three attractive phaseregions: a large number of phase-traversing low-energy region trajectories, which both precedestrong energy resonance (Figure 7(b)) and follow after a strong energy resonance (Figure 7(c)).

Analysis of Seismic Responses of Rock Massif to Explosive Impacts with Using Nonlinear Methods DOI: http://dx.doi.org/10.5772/intechopen.80750

#### Figure 7.

Phase portrait of the response of the state of the array during one of the most powerful mountain impacts at the Tashtagolsky mine, (a) for a time interval of 25.11-29.12 2007, (b) for a period of time before a rock shock (1), and (c) for a period of time after a rock shock (2). The legend for the axes is the same as in Figure 6.

chaos of a given level is, on the one hand, a stable state for the system. On the other hand, this parameter is the control for the transition of the system to a state with another parameter, which is catastrophic for it. After the realization of this catastrophe, the system again creates a chaos region with a parameter close in value to the first. This process differs from the bifurcation process, because in the space of the distributions of phase trajectories studied by us, there is an attractive point, in the plane, the extracted energy, and the time derivative of the logarithm of the extracted energy. Thus, further study of the detailed seismic catalog will allow us to formulate the criteria for predicting the behavior of the rock mass from the point of view of the mathematical theory of synergetics [36]. This approach can also be used to analyze seismological data at seismological landfills (Figure 8).

#### Figure 8.

Comparison of the phase portraits of the response of the state of the array before and after the mountain impacts of different intensity and at different time intervals in 2007. (a) 1-25.11, 2-01.01-13.01, 3-27.09-11.10. (b) 1-25.11-29.12, 2-13.01-28.01, 3-11.10-24.11. The legend for the axes is the same as in Figures 6 and 7.

## 4. Conclusion

At present, theoretical results on the modeling of the electromagnetic and seismic fields in a layered medium with inclusions of a hierarchical structure are in demand. Algorithms for modeling in the electromagnetic case for 3D heterogeneity are constructed, in the seismic case for 2D heterogeneities [39–41]. It is shown that with increasing degree of hierarchy of the medium, the degree of spatial nonlinearity in the distribution of the components of the seismic and electromagnetic fields increases, which corresponds to the detailed monitoring experiments conducted in the shock-hazard mines of the Tashtagolsky mine and the SUBR. The constructed theory demonstrated how the process of integrating methods that use the electromagnetic and seismic field to study the response of a medium with a hierarchical structure becomes more complicated. This problem is inextricably linked with the formulation and solution of the inverse problem for the propagation of electromagnetic and seismic fields in such complex media. The problem of constructing an algorithm for solving the inverse problem using the equation of the theoretical inverse problem for the 2D Helmholtz equation is considered in [41], [42]. The explicit equations of the theoretical inverse problem for the cases of scattering of an electromagnetic field (E and H polarization) and scattering of a linearly polarized elastic wave in a layered conducting and elastic medium with a
