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Purpose: When producing mining operations in high-stress rock massive, technogenic seismicity is manifested. Forecasting and prevention of these events is given much attention in all countries with a developed mining industry. From the point of view of the paradigm of physical mesomechanics, which includes a synergetic approach to changing the state of rock massive of different material composition, this problem can be solved with the help of monitoring methods tuned to the study of hierarchical structural media. Changes in the environment, leading to short-term precursors of dynamic phenomena, are explained within the framework of hierarchical heterogeneity and nonlinearity from observations of wave fields and seismic catalog. For that purpose it is needed to develop new algorithms of modeling wave field propagation through the local objects with hierarchical structure.
Design/Methodology/Approach
: It had been constructed an algorithm for 3D modeling electromagnetic field for arbitrary type of source of excitation in N-layered medium with a hierarchic conductive and magnetic intrusion, located in the layer number
*J*. It had been constructed algorithms for 2D modeling of sound diffraction and linear polarized transversal seismic wave on an anomaly elastic or dense intrusion of hierarchic structure, located in the layer number
* J* of N-layered elastic medium. We used the method of integral and integral-differential equations for a space frequency presentation of wave field distribution.
Findings: From the theory it is obvious that for such complicated medium each wave field contains its own information about the inner structure of the hierarchical inclusion. Therefore it is needed to interpret the monitoring data for each wave field apart, and not mixes the data base.
Practical Value/Implications: These results will be the base for constructing new systems of monitoring observations of dynamical geological systems. Especially it is needed to prevent rock shocks in deep mines by their exploitation or natural hazards.

The phenomenon of zonal disintegration of rocks around underground excavations was first described in [

The Institute of Geophysics of the Ural Branch of the Russian Academy of Sciences has developed a series of devices and interpretation complex for studying the structure and state of a complex geological environment that has potential instability and the ability to rearrange the hierarchy of the structure due to the significant external impact. The basis of this complex is the developed 3D planshet technique of electromagnetic induction studies in the frequency-geometric version, based on one hand on a software-realized system of interpretation of 3D variable electromagnetic fields [

Determining the state and dynamics of a rock massif is a more complex problem than mapping its structure. Individual parts of the massif can be in a different stress state, and the corresponding deformations can be either elastic or plastic. The medium can be multiphase. A powerful change in the state of the blocks can lead to stability loss of the whole massif and to a rock shock. The state change is determined both by natural and technogenic impact on the massif and is manifested, among other things, in the form of formation of man-made cavities and pumping mechanical energy during mass explosions provided for mining technologies. The phenomenon of non-stationary state of the rock massif today is a well-known fact [

At the suggestion of N. P. Vloch, this system was tested on a number of massive, differing in material composition, according to their geological classification (sedimentary, volcanic-sedimentary, and volcanogenic) and in degree of impact hazard. These objects in the Ural were studied: the Magnezitovaya mine, the SUBR, the UUBR, the BKRU-4, the Estyuninsky mine, the Uzelginsky mine; in Siberia, in the Far East: Tashtagol, Nikolaevskij mine (Dalnegorsk). Each of these objects allowed establishing the features of the structure and behavior of the massif, to isolate and rank the factors affecting the stability of the massif. This was possible only with the possibility of comparing various factors within the framework of a single integrated methodology of geophysical and geomechanical research. Consider the results of testing and the effectiveness of the proposed system for monitoring the rock mass at the Magnezitovaya mine (1st (internal) cycle). The experience of geophysical work in underground conditions with the use of various physical fields with the purpose of mapping the zones of disturbance of a rock massif and studying the connection of their dynamic manifestations in the specific physical parameters of the massif indicates the highest efficiency and manufacturability of the use of non-contact electromagnetic methods of investigation.

Full-scale experiments were carried out at the Magnezitovaya mine (Satka, Chelyabinsk Region) during the three years 1997-1999, in February-April of each year to study the structure of the interworking space, assess the degree of heterogeneity of the rock block and the variability of its structure and state over time. During the period of providing electromagnetic investigations, the first-stage chambers were working in the process, when the roof and their walls were represented by an array of rocks (dolomite and magnezite), located across the shock of the magnezite deposit. Electromagnetic induction observations were provided at two mutually parallel levels: at the 297 m horizon in seven mutually parallel excavations (409 - 421) and at the horizon 277 m in two excavations (211 - 213). At the beginning of the experiment in 1997, they were under-roof workings up to 120 m length, 3 m wide and 3 m height. Then, according to the technology of working out the massif, these workings widened to 8 m in the part where the magnezite was located. Where there were interlayers of dolomite, the width of the excavations remained the same―3 m. Then these workings were worked out, their height increased to 10 m, and the inter-working space between the horizons in the process of working the chambers decreased in height from 17 m to 10 m. The observation profiles passed respectively along the workings practically along their middle. Observations of the modules of the three components of the magnetic field at 5 frequencies (from 5 kHz to 80 kHz) were carried out with the help of equipment developed at the Institute of Geophysics of the Ural Branch of the Russian Academy of Sciences (the developer A.I. Chevolevochkov) independently for each hole, and the excitation source was in the same hole, as the receiver. One cycle of observations included multifrequency measurements of two horizontal and vertical components of an alternating magnetic field when the receiver moved with a given step and fixed source position, then the source moved to another point of the profile and the measurement cycle was repeated. In the present experiment, four cycles of observations were made in all the excavations.

After appropriate processing of the data within the framework of a specialized system, developed by us, the distribution of effective resistance as a function of distance was obtained for all frequencies. Data analysis was carried out within the framework of the concept of three-stage interpretation. Thus, using the algorithms for the interpretation of the first stage [

In [

δ ¯ m i = 1 K ∑ k = 1 K δ m k i ; (1)

δ m k i = | H ϕ m i | | H ρ m k i | × 100 % (2)

i―number of frequency (1 - 5 kHz, 2 - 10 kHz, 3 - 20 kHz, 4 - 40 kHz, 5 - 80 kHz); К―the number of movements of the excitation source within the observation section; k is the location number of the source of excitation; m is the location number of the receiver.

The analysis of the results obtained in 1997, 1998 full-scale experiments shows that the effect of changing the geoelectrical heterogeneity parameter over time is significant and fixed in the framework of the observations, and as a rule these changes are larger in absolute magnitude at a frequency of 5 kHz, compared to with the remaining frequencies. To interpret these data, we created an iterative algorithm based on the minimization of the functional, taking into account the mutual lateral influence and the influence of “top-bottom” of the following kind (3):

Q i = 1 N ∑ N 1 M N ∑ m = 1 M N | δ ¯ m i − δ ¯ m T i | ; (3)

where N―is the number of considered interactions in the profile data of the volume observation system, M_{N}―the number of observation points on each observation profile, δ ¯ m T i ―the approximation design or the theoretical average parameter of the geoelectrical heterogeneity at the observation point of the number m [

Geomechanical studies were carried out to test the hypothesis about the nature of anomalous geoelectrical zones associated with excessive fracturing. As a result of the comparison of the results obtained, the following features were revealed: according to the data of geomechanical studies, in the second and third wells, zones of intense fracturing related to the fracture zones were found in the first well of such zones were not found. Electromagnetic studies were carried out earlier than geomechanical studies and, based on the results of their interpretation; a predicted section was constructed, including the position of the inhomogeneous zones [

To solve the problems of geological and geophysical mapping, a model of a layered-block medium with homogeneous and inhomogeneous inclusions in physical properties is currently widely used, within the framework of which apparatus-methodological complexes for studying three-dimensional inhomogeneous media with the corresponding interpretation theory of geophysical data have been created [

Let the local heterogeneity has the following structure: at the first hierarchical level, this is the heterogeneity of the volume V_{1} with the conductivity σ_{a}_{1}; at the second level, these are the heterogeneities located inside the volume V_{1} and occupying the volume V_{2} with the conductivity σ_{aj}_{2} in the general case. We will consider the simpler case, when heterogeneities of the second and higher rank will have the same conductivity within their rank, that is, σ_{а}_{2}. The heterogeneities of the third rank will occupy the volume V_{3} within the volume V_{2} with the conductivity σ_{а}_{3}, etc. The parameters of the host horizontally layered medium have the form {σ_{k}, h_{k}}, where k = 1, ・・・, N, h_{k} are the total thicknesses of the layers, i is the rank or hierarchical level number. The problem is considered for a magneto-homogeneous medium in the quasistationary approximation.

The volume integral equations and, respectively, integral representations for the electric and magnetic field components are written out as:

E i ( M 0 ) = E 0 i − 1 ( M 0 ) + ( σ a i − σ k ( M 0 ) ) ∫ V i E i ( M ) G ^ E ( M , M 0 ) d V i (4)

H i ( M 0 ) = H 0 i − 1 ( M 0 ) + ( σ a i − σ k ( M 0 ) ) i ω μ 0 ∫ V i H i ( M ) G ^ H ( M , M 0 ) d V i (5)

where, i is the number of iterations, and G ^ E ( M , M 0 ) and G ^ H ( M , M 0 ) are the Green’s tensors of the layered medium, which are determined by the known method described in [

An algorithm for simulating the diffraction of sound on a two-dimensional elastic homogeneous inclusion located in the J-layer of an N-layer medium is written in [

( k 1 j i 2 − k 1 j 2 ) 2 π ∬ S c φ ( M ) G S p , j ( M , M 0 ) d τ M + σ j a σ j i φ 0 ( M 0 ) − ( σ j a − σ j i ) σ j i 2 π ∮ C G S p , j ∂ φ ∂ n d c = φ ( M 0 ) , M 0 ∈ S C σ j i ( k 1 j i 2 − k 1 j 2 ) σ ( M 0 ) 2 π ∬ S c φ ( M ) G S p , j ( M , M 0 ) d τ M + φ 0 ( M 0 ) − ( σ j a − σ j i ) σ ( M 0 ) 2 π ∮ C G S p , j ∂ φ ∂ n d c = φ ( M 0 ) , M 0 ∈ S C (6)

where G S p , j ( M , M 0 ) is the source function of the seismic field of the problem under consideration; k 1 j i 2 = ω 2 ( σ j i / λ j i ) ; is the wave number for the longitudinal wave, in the above expression, the index ji denotes the belonging of the medium properties inside the heterogeneity, ja―outside the heterogeneity, the Lamé constant, σ―the density of the medium, ω―circular frequency, -potential of a normal seismic field in a layered medium in the absence of an heterogeneity: φ j i 0 = φ j 0 . The idea presented in the previous paragraph for the electromagnetic field is also realized for a seismic field for a two-dimensional case of propagation of a longitudinal wave through a local heterogeneity with a hierarchical structure located in the j-th layer of the N-layered medium.

( k 1 j i 2 − k 1 j 2 ) 2 π ∬ S c l φ l ( M ) G S p , j ( M , M 0 ) d τ M + σ j a σ j i φ l − 1 0 ( M 0 ) − ( σ j a − σ j i l ) σ j i l 2 π ∮ C l G S p , j ∂ φ l ∂ n d c = φ ( M 0 ) , M 0 ∈ S C l σ j i l ( k 1 j i l 2 − k 1 j 2 ) σ ( M 0 ) 2 π ∬ S c l φ l ( M ) G S p , j ( M , M 0 ) d τ M + φ l − 1 0 ( M 0 ) − ( σ j a − σ j i l ) σ ( M 0 ) 2 π ∮ C l G S p , j ∂ φ l ∂ n d c = φ l ( M 0 ) , M 0 ∈ S C l (7)

G S p , j ( M , M 0 ) ―function of the source of the seismic field of the problem under consideration, it coincides with the function of expression (64). k 1 j i l 2 = ω 2 ( σ j i l / λ j i l ) ―the wave number for the longitudinal wave, in the above expression, the index ji denotes the property of the medium inside the heterogeneity, ja―outside the heterogeneity, the index l = 1, ・・・ L―the number of the hierarchical level, u l = g r a d φ l , φ l − 1 0 ―the potential of the normal seismic field in the layered medium in the absence of heterogeneity of the previous rank, if l = 2, ・・・ L,. φ l − 1 0 = φ l .

If, moving to the next hierarchical level, the two-dimensionality axis does not change, and only the geometry of sections of embedded structures changes, then it is possible to write out an iterative process of modeling the seismic field similarly (4, 5) (the case of the formation of only a longitudinal wave). The iterative process refers to modeling the displacement vector from the previous hierarchical level to the next level. Within each hierarchical level, the integro-differential equation and the integro-differential representation are computed using algorithms (7). If at some hierarchical level the structure of the local heterogeneity breaks down into several heterogeneities, then the double and surface integrals in expressions (7) are taken over all heterogeneities. In this algorithm, the case is considered when the physical properties of the heterogeneities of the same level are identical, only the boundaries of the regions differ.

Similarly to (7), the same process is written for modeling the propagation of an elastic transverse wave in an n-layer medium with a two-dimensional hierarchical structure of arbitrary cross-section morphology using integral relations [

( k 2 j i l 2 − k 2 j 2 ) 2 π ∬ S C l l u x l ( M ) G S s , j ( M , M 0 ) d τ M + μ j a μ j i l u x ( l − 1 ) 0 ( M 0 ) + ( μ j a − μ j i l ) μ j i l 2 π ∮ C l u x l ( M ) ∂ G S s , j ∂ n d c = u x l ( M 0 ) , M 0 ∈ S C l μ j i l ( k 2 j i l 2 − k 2 j 2 ) μ ( M 0 ) 2 π ∬ S C l l u x l ( M ) G S s , j ( M , M 0 ) d τ M + u x ( l − 1 ) 0 ( M 0 ) + ( μ j a − μ j i l ) μ ( M 0 ) 2 π ∮ C l u x l ( M ) ∂ G S s , j ∂ n d c = u x l ( M 0 ) , M 0 ∈ S C l (8)

Thus, the iterative processes (7) and (8) make it possible to determine, for given elasticity modules, the layered medium that encloses the hierarchical heterogeneity and in the heterogeneity at each hierarchical level analyze the spatial distribution of the components of the seismic field. Then, using the known formulas [

The results of active electromagnetic induction monitoring in the shock proof mine of the Tashtagolsky mine allow the following conclusions to be drawn [

・ massif of rocks represents a multi-ranked hierarchical structure; the study of the dynamics of a state and its structure can be conducted only with the help of geophysical methods tuned to such a model of the environment.

・ the use of a multi-level induction electromagnetic method with a controlled source and a corresponding processing and interpretation technique allowed us to trace two hierarchical levels and identify the zones of disintegration that are an indicator of the stability of the array.

・ zones of disintegration in the circumscribed area are asymmetrical in soil and roof and discrete: i.e. there are intervals in the near-service space for their complete absence. The maximum changes in the array under the technogenic influence occur precisely in the morphology of the spatial position of these zones as a function of time.

・ the introduction of a new integral parameter of the intermittent intensity distribution of the disintegration zones makes it possible to proceed to a detailed classification of the array by the degree of stability and introduce quantitative criteria for this array [

・ introduction of the proposed integrated passive and active geophysical monitoring aimed at studying the transient processes of redistribution of the stress-strain and phase states, contributes to the prevention of catastrophic dynamic manifestations during the development of deep-located deposits.

At present, theoretical results on the modeling of the electromagnetic and seismic field in a layered medium with inclusions of a hierarchical structure are claimed [

It is shown that with increasing degree of hierarchy of the medium, the degree of spatial nonlinearity of 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.

Hachay, O., Khachay, A. and Khachay, O. (2018) Accounting Hierarchical Heterogeneity of Rock Massif for Prediction of Mine Seismicity. Open Journal of Geology, 8, 187-200. https://doi.org/10.4236/ojg.2018.83012