2.1 The seismically active layer of the Earth's crust and its connection with the critically stressed layer.
2.1.1 Earthquake source as an area of critically stressed condition of rock
One of the key factors indicating the threat of geodynamic events is the stressed state of the rock [26, 15, 27]. An integral reflection of the stressed condition of the Earth's crust is seismicity. The so-called shallow earthquakes occur in the inner parts of lithospheric plates, the source of such quakes is located within the Earth's crust.
The physics of the processes occurring in the seismic focus is the subject of numerous works, reviews of which are presented in [28, 22, 29]. In general terms, the earthquake focus zone is viewed upon as an area of destruction and the place where a new rupture develops or there is fault reactivation. It follows that the earthquake source at the final stage of the event preparation can be considered as a certain amount of rock in critical stressed condition.
2.1.2 Seismically active layer of the Earth's crust
It has been noticed that in seismic-active regions of the Earth most earthquakes occur at certain depths, which suggests the existence of a specific “seismically active layer” of the Earth's crust [30-33]. A typical distribution of seismic focuses by depth is provided in Figure 1, where it can be seen that their maximum number occur at a definite depth interval. These picture shows that there is a certain maximum depth of crustal earthquake hypocenters for areas inside lithospheric plates.
Generally, it is believed that a seismically active layer lies below the Earth's surface at a certain depth H, which corresponds to the brittle-plastic transition zone in the Earth's crust and approximately coincides with a temperature range of 300-400 ° [30, 33, 36, 37]. Based on statistical analysis of a large sample of data, in the review [33] is indicated that on average the H= 10 km and most earthquakes occurred within this seismically active layer. The source of earthquakes is the stress concentration in this area [30], associated with the interaction of the crust and mantle [31].
2.1.3 M. Petukhov’s hypotheses of the critically stressed condition of the Earth's crust.
Much earlier, the very first results of measuring rock stress showed that horizontal stresses exceed vertical values [38, 39]. This finding was explained by the presence of tectonic processes, and was subsequently confirmed by numerous tests and general conclusions [40]. I.M. Petukhov suggested that due to the strong compression of rock by horizontal forces, the source of which were global tectonic processes, certain areas inside lithospheric plates can accumulate critical stress [25]. By analogy with critically stressed zone in front of longwall (coal face), it was believed that critically stressed area in the Earth's crust extends through a certain layer under the earth's surface (Fig. 2). The depth of this layer depends on the magnitude of horizontal compression and the nature of the interaction between crustal blocks, and can vary from zero to the full thickness of the Earth’s crust.
Understanding of how the processes at the boundaries of plates affect the areas in remote parts of such plates is currently based on theoretical and experimental studies in this area. Geodynamic models have been developed for individual regions, demonstrating gradual transfer of deformations from the plate collision zone to internal parts of the blocks [41, 42].
2.2 Assessment of the thickness of the layer of crustal rock under critically stressed
We devised a calculation method based on a number of assumptions [43] to assess the thickness of the critically stressed layer of the Earth's crust. This calculations show that the thickness of this layer can vary from site to site, but these could not be used for practical purposes. Yet, if at a certain depth the rock accumulates critical stress, then this process should be accompanied by some or other seismic manifestation. It is the transition zone where rock acquires breaking stress that can be the main source of seismic events. Mining practice clearly demonstrates: microshocks and microseismic events occur in zones with maximum abutment pressure, in the transition zones where rock acquires critical stress. This concept of seismic event distribution throughout crustal depths underpins the author’s idea of classifying sections of the Earth’s crust according to the level of geodynamic hazard and risk.
3. Classifying sections of the Earth’s crust according to the level of geodynamic hazard.
3.1 Classification concept and classification attribute.
Rock can accumulate potential energy of elastic compression in critically stressed zones ahead of (coal) faces, where energy level is proportional to the squared value of acting stress and volume of the zone. Any impact on such stressed zone triggers instability, wherby part of the released energy transforms into the energy of geodynamic processes (bumps, spalling, rock bursts and tectonic rock bursts), and the remaining part is redistributed in the surrounding formation, causing rock displacements along the weakened surfaces and shifting stress to adjacent areas. As stress progressively builds up, the size of critically stressed zone increases, and the abutment pressure zone migrates into deeper areas. Hazardous condition is created if there is crushed or fractured material (tectonic fault zones) in those areas that is not able to absorb stress and that impedes movement of the abutment pressure zone depthward. Thus, an area of increased risk is created in front of such weakened zone, since in case of any impact on such stressed zone redistribution of energy into the surrounding formation gets constrained, and the proportion of energy that transforms into geodynamic energy increases.
Similarly, it can be assumed that anthropogenic impact on the deeper earth or the surface also creates instability due to the existence of critically stressed rock layer in the Earth’s crust. The significance of geomechanical effect imposed by engineering structures can be comprehended from the available research results. Observations of induced seismicity show that mining activity can cause earthquakes with epicenters located at 3-30 km distance from the mining area and with hypocenters that are several kilometers deeper [25, 44, 45]. A. McGarr believed that oil production activates the seismic process at great depths by relieving some of the load on fault planes [31]. In his book A. Sheydegger [46] cited F. Steinhauser and M. Caputo who had calculated that filling a dam pond with about 1010 m3 of water brings about a change in the stress condition as far as the Moho discontinuity, i.e. for the entire thickness of the Earth’s crust.
It can be assumed that due to anthropogenic impact on the Earth’s interior or the surface part of the energy accumulated in the critically stressed rock layer transforms into the energy of geodynamic processes, and part is redistributed in the surrounding formation. The thicker is the critically stressed rock layer, the more energy is accumulated there and the larger energy can transforms into the energy of geodynamic processes. In other words, the thicker the critically stressed rock layer, the more hazardous it is to penetrate into underground area or impact to the Earth's surface, i.e. the greater is the geodynamic risk involved in antropogenic influence.
In addition, the thicker is the critically stressed rock layer, and the closer its thickness comes to that of the Earth's crust, the worse is the situation with redistribution of energy into the surrounding rock, since the rock of the upper mantle have a lower viscosity and cannot absorb the stress. In this situation, comparable with impacts on the critically stressed zone near a fault in a mine, the rate of energy redistribution into the surrounding rock may slow down, which will result in escalation of geodynamic threat (Fig. 3).
Consequently, geodynamic impact of engineering structures on critically stressed rock areas evokes immediate response. In some areas there are no extensive zones of critical stress, however, critical stress can be accumulated in sporadic small areas due to interaction of crustal blocks or engineering activities. Then, in response to engineering work geodynamic events might occur in these small critically stressed areas. The uniqueness of this critically stressed crustal layer is that it is not continuous, but includes sporadic sections (volumes) wherein stress has reached critical values; these volumes are distributed to a certain depth.
Next, conditions are created for excessive rock deformation in areas with critically stressed rocks. Under these conditions, the interaction and relative movement of crustal blocks can develop under stress well below the elastic limit. Moreover, deformation build-up (caused by displacement of blocks relative to each other along the boundaries separating them rather than by deformation of the entire rock mass) keeps occuring at ever lower stress values. Therefore, the thicker the layer of critically stressed rock, the easier and more intense the deformation of the Earth's surface can develop along the boundaries of the blocks under additional stress omposed by engineering structures, and the greater is threat to engineering facilities and technological operations.
Based on the foregoing, it is proposed to take - as a quantitative classification criterion - the ratio of the critically stressed rock layer thickness Hs to the thickness of the Earth's crust in this section He.c. : n = Hs/He.c. We can take the critically stressed rock layer thickness Hs in the Earth's crust equal to the depth of the bed of the seismically active layer, i.e. maximum depth of earthquakes in the area.
3.3 Estimation of the critically stressed rock layer thickness using data on the earthquake hypocenter
Since for estimating Hs we focus on the maximum depths of hypocenters, this greatly facilitates the selection of statistical data for analysis. Based on the data review on the maximum depths of hypocenters, the author obtained approximately 200 values of the relative depth of the seismically active layer, unevenly distributed throughout Northern Eurasia and having various errors, Figure 4. The number of points on the map (about 200) is statistically acceptable for testing the idea of classification. The part of data is in the Table 1.
The author focused primarily on the most probable estimate of the earthquake depth, but for some earthquakes, a lower-bound estimate of the depth was used.
3.4 Classification of the Earth's crust areas by degree of geodynamic hazard
Based on the data obtained on the values of seismically active layer relative depth distribution and the block structure of the Earth’s crust, it is possible to map the sections of the Earth’s crust according to the geodynamic threat level. The possible number of map gradations (classification classes) can be selected taking into account the quality of the available factual information.
3.4.1 Defining possible number of gradations (levels).
Since there is only one quantitative attribute in the proposed classification (n=Hs/He.c.), the optimal number r of groups in the classification can be determined by the Sturges' formula (1):
where N is the number of statistical units. In this case, N = 200 and r = 9.
However, the number of groups defined with this formula is obviously overestimated due to the high uncertainty of the classification attribute. In our case, it can be shown that the squared relative error of the classification attribute n = Hs/He.c. is equal to the sum of the squared relative errors Hs and He.c. If we take the relative errors of values of Hs and He.c. as 0.1 (or 10%), then the relative error n will already be approximately 0.15. And since the values of n are in the range [0-1.0], the number of gradations (the number of groups) should be no more than 4 to 6. In addition, the Hs estimation relative errors can be much higher than 0.1, as follows from the materials in Table 1. As for the thickness of the Earth’s crust He.c., there are arguments that relative errors in its estimation can be significantly higher than 0.1.
Furthermore, the error in defining depth Hs increases with the depth value. And this leads to the fact that group intervals become uneven. So, for n > 0.5, the errors in the determination of Hs build-up so that it is no longer possible to divide the interval 0.5-1.0 into smaller groups. All this allows us to arrange the entire set of n values into three unequal intervals: 0-0.25; 0.25-0.5 and 0.5-1.0. In addition, aseismic territories can be represented as territories with a zero value of the critical stressed layer and spin them off into a separate (first) group.
3.4.2 Map of the Earth’s crust sections with geodynamic threat rating
In 1990–2010 work was being done to draw a map of geodynamic zoning (I. Batugin's, I. Petukhov's terminology) for Russia and adjacent territories [25]. Maps were drawn for the territory of the former USSR and China. This work was based on the concept of hierarchically discrete structure of the rock and the Earth's crust as a whole. This concept is recognized at the current stage of the development of science as the most significant advance in geomechanical and geodynamic research made at the end of the last century [47] and is used in current research on geodynamics and rockmechanics [11, 48, 49]. To build a map montage of the Earth’s crust sections with geodynamic threat rating, the author made use of a map of the crustal block structure from [25]. Following criteria were applied to the map montage:
- geometrical configuration of areas with different gradations on the map are selected with due account for the block structure of the Earth's crust. It is assumed that the shape of such areas, due to the fundamental nature of the crustal discrete structure, corresponds to the geometric shapes of individual blocks or groups of blocks
- if the coordinates of several earthquakes coincide, the earthquake with the maximum depth of the hypocenter is displayed on the map
- if earthquakes from different gradation groups fall into the same block of rank I, then the maximum value for the entire block is accepted. Blocks with equal gradations are combined into corresponding areas
Map montage where the above assumptions are taken into account is provided in Figure 5.