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Regression prediction algorithm of suffusion processes development during geoelectric monitoring.


It is known that the intensity of geodynamic changes of certain volumes of geological environment during development of suffusion is far higher than the intensity of its total variations. Accordingly, selective geodynamic monitoring provides information on possible catastrophic changes earlier than monitoring of the environment geodynamics in general [1,2]. Therefore, in practice, to solve the problem of protection of natural and man-made objects against possible consequences of catastrophes in case of suffusion danger, as well as to monitor the bearing capacity of overlying and underlying soil in operation of industrial facilities geomonitoring systems based on use of geoelectric sounding methods should be used [3]. They allow to register geodynamics of research subjects and to make predictive estimate of possible man-made disasters on the basis of informational processing of geoelectric monitoring data algorithms. Consequently, it is relevant to create a technique for prediction of suffusion processes development.

This article discusses the method of development of algorithms for regression processing of geoelectric monitoring data in order to create predictive geodynamic estimates for suffusion processes using geomechanical models of caving.


An organization chart of suffusion processes geoelectric monitoring is shown in Figure 1. It is based on the fact that geodynamics of objects of the analyzed environment is caused by its structure and lithological features of rocks, and the interpretation of recorded variations of geoelectric section transfer function and geodynamic estimate is determined in accordance with the object model [3, 4].

Based on the principle of stationary action and linearity of the geoelectric section, the operational transfer function of the geoelectric section [delta][H.sub.ij](p, [[alpha].sub.1], ... [[alpha].sub.l]) can be estimated with the help of the space functions of an object system [[psi].sub.ij](p) at a nominal value of geodynamic parameters [alpha][R]. Under conditions of an initial balancing of a measuring system and current geodynamic variations of an object:

[DELTA][U.sub.i](p) = [[SIGMA].sup.n.sub.j=1 [DELTA][H.sub.ij](p)[I.sub.j](p),

[DELTA][H.sub.ij](p,[[alpha].sub.x], ...,[[alpha].sub.l]) = K(p)/[S.sub.i](p) [[SIGMA].sup.l.sub.k=1] [[partial derivative][[PSI].sub.ij] (p,[[alpha].sup.0.sub.1],....[[alpha].sup.0.sub.l])/[partial derivative][[alpha].sub.k] [DELTA][[alpha].sub.k] (1)

where [I.sub.i], [delta] [U.sub.i] is the sounding signal and the response of the i-th source ; [delta][[alpha].sub.k] is the vector of geodynamic variations of the object; K(p)is the environments contrast ratio; [S.sub.i] (p) is the function of measuring tract transfer factor. This expression formulates the principle of superposition of sounding signals and thus defines one of the most important aspects of geodynamic objects monitoring organization--an opportunity to highlight the properties of a certain part of the environment (object) by controlling the source parameters [5].

Fig. 1: Block diagram of geoelectric monitoring

It is obvious that the efficiency of geodynamic evaluations during geoelectric monitoring significantly depends on the established models of geodynamic objects and the geological environment and, therefore, this diagram provides algorithmic correction of the selected model based on the current information processing. The need for correction arises in case of qualitative change of the geodynamic object due to a possible redistribution of selected volumes of the geological environment due to suffusion. This qualitative change in the monitoring system is based on the evaluation criteria at the stage of processing and decision-making [6].

Main part:

The process of caving caused by crushing of dispersed rocks takes place over suffusion cavities as a result of their growth and is the result of underground erosion. Caving occurs due to an initial collapse at the moment when a cavity formed as a result of suffusion reaches some certain critical dimensions.

Forecast of suffusion processes development includes an assessment of sizes and location of the expected shows, as well as the rates of its geodynamics in space and time. It is based on geomechanical models of different degree of complexity, which take into account the geological conditions of the process development and the mechanism of its interaction with the technosphere.

Geomechanical estimate of critical dimensions of suffusion cavities can be given on the basis of the applicable geomechanical models. If there are no aquifers in dispersed rocks the critical dimension of the half width of suffusion cavities can be evaluated according to the following equation [7]:

[R.sub.z] = z[B.sub.z] ([[phi].sub.z]) + 2[c.sub.z]/[[lambda].sub.z], (2)

where z is the depth of the top of the suffusion cavity ; [[phi].sub.z] is the angle of internal friction; [c.sub.z] is the specific cohesion ; [[gamma].sub.z] is the specific weight of the rocks; [B.sub.z] ([[phi].sub.z]) is the function defining the lateral pressure. For a radial suffusion cavity

[B.sub.z] ([[phi].sub.z]) = 1 -sin[[phi].sub.z]/1 + sin[[phi].sub.Z] tg[[phi].sub.z].

In other cases, the equation (2) may be more complex, taking into account both singularities of the environmental geology and man-caused impact on it.

From the point of view of geoelectric monitoring and geoelectric control methods use it is necessary to establish a correspondence between spatial functions in the equation for the transfer function of the geoelectric section (1) and geomechanical conditions of the local caving (2). This correspondence can be defined from consideration of the problem of distribution of the point source of the field geoelectric field in the presence of a spherical heterogeneity, by which the suffusion process can be represented very tentatively.

The general equation for potentials of an electric field in the presence of near-surface heterogeneity in the form of a sphere can be traced to Legendre's equation [8] and its solution is as following:

U(r,[theta] = I[[rho].sub.1]/4[pi]d [[SIGMA].sup.[infinity].sub.n=0] [(r/d).sup.n] [P.sub.n](COS[theta] + [[SIGMA].sup.[infinity].sub.n=0] [A.sub.n][r.sup.-(n+1)] [P.sub.n] (COS[theta]), [A.sub.n] = I[[rho].sub.1]/4[pi] K(j[omega]) [a.sup.2n+1]/[d.sub.n+1], (3)

where [P.sub.n] (cos [theta]) is the Legendre polynomial. Coefficient [A.sub.n] is determined by the boundary conditions and the spatial parameters of near-surface heterogeneity: the distance from the sounding site to the center of the heterogeneity cl. the directional angle [theta] and the radius of the sphere a (Fig. 2).

The proportions (3) allow us to solve the problem of determining the sphere occurrence characteristics according to the observed distortions brought by it into the spatial distribution of the geoelectric field potential. Taking into account doubling of the anomalous component of the field the transfer function, which determines the spatial displacement of the equipotential lines of the i-th source, can be expressed as follows:

[DELTA][H.sub.ij] (p,a,h) = K(p)[[PSI].sub.ij] (a,h) = 2K(p) [a.sup.3][r.sub.ij]/[([r.sup.2.sub.ij] + [h.sup.2]).sup.3/2] (4)

where h = z + a is the depth of occurrence of the sphere under the surface of the ground.

On the basis of the proportion (4) we can make an assessment of measurement of the depth of occurrence and dimensions of the near-surface heterogeneity in the form of a sphere and therefore we can use it as an estimate for geodynamics of suffusion processes forecast:

[R.sub.z] = 3[square root of 3[square root of 3][DELTA]H[h.sup.2]/2K(p)]

where [delta] H is the estimated maximum of the equipotential line displacement.

The problem of geodynamic processes forecasting can be solved on the basis of predictive modeling, the initial information for which is the results of the interim geodynamic series regression processing. The geoelectric model of suffusion processes geodynamic development can be represented as the linear discrete system [9], which is determined by the difference equation:

[Y.sub.k][i] + [[SIGMA].sup.n.sub.i=1] [[SIGMA].sup.m.sub.j=1] [a.sub.ij][Y.sub.k][I - j] = [S.sub.k][i], (5)

where [Y.sub.k] [i]-readings of the recorded geodynamic process by the k-th registration point; [a.sub.ij] coefficients of the model ; [S.sub.k][i] --readings of a generated random geodynamic process with the parameters

M{[S.sub.k][i]} = 0, M{[S.sub.k][i][S.sub.k][i]} = [[sigma].sup.2.sub.k][[delta].sub.ij] ([[delta].sub.ij] - weight coefficients of the model).

On the basis of expression (5) a system of initial regression equations can be formed:

[Y.sup.T] [i] = [F.sub.a] [i][a.sup.T] [i] + [s.sup.T] [i], (6)

where [Y.sup.T] [i] = [Y[m +1], ..., Y[[l]].sup.T] ;


[a.sup.T] [i] = [a[1], ..., a[[m]].sup.T] ; [s.sup.T] [i] = [s[m +1], ..., s[[m +1]].sup.T] ; l - depth of the predictive estimate.

The applied regression model of the predictive estimate (6) during the analysis of suffusion processes allows us to take into account both the influence of cyclical planetary factors and man-made influences.


According to the algorithms discussed in this paper a predictive estimate of caving on the models of karstsuffusion processes is provided. Table 1 shows the data grouped into six types of soils in the area of the supposed caving.

Probability of detection of [p.sub.0] and probability of a false alarm [p.sub.1] when using monopolar sounding electrical installation were used as evaluative parameters [10].


As is clear from the data presented proposed algorithms for formation of predictive estimates during geoelectric monitoring allow to define conditions of caving at suffusion karst development with high reliability, even when using single-pole electric installations. The effectiveness of the proposed method increases significantly, increasing the depth of predictive estimates, by means of increasing the quantity of sounding sources used and geoelectric field registration points. Thus, the solution to the problem of protection of natural and man-made objects from possible consequences of catastrophes in case of suffusion danger, as well the solution to the problem of control over the carrying capacity of overlying and underlying soils during the operation of industrial facilities is provided.


The research was made with financial support from the grant of the Russian Foundation for Basic Research 13-05-97506 - r tsentr a.


Article history:

Received 23 January 2014

Received in revised form 19 April 2014

Accepted 6 April 2014

Available online 15 May 2014


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(1)Bykov Artem Aleksandrovich and (2) Kuzichkin Oleg Rudolfovich

(1) Murom Institute (branch) Federal state budgetary Educatioal Institution of Higher Professional Education "Vladimir State University named after Alexader Grigoryevich and Nikolay Grigoryevich Stoletov" 602264, Russia, Murom, Orlovskaya str., 23

(2) Murom Institute (branch) Federal state budgetary Educatioal Institution of Higher Professional Education "Vladimir State University named after Alexader Grigoryevich and Nikolay Grigoryevich Stoletov" 602264, Russia, Murom, Orlovskaya str., 23

Corresponding Author: Bykov Artem Aleksandrovich, Murom Institute (branch) Federal state budgetary Educatioal Institution of Higher Professional Education "Vladimir State University named after Alexader Grigoryevich and Nikolay Grigoryevich Stoletov" 602264, Russia, Murom, Orlovskaya str., 23

Table 1: Model studies results

#     Soil       [[gama].sub.z],   [C.sub.z],   [[phi].sub.z]
                 kN *              kPa          degrees

1     Clay       19,2              31           20
2     Loam       23,1              59           31
3     Dolomite   24,6              198          38
4     Gypsum     23,3              515          32
5     Marl       22,2              114          35
6     Gravel     18,2              2            40

#     [bar.h],   [bar.z],    [bar.           [p.sub.0]   [p.sub.1]
      m          m           [R.sub.z]], m

1     6,5        1,4         3,2             0,943       0,00932
2     7          1,3         3,5             0,951       0,00756
3     8,5        1,5         3,5             0,933       0,00806
4     15         5,2         5,3             0,924       0,00944
5     19         4           6,6             0,913       0,01004
6     6          1,5         3,2             0,953       0,00771
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Author:Aleksandrovich, Bykov Artem; Rudol'fovich, Kuzichkin Oleg
Publication:Advances in Environmental Biology
Article Type:Report
Geographic Code:7IRAN
Date:Apr 1, 2014
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