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Geotomography with the help of a cutter–loader working organ as a source of imaging waves
ARTICLE IN PRESS International Journal of Rock Mechanics & Mining Sciences 46 (2009) 1235–1242
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International Journal of Rock Mechanics & Mining Sciences journal homepage: www.elsevier.com/locate/ijrmms
Technical Note
Geotomography with the help of a cutter–loader working organ as a source of imaging waves Zbigniew Isakow Department of Geophysical Systems, Research and Development Centre for Electrical Engineering and Automation in Mining—EMAG, 40-189 Katowice, Poland
a r t i c l e in fo Article history: Received 6 March 2007 Received in revised form 26 May 2009 Accepted 1 June 2009 Available online 26 June 2009
1. Introduction The abilities of a continuous monitoring of distribution of relative-stress changes in long-face mining, as well as a detection of discontinuous and density faults in front of mine workings, are important issues from the point of view of work performance and safety in hard-coal mines. The continuous monitoring of strata under conditions of coal getting is a fundamental problem for a mining service. An effective solution for this problem should provide low-cost measurements, a high operational reliability, and stability of a measuring system under conditions of intensive mining operations in order to achieve a high resolution and a clear method for interpreting the results. The new Polish intrinsically safe system GEOTOMO/E, developed at the EMAG under direction of the author in Katowice, has been designed for monitoring relative-stress changes that occur in the coal roof and seam in front of a longwall. Rock-mass imaging is achieved by seismic waves generated by the getting element of a cutter–loader. This enables the detection of zones where stress is concentrated, identification of its occurrences, and the hazards they may induce. A seismic signal generated by the getting element of a cutter–loader, the position of which is monitored in the course of penetrating the imaged area, is recorded by a properly configured network of sensors mounted in advanced galleries to provide optimal conditions for signal identification. The process of tomography has been applied for more than 35 years. At first it was used by Hounsfield [1] and Cormack [2] in medicine, in the early 1970s. Then it was used by Dines and Lytle [3] in geology, in 1979. Seismic tomography has been used in the mining industry since 1981 [4,5]. It has been used for representing
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the structure of strata and changes in properties of strata, including research into stress changes by the propagation velocity of seismic waves [6–8]. Westman [9] described laboratory tests that applied velocity tomography to represent changes in stress of rock samples that were being loaded. Westman et al. [10] conducted research similar to the present study. They used attenuation tomography and the Rock Vision system, including analogue transmission, to represent stress concentration in front of a long face. They used a longwall shearer as the source of seismic waves. The frequencies were measured in the range of 80–200 Hz. An assumed tomogram grid was 10 m 15 m, the dimensions of a ‘‘pixel’’ for which the relative attenuation changes were determined. Westman [9] used attenuation tomography for determining the varying stresses of rocks of differing lithologies in an underground coal mine. Active seismic methods used for indirect analysis of relativestress changes are based on a seismic-velocity mining tomography in which the generated signal is a pulse by a hammer or blast. Frequent measuring in terms of advancing a longwall, and in the presence of a gas-explosion hazard, is very difficult and practically impossible. To allow continuous measurement of the relative-stress changes, a measuring system is designed wherein the working organ of a cutter–loader may be regarded as a seismic-noise source and a continuous ground-motion generator. Generated ground motions, after penetrating the tested area of a seam or roof, are registered by seismic sensors and are available for interpretation. Thus, one can achieve a considerable reduction of expenditure for the work that is necessary for imaging, because the measurement cycle is carried out entirely automatically. Control of the entire process is carried out from the surface (e.g., from a geophysical station). One cannot underestimate the fact that another advantage of the fully automated measurement system assures safety to those who do the metering.
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2. Description of the method An elastic wave that propagates in a rock mass is subject to a complex process of amplitude attenuation related to the increasing distance to the wave source and the propagation time. This process relates to factors independent of the mechanical properties of the rock mass, such as increasing wave-front field in time or factors governed by the rock-mass structure. Among these factors are processes that lead to mechanical scattering of elastic energy resulting from inhomogeneity, energy conversion into thermal or electric energy, and many others. As the seismic wavelength ranges from a dozen or so meters to several dozens of meters, whereas the seam thickness is usually less than 3 m, and horizontal dimensions of mine workings are some dozens of meters, a three-dimensional model would be useless. We might assume that the seam has rectangular dimensions of N M meters. Let an attenuation coefficient value be given for every point of this rectangular area of c(x, y)40. Let the signal energy in the source be IT, and the energy of the recorded signal be IR. As attenuation on the ds path is proportional to the length of this path and to the initial signal energy as well, we can write [11,12] dI ¼ Icðx; yÞ ds.
(1)
The solution for the boundary condition I(0) ¼ IT is RT cðx;yÞ ds I ¼ IT e R .
(2)
Taking a receiving point as I(R) ¼ IR, we have RT cðx;yÞ ds IR ¼ IT e R .
(3)
Integration is carried out along the seismic ray propagating from the source to the receiver. It is often assumed that the seismic ray is a straight line. This assumption leads in some cases to errors, which can be avoided by the procedure of tracing the seismic ray to find the real propagation path of the seismic wave. In our case we decided to assume linearity for the sake of a simple calculation. Measurements were made at a small area in front of a long face, taking particularly into consideration the relative changes of energy attenuation at the area around the face in order to detect the trends of these changes in time and space and to draw conclusions on this basis regarding the change of stress. In our case the signal is continuous, in contrast with typical seismic measurements having a pulse signal with a well-defined excitation time. Continuous signal recording can be done in a well-defined short time window. In a given time window, different types of seismic waves can be recorded—direct waves (excitation latest), reflected and refracted waves (excitation earlier), and scattered waves (excitation earliest). Obviously, their propagation rays are different as well as their propagation velocities. The assumption of a rectilinear propagation of a signal energy and simultaneous multiple measurements at the same pixels lead in a sense to averaging of the problem, even though it is approximate and contains errors. Regarding the use of the system for assessment of the rock burst hazard and effectiveness of prevention, the most important is a nearly continuous (after each cutting) observation of the concentration of relative changes in stress in time and in space in front of the face. The basic equation of seismic attenuation tomography is Eq. (3). It can be resolved to linear form by transforming Eq. (3) as follows: Z T IR ¼ cðx; yÞ ds. (4) ln IT R
It follows from Eq. (4) that logarithms of measured attenuation values of energy are linear functions of c(x, y) attenuation coefficients. Formula (4) must be replaced by a discrete equivalent suitable for numerical calculations. Denoting the logarithm of registered signal energy to induced signal energy ratio (i.e., ln(IR/IT)) for a given ith seismic ray as DIi, we can write
DIi ¼
M X
Dsij cj ;
i ¼ 1; . . . ; N,
(5)
j¼1
where Dsij is the ith ray path in the jth cell, and cj is an attenuation coefficient in the jth cell. In every opened short period of time (5 s) and every 2 m of a path traveled by a shearer, the energy induced in the source reaches all sensors; therefore, one may assume that the value of that induction is constant. It may change insignificantly from one measurement to the next. However, this is of no importance because within every measurement cycle new equations are created, which are, after every cutting, the basis for calculating average values of attenuation factors in elementary pixels, and next the standardized relative attenuation factors. The procedure for creating measuring data vector d (see below) allows for calculation of the average energy of induction in the case of multiple passings by the shearer of the same measuring point during cutting. Let d be the vector with components comprising, in particular, DIi the vector of measured data, and m the vector comprising cj attenuation coefficients (the vector of estimated model parameters). The set of Eq. (5) can be written in matrix form as d ¼ Gm.
(6)
The G matrix of Eq. (6) defines the measurement model, and for this case it is in the form 3 2 Ds11 Ds12 Ds13 : : Ds1M 6 Ds : 7 7 6 21 Ds22 Ds23 : : 7 6 7 6 Ds31 Ds32 Ds33 : : : 7 6 6 : : : : : 7 (7) G¼6 : 7. 7 6 7 6 : : : : : : 7 6 6 : : : : : : 7 5 4 DsN1 : : : : DsNM Particular elements of the G matrix are calculated with seismic ray tracing procedures. They allow determination of the path of the seismic wave in each of the particular cells with an assumption of linear or nonlinear propagation. As the induction of a seismic signal is continuous, the sensors record waves of different types within the time window. Different waves propagate along different ray paths (although for some waves encountered in mining conditions the ray theory cannot be applied). Furthermore, each type of wave undergoes different attenuation on its propagation path. Taking into account all these essential differences, along with the unknown character of the seismic wave source, would make an industrial application impossible. In such a case, rectilinear propagation would be the best solution. Furthermore, such an assumption will speed up and simplify significantly the calculations for relatively small dimensions of the area being under control in front of a face and for short ways of the rays. The calculations are made according to the following procedure. The imaged field is divided into cells (rectangular, as a rule) in which attenuation coefficient values are to be determined. Also determined is the path of each ray in each cell for a source from a given excitation point (position of a cutter–loader at a particular longwall point); those paths are the elements of a G matrix given
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SURFACE PART OF THE SYSTEM IBM PC SERVER FOR MONITORING CUTTER-LOADER PARAMETERS
SUPERIOR SERVER
MODEM
RECEIVING PART OF DIGITAL TRANSMISSION
UNDERGROUND PART OF THE SYSTEM
8 1
2 3
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GEOPHONES
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9 10 11 12 13 14 15 16
TRANSMITTERS FOR DIGITAL TRANSMISSION
Y
COMPACT STATION
IBM PC SERVER FOR IDENTIFICATION OF STRESS CHANGES
X
CUTTER-LOADER Fig. 1. Structure of the interconnected systems for monitoring relative changes in stress and the coal getting process. (This figure is an example of sensors in the array scheme for coal-seam geotomography; a scheme for coal-roof geotomography is not shown.)
by Eq. (7). The data vector is obtained after determining the mean energy value of signals recorded by particular sensors for each fixed excitation point. On such a basis the solution of an inverse problem parameter vector (i.e., attenuation values for particular cells) is obtained. Then an up-to-the moment distribution map of the elastic-wave attenuation of a single cutter–loader slice is obtained (from the roof or seam). There are many ways in which the solution of Eq. (6) describes the relation between the distribution of an attenuation coefficient of a rock mass and the energy values of the measured signal. From a formal point of view, those problems can be brought to bear toward finding the so-called inverse of a G matrix—a Gg matrix—which results in the relation mest ¼ Gg d,
(8) est
in which the m symbol denotes a vector of calculated model parameters. The Gg matrix may be treated (in a way) as an inverse of a G matrix. A rough analysis of Fig. 1 and matrix shape given by Eq. (7) brings to light the main problems of determining the Gg matrix by classical methods. The G matrix is a rectangular matrix, which means that, as a rule, there are fewer equations than estimated parameters; in a classical way, then, there is no inverse of the G matrix. Furthermore, G is a sparse matrix—i.e., most of its elements are equal to zero; thus, most mathematical operations may lead to singular problems in this case. The problem defined by Eq. (6) may lead (and often leads) to unstable solutions (i.e., small changes of data vector lead to large changes in estimated parameters). The G matrix has, as a rule, very large dimensions; in many cases it involves limits on available algorithms. It is typical of problems in attenuation seismic tomography that some model parameters (in this case, attenuation values for particular cells) cannot be determined, because some cells are crossed by insufficient seismic rays to determine reliable damping values. On the other hand, some other parameters can be parameterized as a mean value of many values that correspond to cells crossed by many rays. An efficient way for solving the inverse problem should allow for division of all parameters into
two groups: the first, with parameters insufficiently determined, and the second, with element values with an excess of parameterization. To solve the inverse G matrix problem for the case of attenuation in seismic tomography applied to long longwall fronts the matrix decomposition method (singular value decomposition—SVD) [11,13] and the pseudo-inverse rectangular matrix method are used, with the numerical algorithm allowing for effective and numerically stable calculations. Signals detected by sensors installed in the coal roof and seam, after A/D conversion, are transmitted to the GEOTOMO/E seismic device, constructed specially for this purpose, which interfaces with the system that monitors the coal getting process (a system that provides information on the cutter–loader position; Fig. 1). The digital transmission of data ensures a high-quality recording and enables a reduction of both the device-specific noise and noise generated by the telecommunication network. The interpretation of the recorded signal is based on algorithms verified in the analysis of continuous seismic monitoring results in the course of geological drilling [14]. These algorithms are based principally on examination of the energy of the registered signals. The method presented here enables description of the distribution of attenuation factors for elastic waves in rock on the basis of registered decreases in average amplitudes of energy of vibrations generated by the getting element of the operating longwall cutter–loader. For the purpose of determining the energy attenuation coefficients in the elementary cells, into which the monitored regions of the coal bed and roof in front of the longwall have been divided, the inversion algorithm [13,15] was applied, based on matrix decomposition together with the method of solution regularization in cases of high-level random noises. The information obtained, presented in the form of distribution of attenuation of signal energy (being approximately inversely proportional to stress changes) in front of the getting cutter–loader, enables optimization of the performance of powered supports as well as selection of the most appropriate parameters of their operation (supportiveness). Such information also improves work safety in mine workings. The metering results
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0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0
Bed 19 -12-2002 18:09 , 19-12-2002 20:38
Position Y [m]
1
6
50 40
3 30
5
20 4
2 10
0 120
100
80 60 Position X [m]
40
20
0
Day,Time [h]
Track record of a cutter-loader path in wall
Position X [m] Fig. 2. Map representing the relative factors of attenuation of vibration energy in the seam for 19 December 2002 as the result of cutting of wall no. 306 with a cutter–loader within the period 6:09 pm to 8:38 pm. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
can be compared with other data, such as the value of active power consumption of a longwall cutter–loader during cutting. Thus, data can be obtained for calculating the relationships between control of sufficient support, relative-stress distribution within the longwall during cutting, and the energy expenditure necessary for completion of such an operation.
3. Description of the GEOTOMO/E system The GEOTOMO/E system, developed for the purpose of monitoring of relative stress, was designed for automatic assessment of energy attenuation of elastic waves induced by the getting element of the operating cutter–loader, which is approximately inversely proportional to the stress in front of an imaged longwall. The GEOTOMO/E system consists of both underground and surface components. The standard GEOTOMO/E system for monitoring relative changes in stress consists of the following: GVu (geophone made by GeoSpace of type LS11D 4.5 Hz Vertical), geophones of type GHa (made by GeoSpace LS11D 14 Hz Horizontal), NSGA underground transmitters, SP/DTSS surface station with digital OCGA receivers and ST transmission control module, recording server, separating network connector with the Media Converter, and the GEOTOMO/E system’s processing computer.
The feeding of the system’s underground component is realized centrally from the surface with an appropriate, intrinsically safe voltage. Such feeding ensures proper operation of the geophones and transmitters, unaffected by incidental breakdowns in local feeding on the longwall or in close-to-longwall roads. The intrinsically safe underground part of the system consists of seismic geophone GHa sensors installed horizontally in the seam on anchors adapted specifically for that purpose, and seismic geophones of the GVu type installed vertically on anchors in the roof. Sensors are compatible with seismic NSGA transmitters. Each of the sixteen seismic transmitters is compatible with one GHa sensor and one GVu sensor. Sets of GHa/GVu sensors, together with an NSGA transmitter, are installed in both of the advanced galleries, symmetrically against the longwall front in 20-m intervals. Measurement points are established in 20-m intervals, which, on the one hand are appropriate for coverage of the measured area, and on the other hand are sufficient when taking into account the limit of propagation of the seismic signal generated by the working element of a cutter–loader. Signals from thirty-two measurement sensors, after A/D conversion, are transmitted via NSGA transmitters and sixteen teletransmission lines to the SP/DTSS surface transmission station, and then, via the ST control module, are transmitted to the recording server, where they are buffered and stored by a software
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0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0
Roof 19-12-2002 18:09 , 19-12-2002 20:38 9
14
50
Position Y [m]
40 11
13
30 20
10
12
10 0
120
100
60 80 Position X [m]
40
20
0
Day,Time [h]
Track record of a cutter-loader path in wall
Position X [m] Fig. 3. Map representing the relative factors of attenuation of vibration energy in the roof for 19 December 2002 as the result of the cutting of wall no. 306 with a cutter–loader within the period 6:09 pm to 8:38 pm. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
of the DTSS/G Server. This server cooperates with the processing computer via a light pipe connector and the Media Converter. NSGA seismic transmitters serve as programmable ‘‘intelligent’’ underground-measurement concentrators that facilitate control of amplification and filtration of signals, switching of amplification between measurement channels in accord with the commands given from the surface, A/D conversion with dynamics not less than 100 dB, and digital transmission of data to the surface. The joint analysis of measurement data, obtained from the system of monitoring a cutter–loader’s operation parameters (in particular, its position) and from the GEOTOMO/E system for identifying relative-stress changes, enables the assessment of attenuation of the recorded elastic wave in terms of variable positions of a vibration source (i.e., the working element of a cutter–loader) and of nonhomogeneous parameters of elasticwave propagation. The principal purpose of this system is producing maps of isolines proportional to the relative changes in attenuation of energy of induced waves in the coal roof and seam in front of a long face.
4. Results The GEOTOMO/E system was installed and put into operation in longwall no. 306 of coal-seam no. 507 at the Bielszowice Coal
Mine. Because of limitations in the number of telecommunication lines supplied by the coal mine, the number of sensors installed in the coal roof and seam was limited to six. Along with increasing the number of required teletransmission lines supplied by the coal mine, the greater number of metering units composed of NSGA transmitters and GHa/GVu geophones were connected. This network resulted in better coverage of the controlled area with seismic rays and ensured enhanced spatial sensitivity of the method with regard to detection of attenuation changes and improved spatial resolution with regard to the horizontal cross-sections of the coal seam in front of a longwall up to the elementary cells of 5 m 5 m. There was also a need to select optimally the parameters indispensable for correct solution of the opposite issue of determination of attenuation factors in ‘‘pixels’’ into which the areas of a seam and a roof under control have been divided. During validation tests of the software designed for calculation of attenuation factors and plotting the maps of attenuation isolines, experiments were made on a regularization factor as well as on selection of dimensions of elementary areas—pixels (for which average attenuation factors were calculated). The regularization factor may be identified with a certain kind of averaging or attenuation of oscillations of the results of calculations. Research has shown that the algorithm of solution of the opposite problem in the case of a limited network of sensors up to
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Fig. 4. Map representing the relative factors of attenuation of vibration energy in the seam on 18 January 2005 as the result of cutting of wall no. 306 with a cutter–loader within the period 12:11 pm to 12:54 pm, set against the track record of the cutter–loader operating path. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
6 pcs in a seam and up to 6 pcs in a roof resulting in a limited number of seismic rays ‘‘covering’’ the elementary areas—i.e., the pixels—mostly gives results of calculations for an elementary
dimension of the pixel of 5 m 5 m. Only in rare cases was there a need to make a bigger dimension of the elementary area of the pixel of up to 8 8 m. In order to select a regularization factor of
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Fig. 5. Map representing the relative factors of attenuation of vibration energy in the roof on 18 January 2005 as the result of cutting of wall no. 306 with a cutter–loader within the period 12:11 pm to 12:54 pm, set against the track record of the cutter–loader operating path. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
the opposite issue, maps of attenuation were determined for the values of the factors 0.05, 0.1, and 0.5. Next, they were compared with a density of covering of the elementary areas (pixels) with the rays.
It was ascertained that too many amplifications (negative attenuations) occurred for the lowest value of the regularization factor 0.05, and this is physically impossible (this was the result of oscillations of the measuring results). On the basis of many
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different tests it was decided that the value of the regularization factor should be 0.1 for such an experiment. Indeed, for this value of the factor the lowest number of amplifications was observed (negative factors of attenuation). The calculated values of elements of matrix mest of the model before visualization need to be standardized to the values of relative factors of attenuation, whereas the factors should be contained in the range of 0–1. Most of the elementary areas of pixels were well covered with the seismic rays (some of them were covered more than 700 times). This means that results of the inversion have been reliable. However, the results in a triangular area in the center of the longwall faraway from its front (a zone without seismic rays) were absolutely unreliable. The final form of the analyzed map of isolines of relative changes in attenuation of energy of oscillations in a seam, including the history of the traveling shearer, is shown in Fig. 2. The areas with low attenuation, the areas in bad repair, and the stressed areas are seen in a light red color. The zone containing the unreliable results is shown in white. In order to evaluate the reliability and repeatability of the results gained by geotomography, maps of relative factors of attenuation of the energy of oscillations, which were processed in short intervals up to a few dozen hours, were analyzed. The analysis of the next maps of the relative changes of attenuation showed good repeatability of results. The slow processes of creation of a bar of stresses in front of the face were apparent. Such a bar was created, for example, in the center of the longwall in the period 19–20 December 2002. Analyzing Figs. 2 and 3 (the map of 19.12.2002), a clear bar of stresses in the roof at a distance of about 5 m from the front of the face from the sixtieth meter to the ninetieth meter of the longwall can be seen, including an especially dangerous area of stresses in the seam and in the roof at the hundredth meter of the longwall. The analysis of the travel path of the shearer during that time confirmed the problems that occurred at the hundredth meter of the longwall. At this point a roof fall occurred, the cutting head locked, the motor was overloaded, and the shearer was shut down. A consequence of this event was a standstill of the shearer of about 2 h. Relative changes of the attenuation factors of the oscillation energy registered in front of the face by means of fourteen sensors at a depth of about 140 m, taking into account a dead zone in the center of the longwall at a depth of about 70 m are shown in Figs. 4 and 5. 5. Summary Analysis of the results obtained revealed a notable correlation of zones where the effects of stress changes (rock falls, outbursts) were manifested with the zones identified in the course of operation of the system monitoring the attenuation changes (approximately inversely proportional to the relative changes in stress). Such a coincidence is not accidental and positively verifies the operating system with regard to its accuracy in determining tensed or tightened zones (marked with various shades of red color) as well as de-stressed and yield zones (marked with various shades of blue color). Taking into consideration the simplified character of imaging with the GEOTOMO/E system, regarding the energy consumed by a cutter–loader in the working process, the instant values of energy registered in 2-m intervals along the cutter–loader path,
are qualitative in nature. Complete, comprehensive testing requires analysis of the complete recordings of power metered at the time of cutting by the cutter–loader. Initial analysis of the results obtained leads to the following conclusions. The power input of a cutter–loader increases in zones of greater attenuation yield areas, decreases in zones of lower attenuation and tensed or tightened areas, and increases rapidly at the moments of overloading of a getting element. By an appropriate control of hydraulic support resistance it is possible to lower the consumption of energy per coal output unit, with preservation of exploitation safety. Verification tests for the performance correctness of the system for monitoring relative changes of stress in a coal seam and roof in front of a longwall, carried out in operating conditions, have proved the system’s efficient performance and have been considered most promising. The results obtained are stable and indicate a trend of occurring changes. The system may be used for safety. Additionally, it has been proved that the formation of dangerous stress waves in front of a longwall causes rock falls and side outbursts of coal. Diversification of stress is greater in the roof than in the coal seam, although the stress distributions are of similar character. The power input of a cutter–loader depends generally on the compactness of unmined coal and the stress occurring therein. The stress distribution in a coal roof depends on the effectiveness of the hydraulic support. The tests have proved that nonuniform support causes dangerous concentrations of stress in the coal roof and seam. A complete analysis of these relationships will be possible following further research on the basis of more advanced methodology. References [1] Hounsfield GN. Computerized transverse axial scanning (tomography). 1. Description of system. Br J Radiol 1973;46:1016–22. [2] Cormack AM. Reconstruction of densities from their projections, with applications in radiological physics. Phys Med Biol 1973;18:195–207. [3] Dines KA, Lytle JR. Computerised geophysical tomography. Proc IEEE 1979; 67:1065–73. [4] Buchanan DJ, Davis R, Jackson PI, Taylor PM. Fault location by channel wave seismology in United Kingdom coal seams. Geophysics 1981;46:994–1002. [5] Mason IM. Algebraic reconstruction of a two-dimensional velocity inhomogeneity in the High Hazles seam of Thoresby colliery. Geophysics 1981;46: 298–308. [6] Kormendi A, Bodowy T, Hermann L, Dianiska L, Kalman T. Seismic measurements for safety in mines. Geophys Prospect 1986;34:1022–37. [7] Dubin´ski J, Dworak J. Recognition of the zones of seismic hazard in Polish coal mines by using a seismic method. Pure Appl Geophys 1989;129:609–17. [8] Young RP, Maxwell SC. Seismic characterization of highly stressed rock mass using tomographic imaging and induced seismicity. J Geophys Res 1992; 97B9:12,361–73. [9] Westman EC. Use of tomography for inference of stress redistribution in rock. IEEE Trans Ind Appl 2004;40:1413–7. [10] Westman EC, Haramy KY, Rock AD. Seismic tomography for longwall stress analysis. In: Aubertin, Zassani, Mitri, editors. Rock mechanics. Rotterdam: Balkema; 1996. p. 397–403. [11] Menke W. Geophysical data analysis: discrete inverse theory. London: Academic Press; 1984. [12] Peterson JE, Paulsson BNP, McEvilly TV. Applications of algebraic reconstruction techniques to crosshole seismic data. Geophysics 1985;50:1566–80. [13] Golub GH, Reinsch C. Singular value decomposition and the least squares solutions. Numer Math 1970;14:403–20. [14] Rector JW, Marion BP. The use of drill-bit energy as a downhole seismic source. Geophysics 1991;56:628–34. [15] Isakow Z. Initial experience on operation of a system for the continuous monitoring of stress changes in front of a longwall. Mech Autom Mining Ind 2003;1/385:32–53.
Contents lists available at ScienceDirect
International Journal of Rock Mechanics & Mining Sciences journal homepage: www.elsevier.com/locate/ijrmms
Technical Note
Geotomography with the help of a cutter–loader working organ as a source of imaging waves Zbigniew Isakow Department of Geophysical Systems, Research and Development Centre for Electrical Engineering and Automation in Mining—EMAG, 40-189 Katowice, Poland
a r t i c l e in fo Article history: Received 6 March 2007 Received in revised form 26 May 2009 Accepted 1 June 2009 Available online 26 June 2009
1. Introduction The abilities of a continuous monitoring of distribution of relative-stress changes in long-face mining, as well as a detection of discontinuous and density faults in front of mine workings, are important issues from the point of view of work performance and safety in hard-coal mines. The continuous monitoring of strata under conditions of coal getting is a fundamental problem for a mining service. An effective solution for this problem should provide low-cost measurements, a high operational reliability, and stability of a measuring system under conditions of intensive mining operations in order to achieve a high resolution and a clear method for interpreting the results. The new Polish intrinsically safe system GEOTOMO/E, developed at the EMAG under direction of the author in Katowice, has been designed for monitoring relative-stress changes that occur in the coal roof and seam in front of a longwall. Rock-mass imaging is achieved by seismic waves generated by the getting element of a cutter–loader. This enables the detection of zones where stress is concentrated, identification of its occurrences, and the hazards they may induce. A seismic signal generated by the getting element of a cutter–loader, the position of which is monitored in the course of penetrating the imaged area, is recorded by a properly configured network of sensors mounted in advanced galleries to provide optimal conditions for signal identification. The process of tomography has been applied for more than 35 years. At first it was used by Hounsfield [1] and Cormack [2] in medicine, in the early 1970s. Then it was used by Dines and Lytle [3] in geology, in 1979. Seismic tomography has been used in the mining industry since 1981 [4,5]. It has been used for representing
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the structure of strata and changes in properties of strata, including research into stress changes by the propagation velocity of seismic waves [6–8]. Westman [9] described laboratory tests that applied velocity tomography to represent changes in stress of rock samples that were being loaded. Westman et al. [10] conducted research similar to the present study. They used attenuation tomography and the Rock Vision system, including analogue transmission, to represent stress concentration in front of a long face. They used a longwall shearer as the source of seismic waves. The frequencies were measured in the range of 80–200 Hz. An assumed tomogram grid was 10 m 15 m, the dimensions of a ‘‘pixel’’ for which the relative attenuation changes were determined. Westman [9] used attenuation tomography for determining the varying stresses of rocks of differing lithologies in an underground coal mine. Active seismic methods used for indirect analysis of relativestress changes are based on a seismic-velocity mining tomography in which the generated signal is a pulse by a hammer or blast. Frequent measuring in terms of advancing a longwall, and in the presence of a gas-explosion hazard, is very difficult and practically impossible. To allow continuous measurement of the relative-stress changes, a measuring system is designed wherein the working organ of a cutter–loader may be regarded as a seismic-noise source and a continuous ground-motion generator. Generated ground motions, after penetrating the tested area of a seam or roof, are registered by seismic sensors and are available for interpretation. Thus, one can achieve a considerable reduction of expenditure for the work that is necessary for imaging, because the measurement cycle is carried out entirely automatically. Control of the entire process is carried out from the surface (e.g., from a geophysical station). One cannot underestimate the fact that another advantage of the fully automated measurement system assures safety to those who do the metering.
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2. Description of the method An elastic wave that propagates in a rock mass is subject to a complex process of amplitude attenuation related to the increasing distance to the wave source and the propagation time. This process relates to factors independent of the mechanical properties of the rock mass, such as increasing wave-front field in time or factors governed by the rock-mass structure. Among these factors are processes that lead to mechanical scattering of elastic energy resulting from inhomogeneity, energy conversion into thermal or electric energy, and many others. As the seismic wavelength ranges from a dozen or so meters to several dozens of meters, whereas the seam thickness is usually less than 3 m, and horizontal dimensions of mine workings are some dozens of meters, a three-dimensional model would be useless. We might assume that the seam has rectangular dimensions of N M meters. Let an attenuation coefficient value be given for every point of this rectangular area of c(x, y)40. Let the signal energy in the source be IT, and the energy of the recorded signal be IR. As attenuation on the ds path is proportional to the length of this path and to the initial signal energy as well, we can write [11,12] dI ¼ Icðx; yÞ ds.
(1)
The solution for the boundary condition I(0) ¼ IT is RT cðx;yÞ ds I ¼ IT e R .
(2)
Taking a receiving point as I(R) ¼ IR, we have RT cðx;yÞ ds IR ¼ IT e R .
(3)
Integration is carried out along the seismic ray propagating from the source to the receiver. It is often assumed that the seismic ray is a straight line. This assumption leads in some cases to errors, which can be avoided by the procedure of tracing the seismic ray to find the real propagation path of the seismic wave. In our case we decided to assume linearity for the sake of a simple calculation. Measurements were made at a small area in front of a long face, taking particularly into consideration the relative changes of energy attenuation at the area around the face in order to detect the trends of these changes in time and space and to draw conclusions on this basis regarding the change of stress. In our case the signal is continuous, in contrast with typical seismic measurements having a pulse signal with a well-defined excitation time. Continuous signal recording can be done in a well-defined short time window. In a given time window, different types of seismic waves can be recorded—direct waves (excitation latest), reflected and refracted waves (excitation earlier), and scattered waves (excitation earliest). Obviously, their propagation rays are different as well as their propagation velocities. The assumption of a rectilinear propagation of a signal energy and simultaneous multiple measurements at the same pixels lead in a sense to averaging of the problem, even though it is approximate and contains errors. Regarding the use of the system for assessment of the rock burst hazard and effectiveness of prevention, the most important is a nearly continuous (after each cutting) observation of the concentration of relative changes in stress in time and in space in front of the face. The basic equation of seismic attenuation tomography is Eq. (3). It can be resolved to linear form by transforming Eq. (3) as follows: Z T IR ¼ cðx; yÞ ds. (4) ln IT R
It follows from Eq. (4) that logarithms of measured attenuation values of energy are linear functions of c(x, y) attenuation coefficients. Formula (4) must be replaced by a discrete equivalent suitable for numerical calculations. Denoting the logarithm of registered signal energy to induced signal energy ratio (i.e., ln(IR/IT)) for a given ith seismic ray as DIi, we can write
DIi ¼
M X
Dsij cj ;
i ¼ 1; . . . ; N,
(5)
j¼1
where Dsij is the ith ray path in the jth cell, and cj is an attenuation coefficient in the jth cell. In every opened short period of time (5 s) and every 2 m of a path traveled by a shearer, the energy induced in the source reaches all sensors; therefore, one may assume that the value of that induction is constant. It may change insignificantly from one measurement to the next. However, this is of no importance because within every measurement cycle new equations are created, which are, after every cutting, the basis for calculating average values of attenuation factors in elementary pixels, and next the standardized relative attenuation factors. The procedure for creating measuring data vector d (see below) allows for calculation of the average energy of induction in the case of multiple passings by the shearer of the same measuring point during cutting. Let d be the vector with components comprising, in particular, DIi the vector of measured data, and m the vector comprising cj attenuation coefficients (the vector of estimated model parameters). The set of Eq. (5) can be written in matrix form as d ¼ Gm.
(6)
The G matrix of Eq. (6) defines the measurement model, and for this case it is in the form 3 2 Ds11 Ds12 Ds13 : : Ds1M 6 Ds : 7 7 6 21 Ds22 Ds23 : : 7 6 7 6 Ds31 Ds32 Ds33 : : : 7 6 6 : : : : : 7 (7) G¼6 : 7. 7 6 7 6 : : : : : : 7 6 6 : : : : : : 7 5 4 DsN1 : : : : DsNM Particular elements of the G matrix are calculated with seismic ray tracing procedures. They allow determination of the path of the seismic wave in each of the particular cells with an assumption of linear or nonlinear propagation. As the induction of a seismic signal is continuous, the sensors record waves of different types within the time window. Different waves propagate along different ray paths (although for some waves encountered in mining conditions the ray theory cannot be applied). Furthermore, each type of wave undergoes different attenuation on its propagation path. Taking into account all these essential differences, along with the unknown character of the seismic wave source, would make an industrial application impossible. In such a case, rectilinear propagation would be the best solution. Furthermore, such an assumption will speed up and simplify significantly the calculations for relatively small dimensions of the area being under control in front of a face and for short ways of the rays. The calculations are made according to the following procedure. The imaged field is divided into cells (rectangular, as a rule) in which attenuation coefficient values are to be determined. Also determined is the path of each ray in each cell for a source from a given excitation point (position of a cutter–loader at a particular longwall point); those paths are the elements of a G matrix given
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SURFACE PART OF THE SYSTEM IBM PC SERVER FOR MONITORING CUTTER-LOADER PARAMETERS
SUPERIOR SERVER
MODEM
RECEIVING PART OF DIGITAL TRANSMISSION
UNDERGROUND PART OF THE SYSTEM
8 1
2 3
4
5
6
7
GEOPHONES
X
9 10 11 12 13 14 15 16
TRANSMITTERS FOR DIGITAL TRANSMISSION
Y
COMPACT STATION
IBM PC SERVER FOR IDENTIFICATION OF STRESS CHANGES
X
CUTTER-LOADER Fig. 1. Structure of the interconnected systems for monitoring relative changes in stress and the coal getting process. (This figure is an example of sensors in the array scheme for coal-seam geotomography; a scheme for coal-roof geotomography is not shown.)
by Eq. (7). The data vector is obtained after determining the mean energy value of signals recorded by particular sensors for each fixed excitation point. On such a basis the solution of an inverse problem parameter vector (i.e., attenuation values for particular cells) is obtained. Then an up-to-the moment distribution map of the elastic-wave attenuation of a single cutter–loader slice is obtained (from the roof or seam). There are many ways in which the solution of Eq. (6) describes the relation between the distribution of an attenuation coefficient of a rock mass and the energy values of the measured signal. From a formal point of view, those problems can be brought to bear toward finding the so-called inverse of a G matrix—a Gg matrix—which results in the relation mest ¼ Gg d,
(8) est
in which the m symbol denotes a vector of calculated model parameters. The Gg matrix may be treated (in a way) as an inverse of a G matrix. A rough analysis of Fig. 1 and matrix shape given by Eq. (7) brings to light the main problems of determining the Gg matrix by classical methods. The G matrix is a rectangular matrix, which means that, as a rule, there are fewer equations than estimated parameters; in a classical way, then, there is no inverse of the G matrix. Furthermore, G is a sparse matrix—i.e., most of its elements are equal to zero; thus, most mathematical operations may lead to singular problems in this case. The problem defined by Eq. (6) may lead (and often leads) to unstable solutions (i.e., small changes of data vector lead to large changes in estimated parameters). The G matrix has, as a rule, very large dimensions; in many cases it involves limits on available algorithms. It is typical of problems in attenuation seismic tomography that some model parameters (in this case, attenuation values for particular cells) cannot be determined, because some cells are crossed by insufficient seismic rays to determine reliable damping values. On the other hand, some other parameters can be parameterized as a mean value of many values that correspond to cells crossed by many rays. An efficient way for solving the inverse problem should allow for division of all parameters into
two groups: the first, with parameters insufficiently determined, and the second, with element values with an excess of parameterization. To solve the inverse G matrix problem for the case of attenuation in seismic tomography applied to long longwall fronts the matrix decomposition method (singular value decomposition—SVD) [11,13] and the pseudo-inverse rectangular matrix method are used, with the numerical algorithm allowing for effective and numerically stable calculations. Signals detected by sensors installed in the coal roof and seam, after A/D conversion, are transmitted to the GEOTOMO/E seismic device, constructed specially for this purpose, which interfaces with the system that monitors the coal getting process (a system that provides information on the cutter–loader position; Fig. 1). The digital transmission of data ensures a high-quality recording and enables a reduction of both the device-specific noise and noise generated by the telecommunication network. The interpretation of the recorded signal is based on algorithms verified in the analysis of continuous seismic monitoring results in the course of geological drilling [14]. These algorithms are based principally on examination of the energy of the registered signals. The method presented here enables description of the distribution of attenuation factors for elastic waves in rock on the basis of registered decreases in average amplitudes of energy of vibrations generated by the getting element of the operating longwall cutter–loader. For the purpose of determining the energy attenuation coefficients in the elementary cells, into which the monitored regions of the coal bed and roof in front of the longwall have been divided, the inversion algorithm [13,15] was applied, based on matrix decomposition together with the method of solution regularization in cases of high-level random noises. The information obtained, presented in the form of distribution of attenuation of signal energy (being approximately inversely proportional to stress changes) in front of the getting cutter–loader, enables optimization of the performance of powered supports as well as selection of the most appropriate parameters of their operation (supportiveness). Such information also improves work safety in mine workings. The metering results
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0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0
Bed 19 -12-2002 18:09 , 19-12-2002 20:38
Position Y [m]
1
6
50 40
3 30
5
20 4
2 10
0 120
100
80 60 Position X [m]
40
20
0
Day,Time [h]
Track record of a cutter-loader path in wall
Position X [m] Fig. 2. Map representing the relative factors of attenuation of vibration energy in the seam for 19 December 2002 as the result of cutting of wall no. 306 with a cutter–loader within the period 6:09 pm to 8:38 pm. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
can be compared with other data, such as the value of active power consumption of a longwall cutter–loader during cutting. Thus, data can be obtained for calculating the relationships between control of sufficient support, relative-stress distribution within the longwall during cutting, and the energy expenditure necessary for completion of such an operation.
3. Description of the GEOTOMO/E system The GEOTOMO/E system, developed for the purpose of monitoring of relative stress, was designed for automatic assessment of energy attenuation of elastic waves induced by the getting element of the operating cutter–loader, which is approximately inversely proportional to the stress in front of an imaged longwall. The GEOTOMO/E system consists of both underground and surface components. The standard GEOTOMO/E system for monitoring relative changes in stress consists of the following: GVu (geophone made by GeoSpace of type LS11D 4.5 Hz Vertical), geophones of type GHa (made by GeoSpace LS11D 14 Hz Horizontal), NSGA underground transmitters, SP/DTSS surface station with digital OCGA receivers and ST transmission control module, recording server, separating network connector with the Media Converter, and the GEOTOMO/E system’s processing computer.
The feeding of the system’s underground component is realized centrally from the surface with an appropriate, intrinsically safe voltage. Such feeding ensures proper operation of the geophones and transmitters, unaffected by incidental breakdowns in local feeding on the longwall or in close-to-longwall roads. The intrinsically safe underground part of the system consists of seismic geophone GHa sensors installed horizontally in the seam on anchors adapted specifically for that purpose, and seismic geophones of the GVu type installed vertically on anchors in the roof. Sensors are compatible with seismic NSGA transmitters. Each of the sixteen seismic transmitters is compatible with one GHa sensor and one GVu sensor. Sets of GHa/GVu sensors, together with an NSGA transmitter, are installed in both of the advanced galleries, symmetrically against the longwall front in 20-m intervals. Measurement points are established in 20-m intervals, which, on the one hand are appropriate for coverage of the measured area, and on the other hand are sufficient when taking into account the limit of propagation of the seismic signal generated by the working element of a cutter–loader. Signals from thirty-two measurement sensors, after A/D conversion, are transmitted via NSGA transmitters and sixteen teletransmission lines to the SP/DTSS surface transmission station, and then, via the ST control module, are transmitted to the recording server, where they are buffered and stored by a software
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0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0
Roof 19-12-2002 18:09 , 19-12-2002 20:38 9
14
50
Position Y [m]
40 11
13
30 20
10
12
10 0
120
100
60 80 Position X [m]
40
20
0
Day,Time [h]
Track record of a cutter-loader path in wall
Position X [m] Fig. 3. Map representing the relative factors of attenuation of vibration energy in the roof for 19 December 2002 as the result of the cutting of wall no. 306 with a cutter–loader within the period 6:09 pm to 8:38 pm. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
of the DTSS/G Server. This server cooperates with the processing computer via a light pipe connector and the Media Converter. NSGA seismic transmitters serve as programmable ‘‘intelligent’’ underground-measurement concentrators that facilitate control of amplification and filtration of signals, switching of amplification between measurement channels in accord with the commands given from the surface, A/D conversion with dynamics not less than 100 dB, and digital transmission of data to the surface. The joint analysis of measurement data, obtained from the system of monitoring a cutter–loader’s operation parameters (in particular, its position) and from the GEOTOMO/E system for identifying relative-stress changes, enables the assessment of attenuation of the recorded elastic wave in terms of variable positions of a vibration source (i.e., the working element of a cutter–loader) and of nonhomogeneous parameters of elasticwave propagation. The principal purpose of this system is producing maps of isolines proportional to the relative changes in attenuation of energy of induced waves in the coal roof and seam in front of a long face.
4. Results The GEOTOMO/E system was installed and put into operation in longwall no. 306 of coal-seam no. 507 at the Bielszowice Coal
Mine. Because of limitations in the number of telecommunication lines supplied by the coal mine, the number of sensors installed in the coal roof and seam was limited to six. Along with increasing the number of required teletransmission lines supplied by the coal mine, the greater number of metering units composed of NSGA transmitters and GHa/GVu geophones were connected. This network resulted in better coverage of the controlled area with seismic rays and ensured enhanced spatial sensitivity of the method with regard to detection of attenuation changes and improved spatial resolution with regard to the horizontal cross-sections of the coal seam in front of a longwall up to the elementary cells of 5 m 5 m. There was also a need to select optimally the parameters indispensable for correct solution of the opposite issue of determination of attenuation factors in ‘‘pixels’’ into which the areas of a seam and a roof under control have been divided. During validation tests of the software designed for calculation of attenuation factors and plotting the maps of attenuation isolines, experiments were made on a regularization factor as well as on selection of dimensions of elementary areas—pixels (for which average attenuation factors were calculated). The regularization factor may be identified with a certain kind of averaging or attenuation of oscillations of the results of calculations. Research has shown that the algorithm of solution of the opposite problem in the case of a limited network of sensors up to
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Fig. 4. Map representing the relative factors of attenuation of vibration energy in the seam on 18 January 2005 as the result of cutting of wall no. 306 with a cutter–loader within the period 12:11 pm to 12:54 pm, set against the track record of the cutter–loader operating path. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
6 pcs in a seam and up to 6 pcs in a roof resulting in a limited number of seismic rays ‘‘covering’’ the elementary areas—i.e., the pixels—mostly gives results of calculations for an elementary
dimension of the pixel of 5 m 5 m. Only in rare cases was there a need to make a bigger dimension of the elementary area of the pixel of up to 8 8 m. In order to select a regularization factor of
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Fig. 5. Map representing the relative factors of attenuation of vibration energy in the roof on 18 January 2005 as the result of cutting of wall no. 306 with a cutter–loader within the period 12:11 pm to 12:54 pm, set against the track record of the cutter–loader operating path. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
the opposite issue, maps of attenuation were determined for the values of the factors 0.05, 0.1, and 0.5. Next, they were compared with a density of covering of the elementary areas (pixels) with the rays.
It was ascertained that too many amplifications (negative attenuations) occurred for the lowest value of the regularization factor 0.05, and this is physically impossible (this was the result of oscillations of the measuring results). On the basis of many
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different tests it was decided that the value of the regularization factor should be 0.1 for such an experiment. Indeed, for this value of the factor the lowest number of amplifications was observed (negative factors of attenuation). The calculated values of elements of matrix mest of the model before visualization need to be standardized to the values of relative factors of attenuation, whereas the factors should be contained in the range of 0–1. Most of the elementary areas of pixels were well covered with the seismic rays (some of them were covered more than 700 times). This means that results of the inversion have been reliable. However, the results in a triangular area in the center of the longwall faraway from its front (a zone without seismic rays) were absolutely unreliable. The final form of the analyzed map of isolines of relative changes in attenuation of energy of oscillations in a seam, including the history of the traveling shearer, is shown in Fig. 2. The areas with low attenuation, the areas in bad repair, and the stressed areas are seen in a light red color. The zone containing the unreliable results is shown in white. In order to evaluate the reliability and repeatability of the results gained by geotomography, maps of relative factors of attenuation of the energy of oscillations, which were processed in short intervals up to a few dozen hours, were analyzed. The analysis of the next maps of the relative changes of attenuation showed good repeatability of results. The slow processes of creation of a bar of stresses in front of the face were apparent. Such a bar was created, for example, in the center of the longwall in the period 19–20 December 2002. Analyzing Figs. 2 and 3 (the map of 19.12.2002), a clear bar of stresses in the roof at a distance of about 5 m from the front of the face from the sixtieth meter to the ninetieth meter of the longwall can be seen, including an especially dangerous area of stresses in the seam and in the roof at the hundredth meter of the longwall. The analysis of the travel path of the shearer during that time confirmed the problems that occurred at the hundredth meter of the longwall. At this point a roof fall occurred, the cutting head locked, the motor was overloaded, and the shearer was shut down. A consequence of this event was a standstill of the shearer of about 2 h. Relative changes of the attenuation factors of the oscillation energy registered in front of the face by means of fourteen sensors at a depth of about 140 m, taking into account a dead zone in the center of the longwall at a depth of about 70 m are shown in Figs. 4 and 5. 5. Summary Analysis of the results obtained revealed a notable correlation of zones where the effects of stress changes (rock falls, outbursts) were manifested with the zones identified in the course of operation of the system monitoring the attenuation changes (approximately inversely proportional to the relative changes in stress). Such a coincidence is not accidental and positively verifies the operating system with regard to its accuracy in determining tensed or tightened zones (marked with various shades of red color) as well as de-stressed and yield zones (marked with various shades of blue color). Taking into consideration the simplified character of imaging with the GEOTOMO/E system, regarding the energy consumed by a cutter–loader in the working process, the instant values of energy registered in 2-m intervals along the cutter–loader path,
are qualitative in nature. Complete, comprehensive testing requires analysis of the complete recordings of power metered at the time of cutting by the cutter–loader. Initial analysis of the results obtained leads to the following conclusions. The power input of a cutter–loader increases in zones of greater attenuation yield areas, decreases in zones of lower attenuation and tensed or tightened areas, and increases rapidly at the moments of overloading of a getting element. By an appropriate control of hydraulic support resistance it is possible to lower the consumption of energy per coal output unit, with preservation of exploitation safety. Verification tests for the performance correctness of the system for monitoring relative changes of stress in a coal seam and roof in front of a longwall, carried out in operating conditions, have proved the system’s efficient performance and have been considered most promising. The results obtained are stable and indicate a trend of occurring changes. The system may be used for safety. Additionally, it has been proved that the formation of dangerous stress waves in front of a longwall causes rock falls and side outbursts of coal. Diversification of stress is greater in the roof than in the coal seam, although the stress distributions are of similar character. The power input of a cutter–loader depends generally on the compactness of unmined coal and the stress occurring therein. The stress distribution in a coal roof depends on the effectiveness of the hydraulic support. The tests have proved that nonuniform support causes dangerous concentrations of stress in the coal roof and seam. A complete analysis of these relationships will be possible following further research on the basis of more advanced methodology. References [1] Hounsfield GN. Computerized transverse axial scanning (tomography). 1. Description of system. Br J Radiol 1973;46:1016–22. [2] Cormack AM. Reconstruction of densities from their projections, with applications in radiological physics. Phys Med Biol 1973;18:195–207. [3] Dines KA, Lytle JR. Computerised geophysical tomography. Proc IEEE 1979; 67:1065–73. [4] Buchanan DJ, Davis R, Jackson PI, Taylor PM. Fault location by channel wave seismology in United Kingdom coal seams. Geophysics 1981;46:994–1002. [5] Mason IM. Algebraic reconstruction of a two-dimensional velocity inhomogeneity in the High Hazles seam of Thoresby colliery. Geophysics 1981;46: 298–308. [6] Kormendi A, Bodowy T, Hermann L, Dianiska L, Kalman T. Seismic measurements for safety in mines. Geophys Prospect 1986;34:1022–37. [7] Dubin´ski J, Dworak J. Recognition of the zones of seismic hazard in Polish coal mines by using a seismic method. Pure Appl Geophys 1989;129:609–17. [8] Young RP, Maxwell SC. Seismic characterization of highly stressed rock mass using tomographic imaging and induced seismicity. J Geophys Res 1992; 97B9:12,361–73. [9] Westman EC. Use of tomography for inference of stress redistribution in rock. IEEE Trans Ind Appl 2004;40:1413–7. [10] Westman EC, Haramy KY, Rock AD. Seismic tomography for longwall stress analysis. In: Aubertin, Zassani, Mitri, editors. Rock mechanics. Rotterdam: Balkema; 1996. p. 397–403. [11] Menke W. Geophysical data analysis: discrete inverse theory. London: Academic Press; 1984. [12] Peterson JE, Paulsson BNP, McEvilly TV. Applications of algebraic reconstruction techniques to crosshole seismic data. Geophysics 1985;50:1566–80. [13] Golub GH, Reinsch C. Singular value decomposition and the least squares solutions. Numer Math 1970;14:403–20. [14] Rector JW, Marion BP. The use of drill-bit energy as a downhole seismic source. Geophysics 1991;56:628–34. [15] Isakow Z. Initial experience on operation of a system for the continuous monitoring of stress changes in front of a longwall. Mech Autom Mining Ind 2003;1/385:32–53.