A parallel electric field penetration technique for identifying hazardous water sources beneath coal seam mining face floors

In this work, a highly applicable multi-channel parallel electric field penetration technique is proposed to facilitate identification of hazardous water sources beneath coal seam mining face floors. The effects of various parameters on the characteristics of the apparent resistivity curves of a spherical model were analyzed through numerical simulation. It was determined that the proposed technique was sensitive to several model parameters (resistivity, size and spatial location). In addition, physical model experiments were also performed. Resistivity was determined from a three-dimensional inversion of the measurements. The results showed that the proposed technique was highly effective in determining the electrical characteristics and spatial distribution range of the anomalous bodies in the physical model. An engineering application of the proposed technique further demonstrated its effectiveness and reliability. The proposed technique can provide a basis for formulating water disaster prevention and control measures for mining faces.


Introduction
In China, coal-mining operations currently occur in increasingly deeper coal seams where the hydrogeological mining conditions are more complex compared to shallow coal seams. These coal-mining operations are performed under water pressure and thus are significantly threatened by water hazards beneath the mining face floors (Dong 2010;Wang et al. 2012;Xu et al. 2014;Wu et al. 2015). Currently, the main techniques used in identification of water hazards beneath coal seam mining face floors include the transient electromagnetic method (TEM) (Yu et al. 2007;Zhang et al. 2011;Cheng et al. 2013;Chen et al. 2014Chen et al. , 2018Hu et al. 2014), the audio frequency electric penetration method (AFEPM) (Zeng et al. 1997;Zhang et al. 2013) and the direct current resistivity method (DCRM) (Liu et al. 2009;Wu et al. 2010;Li et al. 2015;Zhang et al. 2015;Lu 2016;Sun et al. 2018;Niu et al. 2018) for mines, etc. The TEM is efficient and sensitive to water-bearing bodies. However, the TEM, when used for in-situ detection, is vulnerable to interference from metals and has low data interpretation accuracy. The AFEPM has a high signal-to-noise ratio for field observations and can generate data with a relatively high planar resolution for water-bearing bodies beneath coal seam mining face floors. However, the AFEPM controls the detection depth by varying the frequency. Because the frequency-depth relationship still remains unclear, the AFEPM makes relatively large errors in determining the depths of water-bearing bodies. In addition, the AFEPM also has a short detection range, low efficiency and low field applicability. The theories behind the DCRM for mines are mature. In recent years, a number of observation techniques have been developed, including the double-tunnel monopole electrical penetration technique (Wu et al. 2010), the double-tunnel 3D electrical penetration technique (Zhang et al. 2015) and the multitunnel electrical penetration technique (Lu 2016). Practical applications of these three techniques demonstrate the strengths and weaknesses of each. The first technique is moderately sensitive to water-bearing bodies beneath the floors of the tunnels of double-tunnel mining faces but ineffective in detecting water-bearing bodies within mining face floors. The latter two techniques have relatively good overall detection performance but, restricted by testing equipment, are only applicable to mining faces with relatively small strike and dip lengths. They also have difficulties in collecting data, and low efficiency and applicability when used on mining faces with a large dip width and a long strike length. In view of this, we propose a highly applicable electric field penetration technique that combines the features of various techniques. We demonstrate its reliability in detecting water-bearing bodies beneath mining face floors through theoretical analysis, physical model experiments and a field application to provide a more effective detection method for water disaster prevention and control for mining faces.

Parallel electric field penetration technique
Generally speaking, the water-bearing bodies beneath coal seam floors have relatively low resistivity, whereas the rocks surrounding the coal seam floors have relatively high resistivity -i.e. there is a difference in the electrical conductivity between the water-bearing bodies and surrounding rocks. In particular, there is a significant difference in the resistivity between limestone and water-bearing bodies beneath deep coal seam floors in North China. The electric field penetration technique is based on the theory of a steady-state current field. The geophysical condition for using this technique to detect water-bearing bodies beneath a coal seam floor is the difference in the electrical conductivity that exists between the water-bearing bodies and the surrounding rocks. We and a manufacturer jointly developed an YBT32 parallel electrical penetration system with a pole-dipole survey, which was specifically designed for this technique. This system, consisting of temporally synchronous separated transmitting and receiving units, sets up a number of positive electric current sources (A) at certain intervals in the tunnel on one side of the mining face and a number of electrode assemblies (MN) in the tunnel on the other side of the mining face in the field to receive electric field data in a parallel fashion within a certain angular range. It should be noted that the negative electric current source (B) is placed at infinity invariably, and the arrangement of receiving electrodes (MN) is perpendicular to the tunnel strike (as shown in figure 1). After completing the data collection in one tunnel, the system exchanges the power supply and receiving electrodes, thereby achieving bi-directional 951 coverage and observations. In a practical application, the angular range of observation can be selected based on the width of the mining face and the tunnel conditions. Compared to previous systems, our system employs a time convention-based multi-channel parallel data acquisition method to generate highly synchronized data, which addresses the noise interference problem of data acquired at various times, significantly improves the field work efficiency and reduces the impact of measurement operations on the mining schedule.
To visually reflect the spatial distribution of the waterbearing bodies beneath the floor of a mining face, the proposed technique inverts the measured electric field data. In a steady-state point power source electric field, the potential at any point in the whole space satisfies the following equation (Sasaki 1994;Zhang et al. 1995): where is the resistivity of the medium (Ω m −1 ); U is the potential at any point in the space (V); I is the electric current source (A); is the Dirac delta function; (x, y, z) are the coordinates of the observation point and (x 0 , y 0 , z 0 ) are the space coordinates of the electric current source. The test area is meshed to obtain the resistivity from the inversion because of the non-uniform medium in an authentic exploration space. The partial differential equation (1) is converted by the finite-difference method into a matrix system and a target function of smooth model inversion S(m) is given by Constable et al. (1987) and Degroothedlin & Constable (1990).
(2) where d obs is the measured data vector; g(m) is the predicted data vector; W d is a data weighting matrix; m is the model parameter vector and is a smoothness factor and used to adjust the amount of model roughness imposed on the model in the inversion process.
When S(m) meets the given constraint condition, the inversion process is terminated and the resistivity is extracted from each model block in the finite-difference mesh. In addition, iso-resistivity imaging is performed. The resultant image is used as the detection result obtained from the electric field penetration technique. The resistivity data inversion proceeds in detail as follows.
i. A starting resistivity model is constructed based on the average apparent resistivity.
ii. A forward modeling is carried out for a predicted data set over the starting model, the initial root mean squared (RMS) error at the 0 th iteration can be calculated by the following formula at this step.
where N is the total number of measurements, d Pred is the predicted data and d Meas is the measured data.
iii. Solve the following linearized system of equations iteratively based on the current model and data misfit for a model update (Δm).
where J = g(m)∕ m is a Jacobian (sensitivity) matrix.
iv. Update the resistivity model using a formula like this: The model parameter m consists of electrical conductivity of all model blocks in the finite-difference mesh. The symbol i is the iteration number. v. Run a forward modeling based on the updated model for an updated predicted data set. vi. Calculate a new RMS error between the predicted data and the measured data. vii. If any of inversion stop criteria is satisfied, stop the inversion. Otherwise, repeat the steps (3)- (7).

Whole-space conducting sphere response equation
In figure 2, there is a sphere with a radius a and a resistivity 2 in an infinite homogenous medium with a resistivity 1 . There is also a point power source A with a current intensity I at a distance d from the center of the sphere. Thus, the potential U M and U N outside the sphere can be expressed as (Fu 1990) where P n (cos ) is a Legendre function. Therefore, based on the equation (5), the apparent resistivity of pole-dipole device can be calculated by where K AMN is the electrode geometry and ΔU MN is the potential difference between two receiving electrodes.

Analysis of the characteristics of the apparent resistivity curves
Let a plane at h = 0 with a length of 200 m and a width of 100 m be a mining face, i.e. the coordinate range is as follows: x ∈ [−100, 100] and y ∈ [−50, 50]. The coordinates of the center of the conducting sphere beneath the mining face floor are (x, y, h). Twenty-one power supply points (numbered 1-21, respectively) and 41 receiving points (numbered 1-41, respectively) are set in the two tunnels on the sides of the selected mining face at intervals of 10 and 5 m, respectively. For each power supply point, all 41 receiving points in the tunnel on the other side of the mining face receive the field intensity by a pole-dipole survey along the y-direction, as shown in figure 1. For ease of discussion, the following initial parameters are set: 1 = 100 Ω m −1 ; 2 = 1 Ω m −1 ; a = 10 m and coordinates of the center of the conducting sphere are (0, 0, 20). Thus, the potential at any point outside the sphere when there is a power supply can be calculated by transforming the coordinates using equation (6), to calculate the apparent resistivity. Figure 3 shows the apparent resistivity curves under the aforementioned given parameters (the numbers within the circles represent the power supply points). Clearly, these curves exhibit significant low-value anomalies because of the effects of the sphere. In particular, when power supply point 11 is used to supply power, the apparent resistivity at receiving point 21 is the lowest and the apparent resistivity curve exhibits the most significant anomalous characteristics. When a power supply point on either side of power supply point 11 is used to supply power, the apparent resistivity curve is inversely symmetrical. When a power 953 Figure 4. Apparent resistivity curves corresponding to a 2 of 10,000 Ω m −1 .
supply point on the left side of the sphere is used to supply power, the apparent resistivity curve is high on the left side and low on the right side; when a power supply point on the right side of the sphere is used to supply power, the apparent resistivity curve is high on the right side and low on the left side. In either case, the apparent resistivity curve exhibits a '∞'-shape. In addition, the apparent resistivity at the central intersection is lower than the background resistivity, suggesting that the sphere is a relatively low-resistivity body.

Effects of the resistivity of the model on the characteristics of the apparent resistivity curve.
For ease of discussion, the resistivity of the sphere is set to 10,000 Ω m −1 while the other parameters remain unchanged. Overall, compared to figure 3, the apparent resistivity curves in figure 4 each exhibit an upward convex trend. In addition, for all the '∞'-shaped apparent resistivity curves in figure 4, the apparent resistivity at the central intersection is higher than the background resistivity, indicating a high-resistivity anomaly. Similar to figure 3, the apparent resistivity curve obtained from power supply point 11 supplying power in figure 4 exhibits the most significant anomalous characteristics, and the apparent resistivity at receiving point 21 is the highest. Different from figure 3, in figure 4, the apparent resistivity curve is high on the right side and low on the left side when a power supply point on the left side of the sphere is used to supply power and is high on the left side and low on the right side when a power supply point on the left side of the sphere is used to supply power. Figures 3 and 4 together demonstrate that the electric field penetration technique is effective in distinguishing the electrical characteristics of rocks beneath coal seam floors.
3.2.2. Effects of the model size on the characteristics of the apparent resistivity curve. As demonstrated in figure 5, the distribution patterns of the apparent resistivity curves for various sphere sizes are similar to those in figure 3. However, there is a significant difference in the extent of low-apparent resistivity anomalies between the curves in figures 3 and 5. When a = 5 m (i.e. the volume of the sphere is reduced to 1/8 of the original volume), the extent of low-value anomalies is significantly smaller and the range of the anomalous extensions on the two sides is narrower compared to the original sphere. When a = 20 m (i.e. the volume of the sphere is increased to eight times the original volume), the extent of the low-value anomalies is significantly larger and the range of the anomalous extensions on the two sides is also wider compared to the original sphere. The aforementioned analysis shows that the electric field penetration technique is sensitive to the model size and is effective in identifying the distribution ranges of water-bearing bodies beneath coal seam floors. sphere involves three parameters, namely the distance x in the strike direction, the distance y in the dip direction and the burial depth h. These three parameters are discussed in this section.

Effects of the location
The x-coordinate of the center of the sphere shown in figure 3 varies from x = 0 m to x = 10 m and x = 20 m. Figure 6 shows the resultant apparent resistivity curves, which are similar to those in figure 3 in terms of shape. However, in figure 6a and b, the lowest apparent resistivity occurs when power in supplied using points 12 and 13, respectively, instead of the power supply point 11 in figure 3. The distances between power supply point 11 and power supply points 12 and 13 are 10 and 20 m, respectively. In addition, in figure 6a and b, receiving points 23 and 25, respectively, receive the lowest apparent resistivity instead of receiving point 21 in figure 3; i.e. the central intersection of the '∞'-shaped curve shifts along the x-direction by 10 and 20 m, respectively, in figure 6a and b compared to figure 3. This indicates that the x-coordinate of the model varies consistently with the x-coordinate of the power supply point that generates the largest anomaly in terms of magnitude. Therefore, the locations of the water-bearing bodies along the direction of the tunnels can be determined based on the x-coordinate of the power supply point corresponding to the largest anomaly.
The y-coordinate of the center of the sphere in figure 3 varies from y = 0 m to y = 10 m and y = 20 m. In addition, the tunnel along the positive y-direction is tunnel 1, and the tunnel along the negative y-direction is tunnel 2. Figure 7 shows the resultant apparent resistivity curves, which are similar to those in figure 3 in terms of overall shape. As the sphere shifts along the dip direction, the curves of the apparent resistivity measured in tunnels 1 and 2 gradually become significantly different from one another. The extent of low-apparent resistivity anomalies measured in tunnel 1 gradually increases, whereas the extent of the low-apparent resistivity anomalies measured in tunnel 2 gradually decreases. However, the variation in the range of the low-apparent resistivity anomalies along the tunnel direction is insignificant. Therefore, the distribution of the model along the dip direction of the mining face can effectively be determined based on the difference between the electric field penetration data obtained in the two tunnels.
The h-coordinate of the center of the sphere in figure 3 varies from h = 20 m to h = 10 m and h = 30 m. Figure 8 shows the resultant apparent resistivity curves. Compared to figure 3, the extent of the low-apparent resistivity anomalies is significantly larger when h = 10 m and significantly smaller when h = 30 m. In addition, the range of low-apparent resistivity anomalies decreases in the tunnel direction as h increases, indicating that electric field penetration data are sensitive to the burial depth of the model.
The analysis of the characteristics of the theoretical apparent resistivity curves of various models shows that data volumes obtained using the electric field penetration technique are sensitive to the resistivity, size and spatial location parameters of the model, which provides a good theoretical foundation for its practical application.

System setup and observation
As shown in figure 9, an experiment was conducted in a 2 m × 1.2 m × 0.8 m water tank. Prior to the experiment, a 'U'-shaped glass tunnel with a length of 1.2 m, a dip length of 0.5 m and a square cross-section with a side length of 0.08 m was placed at a distance of 0.4 m from the bottom of the water tank to simulate the tunnels on the two sides of an actual mining face. Then, the water tank was filled with water and the water level was maintained at 0.7 m to 955 Figure 7. Apparent resistivity curves corresponding to various y-coordinates. simulate the whole-space characteristics in the presence of tunnels. Pure water has a relatively high resistivity, contains a large amount of impurities and is inhomogeneous and, consequently, it would affect the simulation results. Therefore, 10 kg of salt was added to the water tank to increase the water conductivity. In addition, an iron ball with a diameter of 0.1 m and a glass cylinder with a diameter of 0.2 m at the bottom and a height of 0.3 m were used as a lowresistivity model and a high-resistivity model, respectively, to represent the hidden electrical anomaly zones beneath an 956 Figure 9. Experimental physical model platform. actual mining face floor. According to the field setup principle of the electric field penetration technique, a total of 11 power supply points and 21 receiving points were set up in the two simulated tunnels at intervals of 0.1 m and 0.05 m, respectively. Each power supply point corresponded to 12 receiving points. Observation data were measured by the poledipole survey along the x-direction. In addition, the locations of the power supply points and receiving points in the tunnels were exchanged to achieve bi-directional electric field coverage.

Experimental simulation and analysis
Based on the theoretical model analysis, two model experiments were designed.
(i) Figure 10a shows the setup for experiment 1. In this experiment, a low-resistivity iron ball and a high-resistivity glass cylinder were placed beneath the floor of two simulated tunnels to evaluate the capability of the electric field penetration technique to distinguish media with various resistivity in three dimensions. 957 Figure 11. Inverse resistivity maps obtained from experiment.
A whole-space 3D inversion was performed on the data obtained in experiment 1. Figure 11a shows the resultant resistivity beneath the floor of the two simulated tunnels. The characteristics of relatively low-resistivity and high-resistivity anomalies can be clearly seen on the resistivity sections at depths of 0.1, 0.15 and 0.2 m. These characteristics are inconspicuous in the section at a depth of 0.05 m. For the iron ball model, its resistivity was relatively low and the range of its resistivity anomalies was relatively wide. However, as shown in the resistivity section of the iron ball model at a depth of 0.15 m, its core zone was consistent with the location of the model. In comparison, the iron ball model cannot be as effectively identified based on the sections at depths of 0.2 and 0.1 m. For these two sections, the shape and core location of the low-resistivity anomaly zones gradually differed from the physical model. Different from the 958 Figure 12. Resistivity of the section at a depth of 50 m from the mining face floor obtained from inversion. iron ball model, the glass cylinder model had high resistivity and could be effectively identified in the sections at depths of 0.1, 0.15 and 0.2 m. In addition, the shape and spatial location of the high-resistivity zones were consistent with the model.
(ii) In experiment 2, two low-resistivity iron balls were placed beneath the simulated mining face floor at locations with different strikes, dips and burial depths to study the capability of the electric field penetration technique to identify the size and spatial location of the models. Figure 10b shows the model setup for experiment 2.
Obviously, two conspicuous low-resistivity zones can be found in figure 11b, which are consistent with the spatial locations of the two iron ball models. However, the specific distribution characteristics of these two models are different from those in experiment 1. In the horizontal direction, compared to experiment 1, the two iron ball models in experiment 2 were placed 0.1 and 0.05 m away in the strike and dip directions, respectively, from the corresponding model in experiment 1. Changes in the two core low-resistivity zones can also be seen on the resistivity sections at depths of 0.05, 0.1 and 0.2 m. These two zones are consistent with the planar locations of the iron ball models. In the vertical direction, because the two iron ball models used in experiment 2 were each placed 0.05 m higher than the corresponding model used in experiment 1, two low-resistivity zones already appear on the resistivity section at a depth of 0.05 m. The low-resistivity zones are the most obvious in the sections at depths of 0.1 and 0.15 m. In comparison, the lowresistivity zones in the section at a depth of 0.2 m are considerably smaller, which makes identifying the iron ball models difficult.
The results of these two experiments demonstrate that the electric field penetration technique is highly capable of identifying media with various resistivity and spatial locations. The experimental results are consistent with the theoretical analysis results. This provides a solid basis for identifying hazardous water sources beneath actual coal seam mining face floors.

Detection analysis
The floor of the No. 1021 coal seam mining face in a mine located in Anhui contains a limestone aquifer. A surface borehole analysis reveals that the stratum is 135 m thick at the thickest location. In addition, 15 layers of limestone are distributed in this stratum, of which the third and fourth layers of limestone are 11 and 11.6 m thick, respectively. These two layers contain developed and highly inhomogeneous karst fissures, and are the main aquifer-containing layers. Based on the available hydrological observation data, this aquifer has a static head of −110 m. The mining face has a minimum elevation of −393 m, a maximum water pressure of 2.83 MPa and a maximum water yield of 117 m 3 h −1 . Therefore, mining operations on this mining face are under water pressure and the aquifer is a disaster-causing water source for mining on this mining face. To ensure safe mining on this mining face, the electric field penetration technique was employed in field detection. A total of 96 and 101 receiving points at intervals of 10 m and 20 and 21 power supply points at intervals of 50 m were placed in the two tunnels on the two sides of the mining face, respectively. Each power supply point corresponded to 21 receiving points.
A 3D inversion of the measurements was performed and a water analysis was performed based on the sections along the bottom boundary depth (average 50 m) of the fourth limestone layer. Based on the mean and variance of the data, a resistivity anomaly threshold of 110 Ω m −1 was determined. Those with resistivity lower than this threshold are resistivity anomaly zones. As shown in figure 12, the low-resistivity anomaly zones are mainly located in the 0-300 m and 550-950 m sections along the strike direction of the mining face. In addition, the low-resistivity anomalies in the 550-950 m section are more significant. Because the coal seam on the mining face is stable and has simple tectonic and geological conditions based on the geological data of the nearby mined faces, it is determined that these two zones contain water and the 550-950 m section is rich in water, which should 959 Figure 13. Low-resistivity anomaly zones and water yields of the boreholes. be treated as the main water disaster prevention and control zone.

Result validation
Based on the detection results, 10 drill sites were set up in the field. A total 65 boreholes were drilled into the mining face from various directions and at various dips until they reached the bottom boundary of the fourth limestone layer. Figure 13 shows the water yields from the boreholes as well as the low-resistivity zones. A statistical analysis reveals that out of 65 boreholes, four had a water yield of 0, 10 had a water yield ranging from 0 to 5 m 3 h −1 , 10 had a water yield ranging from 5 to 10 m 3 h −1 and 41 had a water yield greater than 10 m 3 h −1 . In addition, these boreholes were distributed in a scattered fashion. This indicates that, overall, the limestone layers beneath the mining face floor contain water and are highly inhomogeneous in terms of water content. If a rock layer with a water yield above 10 m 3 h −1 is considered a water-rich layer, 34 of the 41 boreholes with a water yield above 10 m 3 h −1 were located inside or on the boundaries of the low-resistivity zones and the remaining seven were located outside the low-resistivity zones but were all close to the boundaries of the low-resistivity zones. This indicates that the detection accuracy was greater than 82.93%. Moreover, a statistical analysis of the boreholes with a water yield above 10 m 3 h −1 shows that the average water yield was 21.78 m 3 h −1 in the 0-300 m low-resistivity zone and 33.7 m 3 h −1 in the 550-950 m low-resistivity zone. This validates the detected distribution characteristics of the resistivity and further demonstrates the effectiveness and reliability of the electric field penetration technique.

Conclusions and discussion
In this work, to better facilitate detection of hidden hazardous water sources beneath coal seam mining floors, we analyze the deficiencies in the available water detection techniques and propose a highly applicable multi-channel parallel electric field penetration technique. Through a simulation analysis of a theoretical model, it is determined that apparent resistivity curves obtained using the proposed technique each exhibit a '∞'-shape. When the model resistivity is lower than the background resistivity, the apparent resistivity at the intersection of the curve is lower than the background resistivity and low-resistivity anomalies are present. When the model resistivity is higher than the background resistivity, the apparent resistivity at the intersection of the curve is higher than the background resistivity and high-resistivity anomalies are present. The extent and range of apparent resistivity anomalies vary relatively significantly with the size and spatial location of the model. Therefore, the proposed technique responds well to the conductivity, size and spatial location of the model. The results of the physical model experiments demonstrate that the proposed technique is capable of accurately determining the resistivity and spatial distribution range of the models. A field application further verifies the effectiveness and reliability of the proposed technique, which can provide a basis for formulating water disaster prevention and control measures. However, electrical prospecting is significantly affected by volume effects, and there are myriad factors that affect resistivity. Currently, interpretation is still at the qualitative or semi-quantitative level. In practical applications, electrical prospecting often produces errors to varying degrees in determining the range of water-bearing bodies and their water content. Therefore, in-depth research should be performed on water detection techniques for mining face floors (including field operating techniques and data interpretation methods) to improve detection accuracy.