The application of multi-grounded source transient electromagnetic method in the detections of coal seam goafs in Gansu Province, China

Unknown coal seam goafs will pose various safety hazards in construction and engineering designs, thus the accurate detections of coal seam goafs have become engineering problems that urgently require effective solutions. Multi-grounded source transient electromagnetic methods have the advantages of large detection depths and the easy deployment of emission sources. Therefore, they can be used for explorations in such complex areas as mountains, lakes and swamps. Previously, grounded source transient electromagnetic methods had only one emission source arranged on the surface, and were relatively rarely used in field explorations with multi-grounded sources. This study analyses the electromagnetic response differences between multi-grounded sources and a single-grounded source. The results reveal that the electromagnetic responses of multi-grounded sources were larger. Transient electromagnetic signals were be targeted using combinations of multi-grounded sources, which successfully strengthened the detection abilities. As a result, this study was able to achieve the goals of increasing the detection depths and improving the ability to distinguish geological anomalies. In addition, this research investigation referred to the theory of implicit functions and used the z components of the decay voltage to calculate the apparent resistivity. Finally, the results of the field data of a coal goaf located in Gansu Province, China, showed that the applied multi-grounded sources transient electromagnetic method could obtain higher resolution in coal seam goaf resistivity distribution information.


Introduction
At present, as coal resources are exploited on a large scale, particularly by many private small coal kilns, many goafs have been formed underground. These unknown goafs will pose various hazards to the construction of buildings and engineering facilities in the area (Wu et al. 2018;Li et al. 2019;Wen et al. 2019). Therefore, to avoid hazards, the accurate detections of hidden goafs in underground coal seams are of very important practical and economic significance. The traditional transient electromagnetic methods mainly use ground loop source devices to detect coal seam goafs. However, it has been found that in areas with complex topography, such devices are difficult to operate due to low efficiency and high costs Ma et al. 2019). However, when compared with the traditional transient electromagnetic methods, grounded source transient electromagnetic methods have the advantages of high efficiency and large exploration areas, and are known to have incomparable advantages in detection processes conducted in complex areas (Yan et al. 2016;Xue et al. 2018;Li et al. 2021;Ma et al. 2021). Nabighian (1988) proposed a semi-airborne transient electromagnetic method that was based on the device of a horizontal electric dipole. In another related study, Elliott (1996) used the FLAIRTEM system with a large loop as the source and an aircraft to obtain signals. The results of the aforementioned experiment revealed that the electromagnetic field of a large transmitting loop could travel relatively far. However, in areas with severe surface undulations, the processes of laying large loop sources may be difficult. Mogi et al. (1998) developed the GREATEM system, which used a grounded source as the emission source and a helicopter to carry a magnetometer for the purpose of obtaining magnetic field signals. Mogi et al. (2009) and Verma et al. (2010) conducted various experiments using the aforementioned system for the first time in geothermal field surveys in southwestern Japan. The results showed that the topographical undulations had relatively little influencing effects on the magnetic field signals of the device. Allah et al. (2014), along with Allah & Mogi (2016), used the GREATEM system to simulate the three-dimensional resistivity on the Nojima Fault in southeastern Japan, along with volcanoes in northwestern Japan, with satisfactory results obtained. Wang et al. (2013) adopted the SYM8 wavelet method to suppress noise and effectively improve the imaging quality of apparent resistivity for time-domain semi-airborne electromagnetic exploration systems of unmanned airships using long wire sources developed by Jilin University. In addition, Ji et al. (2013) used the system to investigate the impacts of saltwater intrusions in Jiangsu Province. The obtained results were found to be consistent with the local geological and hydrological data, which confirmed the effectiveness of the system.
The emission sources of grounded source transient electromagnetic methods can be single or multiple sources. The use of multiple radiation sources can effectively weaken the influencing effects of random noise. In accordance with the actual situations when working in the field, the signal strength of certain components can be strengthened by adjusting the positions of the emission sources and the directions of the current. In that way, the detection depths and resolution of grounded source transient electromagnetic methods can be improved . Smith et al. (2001) conducted experimental tests in a sulfide mining area in Ontario, Canada, and then compared the signals collected by airborne, semi-airborne and grounded source electromagnetic systems. The results showed that the signal-to-noise ratios of the ground electromagnetic system data were the highest. Therefore, based on those findings, this study focused on application of the multi-grounded source transient electromagnetic method.
At present, the apparent resistivity parameter is still an important parameter known to reflect underground electrical information. Zhang et al. (2015) established a multi-component full-field apparent resistivity interpretation method based on the theory of multi-source transient electromagnetics, and successfully realised definitions for multi-component, full-time and full-space apparent resistivity. In the aforementioned study, the influencing effects of offsets on full-field apparent resistivity were analysed. The resistivity distribution characteristics that were consistent with the design model were obtained by calculating a theoretical model. The results confirmed the effectiveness of the multicomponent full-field apparent resistivity algorithm for multisource transient electromagnetic systems. Ma et al. (2021), proposed the apparent resistivity method based on the imaging technology of grounded source transient electromagnetics, as well as the characteristics of the induced current distributions of the grounded sources. The differences between the horizontal and vertical induced currents, as well as the influencing effects of flight heights on apparent resistivity, were also taken into consideration. Subsequently, based on the distributions and diffusion characteristics of the induced currents, the analytical solutions of uniform half-space magnetic fields and decay voltage were derived. Then, the early, late and full-time apparent resistivity was defined. Finally, the imaging depths of the transverse and longitudinal components were defined based on the analyses of the induced current distributions. The results of the actual measurements in this study's examined coal mining area showed that the target positions had been more precisely located.
In recent years, the application potential of grounded source TEM has attracted increasing attention in the fields of mineral resource exploration, underground cavity detections and coal seam goaf detections (Chen et al. 2017;Xue et al. 2018;Fan et al. 2019). However, the application of multi-grounded source transient electromagnetic methods in engineering detection processes have remained relatively unexplored. In this study, multi-grounded source detection tests were carried out in a coal seam goaf in Gansu Province, China. This study used the excitation of multi-grounded sources and random noise could be weakened. At the same time, the signal strengths were enhanced, deeper electromagnetic signals were obtained and detection depths were improved. Furthermore, the resolution quality of deep abnormal body detection processes was improved ). In the current study, the z component signal-to-noise ratio of the decay voltage is increased and the data quality is improved through the  combination of two emission sources. The test results showed that the multi-grounded source transient electromagnetic method had achieved better detection effects for the examined coal seam goaf.

Theory of multi-grounded source transient electromagnetic methods
Grounded source transient electromagnetic systems generally use one or more grounded sources to emit electromagnetic field signals underground. The data are processed and interpreted according to the theory of transient electromagnetic methods. A schematic diagram of the grounded source transient electromagnetic method device is presented in figure 1.

Response analysis of multi-grounded source transient electromagnetic method
The current study briefly analysed the three-component characteristics of the decay voltage of a single-grounded source and two grounded wire sources. It was assumed that the resistivity of the uniform half-space was 100 Ω ⋅ m −1 ; the resistivity of air was 10 -7 Ω ⋅ m −1 ; the minimum grid length was 10 m; grid expansion factor was 1.4 and the number of grids in three directions was 69 × 56 × 54. The calculated area was 20 × 20 × 20 km. In addition, a single-grounded source, along with two parallel grounded sources with opposite current directions, were set up for the purpose of calculating the three components of the decay voltage. The endpoint coordinates of the single-grounded source were (−500, 50, 0 m) and (500, 50, 0 m). The endpoint coordinates of the two ground wire sources were (−500, 50, 0 m), (500, 50, 0 m) and (500, −50, 0 m), (−500, −50, 0 m), respectively. The receiving point was located on the x axis, and the receiving range was [−200, 200 m]. The point distance was set as 10 m; emission current was 1 A and the time range was [10 -5 , 10 -2 s]. Figure 2 provides a schematic diagram of the emission source on the xoy plane and a model schematic diagram. It can be seen in figure 2 that the anomalous body was a horizontally placed plate-shaped body with a geometric size of 100 × 100 × 20 m, with a resistivity of 1 Ω ⋅ m −1 . The upper interface was located 90 m from the ground surface. Figure 3 shows the three components of the decay voltage of a single-grounded source. Figure 3a details the decay voltage x component, with a positive and negative peak. Figure 3b is the decay voltage y component, with a peak at the center. Figure 3c is the z component of the decay voltage. There was also a positive peak observed at the center position. Figure 4 shows the three components of the decay voltage of two grounded sources with opposite current directions.   Through these analysis results, it was found that if multiple grounded sources were used, the underground anomalous bodies could be explored and analysed from different perspectives, which helped to better identify the targets and understand the characteristics of the underground geological structures. In addition, due to the influencing effects of the current directions on the electromagnetic fields, the grounded sources were reasonably arranged to strengthen the required electromagnetic signals, thereby achieving the purpose of increasing the depths of the explorations and improving the resolution results. The field tests conducted in this study measured the z components of the decay voltage. Then, a principle for calculating the apparent resistivity was successfully determined.

Multi-grounded source transient electromagnetic apparent resistivity principle
In this study, the z component of the decay voltage was B z ( , C, t)∕ t, where C represents the coordinate parameters of the measuring point. In order to ensure fast convergence, a median value within the resistivity range can be used as the initial iteration value according to the actual situation, and the Taylor expansion of B z ( , C, t)∕ t in the field of (0) can be carried out as follows: Then, by retaining the linear principal part of equation (1), the following was obtained: Equation (2) was then rewritten as follows:  The iterative format of equation (3) as follows: where (5) The stopping condition of equation (5) was In equation (6), indicates the error threshold for a given stopping iteration; B z ( , C, t)∕ t represents the decay voltage z component at time t under the specific device parameters; B z ( (i) , C, t)∕ t is the result of a uniform halfspace model with resistivity (i) .

Synthetic model
T reflect the advantages of the apparent resistivity of multigrounded sources, this study designed a complex model of a two-layered goaf as shown in figure 5. The detailed resistivity parameters and geological body size are detailed in Table 1. The number of grids in three directions was set as 80 × 80 × 80. The minimum grid length was 10 m, and the grid expansion factor was set as 1.36. There were two grounded sources.  (Zhou et al. 2018) was used to calculate the electromagnetic responses of the complex model. Figure 6 shows the apparent resistivity of the model with two mined-out water bodies. Figure 6a shows the apparent resistivity of source 1. It can be clearly seen in the figure 6a that there were two areas of low-resistivity anomalies, and the low-resistivity anomaly in the shallow part was weak.   Figure 6b shows the apparent resistivity of source 2. It can also be seen that there are two areas of low-resistivity anomalies, and the deeper anomaly was weak. Figure 6c details the apparent resistivity of the two sources. This study found that when compared with figure 6a and b, it was clear that the apparent resistivity of figure 6c had clearly reflected the resistivity information of both the shallow and deeper parts. 521 Figure 9. Schematic diagram of the survey line.

Case history
The electromagnetic response characteristics of a singlegrounded source and multi-grounded sources were analysed in this study and the principle of the decay voltage z component was presented to define the apparent resistivity. The next section of this study details the processing flow and the results of the field data.

Survey section
This study obtained field data of a coal mine goaf in Gansu Province, China. It was found that the majority of stra-tum in the work area was covered with Quaternary loess, which was basically hidden, and part of the bedrock was exposed. The strata were basically sedimentary rock from top to bottom with no obvious geological movement. The strata layers were mainly composed of Upper Cretaceous, Lower Cretaceous, Upper Jurassic, Middle Jurassic and Upper Triassic strata. The Middle Jurassic was the main coal-measure strata. The Upper Triassic formed the basement of the coalmeasure strata. The southern part of the mining area was characterised by hills, and some of the hilly Cretaceous rock formations were exposed. The northern part of the surface area was observed to be open and gentle, featuring farmland and low hills. There were two seasonal sand rivers in the middle and northern section of the surface area. The target strata in the mining area were coal-bearing strata, which were mainly composed of quartz sandstone, glutenite, carbonaceous mudstone and carbonaceous siltstone. The resistivity of the quartz sandstone was in the range of 83 to 455 Ω ⋅ m −1 . That of the glutenite was in the range of 102 to 486 Ω ⋅ m −1 . The resistivity of the carbonaceous mudstone ranged between 56 and 382 Ω ⋅ m −1 , and that of the carbonaceous siltstone ranged from 75 to 437 Ω ⋅ m −1 . Figure 7 details the geomorphic features of the study area.
The location of the experimental study area is shown in figure 8. The study area measured 3.69 km 2 , and the multi-grounded source transient electromagnetic method was adopted in this study. Due to the lack of instruments   and equipment with multi-grounded sources, this study used a mode of superimposing the electromagnetic responses of multiple single excitation sources. During this study's fieldwork processes, two parallel grounded sources were used, and the instrument was a V8 multi-function electrical device. The current was set at 15 A and fundamental frequency was 8.3 Hz. Then, the decay voltage z components were received.

Data processing
The acquisition data of the multi-grounded source TEM was the decay voltage of each measuring point, which had to be converted into apparent resistivity parameters for further interpretations. The main steps were as follows: (1) Filtering: due to the human electromagnetic noise in the study area, the data was required to be filtered before data processing to eliminate the noise. A slope smooth filtering method was adopted in this study, which was able to effectively suppress the random noise, better suppress the power frequency noise and improve the resolution (Xie et al. 2019).
(2) Smooth: since the data obtained in the field had a tendency to jump up and down, with even some of the data not conforming to the decay law of the electromagnetic field, it was required to undergo an appropriate smoothing process. In this study, a three-point smoothing algorithm was used to smooth the attenuating voltage. (3) Apparent resistivity imaging: according to the theory of implicit functions, an iterative method was used to calculate the apparent resistivity of the multi-grounded sources to show the electrical distribution characteristics of the underground areas. In this study's field test, the transient electromagnetic instrument was adopted to collect the z components of the decay voltage. However, to facilitate the understanding of the underground resistivity distributions, this study obtained the variations of apparent resistivity with depth according to the floating plate theory (Zhang et al. 2016). Figure 10 shows the curves before and after the smoothing of the z components of the decay voltage at the measuring points. It can be seen from figure 10a that the data of some of the time-channels did not conform to the decay characteristics of the electromagnetic fields and needed to be smoothed. In addition, it can be seen in figure 10b that the smoothed curves conformed to the decay characteristics of the electromagnetic fields. Figure 11 details a multi-channel diagram of the z components of the decay voltage of a survey line before and after it was smoothed. As can be seen from figure 11a, the electromagnetic signals featured in the later period were rather disorderly, and there were crossovers and coincidence phenomena among curves. These results were inconsistent with the propagation characteristics of the electromagnetic field. Consequently, filtering and smoothness processes were required. In this study, the field data filtering, smoothness and noise suppression processes were found to be beneficial for the subsequent apparent resistivity imaging.

Apparent resistivity
During the process of calculating the apparent resistivity, this study set the error threshold to terminate the iteration = 10 −3 , and the maximum number of iterations was 500. Then, according to the actual situations, an intermediate value within the resistivity range of the working area was used as the initial value of the iteration. Figure 12 shows a contour map of the coal seam floor of the study area, and figure 13 highlights a plan view of the apparent resistivity of the multigrounded sources. The elevation of figure 13a is 990 m, and the elevation of figure 13b is 1030 m. It can be seen from figure 12 that there were two tunnels at the positions of Line140 and Line160, and two obvious resistivity gradient bands corresponded to the positions of x = 140 and x = 160 m in figure 13. At the same time, as detailed in figure 12, there was also a tunnel at the location of Line340, which was also reflected in figure 13. The apparent resistivity was mainly affected by such factors as the stratum lithology and the water content. The light blue part in figure 13 indicates a low-resistivity zone. It was speculated that a waterfilled goaf had formed after the coal seam was mined making the stratum relatively water-rich, resulting in the low resistivity in figure 13. The lower the resistivity was, the higher the water-rich degree of the stratum would be. The red part indicates that this is a high-resistivity zone; this zone has been caused due to the fact that the goaf at that location was not filled with water or that the coal seam had not been mined out. In addition, as shown in figure 13 the southwest corner of the study area was characterised by high resistance, and the northeast corner was characterised by low resistance, which indicated that the water-bearing goaf of the study area was mainly distributed in the northeast. Then, to further examine the resistivity characteristics of the water-bearing goaf in the study area, this study calculated the apparent resistivity imaging of Line320, Line340 and Line360. involved, this paper selected Line320, Line340 and Line360 as the research objects to calculate the apparent resistivity. In figures 14-16, part (a) is the apparent resistivity of the A1B1 source; (b) shows the apparent resistivity of the A2B2 source and (c) is the apparent resistivity of the two grounded sources. It can be seen in figure 14c, figure 15c and figure 16c that low-resistivity areas existed at x = 180, x = 220, x = 300, x = 380 and x = 460 m in the horizontal direction. Therefore, it can be inferred that water-rich areas may have formed due to the development of rock fractures caused by the collapsing of the coal mined-out areas, forming low-resistivity zones. Each survey line displayed an obvious low-resistivity area between 460 and 500 m. As show in figure 12 that groundwater enrichment may have been caused by fault activities at those positions. In figures 14-16, (a) and (b) only show the 460 to 500 m low-resistivity zone in the x direction, and the reflection of the low resistance areas in the other locations were not adequately detailed. It can be seen from the apparent resistivity images in figures 14-16 that, when compared with a single-grounded source, the method of transient electromagnetic detection with multi-grounded sources had achieved better resolution effects for the low resistance areas of the water-bearing goaf.

Apparent resistivity plan.
3.3.3. 3D Apparent resistivity in the work area. A 3D apparent resistivity diagram of the work area is presented in figure 17. 526 As can be seen in the figure, there are four apparent resistivity profiles along the y axis, from which the shape and location of the anomaly can be clearly seen; along the x direction, there is one apparent resistivity profile (for the intuitiveness of the picture, only a cross-sectional view of the apparent resistivity along the x direction is shown). In figure 17, it can also be seen that there are two obvious resistivity gradient bands near x = 140 and x = 160 m. It can be observed that a low-resistivity zone is located between 460 and 500 m in the y direction. In the current study, through the 3D apparent resistivity map of the study area, the locations of the low resistance areas could be visually delineated, and a reliable goaf position was provided for the subsequent engineering projects in the region.

Conclusions
This study used the analysis results of the transient electromagnetic responses of multi-grounded sources and the processing of the field data to reach the following conclusions: (1) In this study, the numerical simulation results showed that the required electromagnetic response components could be strengthened by reasonably laying the relative positions of the grounded sources. This made use of the influencing effects of the source arrangements and the current directions on the electromagnetic fields in order to increase the exploration depths and improve the resolution ability of the geological target bodies.
(2) This study found that when compared with a singlegrounded source, the apparent resistivity imaging results of the multi-grounded sources displayed more detailed resistivity distribution information.
(3) In addition, the results of field data revealed that using multi-grounded sources transient electromagnetic method to explore and analyse the underground abnormal bodies from different perspectives was helpful for increasing the understanding of the underground electrical characteristics in the study area.