Simulation Research and Application on Response Characteristics of Detecting Water-lled Goaf by Transient Electromagnetic Method

Water inrush disasters poses a great threat to the safe exploitation of coal resources. To solve this problem, the transient electromagnetic method(TEM) was proposed to accurately detect the water accumulation in the goaf. The electromagnetic response characteristics of different water-filled goaves were studied by electromagnetic field theory, numerical simulation and field verification. Through the models of 100% water accumulation, 50% water accumulation, 0% water accumulation, 100% water accumulation with collapsed rock, 50% water accumulation with collapsed rock and 0% water accumulation with collapsed rock goaf, the characteristics of induced voltage attenuation curves were studied. Meanwhile, the relationship between the attenuation voltage value and area of the transmitting coil and the depth of the goaf were also simulated. The results illustrate that the attenuation curve of induced voltage presented a regular exponential decay form in the 0% water accumulation model but existed abnormal exaltation for voltage in water-filled model. Through the linear fitting curve, it can be seen that the abnormal intensity of the induced voltage becomes stronger as the distance between the measuring point and the center of the target decrement. Moreover, the abnormal amplitude of the induced voltage increases with the rise of the water accumulation and collapsed rock will weakly reduce the low-resistance anomalous effect on the wa-ter-accumulated goaf. In addition, the response value of the attenuation voltage increased in second-order as the area of the transmitting coil increases, but decreased in third-order as the depth of the target body increases. The field detection results of the Majiliang coal mine also confirmed the theoretical analysis and the numerical simulation. The conclusions had important guiding significance for accurate detection of coal mine goaf.


Introduction
In China, especially in Shanxi Province, the private mining of coal resources in the past few decades has resulted in a large number of goafs with unclear locations. The accumulation of water will form water-filled goaf, which may lead to serious water disasters during normal mining activities, and bringing immeasurable life safety threats and property losses to the country and people. In view of this, it is particularly critical to propose a method to accurately locate the mined-out area of coal mine water (Wang et al. 2019;Dong 2007). At present, there are many methods for detection. Among them, the transient electromagnetic method(TEM) has the advantages of low economic cost, high efficiency, strong penetrating power of high-resistance rock formations, sensitive reflection of low-resistance bodies and unaffected by terrain conditions (Shan et al. 2009;Liu et al. 2014).Therefore, it is more appropriate to use the TEM to detect the water-accumulated goaf with low resistance response. *Corresponding author: Feng Guorui E-mail: fguorui@163.com As early as the 1980s, David V. Fitterman (1991) studied the electromagnetic field forward simulation calculation problem in the field of groundwater exploration, successfully detected groundwater resources on the piedmont alluvial plain in the eastern part of the city of Alain, UAE by using the ground conductivity method and the transient electromagnetic method.Kendrick Taylor (1992) used transient electromagnetic method to study the characteristics of local groundwater system in arid alluvial environment, and the false change of color apparent resistivity with time to display apparent resistivity data was adopted to determine groundwater characteristics. It can also be used in water accumulation detection. Nek R. Garg (1999) proposed a data processing of TEM based on electromagnetic field filtering to obtain a clearer geoelectric structure to determine the location of the water-filled goaf. Finally, applied it to the field detection experiment on the river plain of Idaho Snake. Jafar Sadi (2013) combined the transient electromagnetic method and the DC resistivity sounding method to identify and mapped the spatial distribution of freshwater and saline groundwater in the shallow mined-out area in the central Azraq Basin, Jordan. Reza Malekian (2019) used the finite-difference time-domain method to calculate the three-dimensional model calculation of the coal mine water goaf. The position of the goaf was distinguished by obtaining its full-space transient electromagnetic response characteristics, and the simulation results of water richness in the goaf was detected and verified in a certain mine environment. Li Chengyou and Liu Hongfu (2007) obtained the characteristics of transient electromagnetic response by analyzing the multi-channel voltage profile of transient electromagnetic and pseudo-resistivity, thereby accurately detected the location of the multi-layer (water accumulation) mined-out area . Jiang Zhihai (2014) proposed a ground-lane transient electromagnetic method (SUTEM) for laying transmitter coils on the surface and receiving by underground tunnels. 3-D unstructured tetrahedral grid vector finite element full-field electromagnetic forward algorithm was used and numerical simulations were carried out on the response of typical 1-D and 3-D water-filled goaf models. Then field tests were carried out to verify the simulation results . Tang Zhenyu (2015) proposed a transient electromagnetic imaging technology, which delineated the abnormal area of water accumulation through the two-dimensional apparent resistivity cross-section map and the slice map. The detection example of the water-accumulated goaf in the 10 # coal seam of Shanxi showed the imaging technology can accurately locate the range and state of the abnormal area of stagnant water. Chang Jianghao (2017) established a full-space geoelectric model of the mined-out area based on the coal-measure stratigraphic data in North China and the Middle East. The convolutional perfectly matched layer (CPML) was chosen as the boundary condition and simulated the overall transient electromagnetic response of the coal mine water-bearing subsidence column at different depths of the stope floor and in front of the driving work with the finite difference time domain method. Yu Chuantao (2018) improved the traditional large fixed source loop device in the ground TEM, and applied it to the detection of the water-filled goaf of a coal mine in Shanxi. The apparent resistivity section was obtained through inversion to obtain the electromagnetic response, and the drilling verification had accurately positioned the buried depth of 300m in the mined-out area with water. Yan Guocai (2020) used electrical source short-offset transient electromagnetic method to detect deep low-resistance water accumulation areas with buried depth of more than 1000m. Response characteristics of regional apparent resistivity and the law of sounding through inversion calculation of the H-type theoretical model were obtained by an improved least square method. Moreover, this method was applied to detect the goaf of the thick conglomerate layered water in the deep part of the North China mining area.
In summary, many achievements about TEM detection of water-filled goafs has been aquired. However, there are relatively few studies on the electromagnetic response characteristics for goaf with complicated accumulated water occurrence states. In this paper, theoretical analysis and numerical simulation are used to obtain the transient electromagnetic response characteristics of the goaf under different water accumulation conditions, and field tests are performed to verify the simulation results. At the same time, the research results provide theoretical and technical support for the accurate detection of water-filled goafs and coal mine safety production.
Three matter equations as follow Where E is electric field intensity(V/m), B is the magnetic induction intensity(Wb/m 2 ), H is the magnetic field intensity (A/m), D is the electric displacement vector(C/m 2 ), j is the current density (A/m 2 ), ρ is the free charge density, σ is the electrical conductivity, μ is the magnetic permeability, ε is the dielectric constant.
Maxwell's equation characterizes the relationship between field strength vector, current density and charge density.

Calculation of transient electromagnetic field response
According to the relevant research of experts (Li 2002;Luo 2012;Bai 2003), based on the calculation theory of the electromagnetic field in the frequency domain, the Fourier inverse solution is the best calculation method, so this research also follows this. In order to simplify the calculation process, the cylindrical symmetry of the electromagnetic field is usually chosen to solve the electromagnetic parameters, and the Hertzian potential function F is also introduced as The expression of the frequency domain electromagnetic field component are follows   When the mined-out area contains water, the dielectric constant ε, magnetic permeability μ and resistivity ρ will change as follows Where a is the radius of the circular coil (if the transmitting coil is a square coil with side length L, then aL  ), u is the comprehensive parameter, 2 ua   , τ is the apparent diffusion parameter, 0 =2 2 t     , μ1 is the permeability of the mined-out layer of water, μ0 is magnetic permeability in vacuum, t is the diffusion time of the transient field, ρw is the resistivity of the groundwater goaf, Φ(u) is the probability integral.

Theoretical calculation
According to equation (10) and (11), MATLAB is used for programming (Tong 2013) to study the transient electromagnetic response characteristics of the goaf under different water accumulation conditions. The basic parameters are set that the coil radius a is 100m, the emission current is 1A, the surrounding rock resistivity of the goaf area is 500Ω·m, μ0 = 4π×10-7 H/m.
The resistance of the mined-out layer are selected as ρ1=5Ω·m(fully-water-filled),ρ2=50Ω·m(half-water-fille d), and ρ3 = 1000Ω·m (water-unfilled) respectively. t is the diffusion time, ranging from 0.1ms to 100ms.The coordinate axis is expressed in double logarithmic form, and the attenuation voltage curves under the three models are shown in Figure 1.
The attenuation trend of the three curves is similar and the attenuation voltage response value is proportional to the amount of water accumulation. It also shows that the greater the amount of water accumulation, the higher the voltage value.

Goaf model of water-filled states
Coal mine goaf is the closed or semi-enclosed space area left behind by the underground coal seam being mined. After the goaf formed, the integrity of the rock strata is destroyed, causing a large area of cracks inside the rock strata. When the goaf is filled with water, its resistivity is lower than the surrounding rock.
When the goaf does not contain water, the regional resistivity is higher than that of the surrounding rock.
Simulation research is carried out based on the physical characteristics (Han 2018, Lian 2020).
The simulation was used Maxwell software for calculation. In order to truly reflect the changes in the water environment in the mined-out area, the plate-shaped structure was selected to simulate the various underground rock layers and 6 goaf models of 100% water accumulation, 50% water accumulation, 0% water accumulation, 100% water accumulation with collapsed rock, 50% water accumulation with collapsed rock and 0% water accumulation with collapsed rock were established. Then the electromagnetic response characteristics were analyzed through the attenuation electromotive force curve and apparent resistivity cross-section obtained by forward and inversion simulation.
In this study, the water-accumulated goaf of  layer, corresponding to the resistivity of each layer is 1000Ω·m, 5Ω·m and 200Ω·m, and the thickness is 100m, 20m and 50m respectively. The rest of the space is considered as the surrounding rock, the resistivity is 500Ω·m while the thickness is infinite, and the subsequent models are also the same.      When the goaf is completely filled with water, an abnormally low-resistance enclosed area appears at the buried depth of -100m to -130m and the measuring point distance of 150m to 350m (water-filled goaf).
The abnormal increment for the induced electromotive force lead to the decrement of apparent resistivity value when the goaf is fully water-filling. Corresponding to the above-mentioned forward modeling results, the apparent resistivity contour lines around are distributed in irregular shapes, as shown in the Figure 5(a). When the goaf contains 50% water, the high-resistance air layer will weaken the abnormal amplitude. Compared with the full-water model, a small anomaly low-resistance enclosed area will generate at the buried depth -105m to -120m and the lateral distance from 175m to 330m, as shown in Figure 5(b). When there is no water in the mined-out area, no obvious enclosed area appear on the apparent resistivity profile diagram, the resistance of each layer is linearly distributed, and the value is high. This is because the induced electromotive force does not increase abnormally, while the apparent resistivity value did not decrease significantly, as shown in Figure 5(c).
For the mined-out area with collapsed rock mass, based on the slight difference of the induced voltage response, and the trend of the apparent resistivity profile obtained from the inversion is almost the same as that mind-out area without collapsed rock. The resistivity value has little increment, as shown in Figure   5(d)-5(f).  to the low resistance characteristics of the water accumulation, the induced voltage curve will produce abnormal "bump" phenomenon within the sampling time of 0.56ms~10ms. The attenuation process is limited and the sequence of the degree of abnormal response is 100% water accumulation goaf > 50% water accumulation goaf > 0% water accumulation goaf. Which implys that the larger the amount of water accumulation, and brought the more obvious the low resistance effect.
Moreover, the attenuation rate of the induced electromotive force response is slower while the response value is higher.

Transient electromagnetic response characteristics of water-filled goaf with different coil sizes
This section studies the electromagnetic response It can be seen from the figure that the initial voltage values of the six models of water-filled goafs increase significantly with the continuous increase of the side length of the transmitting coil. When the coil side length is 100m, the initial value of the attenuation voltage is about 11000~13000μV/A. When the coil side length is 150m, it is about 41000~55000μV/A. When the coil side length is 200m, the voltage value is about 98000~130000μV/A while it rises to 610000~770000μV/A when the side length of the coil is 400m. However, the attenuation trends of the four voltage curves are almost consistent, and the abnormal "upward" amplitudes produced are identical, which indicates that the size of the coil only changes the attenuation voltage value, and does not have a significant impact on the attenuation process and rate.
In order to obtain the relationship between the coil side length and the attenuation voltage value, the voltage values were chosen at the 10th, 12th, 15th and 17th measurement channels within the abnormal response time to fit the relationship between the two, and the corresponding fitting curve is shown in Figure  8(a)-8(f).
The results show that the attenuation voltage response values corresponding to the six types of mined-out areas all increase in a quadratic function with increasing the side length of the transmitting coil. The attenuation voltage values continue to decrease with the passage of sampling time (the number of time channels increases). The tangent slope of the quadratic formula keeps getting smaller, but the overall growth trend has not changed. In addition, the tangent slopes of the fitting curves of the 4 fitting curves under the 100% water-accumulated condition (including the model with the collapsed body) are the maximum. The tangent slopes of the 4 fitting curves under the condition of the 50% water-accumulation (including the collapsed body model) are the mediate. The slope of the tangent line is the minimum under the condition of no water accumulation (including the model with collapsed body). It can be seen that the voltage response value during the whole attenuation process decreases with the increase of the buried depth of the goaf, the abnormal amplitude of the "upward convexity" of the curve is reduced accordingly. At the same time, the abnormality of the curve and the increase in response value decrease with the increase of buried depth. This is because the intensity of the transient electromagnetic field signal gradually weakens when it penetrates the rock formations, and the ability to interpret low re-sistance anomalies will continue to decrease as the depth increases. The shallower the buried depth of the goaf, the shorter the abnormal response duration. When the buried depth reaches 300m, the attenuation voltage response is already extremely weak, and the abnormal phenomenon is not obvious. The above results indicate that the transient electromagnetic exploration has limited detection capabilities for abnormal objects, and the buried depth of the target body will also affect the response value and decay rate of the attenuation voltage.
(e) (f) Fig.9 Attenuated voltage curves of the different water-filled goaf models with different burial depths: (a) Model of the 100% water accumulation goaf, (b) Model of the 50% water accumulation goaf, (c) Model of the 0% water accumulation goaf, (d) Model of the 100% water accumulation with collapsed rock goaf, (e) Model of the 50% water accumulation with collapsed rock goaf, (f) Model of the 0% water accumulation with collapsed rock goaf (e) (f) Fig.10 Fitting curves of the attenuation voltage of with different burial depths: (a) Model of the 100% water accumulation goaf, (b) Model of the 50% water accumulation goaf, (c) Model of the 0% water accumulation goaf, (d) Model of the 100% water accumulation with collapsed rock goaf, (e) Model of the 50% water accumulation with collapsed rock goaf, (f) Model of the 0% water accumulation with collapsed rock goaf In order to obtain the relationship between the buried depth and the attenuation voltage value, the 10th, 12th, 15th and 17th measurement channels of voltage values were seleted within the abnormal response time to fit the relationship between the two, and the corresponding fitting curve is shown in Figure 10

Probe preparation and instrument selection
In this field experiment, the V8 multifunctional    (2) According to the geology background of the Majiliang Coal Mine, goaf model with six water accumulation situation were built as 100% water accumulation, 50% water accumulation, 0% water accumulation, 100% water accumulation with collapsed rock, 50% water accumulation with collapsed rock and 0% water accumulation with collapsed rock goaf models.
The simulation results demonstrate that the TEM detection has strong resolution in the low-resistance water-filled goaf and would generate obvious abnormal reactions. The attenuation curve presents a third-order exponential function distribution, and the distribution form is "S". However, the resolution of the goaf without water content is poor, and there is no abnormality in the curve during the decay process, which follows the normal exponential decay pattern. At the same time, the larger the water accumulation could lead to higher the abnormal amplitude and greater the voltage response value. The collapsed rock wound slightly weaken the low-resistance anomaly effect in the water-accumulated mine-out area.  Model of the water-lled goaf under different states: (a) Model of the 100% water accumulation goaf, (b) Model of the 50% water ac-cumulation goaf, (c) Model of the 0% water accumulation goaf, (d) Model of the 100% water accumulation with collapsed rock goaf, (e) Model of the 50% water accumulation with collapsed rock goaf, (f) Model of the 0% water accumulation with collapsed rock goaf Attenuated voltage curve of water-lled goaves in different states: (a) Model of the 100% water accumulation goaf, (b) Model of the 50% water accumulation goaf, (c) Model of the 0% water accumulation goaf, (d) Model of the 100% water accumulation with collapsed rock goaf, (e) Model of the 50% water accumulation with collapsed rock goaf, (f) Model of the 0% water accumulation with collapsed rock goaf The tting curve of the attenuation voltage of measuring points in 100% water accumulation goaf The apparent resistivity cross-section diagrams of the goaf with water accumulation in different states: (a) Model of the 100% water accumulation goaf, (b) Model of the 50% water accumulation goaf, (c) Model of the 0% water accumulation goaf, (d) Model of the 100% water accumulation with collapsed rock goaf, (e) Model of the 50% water accumulation with collapsed rock goaf, (f) Model of the 0% water accumulation with collapsed rock goaf Attenuated voltage curves of the different water-lled goaf models with different coil sizes: (a) Model of the 100% water accumulation goaf, (b) Model of the 50% water accumulation goaf, (c) Model of the 0% water accumulation goaf, (d) Model of the 100% water ac-cumulation with collapsed rock goaf, (e) Model of the 50% water accumulation with collapsed rock goaf, (f) Model of the 0% water accumulation with collapsed rock goaf   Attenuated voltage curves of the different water-lled goaf models with different burial depths: (a) Model of the 100% water accumula-tion goaf, (b) Model of the 50% water accumulation goaf, (c) Model of the 0% water accumulation goaf, (d) Model of the 100% water accumulation with collapsed rock goaf, (e) Model of the 50% water accumulation with collapsed rock goaf, (f) Model of the 0% water accumulation with collapsed rock goaf  Apparent resistivity pro le of 8# Coal Seam on 8111 Working Face