Seismic Clustering Analysis for Detecting Seismic Hazards Induced by Geological Anomalies and Residual Coal Pillars: A Case Study of Mining in a Protected Coal Seam

Abstract

Seismic hazards in underground coal mines are frequently triggered by geological anomalies and residual coal pillars, posing severe threats to safe mining. A protected seam longwall in a Chinese coal mine was used as a case to analyse the seismic clustering characteristics under the combined influence of the B4 anticline and a 30-m-wide overlying residual chain pillar. A simulation-testing-based source locating accuracy (STSLA) method was used to study the vector characteristics of seismic location errors in the longwall. A new seismic clustering index, the Number of Possible Clustered Events (NPCE), was proposed to quantify fracture connectivity in the coal-rock mass while reducing the influence of locating errors. The spatial–temporal evolution of NPCE, seismic event frequency, and energy magnitude was compared. Results show that NPCE exhibits a strong positive correlation with imminent high-energy seismic events and outperforms conventional indicators in recall rate and overall early-warning performance. The confusion matrix method demonstrates that NPCE achieves a better balance between precision and recall, especially at high pre-warning thresholds. NPCE = 0.7 is determined as the optimal threshold for seismic hazard risk identification. The proposed method provides a reliable approach for seismic-data-based seismic hazard early warning.

1. Introduction

Seismic hazards in underground mines are the potential for ground failures caused by mining-induced strong seismic events, such as rockbursts, coal bursts, and gas outbursts [1]. Over recent decades, catastrophic seismic hazards have been extensively documented in major mining nations worldwide, including China, Australia, Poland, the United States, and South Africa [2,3,4,5]. Although substantial research efforts spanning nearly a century have been devoted to this issue, the challenge of achieving accurate and reliable early warning of seismic hazards remains unresolved. This intractability arises primarily from the highly complex failure mechanisms governing seismic hazards, coupled with significant uncertainties associated with their diverse triggering factors.

Geological anomalies are among the primary factors that induce seismic hazards in underground mines. The existence of geological structures such as faults, folds, collapse columns, etc., can directly alter the stress distribution and structural stability of rock masses and trigger stress concentrations during mining operations, leading to rock fracture or sliding and thereby initiating hazardous seismic events. Many scholars have conducted in-depth research on the influence of geological structure on coal-rock mass stress and seismic hazard under various conditions. For example, Zhang, et al. [6] found that the core of a fold syncline experienced more intense tectonics than other positions, leading to the concentration of local in situ stress and four extremely intense rock bursts. Xiao, et al. [7] studied rock burst control under complex geological conditions and found that seismic events rise as mining nears geological structures. Zhao, et al. [8] found that in a geologically complex coalfield, coal bursts are strongly linked to geological structures, with seismic hazards often occurring in stress-concentrated zones. Guo, et al. [9] found that stress concentration zones exist in regions with variable facies in coal seam thickness, dip angle, and coal quality. Coal bursts result from the superposition of high in situ tectonic stress and abutment pressure from mining activities. Xue, et al. [10] investigated stress evolution in upright fold structure areas of deep mines, which shows periodic sine/cosine-like variations within the folding influence range. The above research findings provide solid references for understanding the seismic hazard mechanisms associated with geological structures. However, for hazard prevention and control, determining the influence range and hazardous state of geological anomalies from real-time monitoring data during mining operations is key to effectively preventing seismic hazards.

Apart from that, residual coal pillars are also a major hazardous source, causing coal bursts or seismic hazards in underground mines. Usually, they are used to support the roof, protect roadways and surface structures, and isolate goafs and areas at risk of water and gas hazards [11]. Some residual coal pillars are passively retained due to mining method sequences, geological structures, safety regulations, technical limitations, or resource recovery strategies. However, these pillars tend to form high-stress concentration zones and accumulate substantial elastic energy, which can easily induce sudden stress changes and energy release, thus significantly increasing the risk of coal bursts and their damage intensity [2]. Li, et al. [12] believed that large residual coal pillars in deep coal mines can accumulate high static and dynamic stress that rises with longwall retreatment, posing significant seismic hazard risks, which can be mitigated through reasonable design and destress measures. Zhang, et al. [13] examined the effects of residual coal pillar width on coal burst and goaf ignition via simulations, defined two risk indices, proposed an optimal width method based on the operating point principle, and verified it with a 7 m field trial in an underground mine. By studying the stability of irregular residual coal pillars via analytical calculation and simulation, Chen, et al. [14] found that residual coal pillars have an absolutely stable width of twice the abutment pressure influence distance, with distinct stability states and graded rock-burst risks. Tan, et al. [15] explored the linkage failure between the residual coal pillar and the rock stratum in multi-seam mining, identifying progressive and dynamic failure modes using safety factor and stiffness ratio, and clarifying key instability-triggering factors and mechanisms. Cao, et al. [16] studied how large residual coal pillars lead to high stress concentration and coal bursts with detectable seismic precursors, and used variable seismic analyses to achieve effective spatiotemporal pre-warning of hazard risks.

Several approaches, including seismic monitoring, geomechanical modelling, and machine learning, have been widely employed to assess seismic hazards in underground coal mines. Among these, seismic monitoring remains the most commonly used and effective technique, as it directly captures real-time fracture evolution within coal-rock masses and supports hazard forecasting, prevention, and control. It detects internal damage by analysing seismic waves generated by coal and rock masses, providing a reliable way to identify dynamic rock failures and assess the instability of geological structures. Several seismic analysis methods have been developed based on different seismicity features. Among them, seismic clustering analysis is commonly used to uncover hidden geological structures within rock masses, where seismic events are often caused by the same damage source with similar mechanisms [17,18]. Seismic clustering describes the spatial grouping of seismic events caused by connected fractures. The analysis on seismic clusters emphasises correlations among seismic events to gain deeper insights into the source of damage [19]. Various principles and algorithms have been developed for seismic clustering, including the Cluster Index Function [20], DBSCAN [21], the two-pass seismic clustering method [19], and sequential spatial clusters [22]. During mining activities near geological structures, large amounts of seismic data are produced. Fractures within the influence zone tend to form clusters, which can be used to effectively evaluate the instability of geological structures and their affected regions. As a result, seismic clustering analysis serves as an ideal indicator for assessing seismic hazard risks and can guide the implementation of seismic hazard prevention and control measures. A seismic cluster shows the spatial pattern of seismic events, making precise event location essential for identifying clustering behaviour.

However, locating seismic sources is challenging due to the flat geometry of geophone arrays, complex geological formations, and high levels of extraction activity in underground coal mines [23]. Most existing methods are susceptible to location accuracy and fail to precisely capture fracture connectivity and unstable coal-rock mass evolution. Gibowicz and Kijko [24] indicated that location errors typically range from 20–50 m or 50–100 m, influenced by the number of sensors and the network’s size and shape. In the Upper Silesian Coal Basin (USCB) in Poland, horizontal location errors are about 50 m, whereas vertical errors can reach 100 m [25]. Monitoring system epicentre errors in one Canadian and one South African mine range from 4 to 61 m, with an average of 15–23 m [26]. Low seismic location accuracy severely distorts fracture distribution patterns, misleads hazard zone identification, and reduces the reliability of seismic clustering-based early warning. Given these significant impacts, it is important to incorporate location uncertainties into seismic clustering analyses.

Therefore, this study proposes a seismic clustering method that accounts for source location errors to investigate the seismic responses and fracture connectivity characteristics of coal-rock masses in longwalls affected by geological anomalies and residual coal pillars. The method is validated using a protected-seam longwall face in a Chinese coal mine, where an anticline lies in the middle of the longwall and a 30-m-wide residual coal pillar exists above the central area. An index called NPCE, which quantifies fracture connectivity while reducing the impact of location errors, is established to examine the evolution of seismic clustering during longwall retreat. Three measurable objectives are proposed: (1) to quantify the vector characteristics of seismic location errors and their influence on clustering analysis; (2) to verify that NPCE outperforms conventional indicators (seismic frequency, energy magnitude) in recall rate and overall early-warning performance; (3) to determine an optimal NPCE threshold for identifying high-risk zones under combined geological anomaly and residual coal pillar conditions. The results of this study can provide an accurate approach to seismic analysis to assess seismic hazard risks during longwall mining.

2. Site Overview

The study site is the Hulushu Coal Mine, located in the Hujite Mining Area of the Dongsheng Coalfield in Erdos City, Inner Mongolia, China, with a production capacity of 8.0 Mt/a. The main coal seams, 2-1 and 2-2, have an inclination of less than 2° and are buried at depths of 650 to 700 m, with a spacing of 24 to 32 m between them.

The longwall under study, LW22103, is the first longwall in the 2-2 coal seam in the first district at Hulushu Coal Mine. LW22103 is 320 m long and has an advanced length of 4084 m. The target 2-2 coal seam has an average thickness of 2.8 m, and the average mining depth is approximately 662 m. The coal exhibits a uniaxial compressive strength of 20.25 MPa and an elastic modulus of 1.31 GPa. The coal seam is overlain by medium-grained sandstone with a thickness of 20 m, uniaxial compressive strength of 52.22 MPa, and elastic modulus of 5.56 GPa. It is underlain by sandy mudstone with a thickness of 8.9 m and an uniaxial compressive strength of 32.17 MPa. Within LW22103, several minor faults of varying sizes, mostly normal, occur, and their locations and parameters are shown in Figure 1. Additionally, a B4 anticline with an amplitude of 15 m develops in the middle of the longwall, and its two wings are essentially symmetrical.

The 2-1 coal seam above LW22103 has been fully mined: LW21102 (mining ended in June 2018) and LW21103 (mining ended in October 2019). Therefore, LW22103 is also referred to as a protected-seam longwall face. Above the middle portion of LW22103, a 30 m-wide residual chain pillar lies between the goafs of LW21102 and LW21103, located 174 m from the maingate and 105 m from the tailgate of LW22103.

The mine is equipped with the Polish ARAMIS M/E seismic monitoring system, which comprises 32 geophones, data acquisition and transmission modules, and analysis software. Nine geophones were deployed around the LW22103 face, with a sampling frequency of 500 Hz and a recording frequency range of 0–150 Hz. The system supports mobile monitoring, with geophones relocated forward by 200–400 m as mining advances, ensuring continuous and stable data acquisition.

As LW22103 is a protected-seam longwall face, geo-stress in the 2-2 coal seam has been partially relieved, thereby reducing seismic hazard risks [27]. However, several factors result in persistent seismic hazard risks during LW22103 retreat:

(1) The No. 2-2 coal seam exhibits physical and mechanical properties indicative of strong bursting liability, with an average uniaxial compressive strength exceeding 20 MPa and an average elastic energy index greater than 12;

(2) The overlying 30-m-wide residual coal pillar transfers overburden pressure to the coal-rock mass of LW22103, leading to a high degree of stress concentration in the corresponding area;

(3) The B4 anticline lies in the middle of LW22103. During retreat towards the anticline, the horizontal in situ stress increases sharply, causing a high accumulation of elastic strain energy within the coal and rock mass.

Seismic events with energy ranging from 0.1 kJ to 10 kJ were used for methodology testing, covering both low-energy microfracturing events and high-energy events associated with unstable coal-rock mass failure. Figure 1 shows the distribution of seismic activity before and after LW22103 retreated through the B4 anticline, i.e., from February to June 2024. It can be seen that when LW22103 retreated to 500 m away from the B4 anticline, the frequency of seismic events with energy greater than 1 kJ increased significantly. Two strong seismic events with energy exceeding 10 kJ occurred when the longwall retreated directly into the anticline. The frequency of seismic events with energy greater than 1 kJ decreased noticeably only after the longwall retreated approximately 400 m away from the B4 anticline, indicating a high level of seismic hazard risk in this region.

The term geological anomalies in this study specifically refers to structural geological features that induce stress concentration and seismic activity, including the B4 anticline, local small-scale normal faults, and the overlying residual coal pillar, which collectively control the spatial distribution of mining-induced seismicity.

3. Methodology

3.1. Simulation-Testing-Based Source Locating Accuracy (STSLA) Analysis

Given the randomness of errors in wave-velocity and arrival-time picking when locating seismic events, numerical forward-modelling simulations are used to investigate the spatial distribution of source-location errors [28]. For a given seismic network, assuming a seismic event occurs at $(x_0, y_0, z_0)$ at time $t_0$, the theoretical arrival time $t_i$ of the seismic wave at each geophone i, located at (x_i, y_i, z_i), is calculated using the classical Geiger locating method [29] with a constant-velocity model at velocity $v_p$:

$$t_i=t_0+{\displaystyle \frac{\sqrt{{(x_0-x_i)}^2+{(y_0-y_i)}^2+{(z_0-z_i)}^2}}{v_p}}$$

(1)

Based on the statistical error distributions of arrival times and wave velocities in seismic waves, artificial arrival-time error ${\delta }_p$, and wave-velocity error ${\delta }_v$ are randomly added to each geophone. For Geophone $\#i$, its residual arrival time ${r_i}^{\prime }$ under the influence of the two errors is:

$${r_i}^{\prime }=t_i+{\delta }_{ip}-t_0-{T_i}^{\prime }(x_0,y_0,z_0)$$

(2)

$${T_i}^{\prime }(x_0,y_0,z_0)={\displaystyle \frac{\sqrt{{(x_0-x_i)}^2+{(y_0-y_i)}^2+{(z_0-z_i)}^2}}{v_p+{\delta }_{iv}}}$$

(3)

where ${\delta }_{ip}$ and ${\delta }_{iv}$ are the arrival-time and wave-velocity errors for Geophone $\#i$, respectively. Using the least squares method, the error-influenced source location (x₀′, y₀′, z₀′) can be determined by minimising the sum of the squared residual arrival times r_i′ across all available geophones:

$$\Phi ({t_0}^{\prime },{x_0}^{\prime },{y_0}^{\prime },{z_0}^{\prime })={\displaystyle \sum _{i=1}^n{{r_i}^{\prime }}^2}$$

(4)

Following the above procedure, the location of the seismic event, considering ${\delta }_p$ and ${\delta }_v$ is repeatedly calculated, typically 1000–3000 times, to obtain an elliptical spatial distribution of the source-location error scatter [30]. This ellipse characterises the vector properties of the source-location error of the seismic network in the area of interest.

In this study, an average P-wave velocity of 3700 m/s was adopted, calibrated via controlled blasting tests for source locating. Both ${\delta }_p$ and ${\delta }_v$ followed a Gaussian distribution, the standard form for random measurement noise in source-locating analyses. The arrival-time errors ${\delta }_p$ were assigned a standard deviation of 0.006 s, derived from statistical analysis of on-site seismic records. The wave-velocity error ${\delta }_v$ was set to 100 m/s, calibrated against typical underground velocity variations. Simulations were performed on 50 m × 50 m grids in the area of interest, with 2000 simulation tests conducted per grid point to ensure stable and reliable statistical results.

3.2. Number of Possible Clustered Events (NPCE)

Laboratory experiments and engineering practices have shown that, before reaching its strength limit, a loaded coal-rock mass exhibits clustering of seismic events around the macroscopic fracture surface, which can serve as a precursor to instability [19,31,32]. However, in practical coal mine applications, constrained by the seismic network’s source-locating accuracy, initial source location results struggle to accurately characterise fracture development features, thereby hindering further improvement in the accuracy of impact ground pressure warnings. Therefore, based on the characteristics of the location error distribution derived in Section 3.1, an index, the Number of possible clustered events (NPCE), is proposed. NPCE characterises the degree of coal-rock mass fracture development by evaluating the connectivity probability of adjacent micro-fractures within their respective regional location error ranges, thereby minimising the adverse impact of network positioning accuracy on the description of the seismic response characteristics of coal-rock masses. In physical terms, NPCE reflects the real-time fracture connectivity and the degree of stress-induced instability of the coal-rock mass. A higher NPCE value indicates that more micro-cracks have initiated, propagated, and interconnected under mining and tectonic stress, forming a network of penetrating fractures. This means the coal-rock mass is closer to unstable failure, which corresponds to a higher risk of seismic hazards. Thus, NPCE can provide a clear geomechanical meaning for quantifying the hazard level.

The energy of seismic waves from seismic events is positively correlated with the radius of the rupture surface [24]. Jager and Ryder derived an empirical relationship between source energy and rupture radius from extensive field observations [33].

$$r_0={10}^{(1+M_L/2)}/2$$

(5)

In Equation (5), $r_0$ represents the source radius, and $M_L$ denotes the event magnitude. This empirical relationship is widely used for mining-induced seismic events. Although field measurements of source radius for events with different magnitudes and energy levels are lacking, it remains suitable for the low-to-moderate energy range (0.1–10 kJ) monitored in this study.

During the seismic fracturing process, the area within twice the source radius of the epicentre is termed the near-field zone, where rock mass damage is about to occur. Consequently, the two seismic events can be clustered if their distance d is less than twice the sum of their source radii $r_{0\left(1\right)}$ and $r_{0\left(2\right)}$:

$$d\le 2(r_{0\left(1\right)}+r_{0\left(j2\right)})$$

(6)

Equation (6) defines the critical distance for two seismic events to be regarded as clustered, representing the potential fracture connection range. Based on the failure mechanism, Vasak, Suorineni, Kaiser, and Thibodeau [17] identified four typical failures of seismic clusters around excavations during mining. The propagation, connection, and excavation-intersecting of geological structures can be illustrated by the clustering of seismic events.

However, due to source location errors, even if the fractures of two events have already connected, their distance may still exceed twice the sum of their source radii, thereby failing to effectively identify the incipient failure process. To address this issue, the NPCE is established to represent the probability of rupture interconnection between adjacent seismic events within their respective location error ellipses, which describe the spatial range where the real seismic source may exist.

For two adjacent seismic events $i$ and $j$, with their respective source radii being $r_{0\left(i\right)}$ and $r_{0\left(j\right)}$, three mutually exclusive cases are defined based on their source distance and location error ellipses:

Case I: Definitely clustered (NPCE = 1)

The distance $d$ between the two events satisfies $d\le 2(r_{0\left(i\right)}+r_{0\left(j\right)})$. The fractures are definitely connected even without considering location errors, as shown in Figure 2a.

Case II: Potentially clustered (0 < NPCE < 1)

The nominal distance $d$ exceeds the clustering threshold, but the events could become clustered when movement within their respective location error ellipses is allowed. NPCE quantifies this connection probability, as shown in Figure 2b. In this case, NPCE is:

$$F{p}_{(ij)}={\displaystyle \frac{p_i}{p_{\max }^i}}·{\displaystyle \frac{p_j}{p_{\max }^j}}$$

(7)

Case III: Definitely unclustered (NPCE = 0)

Even after accounting for the full location error ellipses, the events still cannot satisfy the clustering condition. No possible fracture connection exists, as shown in Figure 2c.

Based on the calculation method for NPCE for two adjacent seismic events mentioned above, and assuming there are m seismic events surrounding seismic event i, the Number of Possible Clustered Events index for the region where seismic event i is located, NPCE(i), is expressed as:

$${\mathrm{NPCE}}_{(i)}={\displaystyle \sum _{j=1}^m{\mathrm{NPCE}}_{(ij)}}$$

(8)

Compared with conventional seismic clustering methods that neglect location errors, the proposed STSLA-NPCE method uses error ellipses to quantify anisotropic locating uncertainty and applies the NPCE index to evaluate fracture connectivity within these ellipses, thereby improving the reliability of seismic hazard assessment.

Of particular note is to clearly distinguish between seismic clustering, fracture connectivity, and seismic hazard. Seismic clustering denotes seismic aggregation, fracture connectivity reflects crack coalescence, and seismic hazard denotes actual coal burst risks. High NPCE serves as an indirect indicator of enhanced fracture connectivity and unstable coal-rock mass, not a direct measurement. This interpretation is mechanistically reasonable but inferential, as NPCE is derived from seismic patterns rather than from direct crack observations. Cavalieri, et al. [34] note that seismic indicators reflect degradation but cannot replace direct evidence such as borehole data, stress monitoring, and numerical modelling. Thus, NPCE is adopted as a supplementary early-warning proxy for fracture connectivity and potential seismic hazard.

4. Results

4.1. Seismic Location Error Characteristics

Figure 3 shows the distribution of error ellipses for seismic source location in LW22103 during retreat from February 2024 to June 2024. The figure shows that location accuracy and error orientation vary significantly across the longwall. The region with the minimum location error lies within the X-coordinate range of 1300–2100 m and the Y-coordinate range of 900–100 m, where the horizontal location error ranges from 36.5 m to 40.3 m. Within the longwall face and near the B4 anticline, the major axes of the error ellipses are oriented southwest–northeast, indicating that location errors for seismic activity in this zone are larger in the southwest–northeast direction than in the northwest–southeast direction.

In contrast, due to insufficient geophones to form a network envelope, the seismic location error in the western part of the longwall, i.e., the Y-coordinate range of approximately 400–600 m, is 60 m to 85.3 m. From north to south, the major axis of the error ellipse gradually rotates from northwest–southeast to southwest–northeast, indicating substantial directional differences. Similarly, in the eastern part of the longwall, i.e., the Y-coordinate range of approximately 1200–1400 m, the seismic location error is about 50 m to 78.6 m, and the major axis of the error ellipse is oriented east–west, suggesting that seismic events in this zone may exhibit large location errors in the east–west direction.

The results above indicate that during the LW22103 retreat, the seismic network’s location accuracy is relatively low, and the vector characteristics of location errors across different longwall zones are pronounced, likely causing serious deviations in seismic early warning for seismic hazards. Compared with the traditional scalar value of location error, error ellipses can more comprehensively describe the vector characteristics of seismic network location accuracy, providing a data basis for improving the accuracy of early warning for seismic hazards.

4.2. NPCE Results

In this study, seismic events recorded in LW22103 during its passage through the B4 anticline from 23 February to 13 June 2024 were analysed. The evolution of the seismic activity distribution in LW22103 is shown in Figure 4, using a 2-week time window and a 2-week step size for seismic data analysis.

As shown in Figure 4a, when the longwall was approximately 700 m from the B4 anticline, few seismic events with energy greater than 1 kJ occurred, and seismic activity was mainly confined to the overlying residual coal pillar zone. This indicates a high degree of stress concentration in the coal-rock mass beneath the residual coal pillar. As the longwall gradually approached the B4 anticline (see Figure 4b to Figure 5e), seismic activity spread from the overlying residual coal pillar to the entire longwall face area. This suggests that the temporal and spatial evolution of seismic activity is closely controlled by the combined geological constraints of the B4 anticline and the overlying residual coal pillar. The residual pillar induces persistent vertical stress concentration in the underlying coal-rock mass, while the anticline amplifies horizontal tectonic stress as the longwall advances. This dual-stress superposition drives progressive fracture initiation, propagation, and interconnection, which, in turn, leads to a gradual increase in seismic event frequency and the expansion of high-NPCE zones. As the anticline is approached, the intensified tectonic stress accelerates fracture connectivity, leading to frequent high-energy seismic events and a sharp rise in seismic hazard risk.

When the distance to the anticline was less than 100 m (see Figure 4f), the B4 anticline zone and the overlying residual coal pillar zone exhibited frequent, intense high-energy seismic events, indicating a rapid increase in seismic hazard risk. During passage through the B4 anticline, two strong seismic events with energy exceeding 10 kJ occurred (see Figure 4g), indicating that the coal-rock mass was in a highly unstable state, with seismic hazard risk at its peak. After retreating past the B4 anticline, the frequency of seismic activity at the longwall decreased significantly, indicating that the abnormal influence of tectonic stress induced by the B4 anticline gradually weakened and the seismic hazard risk correspondingly diminished.

Figure 5 shows the NPCE distribution in LW22103 during the retreat from 23 February to 13 June 2024. To quantitatively compare the clustering degree of seismic activity across periods, the NPCE results were normalised. For the $i^{th}$ grid or the $i^{th}$ event, the normalised value $R_{para\left(i\right)}$ of its pre-warning indicator $para\left(i\right)$ is as follows:

$$Rpar{a}_{(i)}={\displaystyle \frac{par{a}_{(i)}-\min para}{\max para-\min para}},$$

(9)

where $\mathrm{m}\mathrm{a}\mathrm{x}para$ and $\mathrm{m}\mathrm{i}\mathrm{n}para$ are the maximum and minimum indicator results during the study period, respectively.

As shown in Figure 5a, when LW22103 face was far from the B4 anticline, high NPCE values were mainly concentrated in the overlying residual coal pillar zone, which is basically consistent with the seismic activity distribution in Figure 4a. Similarly, in Figure 5b,c, as the longwall face was affected by the geological anomaly, accompanied by a gradual increase in horizontal tectonic stress, the range of high-NPCE zones gradually expanded, which is generally consistent with the distribution characteristics of seismic events with energy greater than 1 kJ in Figure 4b,c.

However, the NPCE distribution patterns in Figure 5d differ significantly from those of seismic events with energy greater than 1 kJ in Figure 4d. Figure 5d shows that the seismic cluster was still highly concentrated in the overlying residual coal pillar zone with an expanded range, where the maximum NPCE exceeded 140, while the seismic clustering degree in other areas remained low with NPCE values of only about 20–40. In Figure 4d, seismic events with energy greater than 1 kJ had already appeared near the maingate of the longwall, but their corresponding NPCE values were still low, at only approximately 50.

Similar phenomena were also observed during the period when the LW22103 retreated from 200 m away from the B4 anticline to passing through it (see from Figure 5e–g). During this period, high NPCE values were mainly concentrated at the intersection of the overlying residual coal pillar and the B4 anticline, whereas seismic events with energy greater than 1 kJ had spread across the entire longwall face (see from Figure 4e–g). This indicates that under the combined influence of overburden vertical pressure and horizontal tectonic stress from the geological anomaly, internal fractures in the coal-rock mass in the middle of the longwall had become fully connected, unstable failure was likely to occur, and the risk of seismic hazards induced by strong seismic events peaked. After passing through the B4 anticline, NPCE values decreased substantially, and the seismic hazard risk was reduced.

The results in Figure 5 demonstrate that NPCE does not have a one-to-one correspondence with high-energy seismic events. This discrepancy mainly occurs in two scenarios. First, scattered high-energy events induced by local small faults may occur without widespread fracture connectivity, leading to high energy but low NPCE. Second, high NPCE values can appear in regions with fully connected microcracks but insufficient energy accumulation for immediate high-energy release, reflecting early-stage instability before strong events. This distinction indicates that NPCE characterises fracture connectivity, while high-energy events reflect sudden energy release, representing different stages of the failure process.

The temporal evolution of normalised event frequency, seismic energy, and NPCE during mining toward the B4 anticline is shown in Figure 6. Before approaching the B4 fold (7-Mar to 18-Apr), event frequency rises rapidly to a normalised value of 1.0, while seismic energy and NPCE increase gradually to 0.33 and 0.72, respectively. This trend reflects the initial accumulation of stress and microcrack propagation under the combined influence of the residual coal pillar and advancing mining.

As mining advances to the B4 fold position (18-Apr to 16-May), event frequency remains high, between 0.9 and 1.0, and NPCE peaks at 1.0, indicating widespread fracture connectivity. Seismic energy fluctuates between 0.3 and 0.6, corresponding to moderate energy release during progressive crack coalescence. The synchronous elevation of event frequency and NPCE confirms that the B4 anticline amplifies tectonic stress, driving the formation of a connected fracture network.

After passing the B4 fold (16-May to 27-Jun), event frequency and NPCE decline steadily, while seismic energy first surges to 1.0 on 30-May before dropping sharply. This transient energy peak indicates a sudden release of accumulated elastic energy after the working face clears the anticline, while the gradual decrease in NPCE reflects the gradual closure of fractures and reduction in connectivity as stress redistributes. These quantitative changes establish a clear causal link between geological controls (B4 anticline + residual coal pillar) and the evolution of seismic activity and fracture connectivity.

Also, Pearson correlation coefficients and key statistics were calculated for the time series (February–June 2024). NPCE shows a strong positive correlation with event frequency (r = 0.82, p < 0.01) and a moderate correlation with seismic energy (r = 0.67, p < 0.01), while frequency and energy are weakly correlated (r = 0.59, p < 0.01). This indicates that NPCE primarily reflects fracture connectivity rather than sudden energy release. Normalised statistics show NPCE has a mean of 0.58 and a standard deviation of 0.29, balancing sensitivity and stability. Consistent with Figure 6, NPCE and frequency rise synchronously near the anticline, whereas energy peaks later, reflecting delayed energy release after fracture network formation.

4.3. Seismic Hazard Pre-Warning Performance Assessment

To quantitatively compare the pre-warning performance of NPCE, seismic event frequency, and energy magnitude for seismic hazards, the study analysed the relationship between the distributions of each indicator during mining near the B4 anticline influence zone from 19 April to 16 May 2024, and the locations of 25 strong seismic events with energy greater than 5 kJ that were imminent from 3 May to 30 May 2024.

Figure 7 shows the distribution of NPCE and normalized NPCE (hereafter referred to as $R_{NPCE}$) in LW22103 from 19 April to 2 May 2024 and from 3 May to 16 May 2024, respectively. The pink pentagrams represent the planar locations of strong seismic events with energy greater than 5 kJ that occurred within the following two weeks. As shown in Figure 7a, based on the NPCE results from 19 April to 2 May 2024, 6 out of 7 imminent strong seismic events were concentrated in the overlying residual coal pillar zone, where NPCE values were all greater than 100 and the corresponding $R_{NPCE}$ reached above 0.78. Only one high-energy event near the small fault group had a low NPCE value of 23.84 and $R_{NPCE}$ of 0.18. As shown in Figure 7b, based on the NPCE results from 3 May to 16 May 2024, there were 18 imminent strong events, mainly distributed at the intersection of the overlying residual coal pillar and the B4 anticline. Among them, 12 events were located in the medium-to-high NPCE zone, with NPCE values greater than 82 and $R_{NPCE}$ greater than 0.7. Three events were located in the medium NPCE zone, with $R_{NPCE}$ ranging between 0.5 and 0.7. The remaining three high-energy events showed poor correspondence with NPCE, as the $R_{NPCE}$ in their corresponding zones were less than 0.5. The above results indicate that the NPCE distribution in LW22103 exhibits a strong positive correlation with strong seismic events imminent in the short-term future, and thus, can be used as an ideal periodic pre-warning evaluation indicator for seismic hazards.

Figure 8 shows the distribution of seismic frequency and its normalised value (hereafter referred to as $R_{Freq}$) in LW22103 for the periods from 19 April to 2 May 2024, and from 3 May to 16 May 2024. Compared with the NPCE results, the regions with high seismic frequency are more concentrated. In Figure 8a, the medium-to-high seismic frequency zones are also located in the overlying residual coal pillar area. However, only one imminent strong seismic event has a $R_{Freq}$ value exceeding 0.6, while the $R_{Freq}$ of the other 6 strong events range from 0.3 to 0.5. In Figure 8b, the medium-to-high seismic frequency zones are still mainly distributed in the residual coal pillar but do not cover the B4 anticline area, resulting in a weak correlation between $R_{Freq}$ and future strong seismic events. Among the 18 strong seismic events, only 4 have relatively high $R_{Freq}$ values of 0.9 and 0.64, respectively, while the remaining $R_{Freq}$ range from 0.01 to 0.59. This indicates that the correlation between seismic events frequency and short-term future strong seismic activity is significantly weaker than that of NPCE.

Figure 9 illustrates the distribution of seismic energy magnitude and its normalised value (hereafter referred to as $R_{ML}$) in LW22103 from 19 April to 2 May 2024, and from 3 May to 16 May 2024. As shown in the figure, compared with the NPCE results, the area with high $R_{ML}$ is considerably larger. In Figure 9a, zones with high energy magnitude ($R_{ML}$> 0.7) remain mainly within the overlying residual coal pillar area, but their coverage length has approached 300 m. Of the 7 strong seismic events in the subsequent period, 4 occur in zones with $R_{ML}$ > 0.7 and 2 in zones with 0.5 < $R_{ML}$ < 0.7. Similarly, in Figure 9b, zones with high energy magnitude extensively cover the intersection area of the overlying residual coal pillar and the B4 anticline. Of the 18 strong seismic events in the subsequent period, 7 occur in zones with $R_{ML}$ > 0.7, 6 in zones with 0.5 < $R_{ML}$ < 0.7, and 5 in zones with <0.5. These results indicate that the energy magnitude distribution in LW22103 shows a strong positive correlation with imminent strong events in the short term. However, the excessively large area of high-value zones may reduce pre-warning efficiency.

To quantitatively compare the performance of NPCE, seismic event frequency, and energy magnitude in predicting high-energy events, the confusion matrix method [35] was used to analyse the precision P, recall rate R, and F-score of the three normalised indicators across different pre-warning thresholds. In this research, the precision P is defined as the ratio of the number of grids with strong seismic events that exceed the pre-warning indicator threshold to the total number of grids that exceed the relative pre-warning indicator threshold:

$$P={\displaystyle \frac{Nu{m}_{grid-events}}{Nu{m}_{grid-\mathrm{thres}}}}.$$

(10)

The recall rate R is defined as the ratio of the number of strong seismic events exceeding the relative pre-warning parameter threshold to the total number of such events:

$$R={\displaystyle \frac{Nu{m}_{events}}{Nu{m}_{events-total}}}$$

(11)

P reflects the pre-warning efficiency of each indicator for strong seismic events. A higher P indicates a smaller pre-warning area and thus higher pre-warning efficiency. R characterises the pre-warning accuracy of each indicator for strong seismic events, and a higher R corresponds to greater pre-warning accuracy.

Given that P and R are mutually constrained, the F-Score was used to assess pre-warning performance:

$$F_{Score}=(1+{\beta }^2){\displaystyle \frac{P·R}{{\beta }^2·P+R}}$$

(12)

where β is a constant representing the relative importance of precision P and recall rate R. Since P and R are equally important for seismic hazards early warning, β = 1.

To ensure a robust statistical basis for early-warning performance evaluation, the grid size was set to 50 m × 50 m, consistent with the spatial resolution of seismic location error analysis. The warning area was defined as the entire longwall panel. A seismic event was associated with a grid if its epicentre fell within the grid boundary. True positives (TP) were defined as grids exceeding the warning threshold that contained at least one subsequent high-energy event (>5 kJ). False positives (FP) were grids exceeding the threshold without subsequent high-energy events. False negatives (FN) were grids containing high-energy events that did not exceed the threshold. True negatives (TN) were grids without high-energy events and below the threshold.

Figure 10 shows the pre-warning precision and recall rates of the normalised NPCE, seismic event frequency, and energy magnitude for strong seismic events under different pre-warning thresholds. In terms of recall rate, the R-values of all three indicators gradually decrease as the pre-warning threshold increases. The R-value of $R_{NPCE}$ is consistently higher than those of $R_{Freq}$ and $R_{ML}$ across all pre-warning thresholds, and this advantage of $R_{NPCE}$ becomes increasingly pronounced with higher thresholds. This indicates that NPCE can significantly improve the accuracy of predicting strong seismic events compared to the two conventional indicators. In terms of precision rate, the p-value of $R_{NPCE}$ increases gradually as the pre-warning threshold rises. For thresholds from 0.1 to 0.8, the p-value of $R_{NPCE}$ is higher than that of $R_{ML}$ but lower than that of $R_{Freq}$. At a threshold of 0.9, however, the p-value of $R_{NPCE}$ peaks at 0.71, making it the highest among the three indicators. Meanwhile, the p-values of $R_{Freq}$ and $R_{ML}$ drop sharply, falling to 0.33 and 0.09, respectively. These results demonstrate a strong positive correlation between NPCE and the probability of strong seismic event occurrence, with its high recall rate a prominent advantage. Although the event frequency boasts a high precision rate, its low recall rate leads to a significant increase in missed alarms. Conversely, the poor precision rate of energy magnitude makes it prone to generating a high number of false alarms.

Figure 11 shows the F-score of the three normalised pre-warning indicators for strong seismic events across different pre-warning thresholds, calculated using Equation (12). At low warning thresholds (0.1–0.5), NPCE exhibits inferior overall performance compared with seismic frequency, driven by three key mechanisms. First, weak differentiation of fracture connectivity: low thresholds include nearly all micro-seismic events, most of which correspond to isolated, non-connected microcracks. NPCE is designed to quantify connected fracture networks, so it cannot effectively distinguish between trivial, scattered micro-events and early-stage connected fractures at low thresholds, leading to high false-positive rates. Second, amplified interference from location errors: at low thresholds, the probabilistic clustering calculation in NPCE is highly sensitive to minor deviations within error ellipses, which artificially inflate potential clustering probabilities for isolated events and reduce the reliability of hazard differentiation. Third, over-sensitivity to low-energy noise: NPCE counts potential clustered events regardless of event energy, so low-energy, non-hazardous micro-events dominate the index value at low thresholds, masking the true signal of hazard accumulation.

Quantitative comparison across the low-threshold range (0.1–0.5) confirms this performance gap. As shown in Figure 10 and Figure 11, at a threshold of 0.3, the F-score for seismic frequency reaches 0.39, whereas NPCE achieves only 0.26. At a threshold of 0.5, seismic frequency still maintains an F-score of 0.36, whereas NPCE rises to 0.36 (equal performance). In contrast, energy magnitude performs poorly throughout the low-threshold range, with an F-score below 0.12 at all thresholds ≤0.5, due to excessive false alarms from scattered low-energy events. These results confirm that seismic frequency is more suitable for preliminary hazard screening at low thresholds.

However, when the pre-warning threshold exceeds 0.5, the comprehensive pre-warning capability of $R_{NPCE}$ remains consistently high, with its maximum F-score reaching 0.39. In contrast, the comprehensive pre-warning performance of $R_{Freq}$ drops sharply when the pre-warning threshold exceeds 0.5: its F-score is approximately 0.15 at a threshold of 0.8 and decreases to nearly 0 at a threshold of 0.9. This indicates that the pre-warning capability of $R_{Freq}$ is significantly weakened as the pre-warning threshold increases. Accordingly, the comprehensive pre-warning performance of NPCE is significantly superior to that of event frequency and energy magnitude at high pre-warning thresholds, and it better balances recall and precision for early warning of high-energy events. Meanwhile, since NPCE already achieves the maximum F-score of 0.39 at a pre-warning threshold of 0.7, this value can be set as the criterion for identifying seismic hazards.

5. Discussion

5.1. Method Limitations

The versatility of the NPCE method is closely tied to geological settings. Under simple geological conditions (gently dipping seams, minor faults, single residual pillars), NPCE performs robustly and reliably captures fracture connectivity induced by mining stress and pillar loading, as validated in this study. In complex geological conditions (steeply inclined seams, multiple intersecting faults, karst collapse columns, or igneous intrusions); however, highly heterogeneous stress fields and scattered seismic events may weaken the correlation between NPCE and large-scale fracture networks, potentially reducing early-warning accuracy. For multi-seam mining with overlapping residual pillars, NPCE can still identify concentrated fracture zones but may require refined spatial windows to distinguish pillar-induced from tectonic-induced clustering.

For seismic network configurations, NPCE relies on sufficient geophone coverage to constrain location error ellipses. In dense, well-distributed networks, location uncertainty is low, and NPCE provides precise quantification of fracture connectivity. In sparse or asymmetric networks (e.g., limited geophones in one direction), larger error ellipses inflate the potential for clustering, increasing false positives. In complex tectonic settings (fold groups, thrust faults, or intense tectonic stress), NPCE excels at tracking progressive fracture coalescence driven by stress superposition, but it cannot directly differentiate between tectonic and mining-induced seismicity. Thus, NPCE is best applied as a complementary tool alongside geological mapping, stress monitoring, and numerical modelling, rather than as a standalone solution, to enhance reliability across diverse mining environments.

5.2. Comparison with Alternative Methods and Practical Applicability

Compared with alternative seismic hazard assessment methods, the proposed NPCE index exhibits distinct advantages and limitations in terms of computational complexity, robustness, and practical implementation.

Geomechanical modelling methods (e.g., finite element or discrete element modelling) require detailed geological parameters, complex mesh generation, and long computation times, which limit their real-time monitoring capability in dynamic mining environments. Their performance is highly dependent on parameter calibration, resulting in poor robustness to unknown geological anomalies.

Machine learning methods rely on large, high-quality labelled datasets and require complex model training and tuning processes. Although they can achieve high accuracy under ideal conditions, they often suffer from poor generalisation ability when applied to new mines or complex geological structures, and their black-box nature reduces interpretability for on-site engineers.

In contrast, the NPCE method directly uses raw seismic monitoring data and has low computational complexity, enabling real-time calculation. It explicitly accounts for seismic location errors, significantly improving robustness to noise and inaccurate positioning. The index has a clear physical meaning (fracture connectivity), which facilitates practical implementation and on-site interpretation. The main limitation of NPCE is that it focuses on fracture connectivity and cannot fully replace geomechanical modelling for stress field analysis or machine learning for multi-factor hazard prediction.

6. Conclusions

This study presents a seismic clustering method, NPCE, that accounts for location errors to evaluate seismic hazard risk during the LW22103 retreat, which overlies a residual coal pillar passing through an anticline. The main conclusions are:

(1) Seismic source locations in LW22103 exhibit strong directional characteristics, with horizontal errors ranging from 36.5 m to 85.3 m and variable error ellipse orientations. The uneven distribution of geophones leads to large deviations in source location, which may significantly distort seismic indicators and reduce early-warning reliability.

(2) Under the superposition of the overlying residual coal pillar and the B4 anticline, coal-rock fractures in LW22103 become fully connected, and seismic hazard risk peaks as the longwall passes through the anticline. NPCE decreases significantly after the longwall passes the anticline, indicating a reduced seismic hazard risk.

(3) The NPCE index effectively mitigates the effects of location errors and characterises the fracture connectivity of coal-rock masses in an unstable state. High NPCE zones are highly consistent with areas where high-energy seismic events occur, whereas seismic event frequency and energy magnitude show weak or dispersed correlations.

(4) Quantitative assessment using precision, recall rate, and F-score demonstrates that NPCE outperforms seismic frequency and energy magnitude in overall early-warning performance. NPCE maintains a high recall rate across all thresholds and achieves the highest precision of 0.71 at a threshold of 0.9. The optimal early-warning threshold for NPCE is 0.7, enabling accurate and efficient identification of seismic hazards.

Compared with traditional seismic frequency and energy indicators, the proposed NPCE method incorporates seismic location uncertainties and better reflects fracture connectivity, providing more reliable seismic hazard assessment. It can be widely applied to early warning in mines affected by geological anomalies and residual coal pillars. However, this study has some limitations. The method performs worse than seismic frequency at low warning thresholds and has only been verified under the combined influence of an anticline and a residual coal pillar in a single longwall. Further verification under more complex geological conditions and comparisons with other seismic clustering methods are required to improve its universality.