Kijko and Sciocatti (1995) conducted comprehensive research on microseismic location theory in order to optimize the spatial arrangement of mining seismic stations. They proposed the D-value theory to enhance microseismic observation systems (Zhao et al., 2022), as shown below.

The microseismic arrival time t i recorded by the ith detector satisfies Equation 2: t i = t 0 + T h , s i + ε i (2) where h = x 0 , y 0 , z 0 and s i = x i , y i , z i represent the coordinates of the source and seismic station in the Cartesian coordinate system, ε i denotes the picking error of the seismic wave recorded by the ith detector, where i=1,…, n, n is the total number of detectors, and T h , s i is the source.

The issue of microseismic location can be reformulated as the following mathematical optimization problems as shown in Equation 3: Φ X = ∑ i n t i − t 0 − T h , s i p (3) where X = x 0 , y 0 , z 0 , t 0 , p is the norm (p ≥ 1). When p=2, Φ X is the least squares estimate, and when p=1, Φ X is the sum of absolute residual values.

Kijko and M Sciocatti believes that the effectiveness of an observation system should be determined by the covariance matrix of the parameter X = x 0 , y 0 , z 0 , t 0 to be inverted for microseismic events. Consequently, the optimization problem for microseismic observation systems can be formulated as a mathematical problem, as presented in Equation 4: min ⁡ f C x   s ∈ f C x (4) where C x is the covariance matrix of the microseismic event parameter X, S = S 1 , S 2 , … , S n represents the coordinate set of each detection point in the microseismic observation system, and g denotes the spatial domain set of potential source location.

The expression of function f ⋅ varies depending on the specific problem, with the D-value optimization being the most common approach, aiming to minimize the value of column C X . John and Draper (1975) provided an in-depth discussion on the selection of D-value criterion parameters. The approximate confidence ellipsoid of the X parameter is represented by Equation 5: X − X ^ C X − 1 X − X ^ T ≤ constant (5) where X ^ is the estimated value of X, constant is the appropriate quantity, and matrix operator T represents transpose.

The steps of the ellipsoid depicted in Equation 5 are proportional to det ⁡ C X . Therefore, a clear optimization criterion is to minimize the ellipsoid shown in Equation 5 by minimizing the source parameter C X . The microseismic observation system achieves this minimization is referred to as D optimization.

Disregarding error factors such as coordinate measurements of detection points and arrival time picking, the Equation 6 for seismic wave travel time is given by: T i H , V p , X i = t i − t 0 = x i − x 0 2 + y i − y 0 2 + z i − z 0 2 V p (6) where t i is the seismic wave travel time recorded by detector i, X i x i , y i , z i is the spatial coordinate of detector i, i=1, 2, ····, n, X = x 0 , y 0 , z 0 , t 0 is the parameter x 0 , y 0 , z to be inverted for microseismic events, 0 is the spatial coordinate of the source, t 0 represent the time of the earthquake, and V p is the P-wave velocity. The seismic wave travel time T i is a function of X , V P , X i .

The covariance matrix C X of the source parameter X is presented in Equation 7: C = k A T A − 1 (7) where k is a constant and A is a partial differential matrix.

According to the basic properties of the determinant, C X satisfies the following Equation 8: det C X = det C X − 1 − 1 (8)

Therefore, the minimization problem of det C X is equivalent to the problem of det A T A . The actual microseismic location problem is much more complex than the D-value optimization theory. Matrix A and the corresponding covariance matrix C X are functions of the unknown actual source parameter X, which are unsolvable quantities. For this purpose, the partial derivative matrix A is generally calculated at the initial guess value of the actual source parameter X.

If Ω h is the spatial domain set of all microseismic events, and the probability of microseismic event H j occurring at location j is P H j , then Equation 9 holds: ∫ Ω h p h h dh = 1 (9)

Considering the randomness of the source coordinates, the average value within the location range Ω h Equation 10 can be used to replace f C X in Equation 4. f C X ¯ = ∫ Ω h p h h f C X d h (10)

Considering that the probability of microseismic events occurring at different points in the spatial domain Ω h varies, the optimal estimation of the microseismic event parameter X is ensured when the observation point s satisfying the following conditions, as shown in Equation 11: min ⁡ ∫ Ω h p h h f C X d h   s ∈ Ω s (11)

In the above derivation process, it is assumed that all n detectors in the microseismic observation system are triggered by one event. For all events, the partial derivative matrix A has the same number of rows, equal to the total number of microseismic detectors n. The fundamental assumption underlying this approach is that the energy emitted by microseismic events must be sufficiently substantial for all detectors to reliably capture the stress waves. To address this stringent assumption, Kijko and Sciocatti (1993) integrated Equation 12 within a certain range of seismic energy: min ⁡ ∫ Ω h ∫ E min E max p h h P E E f C X d E d h   s ∈ Ω s (12) where E min and E max are the minimum and maximum microseismic energies, respectively, and P E E is the probability density distribution function of the energy.

According to the basic theory of seismic wave propagation, both microseismic energy and the covariance matrix C X are functions of detection distance r. The relationship between microseismic event energy E and detection distance r as shown in Equation 13: E = c o n s t r q (13) where q is approximately equal to 2.

According to Rikitake (1976) derivation of seismic energy distribution, the probability density distribution function P r r for the detectable distance r is given in Equation 14: P r = − b d d r max − b q / d − r r min − b q / d r − 1 + b q / d (14) where b is the b value related to magnitude m and the number of events in the Gutenberg Richter equation, and d is the d value in the relationship between seismic energy E and magnitude m shown in Equation 15: log ⁡ E = c + d m (15) where d equals 1.5, and the value of b depends on the specific mine, generally ranging from 0.6 to 1.2.

Based on the above factors, the criteria for determining the optimal observation system can be obtained shown in Equation 16: min ⁡ ∫ Ω h ∫ r min r max p h h P r r f C X d r d h   s ∈ Ω s (16) where r max is the maximum detection distance, corresponding to the maximum energy release r max within the energy range. It is important to ensure that r min < r max must be ensured.

The expected standard error diagram of microseismic event parameter C X is generally used to evaluate the quality of the observation system. This method accounts not only for time error but also for uncertainties in the velocity model. The diagonal elements of matrix C X represent the variance of the seismic event parameter x 0 , y 0 , z 0 , t 0 . The standard error of the epicenter location is defined as the radius of a circle, the area of which is equivalent to the area of the ellipsoid representing the standard error of coordinate x 0 , y 0 . This standard error of the epicenter location defined in this way is expressed by Equation 17: σ x y = C x 22 C x 33 − C x 23 2 1 / 4 (17)

Due to the eigenvalues λ x 0 , λ y 0 of the covariance matrix corresponding to the two axes of the ellipse, Equation 17 can be rewritten as Equation 18: σ x y = λ x 0 λ y 0 (18)

Gong et al. (2010) proposed the calculation formula for seismic source error based on Equation 19: σ x y = λ x 0 λ y 0 λ z 0 3 (19) where λ x 0 , λ y 0 , λ z 0 corresponds to the X-axis, Y-axis, and Z-axis of the ellipsoid, respectively.

Installing detectors in deep holes within the coal seam floor positions them in the rock layers beneath, bringing them closer to the target location area and potential micro-seismic events. Based on the theory of micro-seismic localization theory, this closer proximity is expected to enhance localization accuracy. However, installing detectors in deep boreholes is complex, non-recoverable, and results in high construction costs. To strike a balance between location costs and accuracy, we utilize the D-value optimization criterion to simulate the localization error of micro-seismic events under two observation systems: the bottom-plate-depth hole observation system and the tunnel observation system.

Building on the preferred borehole-tunnel observation system, we conducted simulations to assess the spatial localization accuracy of micro-seismic location at the wellbore joint bottom plate. The simulations were performed under three P-wave arrival time picking variances: 1 ms, 5 ms, and 10 ms, while keeping consistent parameters for location range, average P-wave velocity, and P-wave velocity variance. Results for the 1 ms variance are depicted in Figure 6B, and while results for the 5 ms and 10 ms variances are illustrated in Figure 7. With picking variances of 1 ms, 5 ms, and 10 ms, the average micro-seismic location accuracy were 5.63 m, 16.67 m, and 32.04 m, respectively.

The experiment demonstrates that the precision of P-wave arrival time picking has a significant impact on micro-seismic localization accuracy. Enhancing source localization accuracy requires filtering out P-wave arrival time picks with lower precision before determining source location. To address this, this study applies deep learning techniques to identify and eliminate erroneous P-wave arrival time picks, ultimately improving the accuracy of microseismic source localization.

Building on the selected borehole-tunnel observation system, simulation were conducted to assess the spatial location accuracy for micro-seismic location at the wellbore joint bottom plate under three conditions of P-wave velocity variance:500 m/s², 200 m/s², and 20 m/s². The results of these simulations are presented in Figure 8.

According to the simulation results, when the P-wave velocity variance is 500 m/s², the source location error in the location area ranges from 10 to 50 m, with an average location accuracy of 21.52 m, which does not meet the accuracy requirements of bottom plate source location. At a P-wave velocity variance of 200 m/s², the average source location accuracy in the location area improves to 9.35 m; while a variance of 20 m/s² further reduces the average error to 3.33 m. To reliably monitor micro-seismic events on the bottom plate, micro-seismic location at the well hole joint bottom plate must be based on a high-precision velocity model.

CNNs are a prominent algorithm in deep learning, specifically a type of feedforward neural network known for its convolutional operations and deep structure. Since 2010, CNNs have achieved significant success in image and video recognition applications, including facial recognition, medical imaging, and autonomous driving. Recently, geophysicists have begun applying deep learning techniques, such as CNNs, in geophysical research. CNN models consist of input layers, multiple convolutional layers, pooling layers, fully connected layers, and output layers. An example architecture of a CNNs architecture is shown in Figure 9. The convolutional layers are responsible for feature extraction, pooling layers reduce image spatial dimensions, and fully connected layers establish connections between adjacent layers, respectively (Huang et al., 2018; Jafari et al., 2023; Viatkin et al., 2021).

The purpose of quality control for P-wave arrival time picks is to use computer intelligence to distinguish between correct and incorrect values. Building large-scale training and testing datasets is essential for developing and evaluating models to control P-wave pick quality. Using micro-seismic location waveform data from a certain mine, the AIC algorithm and manual methods were applied to pick the P-wave arrival times of micro-seismic signals. Based on the picking accuracy for each micro-seismic waveform, correct and erroneous P-wave arrival times were identified. The results of automatic picking were saved as images (Figures 10, 11) to serve as input data for the CNNs. Figures 10A, B show typical low signal-to-noise ratio (SNR) signals with P-wave picking errors, commonly due to weak microseismic signals, long propagation distances, or detector failures. Figures 10C, D show incorrect arrival time picks values for medium to high SNR signals, often caused by strong energy of S-wave energy, which conventional algorithms struggle to separate from P-wave arrivals. Figure 11 shows an example of an accurate P-wave arrival time pick with a high SNR.

As shown in Table 3, this study used 13,540 data samples collected from micro-seismic location at the 81,307 working face of a certain mine. The dataset includes 6,720 correct and 6,820 incorrect P-wave picks, with an approximate 1:1 ratio. The dataset was divided training and test sets at a 7:3 ratio, with both correct and incorrect picks proportionately distributed. The training set contains a total of 9,478 samples, comprising 4,704 correct and 4,774 incorrect picks. The test set includes 4,062 samples, with 2,016 correct and 2,046 incorrect P-wave picks.

To compare the differences in identifying incorrect P-wave pickup values among different convolutional neural network models, this study used four network models to train P-wave pickup value quality control models, including VGG-16, ResNet-50, VGG-SENet, and ResNet-SENet.

This study employs four convolutional neural network models—VGG-16, ResNet-50, VGG-SENet, and ResNet-SENet—to train P-wave pickup quality control models, allowing for a comparative analysis of each model’s effectiveness in identifying incorrect P-wave pickup values.

The input P-pickup image is set to a width and height of 128 pixels. During the training process, adjust the learning rate and evaluate the model performance by location val-acc (validation accuracy). The parameters that need to be optimized include patient, factor, and minimum learning rate (min_lr). Set the initial patient=2, factor=0.1, and min_lr=1e⁻¹⁰. The training accuracy curves of four convolutional neural network models are shown in Figure 12.

The input P-wave pickup images are configured to a resolution of 128x128 pixels. During training, the learning rate is adjusted, and model performance is evaluated by tracking validation accuracy (val-acc). Key parameters to optimize include “patience,” “factor,” and “minimum learning rate (min_lr),” initially set to ‘patience=2′, ‘factor=0.1′, and ‘min_lr=1e-10`. The training accuracy curves for the four convolutional neural network models are illustrated in Figure 12.

The training results of four CNNs models are shown in Table 4. The accuracy scores for the VGG-16,ResNet-50,VGG-SENet, and ResNet-SENet models are 0.915, 0.821, 0.848, and 0.858, respectively, with corresponding precision scores of 0.905, 0.712, 0.733, and 0.802. Among these, the VGG-16 model achieved the highest accuracy and precision for P-wave pickup quality control. Therefore, this study chose the P-wave pickup quality control model trained on VGG-16.

The frequency chart of micro-seismic events in front of the coal wall in the 81,307 working face is shown in Figure 18. Within a range of 0–40 m in front of the coal wall, micro-seismic events account for 55% of the total, with their frequency remaining relatively stable. In the range of 40–70 m, the occurrence of micro-seismic events gradually decrease. Beyond 70 m in front of the coal wall, there is a sharp decline in the number of micro-seismic events.

The trend chart showing the distance from the bottom plate micro-seismic event to the return airway plane of the 81,307 working face is shown in Figure 19. Micro-seismic events are mainly concentrated within 90 m of the second side of the return airway, accounting for 94% of the events in this area. As the distance from the return airway increases, the number of micro-seismic events decreases sharply.

The trend chart depicting the distance from the coal seam floor micro-seismic events to the coal seam floor of the 81,307 working face is shown in Figure 20. The micro-seismic events related to the coal seam floor are primarily concentrated in the area more than 30 m below the coal seam, accounts for 80% of the total events. In contrast, there are significantly fewer micro-seismic events observed in the area further than 30 m below the coal seam floor.