Deep mine earthquake probability prediction method, system and equipment based on non-stationary epidemic aftershock sequence model

Abstract

The application discloses a deep mine earthquake probability prediction method, system and equipment based on a non-stationary epidemic aftershock sequence model, and relates to the field of mine earthquake disaster early warning. The method comprises the following steps: obtaining mine earthquake data of a target deep mine area; calculating mine earthquake cascade triggering intensity and mine earthquake non-stationary background intensity based on the mine earthquake data of the target deep mine area; constructing a non-stationary ETAS model based on the mine earthquake cascade triggering intensity and the mine earthquake non-stationary background intensity; calibrating parameters in the non-stationary ETAS model based on standardized mine earthquake data; determining an expected number of high-energy mine earthquake events in a future prediction window based on the non-stationary ETAS model after parameter calibration; and determining a probability of occurrence of at least one high-energy mine earthquake in the future prediction window based on the expected number of high-energy mine earthquake events in the future prediction window. The application can accurately predict the probability of occurrence of a high-energy mine earthquake in the future prediction window of a deep mine.

Description

Technical Field

[0001] This application relates to the field of mine earthquake disaster early warning, and in particular to a method, system and equipment for predicting the probability of deep mine earthquakes based on a non-stationary aftershock sequence model. Background Technology

[0002] High-energy mine tremors are typical dynamic hazards during deep longwall coal mining, especially in geologically complex areas where their frequency and destructive intensity are significantly increased, becoming a key risk factor restricting safe mine production. Mine tremors are usually caused by underground stress concentration and rock strata fracturing resulting from mining activities. With the continuous advancement of the working face, mine tremor activity exhibits significant spatiotemporal aggregation and non-stationary evolution characteristics, leading to frequent high-energy mine tremor events. These disasters not only directly threaten the lives of underground workers but also severely damage roadway support, mining equipment, and the stability of the mine structure, disrupting normal production and significantly increasing the costs of mine safety management and disaster mitigation.

[0003] Currently, mine dynamic disaster monitoring and early warning are mostly based on microseismic monitoring data, relying on empirical indicators such as microseismic event frequency, cumulative energy release, b-value evolution, apparent stress, and spatiotemporal clustering characteristics. Disaster hazard assessment is achieved by constructing a risk index through the fusion of multiple indicators. While this method has strong engineering applicability, it has significant technical limitations: various indicators are analyzed independently for temporal, spatial, and magnitude characteristics, lacking a unified spatiotemporal coupling analysis framework, making it difficult to achieve refined probabilistic modeling of mine seismic activity; for the core prediction problem of the probability of at least one high-energy mine seismic event exceeding a set magnitude occurring in a specific area surrounding the working face within a future prediction window, which is of great concern to engineering sites, it cannot provide a rigorous statistical solution, resulting in early warning results that are biased towards qualitative judgments and insufficient quantitative prediction and risk probability assessment capabilities.

[0004] The Epidemic-Type Aftershock Sequence (ETAS) model, widely used in the field of natural seismology, characterizes the triggering relationship between mainshocks and aftershocks, providing a mature technical approach for probabilistic prediction of seismic activity. However, in the environment of deep coal mining, mine-induced seismic activity is significantly non-stationary due to the coupled influence of multiple factors such as the working face advance speed, geological structure distribution, and mining disturbance intensity. Traditional ETAS models are difficult to adapt to dynamic mining disturbance scenarios, resulting in low accuracy when applied directly. Existing research mainly focuses on simple model transplantation or parameter improvement, failing to fully integrate key covariates such as mining activities and geological conditions. There is still a significant technological gap in probabilistic prediction methods for mine-induced seismic activity that are tailored to actual mine production needs, have clear physical mechanisms, and are engineering-applicable, thus failing to meet the practical engineering requirements for quantitative probabilistic early warning of high-energy mine-induced seismic activity in deep mines. Summary of the Invention

[0005] The purpose of this application is to provide a method, system, and device for predicting the probability of high-energy mine tremors in deep mines based on a non-stationary, popular aftershock sequence model, which can accurately predict the probability of high-energy mine tremors occurring in deep mines within a future prediction window.

[0006] To achieve the above objectives, this application provides the following solution: Firstly, this application provides a method for predicting the probability of deep mine earthquakes based on a non-stationary, prevalent aftershock sequence model. The method includes: Acquire mining seismic data, which includes: the occurrence time of historical mining seismic events in the target deep mining area, the spatial location of the epicenter of historical mining seismic events, the magnitude information of historical mining seismic events, historical mining face advancement data, and historical geological fault spatial distribution data; The intensity of cascading mine seismic events is calculated based on the occurrence time, spatial location of the epicenter, and magnitude information of the historical mine seismic events. The non-stationary background intensity of mining earthquakes is calculated based on the occurrence time of the historical mining earthquake events, the spatial location of the epicenter of the historical mining earthquake events, the historical mining face advancement data, and the historical geological fault spatial distribution data. Based on the cascade triggering intensity of the mine earthquake and the non-stationary background intensity of the mine earthquake, a non-stationary popular aftershock sequence ETAS model is constructed. The parameters in the non-stationary ETAS model are calibrated based on standardized seismic data. The expected number of high-energy mine tremor events within the future prediction window is determined based on the non-stationary ETAS model after parameter calibration. The probability of at least one high-energy mineral tremor occurring within the future prediction window is determined based on the expected number of high-energy mineral tremors within the future prediction window.

[0007] Secondly, this application provides a deep mine earthquake probability prediction system based on a non-stationary, prevalent aftershock sequence model, including: The data acquisition module is used to acquire mine seismic data, which includes: the occurrence time of historical mine seismic events in the target deep mining area, the spatial location of the epicenter of historical mine seismic events, the magnitude information of historical mine seismic events, historical mining face advancement data, and historical geological fault spatial distribution data. The mine earthquake cascade triggering intensity calculation module is used to calculate the mine earthquake cascade triggering intensity based on the occurrence time of the historical mine earthquake events, the spatial location of the source of the historical mine earthquake events, and the magnitude information of the historical mine earthquake events. The non-stationary background intensity calculation module for mine earthquakes is used to calculate the non-stationary background intensity of mine earthquakes based on the occurrence time of the historical mine earthquake events, the spatial location of the epicenter of the historical mine earthquake events, the historical mining face advancement data, and the historical geological fault spatial distribution data. The non-stationary ETAS model construction module is used to construct a non-stationary popular aftershock sequence ETAS model based on the cascade triggering intensity of the mine earthquake and the non-stationary background intensity of the mine earthquake. The parameter calibration module is used to calibrate the parameters in the non-stationary ETAS model based on standardized seismic data. The expected number determination module is used to determine the expected number of high-energy mining tremor events within the future prediction window based on the non-stationary ETAS model after parameter calibration. The probability prediction module is used to determine the probability that at least one high-energy mineral tremor will occur within the future prediction window based on the expected number of high-energy mineral tremor events within the future prediction window.

[0008] Thirdly, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the deep mine earthquake probability prediction method based on a non-stationary popular aftershock sequence model as described above.

[0009] According to the specific embodiments provided in this application, this application has the following technical effects: The physical mechanism is clear: By introducing a non-stationary background intensity, this application can more clearly decompose the cascading triggering process between the background stress loading caused by mining activities and seismic events, thereby enhancing the interpretability and physical basis of the prediction results.

[0010] High prediction accuracy: This application constructs a non-stationary ETAS model based on the cascade triggering intensity of mine seismic events and the non-stationary background intensity of mine seismic events. It can truly reflect the non-stationary, time-varying, and spatially varying laws of mine seismic activity as mining progress and stress migration occur. Compared with the traditional stationary ETAS model, it is more consistent with the occurrence mechanism of mine seismic events in deep coal mines. Using a standardized mine seismic dataset as input, the parameters in the non-stationary ETAS model are calibrated by maximizing the log-likelihood function, thereby improving the accuracy of model prediction.

[0011] Strong spatial positioning capability: The non-stationary ETAS model of this application introduces non-stationary background intensity, which can dynamically locate high-risk areas in front of the work area. The predicted location of high-energy vibrations is highly consistent with the actual situation, providing guidance for taking precise local prevention and control measures.

[0012] Highly practical: This application directly utilizes existing microseismic monitoring data from the target mine, with a systematic modeling framework and standardized evaluation process, providing an operable technical foundation for dynamic and quantitative short-term disaster early warning in deep longwall coal mines.

[0013] Comprehensive Risk Assessment: This application can integrate the occurrence time of historical mining earthquake events, the spatial location of the epicenter of historical mining earthquake events, the magnitude information of historical mining earthquake events, the advance data of historical mining faces, and the spatial distribution data of historical geological faults, overcoming the limitations of single model data processing and achieving a more comprehensive and reliable risk zoning. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 A flowchart illustrating a method for predicting the probability of deep mine earthquakes based on a non-stationary, popular aftershock sequence model, provided in Embodiment 1 of this application; Figure 2(a) is a schematic diagram of the daily microseismic events and the time distribution of high-energy events at the 6306 working face of the Dongtan Coal Mine provided in Embodiment 2 of this application; Figure 2(b) is a schematic diagram of the local magnitude distribution of microseismic events at the 6306 working face of the Dongtan Coal Mine over time provided in Embodiment 2 of this application; Figure 2(c) is a schematic diagram of the cumulative frequency-magnitude distribution of microseismic events at the 6306 working face of the Dongtan Coal Mine provided in Embodiment 2 of this application; Figure 2(d) is a schematic diagram of the temporal evolution of the integrity magnitude at the 6306 working face of the Dongtan Coal Mine calculated based on a sliding 60-day window provided in Embodiment 2 of this application. Figure 3(a) is a schematic diagram of the total information gain of the stationary ETAS model and the non-stationary ETAS model provided in Embodiment 2 of this application relative to the smooth Poisson model; Figure 3(b) is a schematic diagram of the time rescaling residual of the non-stationary ETAS model provided in Embodiment 2 of this application; Figure 3(c) is a schematic diagram of the evolution of the daily background rate of the non-stationary ETAS model provided in Embodiment 2 of this application over time. Figure 4(a) is a statistical diagram of the number of daily observed microseismic events at the 6306 working face of Dongtan Coal Mine provided in Embodiment 2 of this application; Figure 4(b) is a schematic diagram of the number of daily background events and the number of triggered events based on the non-stationary ETAS model decomposition provided in Embodiment 2 of this application; Figure 4(c) is a schematic diagram of the daily branch ratio time series curve of the number of triggered events and the total number of observed events on the same day provided in Embodiment 2 of this application. Figure 5(a) is a background-weighted planar schematic diagram of seismic activity at the 6306 working face of the Dongtan Coal Mine provided in Embodiment 2 of this application; Figure 5(b) is a background-weighted cross-sectional schematic diagram of seismic activity at the 6306 working face of the Dongtan Coal Mine provided in Embodiment 2 of this application; Figure 5(c) is a triggered-weighted planar schematic diagram of seismic activity at the 6306 working face of the Dongtan Coal Mine provided in Embodiment 2 of this application; Figure 5(d) is a triggered-weighted cross-sectional schematic diagram of seismic activity at the 6306 working face of the Dongtan Coal Mine provided in Embodiment 2 of this application; Figure 5(e) is a magnitude distribution map of triggered events, non-triggered parent events, and non-triggered isolated events provided in Embodiment 2 of this application; Figure 5(f) is a distance distribution map of triggered events, non-triggered parent events, and non-triggered isolated events from the working face provided in Embodiment 2 of this application. Figure 6(a) is a schematic diagram of the 24-hour high-energy mine earthquake prediction probability time series of the non-stationary ETAS model and the stationary ETAS model provided in Embodiment 2 of this application; Figure 6(b) is a schematic diagram of the hit rate and false alarm rate of the non-stationary ETAS model provided in Embodiment 2 of this application under different probability thresholds. Figure 7(a) is a schematic diagram of spatial probability prediction of the non-stationary ETAS model provided in Embodiment 2 of this application in the first representative mining stage; Figure 7(b) is a schematic diagram of spatial probability prediction of the non-stationary ETAS model provided in Embodiment 2 of this application in the second representative mining stage; Figure 7(c) is a schematic diagram of spatial probability prediction of the non-stationary ETAS model provided in Embodiment 2 of this application in the third representative mining stage; Figure 7(d) is a schematic diagram of spatial probability prediction of the non-stationary ETAS model provided in Embodiment 2 of this application in the fourth representative mining stage. Figure 8(a) is a schematic diagram of the distance-time evolution of the 24-hour high-energy seismic probability along the working face normal of the non-stationary ETAS model provided in Embodiment 2 of this application; Figure 8(b) is a schematic diagram of the comparison curve of the high-energy event spatial prediction coverage between the non-stationary ETAS model and the stationary ETAS model provided in Embodiment 2 of this application. Detailed Implementation

[0016] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0017] The non-stationary ETAS model constructed in this application is used for short-term probability early warning of high-energy mine-induced tremors in deep longwall coal mines. This model incorporates mining-related variables into a spatiotemporal point process framework, constructing a driving model that dynamically changes the background seismic activity rate with mining conditions, thus achieving accurate modeling of non-stationary seismic activity in the mining area. After parameter calibration based on a high-quality microseismic catalog, the model can make short-term probability predictions for high-energy mine-induced tremors (ML≥1.0), achieving a hit rate of 94.25% within a 24-hour prediction window, and can accurately identify high-risk areas ahead of the working face. By further integrating ETAS probability results, Coulomb stress changes, and precursor event density, a composite hazard assessment model is constructed to achieve stable identification of high-risk areas underground.

[0018] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0019] Example 1: In one exemplary embodiment, such as Figure 1 As shown, a method for predicting the probability of deep mine earthquakes based on a non-stationary, circulating aftershock sequence model is provided. This method is executed by computer equipment, specifically by a terminal or server alone, or by both a terminal and a server. In this embodiment, the method for predicting the probability of deep mine earthquakes based on a non-stationary, circulating aftershock sequence model includes steps 1 to 7. Wherein: Step 1: Obtain mining seismic data, which includes: the occurrence time of historical mining seismic events in the target deep mining area, the spatial location of the epicenter of historical mining seismic events, the magnitude information of historical mining seismic events, historical mining face advancement data, and historical geological fault spatial distribution data.

[0020] Step 2: Calculate the cascading trigger intensity of the mine earthquake based on the occurrence time, spatial location of the epicenter, and magnitude information of the historical mine earthquake events.

[0021] Step 3: Calculate the non-stationary background intensity of mining earthquakes based on the occurrence time of the historical mining earthquake events, the spatial location of the epicenter of the historical mining earthquake events, the historical mining face advancement data, and the historical geological fault spatial distribution data.

[0022] Step 4: Construct a non-stationary ETAS model based on the cascade triggering intensity of the mine seismic event and the non-stationary background intensity of the mine seismic event.

[0023] Step 5: Calibrate the parameters in the non-stationary ETAS model based on standardized seismic data; This embodiment also employs the parameter bootstrap method to perform uncertainty and correlation analysis on the non-stationary ETAS model after parameter calibration, obtains parameter confidence intervals, and quantifies and verifies the uncertainty of the non-stationary ETAS model.

[0024] Step 6: Determine the expected number of high-energy mine seismic events within the future prediction window based on the non-stationary ETAS model after parameter calibration.

[0025] In this embodiment, the expected number of high-energy seismic events within the future prediction window is determined based on a parameter-calibrated non-stationary ETAS model. Specifically, this includes: setting a high-energy magnitude threshold; and using a Gutenberg-Richter magnitude distribution model to fit the magnitude information of the historical seismic events. Value; based on the high-energy magnitude threshold and The value is used to calculate the proportion of events exceeding the high-energy magnitude threshold; based on the proportion of events exceeding the high-energy magnitude threshold, the conditional intensity of the high-energy mining earthquake event is calculated; based on the conditional intensity of the high-energy mining earthquake event, the expected number of high-energy mining earthquake events within the future prediction window is calculated.

[0026] Step 7: Determine the probability that at least one high-energy mineral tremor will occur within the future prediction window based on the expected number of high-energy mineral tremor events within the future prediction window.

[0027] In this embodiment, after determining the probability of at least one high-energy mine tremor occurring within the future prediction window based on the expected number of high-energy mine tremor events within the future prediction window, the method further includes: converting the probability of at least one high-energy mine tremor occurring within the future prediction window into a binary observation value, and calculating the Brier score, information gain, hit rate, and false alarm rate based on the binary observation value and the original probability value of at least one high-energy mine tremor occurring within the future prediction window to evaluate the prediction performance of the non-stationary ETAS model.

[0028] Example 2: In an exemplary embodiment, taking the 6306 working face of the Dongtan Coal Mine as an example, the deep mine earthquake probability prediction method based on the non-stationary aftershock sequence model in this application will be further explained and described in detail below: S1: Create a dataset; the dataset includes: the occurrence time of historical mining earthquake events in the target deep mining area, the spatial location of the epicenter of historical mining earthquake events, the magnitude information of historical mining earthquake events, historical mining face advancement data, and historical geological fault spatial distribution data; the data in the dataset comes from the earthquake catalog.

[0029] The earthquake catalog analyzed in this embodiment spans from December 3, 2024 to November 5, 2025. During this period, a total of 6,575 microseismic events and 115 high-energy events were detected and reliably located. High-energy vibrations are defined as ML ≥ 1.0 according to mine operation standards. To ensure the accuracy of the dataset in terms of time and magnitude, a rigorous quality control procedure was adopted, including removing duplicate events, correcting for time errors, and cross-validating with multiple stations to ensure the completeness and reliability of the dataset.

[0030] Specifically, as shown in Figure 2(a), the temporal evolution of the catalog exhibits significant non-stationarity. Daily event rates fluctuate by more than two orders of magnitude, closely correlated with longwall advance, temporary shutdowns, and subsequent mining resumption cycles. As shown in Figure 2(b), high-energy events occur sporadically during monitoring, typically concentrated in phases of high seismic productivity. This pattern suggests that slow stress accumulation and rapid stress redistribution jointly drive seismic excitation in this dynamic stress environment. As shown in Figure 2(c), the catalog's integrity was assessed using the cumulative frequency-magnitude distribution. It can be seen that for magnitudes above Mc = -0.42, a stable Gutenberg-Richter linear segment is obtained, with a b-value of approximately 1.20. Such a high b-value is characteristic of highly fractured layers affected by stress disturbances caused by continuous mining. As shown in Figure 2(d), to capture possible temporal variations in detection capability, this embodiment further quantifies integrity within a sliding 60-day window, resulting in Mc(t) fluctuating between approximately -0.7 and -0.3. The temporary decrease in integrity coincides with the production interruption in early 2025, subsequently recovering gradually as mining progresses and sensor performance stabilizes. Despite the temporal variations in seismic data, the catalog remained sufficiently complete throughout the study period to support robust calibration of the non-stationary ETAS model.

[0031] S2: Based on the dataset, calculate the cascade triggering intensity of mine seismic events and the non-stationary background intensity of mine seismic events, and construct a non-stationary ETAS model based on the cascade triggering intensity of mine seismic events and the non-stationary background intensity of mine seismic events. In this embodiment, the mine tremors caused during the mining process are considered as a spatiotemporal point process, and the ETAS conditional intensity is used for modeling to obtain a non-stationary ETAS model: ; in, This indicates the impact of all historical mining earthquake events. This indicates the impact of all historical mining earthquake events. time The strength of the conditions at the location, Indicates in time The non-stationary background intensity of the mine seismic activity at the location. Indicates the first The magnitude of the mine earthquake event. Indicates the first Productivity of a single mining earthquake event Indicates the first The mining earthquake event from the moment of occurrence Up to the current moment The time-triggered kernel function, Indicates the first Under the influence of the magnitude of the first mining earthquake event The earthquake event was caused by the location of the epicenter. To the current location Space-triggered kernel function, .

[0032] Productivity parameterization is as follows: ; in, For reference productivity, This is a magnitude scaling parameter used to control the dependence of the expected number of sub-events on the magnitude. This is the minimum triggering magnitude.

[0033] Time-triggered kernels follow a modified Omori-Utsu law: ; in, Indicates time offset. Indicates the time decay exponent. , .

[0034] If the data requires, long-term exponential decay or fractional power tails can be tested, but benchmark analysis uses the standard Omori-Utsu form.

[0035] In this embodiment, the spatial kernel function is defined in a local coordinate system aligned with the strike of the working face or fault, including the strike direction (s) and the vertical direction (n). The relative displacements between events are obtained by transforming the microseismic event locations from the global coordinate system to this local coordinate system. .

[0036] The formula for the space-triggered kernel function is as follows: ; in, , It is a normalization function. This is the spatial attenuation coefficient, used to control spatial attenuation. Characteristic length along the working face or fault strike and the characteristic length perpendicular to the working face or fault strike direction. As the magnitude changes, the formula is expressed as: ; in, (i.e., the characteristic length along the working face or fault strike) Or a characteristic length perpendicular to the working face or the strike direction of the fault. ), (i.e., the reference spatial trigger length along the working face or fault direction) Or the reference spatial trigger length perpendicular to the working face or fault strike. ), Controls the scaling of the space coverage area.

[0037] In this embodiment, the event magnitude is assumed to follow a Gutenberg-Richter distribution and be greater than 1. : ; in, This indicates that the event magnitude is greater than or equal to the minimum triggering magnitude. Under the premise that the magnitude is exactly equal to The probability density, The exponential attenuation coefficient of the magnitude distribution. and Value related, To better represent the high-energy tail and ensure model stability under large earthquake events, a modified GR distribution can be used in the sensitivity test.

[0038] In this embodiment, condition strength Decomposed into background items And triggering contribution factors. For fully mechanized mining faces, the background rate cannot be considered stationary because seismic activity is strongly influenced by the advance of the coal mining front and existing faults. Therefore, this embodiment will... Modeled as an explicit function of mining and structural covariates.

[0039] In the background item In the calculation process, a local coordinate system aligned with the working face is first established. Using an inclination angle of approximately 10° to the global X-axis and the cumulative advance of the upper and lower roadways, the daily position of the working face segment is reconstructed from the footage. For each occurrence... For each event, calculate its signed normal distance to the current working face: ; in, express time Enter the work area in front of the work station. Indicates the direction of the normal relative to the midpoint of the working surface. Projection; positive values ​​indicate the face is located in front of the working face, and negative values ​​indicate the face is located in the goaf. In addition, the footage also provides the daily working face advance rate: ; in, This indicates the daily increase in the advance of the return airway. This indicates the daily increase in the advance of the transport tunnel. express The speed of the working face advance at any given moment reflects the time... Mining intensity at any given moment.

[0040] To account for structural features, this embodiment extracts the fault strike from the detailed mine map and calculates the location of each seismic source. Minimum horizontal distance to the plotted fault: ; in, Indicates the location of the earthquake source. Minimum horizontal distance to the fault This represents a collection of faults within a mining area. Indicates the first Fault, Indicates the location of the earthquake source. The minimum horizontal distance to the fault. Combining these covariates, the non-stationary background rate can be written as a log-linear function: ; in, Indicates in time The non-stationary background intensity of the mine seismic activity at the location. , , , This represents the regression coefficients jointly estimated with the ETAS trigger parameters. for time A scaled representation of the position of the worker in front of the work position. for A standardized representation of the working face advance speed at any given moment. for Scaled representation of the minimum horizontal distance from location to fault, including covariates , , Converting to a scaled version improves numerical stability.

[0041] S3: Using a standardized seismic dataset as input, the parameters in the non-stationary ETAS model are calibrated by maximizing the likelihood function; In this embodiment, the parameter vector in the non-stationary ETAS model is By using a fixed global integrity magnitude Under the given conditions, the log-likelihood function of the earthquake catalog data is maximized and estimated, where At the same time, as the minimum triggering magnitude .

[0042] Integrity Magnitude in this Embodiment The minimum trigger magnitude is obtained by fitting the magnitude frequency distribution in Figure 2(c) and estimating within the sliding time window shown in Figure 2(d), and is used to reflect the detection capability of the monitoring system. Usually taken as Or its stable estimate, to ensure that the model parameter estimation is based on the complete sample.

[0043] The log-likelihood of the spatiotemporal point process in this embodiment is: ; in, The output value of the likelihood function. For the first The logarithmic conditional strength of each observed event at its time and location is used to characterize how well the model fits the observed events. In the collection of historical events The spatiotemporal condition intensity function under certain conditions is used to describe the occurrence rate of events per unit time and unit space. As a window for future prediction, For a specific spatial region.

[0044] In this embodiment, the calibration of the non-stationary ETAS model demonstrates its ability to capture the main temporal patterns of microseismic activity at the 6306 working face, while providing a physically interpretable decomposition of background loading and source triggering.

[0045] Table 1 shows the comparison of the fitting performance of the smooth Poisson model, the stationary ETAS model, and the non-stationary ETAS model on the same dataset. The results in Table 1 are based on the microseismic event catalog data of the 6306 working face of the Dongtan Coal Mine. First, the parameters of the smooth Poisson model, the stationary ETAS model, and the non-stationary ETAS model were estimated using all microseismic events (including occurrence time, spatial location, and magnitude information) during the study period. For each model, the optimal parameters were obtained by maximizing the log-likelihood function of the spatiotemporal point process, and the corresponding log-likelihood value was calculated. Based on this, the AIC and BIC information criteria were further calculated to evaluate the balance between fitting accuracy and complexity of the model. At the same time, using the smooth Poisson model as a benchmark, the single-event information gain was calculated to quantify the improvement of the ETAS model relative to the benchmark model.

[0046] Table 1 Comparison of Model Variants

[0047] As shown in Table 1, the comparison between the non-stationary ETAS model constructed in this embodiment and the uniform Poisson process and stationary ETAS models highlights the strong clustering of mine-induced earthquakes. The total information gain of the two ETAS models is significantly better than that of the Poisson baseline model, as shown in Figure 3(a), where the total information gain (ΔlogL) of the non-stationary ETAS model is 4213.7. Although the stationary ETAS model achieves a slightly higher likelihood value, this difference reflects its tendency to attribute all temporal variations to triggering cascades. In contrast, the non-stationary ETAS model redistributes some temporal variations to the temporally varying background event rate, thus providing a seismic activity representation that is more consistent with the evolution of the stress environment induced by mining.

[0048] As shown in Figure 3(b), the adaptability of the non-stationary ETAS model is validated by its time-reconstructed residuals, which approximate the expected uniform distribution. The absence of systematic bias indicates that the model can capture both rapid triggering dynamics and the slower changes in mining-driven seismic rates, providing statistical support for the introduction of a time-varying background term. As shown in Figure 3(c), a key feature of the non-stationary ETAS model is the reconstruction of its background rate variations. The inferred time-varying background term exhibits large-scale structural fluctuations—ranging from approximately 1 to more than 4 events / day—corresponding to known mining cycles, including working face shutdown, recovery, and accelerated mining phases. These changes precede changes in overall seismic productivity and the occurrence of high-energy events, revealing that background loading, rather than simple cascading triggering, dominates the accumulation of seismic hazard. Stationary background rates cannot reproduce these dynamics, highlighting the necessity of non-stationary modeling.

[0049] S4: The parameter bootstrap method is used to perform uncertainty and correlation analysis on the non-stationary ETAS model after parameter calibration, and the parameter confidence interval (95% bootstrap confidence interval) is obtained to quantify and verify the uncertainty of the non-stationary ETAS model.

[0050] In this embodiment, due to the relatively short and non-stationary nature of the seismic catalog, the asymptotic standard error may be unreliable. To assess the uncertainty of the parameters and its impact on prediction, a synthetic catalog is simulated from the fitted ETAS model using a parameter bootstrap method. Parameters are re-estimated for each realization, and confidence intervals are constructed using the empirical distribution estimated by the bootstrap method. This propagates the uncertainty to the conditional intensity of high-energy seismic events. The probability of at least one high-energy mineral tremor occurring within the future prediction window is determined by the expected number of high-energy mineral tremors within the future prediction window. middle.

[0051] In this embodiment, parameter uncertainty is assessed using the bootstrap method. The parameter estimation results and their uncertainty analysis are shown in Table 2. It can be seen that the estimated values ​​of each parameter are concentrated and have a limited range of fluctuation, without obvious multimodal or abnormal skewness phenomena, indicating that the non-stationary ETAS model parameters in this embodiment have good stability and reliability.

[0052] Table 2. Calibration parameters of the preferred non-stationary ETAS model for the 6306 working face.

[0053] The parameter estimates in Table 2 indicate that the model's triggering parameter ( ≈ 0.040, ≈ 1.60, ≈ 0.016 days The value ≈ 0.083 falls within the range of mine seismic characteristics, indicating that the aftershock sequence has moderate productivity and rapid decay. Mining covariates have a statistically significant and physically interpretable impact on seismic activity: as the working face approaches a certain location ( <0), daily advance rate increases ( >0), and enhancement when near the fault ( >0). These effects quantify how mining geometry and geological structure modulate the... The captured background is loading.

[0054] S5: Based on the parameter-calibrated non-stationary ETAS model, determine the expected number of high-energy mineral seismic events within the future prediction window, specifically including: S501: Set the high-energy magnitude threshold; S502: Obtained by fitting the magnitude information of the historical mining seismic events using the Gutenberg–Richter magnitude distribution model. value; S503: Based on the aforementioned high-energy magnitude threshold and The value is used to calculate the proportion of events exceeding the high-energy magnitude threshold, expressed by the formula: ; in, Indicates the magnitude of the mining earthquake event. Indicates the high-energy magnitude threshold. This indicates that the high-energy magnitude threshold has been exceeded. The proportion of events, , Indicates the minimum triggering magnitude; S504: Based on the proportion of events exceeding the high-energy magnitude threshold, calculate the conditional intensity of high-energy mine-related seismic events, expressed by the formula: ; in, This indicates the impact of all historical mining earthquake events. This indicates the impact of all historical mining earthquake events. time The conditional intensity of high-energy mineral seismic events at the location. This indicates the impact of all historical mining earthquake events. time Conditional strength at the location; S505: Based on the conditional intensity of the high-energy seismic events, calculate the expected number of high-energy seismic events within the future prediction window, expressed by the formula: ; in, Indicates the future prediction window [ , ] and spatial regions The expected number of high-energy seismic events in the interior. .

[0055] S6: Determine the probability of at least one high-energy mineral tremor occurring within the future prediction window based on the expected number of high-energy mineral tremors within the future prediction window, expressed by the formula: ; in, Indicates the future prediction window [ , ] and spatial regions The probability of at least one high-energy mine tremor occurring within the area.

[0056] In this embodiment, in order to analyze the triggering structures associated with the long wall, a nearest neighbor network was constructed, using spatiotemporal magnitude distance, and events were classified into triggering events, non-triggering parent events (NT-parent), and non-triggering isolated events (NT-isolated). The distribution patterns of potential parent events and isolated small events in the compressive stress zone were analyzed, and patterns similar to foreshock-mainshock structures in the long wall were identified.

[0057] Specifically, the non-stationary ETAS model provides a physically based decomposition of seismic activity, dividing it into background loading and cascaded triggering events. The temporal evolution of this decomposition is shown in Figures 4(a)–4(c). As shown in Figure 4(a), the observed number of diurnal seismic events is primarily dominated by highly intermittent bursts, which the model attributes mainly to triggering events. As shown in Figure 4(b), the expected background contribution remains relatively low and changes slowly, while triggering activity rises sharply during clustering, producing the typical pulse-like behavior of mine seismic events. As shown in Figure 4(c), the diurnal branching ratio frequently approaches or exceeds 0.8, indicating that once stress disturbances are introduced, the system evolves through a cascaded amplification mechanism, rather than simply external forcing. Such a high branching ratio reflects a rock mass with critical stress, where small disturbances can propagate rapidly.

[0058] Spatial patterns further clarify the interaction between loading and triggering. As shown in Figures 5(a) and 5(b), background-weighted seismic activity is concentrated near the advancing working face and in structurally heterogeneous regions, representing a long-term stress redistribution caused by mining. In contrast, as shown in Figures 5(c) and 5(d), triggered events form compact and spatially coherent clusters, which typically appear at the edges of high background areas or in areas of geometric stress concentration. High-energy vibrations tend to occur in areas where background loading overlaps with strong triggering potential, consistent with a two-stage nucleation process in which sustained stress accumulation activates the system, and cascading propagation increases the probability of local failure. As shown in Figures 5(e) and 5(f), different categories of events exhibit systematic differences in magnitude and distance from the working face. Triggered events and their non-triggered parent events are mainly distributed in the medium to large magnitude range and are generally more concentrated near the working face, indicating higher stress concentration levels and stronger rupture connectivity in these areas. In contrast, non-triggered isolated events are typically smaller in magnitude and more spatially dispersed, possibly corresponding to areas with lower stress levels or weaker mechanical coupling. This differentiation indicates that the background-dominant activities, cascade-dominant propagation, and event chain initiation processes in the seismic system have distinguishable characteristics in statistical distribution.

[0059] To reveal the internal structure of these cascades, as shown in Table 3, this embodiment classifies each event into triggering events, NT-parent events, or NT-isolated events. This classification comes directly from the posterior triggering probabilities calculated by the model and the inferred parent-child event network. Triggering events have a probability ptrig ≥ 0.5 and a valid parent event index, indicating that their occurrence is primarily driven by interactions with the aforementioned events. Events that do not meet this criterion but are the parent events of at least one triggering event are labeled as NT-parent events; although they originate from background processes, their position in the developing stress field gives them dynamic influence, enabling them to initiate numerous triggering cascades. The remaining events, which neither trigger nor are triggered by other events, form the NT-isolated class, representing background responses that do not participate in the broader cascade dynamics.

[0060] Table 3. Classification of Triggering Events, NT-parent Events, or NT-isolated Events

[0061] S7: Convert the probability of at least one high-energy mineral tremor occurring within the future prediction window into a binary observation value, and calculate the Brier score, information gain, hit rate, and false alarm rate based on the binary observation value and the original probability value of at least one high-energy mineral tremor occurring within the future prediction window to evaluate the prediction performance of the non-stationary ETAS model.

[0062] This embodiment evaluates the time prediction performance of three models: a smoothed Poisson baseline model, a static ETAS model, and a non-stationary ETAS model based on mining area covariates. Based on mining area experience, the model selected... (Approximately 10⁵ joules of energy) is used as the threshold for high-energy events. For each model, at least one high-energy event is calculated to occur. In the prediction window The probability within each prediction window, and for each prediction window Define a binary observation for: ; The three models output their respective probabilities. ,Right now The probability of.

[0063] To quantify the quality of probabilistic predictions, this embodiment uses the Brier score and log-likelihood value, and employs a probability-based threshold to evaluate binary alarms. Hit rate and false alarm statistics.

[0064] Brier's score is defined as: ; in, It represents the number of prediction windows. It measures the mean squared error of probabilistic predictions; a smaller value indicates better calibration and sharpness.

[0065] The log-likelihood of Bernoulli observations with given probabilities is: ; In this embodiment, the information gain of the non-stationary ETAS model or the stationary ETAS model relative to the smooth Poisson baseline model for each window can be calculated using the following formula: ; in, This represents the information gain of a non-stationary or stationary ETAS model relative to a smooth Poisson baseline model per window. A positive value indicates that the model provides more information than the time-independent Poisson baseline. This represents the total log-likelihood value across the entire prediction window for both non-stationary and stationary ETAS models. This represents the total log-likelihood of the smoothed Poisson baseline model across all prediction windows.

[0066] To evaluate alarm performance, this embodiment converts the probability into a binary alarm using a threshold pthresh. If the window... of An alarm will be issued if the alarm is triggered. The alarm will be compared with the observed value. By comparing the results, we can identify four categories: hit: alerts and events ( ); Miss (missed report): An event occurred without an alert. ); False alarm: An alarm is triggered but no event occurs. ); Correct negative: No alarms and no events. ).

[0067] Hit rate and false alarm rate are defined as follows: ; ; Hit rate measures the proportion of event windows that are successfully predicted, while false alarm rate measures the proportion of all prediction windows that issue an alert but no event occurs.

[0068] This embodiment explores different prediction window lengths ΔT, ranging from several hours to two days, and calculates the Brier score and information gain for three models for each prediction window length ΔT. For the non-stationary ETAS model, this embodiment also scans the alarm threshold pthresh ∈ [0.01, 0.50] with a step size of 0.01, evaluating the corresponding hit rate and false alarm rate. Under the daily prediction scheme, very short windows of 1-6 hours contain too few positive windows to generate stable statistics, while very long windows of 36-48 hours lead to excessive window overlap, obscuring the interpretation of alarm statistics. The most robust and operationally meaningful configuration is a 24-hour prediction window. To evaluate the prediction model's ability to predict hazardous periods, this embodiment divides the catalog into 336 non-overlapping 24-hour windows, of which 87 windows contain at least one high-energy (HE) event.

[0069] As shown in Figure 6(a), the non-stationary ETAS model produces a significant probability surge, closely tracking the onset of high-energy seismic clusters, accurately capturing most dangerous periods, and exhibiting clear and interpretable peaks. In contrast, the static model reacts more slowly, systematically assigning lower probabilities before several high-energy events occur. Under the non-stationary model, missed events (red crosses) are few, mainly occurring as isolated events outside the main activation period. False alarms (orange triangles) mostly appear in the decay phase after large clusters, consistent with the ETAS triggering mechanism, where conditional strength persists after significant events.

[0070] Figure 6(b) illustrates the threshold dependence; as the threshold increases, both the hit rate and false alarm rate decrease monotonically. The selected pthresh=0.05 value falls within a region where the non-stationary ETAS model maintains a high hit rate while keeping the false alarm rate manageable, providing a practical balance for daily short-term hazard assessment.

[0071] Table 4 Predicted performance indicators of the 6306 working face

[0072] As shown in Table 4, within a 24-hour prediction window, with pthresh=0.05, the non-stationary ETAS model exhibited the strongest predictive ability, successfully identifying 82 out of 87 high-energy windows, achieving a hit rate of 94.25%. Simultaneously, it generated 123 false positives and 126 correct negatives, resulting in a false positive rate of 36.61% and an overall accuracy of 61.90%. This performance demonstrates that the mine-induced non-stationarity captured through covariate-driven background rates provides crucial predictive information, enabling the model to respond rapidly to constantly changing stress conditions.

[0073] The static ETAS model lacks covariate-based adjustment, exhibiting a weak response to seismic changes. It detected 66 high-energy windows (75.86% hit rate), missed 21, generated 105 false alarms and 144 correct negatives, with a false alarm rate of 31.25% and an accuracy of 62.50%. Although superior to the Poisson model, its smoother and less sensitive probability field led to the missed detection of several high-energy days and its inability to identify emerging seismic clusters in a timely manner.

[0074] The smoothed Poisson baseline model issued alarms almost continuously, detecting all high-energy windows, resulting in 87 hits and 0 false negatives, but also 249 false positives and 0 correct negatives—a false positive rate of 74.11% and an accuracy of only 25.89%. Due to its lack of time adaptability, despite its perfect hit rate, it is not suitable for practical use.

[0075] In summary, the non-stationary ETAS model in this embodiment offers a significant improvement in representing the temporal dynamics of high-energy mine-induced seismic events. By allowing the background rate to evolve with mining activity and stress redistribution, the model produces sharper and more responsive probability peaks, enabling high-fidelity prediction of hazardous clusters and maintaining a significantly higher hit rate than any static model. The alignment of predicted surges with observed seismic sequences, along with a significant reduction in missed events, confirms the criticality of incorporating mine-induced non-stationarity into predictions for reliable short-term high-energy mine-induced seismic events. This makes the non-stationary ETAS model a reliable basis for operational early warning strategies in deep longwall mining environments.

[0076] This embodiment uses a sliding window of the mining timeline of the coal face to estimate ETAS parameters from historical data and generate future parameters. of , and The forecasting ability is evaluated by using the log-likelihood of time-point processes and the information gain compared to a simple reference model. The prediction of event occurrence, quantity, spatial distribution, magnitude distribution and clustering structure is evaluated using likelihood-based marginal and conditional scores, respectively. This avoids the limitations of grid-based Poisson tests and is more suitable for clustered mine seismic activity on the working face.

[0077] In this embodiment, the spatial performance of the non-stationary ETAS model is evaluated through four representative working face advancement stages, which represent various geological structures encountered during longwall mining: the first representative mining stage – the working face approaches but has not yet interacted with the nearest normal fault; the second representative mining stage – initial contact with the fault; the third representative mining stage – complete passage through the fault zone; and the fourth representative mining stage – crossing the fault into a more homogeneous formation. These four representative mining stages cover the major transitions in frontal stress concentration, structural disturbance, and seismic response.

[0078] As shown in Figures 7(a)-7(d), in these four representative mining stages, the non-stationary model generated distinctly localized, forward-looking probability bands that closely adhered to the active working face and intensified with fault approach and stress gradient changes. The predicted hazards migrated consistently with the advancement of the working face, reproducing the anticipated forward stress amplification and structural modulation by normal faults. Except for the initial case (when overall seismic activity was low and the working face had not yet approached strong structural differences), the high-energy (HE) vibrations observed within the prediction window all fell within these predicted high-probability regions. This spatial consistency indicates that the non-stationary ETAS model captures the main physical factors controlling the localization of high-energy vibrations in longwall environments.

[0079] In contrast, the probability distribution generated by the stationary ETAS model is primarily dominated by short-term earthquake clustering, rather than the influence of mining area geometry or structural background. High-probability areas persist over the previous day's microseismic clusters, even after significant migration of the active working face, and the model fails to reproduce the steep spatial asymmetry characteristic of stress concentration caused by mining. While both models generate probabilistic predictions, the probability value of the stationary ETAS model drops to an extremely small value (approximately 10). -6 These values ​​are statistically consistent with the homogeneous background assumption, but are not very effective in identifying space hazards in practical applications. The probabilities of the non-stationary model (0-12%) remain interpretable and are highly consistent with observed high-energy vibrational modes.

[0080] As shown in Figure 8(a), projecting the predictions onto surface normal coordinates further clarifies these differences. The non-stationary model produces a persistent, vertically consistent high-probability band extending approximately 0–150 meters ahead of the working face and smoothly migrating with mining progress. Observed high-energy events are highly consistent with this band throughout the entire mining cycle, including phases of rapid advance and strong structural interaction. The stationary model, lacking such geometric consistency, instead produces a diffusion band dominated by short-term clusters rather than by the evolution of the stress field.

[0081] As shown in Figure 8(b), the coverage statistics provide a quantitative indicator of spatial discrimination capability. The non-stationary ETAS model captured nearly 90% of high-energy events within the top 10% of the predicted high-probability areas, achieving near-complete coverage with only about 12-15% of the area. In contrast, the stationary model requires more than twice the area to achieve a similar level of event capture. This stark contrast demonstrates that incorporating mining area covariates such as face distance, advance rate, and fault proximity can significantly improve spatial prediction capabilities, concentrating hazards in physically significant areas.

[0082] In summary, Figures 7(a)-7(d), 8(a), and 8(b) demonstrate that the nonstationary ETAS model provides a physically sound and statistically superior description, accurately predicting the migration and spatial localization of high-energy vibrations during longwall mining. In contrast, the stationary model, lacking mine-specific covariates, systematically fails to predict the dangerous redistribution driven by face advance and structural heterogeneity.

[0083] An example of the 6306 working face of Dongtan Coal Mine shows that the high-energy vibration prediction accuracy within a 24-hour time window can reach 94.25%, and its spatiotemporal prediction performance is significantly better than the traditional stationary ETAS model and Poisson model.

[0084] This embodiment constructs a non-stationary ETAS model driven by mining variables, aiming to achieve short-term probabilistic early warning of high-energy seismic events in deep longwall coal mines. First, a comprehensive case study was conducted on the 6306 working face of the Dongtan Coal Mine, a region typically experiencing strong tectonic-mining coupling and frequent high-energy seismic events. Subsequently, a non-stationary ETAS model was constructed, in which the background seismic activity rate was explicitly parameterized through key mining variables (such as working face distance and advance rate). This model can not only predict the spatiotemporal probability of high-energy events (ML≥1.0), but also decompose seismic activity into mechanistic components of background loading and triggering cascades. This embodiment systematically constructed and quality-controlled a complete seismic catalog, calibrated the variable-driven ETAS model, quantified its uncertainty, generated and evaluated short-term probabilistic predictions, analyzed the physical nucleation hierarchy of high-energy seismic events using model decomposition, and proposed a composite hazard assessment model. This model can not only be applied to the 6306 working face case of the Dongtan Coal Mine, but also provides a transferable technical basis for probabilistic short-term hazard assessment in deep longwall coal mines.

[0085] Based on the same inventive concept, this application also provides a deep mine earthquake probability prediction system based on a non-stationary, trending aftershock sequence model. The solution provided by this system is similar to the solution described in the above method. Therefore, the specific limitations of one or more embodiments of the deep mine earthquake probability prediction system based on a non-stationary, trending aftershock sequence model provided below can be found in the limitations of the deep mine earthquake probability prediction method based on a non-stationary, trending aftershock sequence model described above, and will not be repeated here.

[0086] In an exemplary embodiment, this application provides a deep mine earthquake probability prediction system based on a non-stationary popular aftershock sequence model. The system includes: a data acquisition module, a mine earthquake cascade triggering intensity calculation module, a mine earthquake non-stationary background intensity calculation module, a non-stationary ETAS model construction module, a parameter calibration module, an expected quantity determination module, and a probability prediction module. Wherein: The data acquisition module is used to acquire mine seismic data, which includes: the occurrence time of historical mine seismic events in the target deep mining area, the spatial location of the source of historical mine seismic events, the magnitude information of historical mine seismic events, historical mining face advancement data, and historical geological fault spatial distribution data.

[0087] The mine earthquake cascade triggering intensity calculation module is used to calculate the mine earthquake cascade triggering intensity based on the occurrence time of the historical mine earthquake events, the spatial location of the source of the historical mine earthquake events, and the magnitude information of the historical mine earthquake events.

[0088] The non-stationary background intensity calculation module for mine earthquakes is used to calculate the non-stationary background intensity of mine earthquakes based on the occurrence time of the historical mine earthquake events, the spatial location of the epicenter of the historical mine earthquake events, the historical mining face advancement data, and the historical geological fault spatial distribution data.

[0089] The non-stationary ETAS model construction module is used to construct a non-stationary popular aftershock sequence ETAS model based on the cascade triggering intensity of the mine earthquake and the non-stationary background intensity of the mine earthquake.

[0090] The parameter calibration module is used to calibrate the parameters in the non-stationary ETAS model based on standardized seismic data.

[0091] The expected number determination module is used to determine the expected number of high-energy seismic events within the future prediction window based on a non-stationary ETAS model after parameter calibration.

[0092] The probability prediction module is used to determine the probability that at least one high-energy mineral tremor will occur within the future prediction window based on the expected number of high-energy mineral tremor events within the future prediction window.

[0093] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal. The computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is connected to the system bus via the I / O interfaces. The processor of the computer device provides computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The database of the computer device stores data used for deep mine seismic probability prediction. The I / O interfaces of the computer device are used for exchanging information between the processor and external devices. The communication interface of the computer device is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements a deep mine seismic probability prediction method based on a non-stationary, circulating aftershock sequence model.

[0094] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0095] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for predicting the probability of deep mine earthquakes based on a non-stationary, prevalent aftershock sequence model, characterized in that, The method for predicting the probability of deep mine earthquakes based on a non-stationary, prevalent aftershock sequence model includes: Acquire mining seismic data, which includes: the occurrence time of historical mining seismic events in the target deep mining area, the spatial location of the epicenter of historical mining seismic events, the magnitude information of historical mining seismic events, historical mining face advancement data, and historical geological fault spatial distribution data; The intensity of cascading mine seismic events is calculated based on the occurrence time, spatial location of the epicenter, and magnitude information of the historical mine seismic events. The non-stationary background intensity of mining earthquakes is calculated based on the occurrence time of the historical mining earthquake events, the spatial location of the epicenter of the historical mining earthquake events, the historical mining face advancement data, and the historical geological fault spatial distribution data. Based on the cascade triggering intensity of the mine earthquake and the non-stationary background intensity of the mine earthquake, a non-stationary popular aftershock sequence ETAS model is constructed. The parameters in the non-stationary ETAS model are calibrated based on standardized seismic data. The expected number of high-energy mine tremor events within the future prediction window is determined based on the non-stationary ETAS model after parameter calibration. The probability of at least one high-energy mineral tremor occurring within the future prediction window is determined based on the expected number of high-energy mineral tremors within the future prediction window.

2. The method for predicting the probability of deep mine earthquakes based on a non-stationary, circulating aftershock sequence model according to claim 1, characterized in that, The step between calibrating the parameters in the non-stationary ETAS model based on standardized seismic data and determining the expected number of high-energy seismic events within the future prediction window based on the parameter-calibrated non-stationary ETAS model further includes: Uncertainty and correlation analysis were performed on the non-stationary ETAS model after parameter calibration using the parameter bootstrap method to obtain parameter confidence intervals, thereby quantifying and verifying the uncertainty of the non-stationary ETAS model.

3. The method for predicting the probability of deep mine earthquakes based on a non-stationary, circulating aftershock sequence model according to claim 1, characterized in that, The formula for the non-stationary background intensity of mine seismic events is expressed as follows: ； in, Indicates in time The non-stationary background intensity of the mine seismic activity at the location. , , , This represents the regression coefficients jointly estimated with the ETAS trigger parameters. for time A scaled representation of the position of the worker in front of the work position. for A standardized representation of the working face advance speed at any given moment. for Scaled representation of the minimum horizontal distance from the location to the fault.

4. The method for predicting the probability of deep mine earthquakes based on a non-stationary, circulating aftershock sequence model according to claim 1, characterized in that, The formula for the nonstationary ETAS model is expressed as: ； in, This indicates the impact of all historical mining earthquake events. This indicates the impact of all historical mining earthquake events. time The strength of the conditions at the location, Indicates in time The non-stationary background intensity of the mine seismic activity at the location. Indicates the first The magnitude of the mine earthquake event. Indicates the first Productivity of a single mining earthquake event Indicates the first The mining earthquake event from the moment of occurrence Up to the current moment The time-triggered kernel function, Indicates the first Under the influence of the magnitude of the first mining earthquake event The earthquake event was caused by the location of the epicenter. To the current location Space-triggered kernel function, .

5. The method for predicting the probability of deep mine earthquakes based on a non-stationary, circulating aftershock sequence model according to claim 1, characterized in that, The expected number of high-energy mineral seismic events within the future prediction window is determined based on a parameter-calibrated non-stationary ETAS model, specifically including: Set a high-energy seismic magnitude threshold; The Gutenberg–Richter magnitude distribution model was used to fit the magnitude information of the historical mining earthquake events. value; Based on the high-energy magnitude threshold and The value is used to calculate the proportion of events exceeding the high-energy magnitude threshold. The conditional intensity of high-energy mine seismic events is calculated based on the proportion of events exceeding the high-energy magnitude threshold. Based on the conditional intensity of the high-energy mine seismic event, the expected number of high-energy mine seismic events within the future prediction window is calculated.

6. The method for predicting the probability of deep mine earthquakes based on a non-stationary, circulating aftershock sequence model according to claim 5, characterized in that, Based on the high-energy magnitude threshold and The value is used to calculate the proportion of events exceeding the high-energy magnitude threshold, expressed by the formula: ； in, Indicates the magnitude of the mining earthquake event. Indicates the high-energy magnitude threshold. This indicates that the high-energy magnitude threshold has been exceeded. The proportion of events, The exponential attenuation coefficient of the magnitude distribution. , Indicates the minimum triggering magnitude; Based on the proportion of events exceeding the high-energy magnitude threshold, the conditional intensity of high-energy mine-seismic events is calculated, expressed by the formula: ； in, This indicates the impact of all historical mining earthquake events. This indicates the impact of all historical mining earthquake events. time The conditional intensity of high-energy mineral seismic events at the location. This indicates the impact of all historical mining earthquake events. time Conditional strength at the location; Based on the conditional intensity of the high-energy mineral seismic event, the expected number of high-energy mineral seismic events within the future prediction window is calculated, as expressed by the formula: ； in, Indicates the future prediction window [ , ] and spatial regions The expected number of high-energy seismic events in the interior. .

7. The method for predicting the probability of deep mine earthquakes based on a non-stationary, circulating aftershock sequence model according to claim 6, characterized in that, The probability of at least one high-energy mineral tremor occurring within the future prediction window is determined based on the expected number of such events, expressed by the formula: ； in, Indicates the future prediction window [ , ] and spatial regions The probability of at least one high-energy mine tremor occurring within the area.

8. The method for predicting the probability of deep mine earthquakes based on a non-stationary, circulating aftershock sequence model according to claim 1, characterized in that, After determining the probability of at least one high-energy mineral tremor occurring within the future prediction window based on the expected number of high-energy mineral tremor events within the future prediction window, the method further includes: The probability of at least one high-energy mineral tremor occurring within the future prediction window is converted into a binary observation value. Based on the binary observation value and the original probability value of at least one high-energy mineral tremor occurring within the future prediction window, the Brier score, information gain, hit rate, and false alarm rate are calculated to evaluate the prediction performance of the non-stationary ETAS model.

9. A deep mine earthquake probability prediction system based on a non-stationary, prevalent aftershock sequence model, characterized in that, The deep mine earthquake probability prediction system based on a non-stationary, popular aftershock sequence model includes: The data acquisition module is used to acquire mine seismic data, which includes: the occurrence time of historical mine seismic events in the target deep mining area, the spatial location of the epicenter of historical mine seismic events, the magnitude information of historical mine seismic events, historical mining face advancement data, and historical geological fault spatial distribution data. The mine earthquake cascade triggering intensity calculation module is used to calculate the mine earthquake cascade triggering intensity based on the occurrence time of the historical mine earthquake events, the spatial location of the source of the historical mine earthquake events, and the magnitude information of the historical mine earthquake events. The non-stationary background intensity calculation module for mine earthquakes is used to calculate the non-stationary background intensity of mine earthquakes based on the occurrence time of the historical mine earthquake events, the spatial location of the epicenter of the historical mine earthquake events, the historical mining face advancement data, and the historical geological fault spatial distribution data. The non-stationary ETAS model construction module is used to construct a non-stationary popular aftershock sequence ETAS model based on the cascade triggering intensity of the mine earthquake and the non-stationary background intensity of the mine earthquake. The parameter calibration module is used to calibrate the parameters in the non-stationary ETAS model based on standardized seismic data. The expected number determination module is used to determine the expected number of high-energy mining tremor events within the future prediction window based on the non-stationary ETAS model after parameter calibration. The probability prediction module is used to determine the probability that at least one high-energy mineral tremor will occur within the future prediction window based on the expected number of high-energy mineral tremor events within the future prediction window.

10. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement a method for predicting the probability of deep mine earthquakes based on a non-stationary, popular aftershock sequence model, as described in any one of claims 1-8.

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