A Principal Component Analysis Framework for Evaluating Mining-Induced Risk: A Case Study of a Chilean Underground Mine

Abstract

Mining-induced seismicity presents significant challenges to the safety and operational continuity of underground mines, particularly in deep and highly stressed environments. This study proposes a methodological framework for seismic risk evaluation inspired by predictive-maintenance principles and applied to a high-resolution microseismic catalog from a Chilean underground mine. Using a combination of data filtering and correlation analyses, we identify the seismic parameters that control the most variability in the dataset: moment magnitude, frequency corner, and both dynamic and static stresses. Based on this, we perform a Principal Component Analysis (PCA), which clearly demonstrates the physical interconnection between the selected parameters, thereby helping to better characterize the seismic events and the mining environment. Using these results, a PCA-based risk map is constructed, enabling the delineation of zones with different levels of seismic risk. Additionally, a temporal tracking of potentially hazardous seismicity is included. The proposed methodology demonstrates that microseismic behavior can be effectively represented in a reduced-dimension space, offering a promising foundation for predictive and data-driven risk-assessment tools capable of supporting real-time decision-making in underground mining operations.

1. Introduction

Mining-induced seismicity represents one of the primary challenges for the safety and efficient operation of underground mines. These events not only pose significant risks to personnel safety but can also cause substantial structural damage and critical production interruptions [1]. Published statistics from the United States, Canada, Chile, South Africa, Poland, and China suggest that, worldwide, a few tens of accidents per year are directly attributed to seismicity [2,3,4,5,6,7]. This year, a potentially mining-induced earthquake of magnitude Mw 4.1 at the El Teniente mine, located in central Chile and one of the largest underground mines in the world, caused six fatalities and large economic losses [8]. The standard seismic risks linked to mineral exploitation can also be amplified if we consider natural phenomena associated with climate change: it is possible to foresee rapid and unexpected changes in the geomechanical response of the mine, due to an increase in extreme events such as heavy rain, heat waves, cold waves, and droughts [9].

The influence of geomechanical properties on mining seismicity is highly mine-specific, as it depends on the local stress regime, rock mass stiffness and strength, excavation geometry and sequencing, and the presence of geological discontinuities such as faults or dykes. Consequently, seismicity rates and source characteristics may vary significantly from one operation to another, even under similar production conditions. For this reason, the selection of appropriate seismic risk indicators and the design of monitoring and forecasting methodologies must be adapted to each mine, combining site knowledge with seismic observations to ensure meaningful hazard characterization and decision support [10,11,12].

Several methodologies have been used to perform seismic risk analysis in mines. These include classical approaches such as the Gutenberg–Richter law, the maximum expected magnitude [13,14,15], the use of frequency–magnitude distributions to infer the stress state of the rock mass [16], and probabilistic hazard models that quantify the likelihood of exceeding predefined levels of energy over time [17,18]. Nevertheless, the predictive capability of such techniques becomes limited when the seismic regime evolves rapidly because of underground mining activities [17,19]. Accordingly, alternative methods have been developed to evaluate the spatial and temporal behavior of seismicity, providing tools for its management. These include clustering analyses to identify seismically active domains [20], mapping of accumulated energy release to detect zones of stress concentration [11], microseismic monitoring techniques that allow the temporal tracking of seismic activity such as re-entry protocols [21,22,23], and the development of seismic indicators that define periods of elevated seismic risk in the mine [24,25]. These approaches aim to characterize spatial and temporal patterns preceding higher-magnitude events. More recently, machine-learning methodologies have been incorporated to better understand the microseismic behavior and assess its seismic risk through predictive and classification-based models [26,27,28,29,30]. Supervised learning methods (e.g., neural networks, support vector machines, and ensemble learning) have been successfully applied to classify and predict the likelihood of rockbursts in underground mines, often outperforming conventional deterministic methods [31].

In this study, we propose a novel approach inspired by techniques originally developed for predictive maintenance [22,32,33]. Analogous to how predictive-maintenance systems assess equipment condition to identify degradation patterns and anticipate failures in critical machinery, seismic monitoring in mining environments enables the detection of subtle variations in catalog parameters that may precede events with magnitudes that pose risks to the workers’ safety and mining infrastructure. This forecast-based approach, supported by data-analysis and machine-learning techniques, facilitates a transition from reactive to predictive seismicity management, thereby enhancing operational continuity and enabling more informed decision-making within the mining exploitation site.

The main contribution of this work is the presentation of a full methodological framework based on data processing, correlation, and normalization techniques, and Principal Component Analysis (PCA), which is used to characterize spatial and temporal mining risk linked to large earthquakes. The PCA, which constitutes the main step of this framework, is a technique initially introduced in the early twentieth century by Pearson [34]. PCA is a multivariate statistical method used to reduce the dimensionality of a dataset while preserving as much of its variance as possible [35]. Its objective is to transform a set of possibly correlated variables into a new set of uncorrelated variables, known as principal components, which are linear combinations of the original variables and are ordered according to the proportion of explained variance. In seismological and geomechanical studies, PCA has been widely applied to identify patterns and relationships among seismic parameters [36], thereby facilitating the interpretation of large datasets and the selection of relevant variables for predictive models [37,38,39]. This technique enables the simplification of complex seismic catalogs and the extraction of representative parameters describing the temporal or spatial evolution of induced seismic activity.

The following sections present the development of this methodological framework, where the first step is to derive the principal components from microseismic parameters of a mining seismic catalog. Then, we characterize seismic hazard within the principal component space—including the establishment of hazard levels—and finally, we examine the temporal behavior of seismicity in this transformed space.

2. Materials and Methods

The proposed approach consists of the following steps: (1) data processing and filtering, (2) correlation and normalization, and (3) PCA, including the determination of the contribution of each selected variable to the principal components. Each of these steps is described in detail in Figure 1.

The case study is based on seismic information recorded in an underground Chilean mine during the period covering January to March 2016. During this interval, a total of 45,143 seismic events (Figure 2a) were detected by the monitoring system installed at the site, which includes uniaxial and triaxial geophones and accelerometers, with good coverage of the study area. The events were distributed within a volume of 7.1 × 10⁹ m³ (2098 × 2147 × 1572 m). The moment magnitude (Mw) was calculated directly from the seismic moment (Mo) using the equation proposed by Hanks and Kanamori (1979) [40]:

$$Mw={\displaystyle \frac{2}{3}}log \left(Mo\right)-6.07$$

(1)

According to this, Mw values vary from −2.4 to 1.7 (Figure 2b).

The frequency–magnitude distribution for these events is shown in Figure 2b. Within the study area and according to mine operations, events with Mw ≥ 0.8 are defined as critical events because they pose a direct risk of damaging the mine, with serious implications for both safety and operational continuity.

For each of these events, the seismic catalog includes: date, time, hypocenter, location error, number of triggered sensors, and the following seismic parameters: seismic moment, energy, P-wave moment, P-wave energy, S-wave moment, S-wave energy, corner frequency, static stress drop, dynamic stress drop, moment uncertainty, energy uncertainty, and S-wave corner frequency. The seismic parameters and their descriptive statistics are presented in

Table 1. Stats summary from the seismic parameters included in the micro-seismic catalog.

	Minimum	Maximum	Average	Std. Dev.	Unit
Moment (Mo)	2.7 × 105	5.1 × 1011	3.3 × 108	4.5 × 109	Nm
Energy (E)	0.0	1.9 × 106	164.7	1.2 × 104	J
Moment P (MoP)	5.9 × 104	8.8 × 1011	5.0 × 108	6.8 × 109	Nm
Energy P (Ep)	0.0	1.9 × 105	28.6	1.6 × 103	J
Moment S (MoS)	1.3 × 105	5.2 × 1011	2.5 × 108	3.7 × 109	Nm
Energy S (Es)	0.0	1.7 × 106	136.2	1.1 × 104	J
Corner frequency (fc)	10.5	2520.0	126.3	1.3 × 102	Hz
Static stress drop (Δσs)	4.7	7.9 × 106	2.7 × 104	1.4 × 105	Pa
Dynamic stress drop (Δσd)	82.4	3.0 × 107	6.1 × 104	3.7 × 105	Pa
Moment deviation (ΔM)	0.0	3.4 × 1011	2.2 × 108	1.0 × 1010	Nm
Energy deviation (ΔE)	0.0	9.5 × 105	103.8	6.9 × 103	J
Corner frequency S (fcS)	10.5	2520.0	126.3	1.3 × 102	Hz

, where it is possible to observe that the different variables exhibit high dispersion, so a normalization process is required to ensure they are comparable and suitable for further analysis.

2.1. Filtering

Before proceeding with normalization, three filters were applied to the dataset: magnitude of completeness (Mc), location error, and number of triggers. This filtering process ensures the reliability and physical consistency of the seismic parameters used in the multivariate analysis.

The magnitude of completeness (Mc) was determined using the Goodness of Fit (GoF) method [41,42]. This method compares the frequency-magnitude distribution with a theoretical distribution, which is calculated using the a and b values of the Gutenberg–Richter law [13], that are estimated by the maximum likelihood method.

The goodness of fit is defined by (Equation (2)):

$$GoF={\displaystyle \frac{{\sum }_{Mi}^{M_{max}}\left|B_i-S_i\right|}{{\sum }_{Mi}^{M_{max}}{B}_i}}100$$

(2)

where B_i and S_i are the observed and predicted cumulative number of events in each magnitude bin, respectively. The GoF threshold of 85% was selected as a compromise between ensuring catalog completeness and retaining enough events for robust statistical analysis. Previous studies have shown that overly strict GoF criteria (e.g., ≥90–95%) can systematically overestimate Mc, particularly in the presence of magnitude uncertainties, leading to unnecessary data loss with limited improvement in parameter stability [43]. Consequently, the adopted threshold provides a reliable fit to the Gutenberg–Richter distribution while preserving statistical representativeness. In this case, Mc = −1.1 (Figure 3).

The next data-filtering step consists of determining the minimum acceptable location error for seismic events. To this end, we analyze a plot of location errors versus the number of sensors (triggers) detecting each microseismic event (Figure 4). As expected, a lower number of triggers results in higher location errors and greater variability. The mean location error, which reaches 22 m, is adopted as the reference value. Subsequently, the minimum number of triggers that satisfy the maximum acceptable error is identified as five.

Applying these three filters, the new catalog is composed of 21,515 events (Figure 5).

2.2. Correlation and Normalization

Before the PCA and to explore the correlation among the 12 parameters available for each microseismic event, we generated a correlation (ρ) matrix including all attributes (

Table 2. Correlation (ρ) matrix for the seismic parameters.

	Mo	E	MoP	Ep	MoS	Es	fc	Δσs	Δσd	ΔM	ΔE	fcS
Mo	1	0.79	0.96	0.89	0.98	0.73	−0.07	0.02	0.02	0.95	0.77	−0.07
E		1	0.61	0.75	0.89	0.99	−0.01	0.05	0.05	0.66	1	−0.01
MoP			1	0.84	0.88	0.53	−0.10	0.01	0.02	0.98	0.57	−0.07
Ep				1	0.88	0.67	−0.01	0.08	0.07	0.80	0.74	−0.01
MoS					1	0.84	−0.07	0.02	0.02	0.89	0.87	−0.07
Es						1	−0.01	0.04	0.04	0.60	0.99	−0.01
fc							1	0.41	0.30	−0.06	−0.01	1
Δσs								1	0.82	0.01	0.05	0.41
Δσd									1	0.02	0.05	0.30
ΔM										1	0.62	−0.06
ΔE											1	−0.01
fcS												1

). Some of these attributes exhibit a high positive correlation (ρ > 0.8), while other combinations seem to be weakly correlated.

Based on this analysis and taking as a reference parameter the scalar seismic moment (Mo), a subset of three extra representative variables was selected: corner frequency (fc) (ρ = −0.07), static stress drop, (Δσs) (ρ = 0.02), and dynamic stress drop (Δσd) (ρ = 0.02).

Furthermore, due to the high dispersion observed in the distribution of the selected variables—reflected in their high coefficients of variation (Figure 6)—these were log-transformed and subsequently normalized prior to performing the PCA. The effect of this transformation is illustrated in Figure 7.

2.3. Principal Component Analysis (PCA) Applied to Mining-Induced Data

To avoid redundancy among the seismic parameters and to explore the internal relationships within the dataset, a PCA is applied to the selected four variables: Mo, fc, Δσs, and Δσd. Prior to the analysis, all variables were standardized to a zero mean and unit variance (X in Equation (3)) to eliminate differences in scale and ensure an equal contribution to the covariance structure. After standardization, the covariance matrix (C in Equation (3)) of the dataset was computed.

$$C={\displaystyle \frac{1}{n-1}}{X}^{T}X$$

(3)

where n is the number of seismic events.

Then its eigenvalues and eigenvectors were extracted to form the principal components (Equation (4)). The eigenvalues (λ_i) quantify the proportion of total variance explained by each component, whereas the eigenvectors (v_i) define the directions in parameter space that represent the most meaningful combinations of source characteristics [37].

$$C{v}_i={\lambda }_i{v}_i$$

(4)

Finally, the score values are calculated, which correspond to the projection of the standardized data onto the new orthogonal axes:

$$score=X coeff$$

(5)

where coeff are the contribution coefficients for each principal component per variable of interest.

3. Results

When applied to the filtered dataset, the procedure reveals that the first two principal components account for approximately 95% of the total variance (Figure 8), demonstrating that the four source parameters can be robustly described within a two-dimensional reduced space.

The dimensionality reduction enables the synthesis of multivariable information into a two or three-dimensional space, thereby facilitating the visualization of cluster structures and the identification and interpretation of the microseismic behavior. The microseismic data represented in the principal component space are shown in 2D and 3D in Figure 9. From the PCA (Figure 8), we can observe that PC1 is dominated by the static and dynamic stresses and the corner frequency, whereas the moment magnitude, highly independent of the other variables, is reflected in PC2. PC3 and PC4, on the other hand, reflect the interaction between the corner frequency and dynamic and static stresses, respectively.

3.1. Seismic Risk Zones Definition

To identify risk zones within the principal component space, a reference threshold was defined based on critical events with moment magnitude Mw ≥ 0.8. Although risk zones could be delineated using additional parameters such as the corner frequency and/or the stress drops, we will base our analysis on the moment magnitude as it is usually utilized for this purpose [44]. Events with Mw ≥ 0.8 are then highlighted in the principal component plane in Figure 10a. Based on this criterion, we delineated the high-risk region with a red color in Figure 10b.

3.2. Spatio-Temporal Analysis

To perform the seismic risk analyses, both the spatial and temporal behavior of seismicity were examined. For spatial analysis, we used local and regional approaches to characterize zones with higher risk in areas where hazardous seismicity is most likely to occur. The local approach consists of analyzing the seismic events surrounding an arbitrary reference point. The distance from each hypocenter to the reference point is then computed, and events located within a sphere of 450 m radius are retained. The center of the sphere and its radius are arbitrary, simply to show how the proposed seismic risk criterion can be implemented. However, the definition of the radius ensures the volumetric influence that a large-magnitude seismic event could have in the mine The events retained are then projected both in three-dimensional coordinates (Figure 11a) and within the principal component space (Figure 11b), mapping them onto the low-, moderate-, and high-risk zones. An example of this procedure is shown in Figure 11, where the 450 m radius zone defined by the arbitrary sphere is cataloged as low risk, as most events fall into the green category (783 events with Mw ≤ 0) versus 78 and 1 events in the yellow and red categories, respectively.

The regional approach explores the presence of potentially harmful sites by analyzing the whole volume covered by the selected events. For this, we applied a k-means clustering algorithm to the coordinates of the filtered catalog, using a testing value of 3 clusters. The selection of three clusters corresponds to three productive sectors of the mine: north, east, and south. The spatial distribution is represented in 3D in Figure 12a. The clusters were then mapped onto the principal component space, enabling a connection between the clusters and specific regions of the PCA plane, and allowing the identification of zones associated with higher seismic risk (Figure 12b). Although difficult to identify through visual inspection, cluster 3 exhibits the greatest potential for high seismic risk (Figure 12c), which is also spatially located close to the main faults (Figure 12d).

To identify periods with higher seismic risk, the temporal evolution of the seismic events is assessed by tracking them over time, examining how they are projected onto the principal component plane. Figure 13 illustrates the trajectory of 6 low-risk consecutive events and how their temporal behavior is reflected within the PCA space. All of them remain in the green zone, indicating no major risk in the period ranging from 1 January 2016 at 00:06:00 to 1 January 2016 at 01:30:32. On the other hand, Figure 13b shows 7 other consecutive events reaching the red zone from 4 January 2016 at 16:09:40 to 4 January 2016 at 16:27:49, then potentially compromising operations during that time.

4. Discussion

The four selected source parameters—seismic moment $M_0$, corner frequency $f_c$, static stress drop $\mathsf{\Delta }{\sigma }_s$, and dynamic stress $\mathsf{\Delta }{\sigma }_d$—provide a good basis for evaluating seismic risk in induced environments. Although P- and S-wave energy are also commonly used in seismic risk studies, we do not focus on them here as they have been extensively explored in the literature, and our objective is to highlight the complementary information contained in these four different source parameters [45,46]. They capture complementary aspects of the rupture process that govern the potential for damaging ground motion: $M_0$ represents the overall event size and therefore the total energy and $f_c$ reflects the characteristic rupture duration and high-frequency content, which are critical for assessing the severity of near-source ground motion. On the other hand, the static stress drop $\mathsf{\Delta }{\sigma }_s$ constrains the intensity of the stress released on the fault, while the dynamic stress $\mathsf{\Delta }{\sigma }_d$ is directly linked to peak velocities and local impact potential.

The PCA results (Figure 8 and Figure 9) define a space that captures the physical diversity of the seismic parameters and reflects their underlying meaning and interactions. PC1, dominated by static stress drop, dynamic stress, and corner frequency, characterizes the rupture behavior in terms of stress level, rupture compactness, and the event’s frequency content. We have observed that events with high scores on PC1 correspond to high-stress, compact ruptures with elevated corner frequencies. On the contrary, events with a low PC1 score reflect low stresses and low corner frequencies (Supplementary Materials). This allows us to separate these data into two different kinds of events: those with short-duration and compact ruptures under high stresses, such as energetic brittle failures observed in rockbursts, and slower ruptures, with less stress release and less energetic rupture, such as background microseismicity and/or mining-tectonic interaction events (Supplementary Materials).

Regarding the PC1 loading, static and dynamic stress drops exhibit contrasting behavior in the principal component space (Figure 9b). Although both parameters are strongly correlated, the PCA projects them in opposite directions along PC1, which means their contributions are also opposite in sign (negative for Δσs and positive for Δσd). This might arise from the following:

(i)

The sign indeterminacy inherent to PCA, which captures both shared variance and contrasting patterns between correlated variables. Consequently, the opposite orientations reflect how PCA defines the direction of maximum variance within the stress domain rather than a physical contradiction between the parameters.

(ii)

Even considering that both stresses increase systematically with PC1 score (Supplementary Materials), the opposite loadings between Δσs and Δσd indicate that PC1 also captures the relative contrasts between both stresses. PC1 values also show events with higher dynamic stress drops relative to the static stress drop, and events where the static stress drop is dominant. This relates to the two rupture modes found in the PC1 score analyses (Supplementary Materials), where energetic, high-frequency events -rockburst- and low-frequency, less impulsive background seismicity were identified.

PC2 is primarily controlled by the seismic moment and highlights its inverse relationship with corner frequency, consistent with the classical $f_c\propto M_0^{-1/3}$ scaling [47], which appears here as opposite vector orientations in the PCA space. PC3 and PC4 both capture secondary variability related to the link between corner frequency and dynamic or static stress, respectively. PC3 reflects how $f_c$ tracks rupture duration, with opposite axes indicating that short, impulsive ruptures generate higher corner frequencies. Finally, PC4 isolates a distinct contrast between static stress drop and corner frequency: its strong positive loading on $\mathsf{\Delta }{\sigma }_s$ and negative loading on $f_c$ reveals events with low static stress but unusually high corner frequencies, characteristic of small, sharp, high-frequency failures [47].

Regarding the spatial characterization of seismic risk, and although filtering techniques are widely used in terms of seismic indicators [48,49], it is worth noting that filtering processes keep out thousands of events (Figure 5), restricting the analyzed space and excluding areas where seismic risk may be equally high or even higher than in the region examined here. Although the application of these filters significantly reduces the number of retained events, the objective is to ensure the reliability of the seismic parameters used in the PCA analyses. Events recorded with a low number of triggered sensors or large location uncertainties might introduce bias and noise into the PCA, potentially obscuring meaningful patterns associated with the physical parameters. While it is acknowledged that areas with lower sensor coverage or higher attenuation may be underrepresented after filtering, the proposed framework is intended as a methodological approach for characterizing seismic risk under well-instrumented conditions. Its extension to more complex mining environments would require an adaptation of the filtering thresholds and sensor configuration.

The spatial risk analyses, such as the local approach and the clustering technique (Figure 11 and Figure 12), highlight the potential of PCA as a real-time decision-support tool, in which newly recorded events could be rapidly projected onto the PCA space to assess their proximity and correspondence to high-risk zones, also establishing correlations with the local tectonic structures (Figure 12d). Such an approach differs fundamentally from classical frequency–magnitude or time-based indicators, as it emphasizes the multi-parameter structure of seismicity rather than relying on single variables.

Temporal tracking of micro-seismicity in the PCA plane reveals migration patterns that reflect evolving seismic conditions (Figure 13). The temporal examples presented in this study show how micro-seismic events evolve within the principal component space, defining periods of time with higher risk. If an alarm state is set as soon as an event enters the high-risk zone, this could be used to identify consistent precursory patterns. Advancing this understanding would strengthen the potential of PCA-based monitoring to support predictive frameworks, enabling informed decision-making and enhancing operational safety.

Based on these findings, an integrated seismic risk surveillance methodology can be proposed by combining source-parameter analysis with the PCA framework. In this approach, each newly recorded microseismic event is first characterized in terms of $M_0$, $f_c$, $\mathsf{\Delta }{\sigma }_s$, and $\mathsf{\Delta }{\sigma }_d$, and then projected into the established PCA space, where its position relative to the previously identified high-risk zones can be immediately assessed. Events falling within regions associated with high PC1 values, strong dynamic behavior (PC3), or anomalous stress–frequency patterns highlighted by PC4 can be flagged as higher-risk, while temporal trajectories in PCA space can be monitored to detect the emergence of persistent or accelerating precursory trends. Integrating these elements enables a unified workflow in which spatial patterns, temporal evolution, and multi-parameter rupture characteristics are jointly evaluated in real time.

5. Conclusions

This study introduces a novel methodological framework for evaluating mining-induced seismic risk based on the projection of micro-seismic parameters into a principal component space. By combining data filtering, variable correlation, and Principal Component Analysis, the proposed framework provides a good representation of the microseismic behavior in terms of mining seismic risk evaluation.

Overall, the results confirm that PCA provides a powerful tool for simplifying the complexity of microseismic catalogs and identifying patterns associated with elevated seismic risk. Although this work represents an initial methodological development, the findings indicate promising directions for future research. Potential extensions include integrating geological and geotechnical information, refining seismic risk thresholds, and incorporating machine learning models for real-time classification and forecasting. The proposed approach offers a foundation for developing predictive, data-driven seismic risk monitoring systems capable of enhancing safety and risk mitigation in underground mining environments.

While machine learning methods have shown strong predictive capabilities in seismic risk analysis, they often require large training datasets, extensive parameter tuning, and limited physical interpretability. In contrast, the proposed PCA-based approach is intended as a complementary tool that can support or precede machine learning models by providing a robust, physics-informed representation of seismic behavior. The PCA framework is particularly well-suited for scenarios where interpretability, rapid implementation, and adaptability to site-specific conditions are critical, such as real-time monitoring, early-warning support, and the preliminary assessment of evolving seismic regimes.

Beyond the methodological contribution, this work underscores the urgent need for developing disruptive monitoring and forecasting technologies capable of anticipating hazardous seismic conditions before they escalate into major incidents. Recent catastrophic events—such as the Mw 4.1 mining-induced earthquake in El Teniente mine, which resulted in multiple fatalities and significant operational losses—highlight the limitations of current monitoring strategies and the high societal and economic cost of underestimating evolving seismic hazard. Advancing towards real-time, multi-parameter, and predictive frameworks is therefore essential not only for improving seismic risk management but also for preventing future large-scale accidents in increasingly deeper and more complex mining environments.

Although this study focuses on a single, well-instrumented underground mine and a fixed magnitude threshold, the framework is inherently adaptable to other mining environments. Future research should explore the integration of geological and geotechnical information, the calibration of site-specific risk thresholds, and the coupling of the PCA space with supervised learning algorithms for automated risk forecasting. Additionally, sensitivity analyses on temporal resolution and spatial influence scales would further enhance the operational applicability of the method.