Multi-Source-Data-Fusion-Based Susceptibility Assessment of Tunnel Geothermal Hazards: A Case Study of the Nige Tunnel

Abstract

Tunnel construction in tectonically active mountainous regions is frequently hampered by elevated geothermal conditions, threatening construction safety and long-term infrastructure performance. In the Yunnan–Guizhou Plateau, characterized by complex fault systems and intense hydrothermal activity, rigorous assessment of geothermal hazard susceptibility along tunnel corridors is of critical engineering importance. However, the sparsity of geothermal observational data renders conventional assessment approaches insufficient, as they fail to quantify predictive uncertainty, which is essential for reliable risk decision-making. To address this gap, this study proposes a three-stage framework that integrates multi-source data fusion with Monte Carlo-based uncertainty quantification, using the Nige Tunnel as a case study. Ten conditioning factors were incorporated, with temperature-weighted positive samples constructed from field-surveyed hot springs. Gaussian noise injection and fractal buffer randomization were applied across 500 Monte Carlo iterations of an L2-regularized logistic regression model, evaluated by leave-one-out cross-validation. The three-stage assessment framework achieved robust predictive performance (mean leave-one-out cross-validation area under the curve (LOO-AUC) = 0.824) under sparse-sample conditions. High and Very High susceptibility zones account for 14.2% of the study area, concentrated along fault traces and collocated with hydrothermal discharge locations, with the Nige Tunnel traversing predominantly High to Very High susceptibility zones. Fault distance emerges as the dominant predictive factor, surpassing heat flow and Moho depth, indicating that structural permeability is the rate-limiting control on geothermal fluid enrichment in fault-dominated systems. The findings offer scientific support and methodological insights for risk zoning and hazard mitigation design in tunnel engineering projects in comparable geological settings.

1. Introduction

In mountainous or heavily hilly terrain, tunnel solutions are frequently adopted to satisfy transportation demand. In recent years, however, a substantial number of high-geothermal-temperature tunnels have been encountered in traffic and hydraulic engineering projects [1,2]. Elevated geothermal conditions pose numerous challenges for tunnel construction, including harsh working environments, adverse health effects on personnel, reduced efficiency of mechanical equipment, and cracking of concrete linings [3,4,5,6]. These challenges may multiply project investment many times over and severely compromise the safety and economic viability of tunnel construction and operation, thereby presenting formidable obstacles to tunnel engineering [7]. Accordingly, predicting geothermal hazard susceptibility in tunnel corridors holds considerable guidance value for engineering practice.

In the geotechnical investigation of tunnel projects, the core challenge in assessing geothermal hazard susceptibility is the sparsity of geothermal samples. Hot spring outcrops are typically limited in number and spatially clustered, which may render results from certain conventional methods less interpretable [5]. Geothermal hazard susceptibility prediction generally requires incorporating geological background information or observational data to support classification. For instance, Meng et al. selected five factors, namely, shallow ground temperature, fault lineaments, hot spring locations, distance to basalt, and distance to subsidence grabens, and delineated geothermally favorable zones through a GIS-based multi-criteria decision-making approach combining analytic hierarchy process and entropy weighting [8]. Bian et al. selected geological indicators, geological structures, digital elevation models, and lithological data as input variables and produced potential geothermal resource maps using support vector machines and a multilayer perceptron [9]. Beyond these factors, a number of researchers have incorporated additional information, including peak ground acceleration, aeromagnetic anomalies, and Moho depth, to further refine geothermal hazard susceptibility assessments [10,11,12]. The integrated use of multi-source heterogeneous data partially compensates for the informational limitations inherent in single-source datasets under sparse-sample conditions, providing a feasible technical pathway for conducting geothermal hazard susceptibility evaluations in regions with limited observational records [13,14].

The methods described above provide qualitative or quantitative assessments of geothermal resources, yet they lack quantification of the uncertainty associated with these evaluations [15]. When the number of available samples is extremely limited, model parameters become highly sensitive to input perturbations, and a single deterministic prediction cannot distinguish between regions that are genuinely high-risk according to the model and those that exhibit elevated uncertainty due to insufficient observational constraints. These two conditions are fundamentally distinct from the perspective of engineering risk decision-making [16,17]. The absence of uncertainty quantification not only undermines the credibility of susceptibility maps as a basis for engineering decisions but may also lead to systematic underestimation or overestimation of risk in high-uncertainty areas, thereby compromising the safety and economic performance of tunnel construction [18]. Monte Carlo ensemble methods offer an effective means of achieving both predictive accuracy and uncertainty quantification under sparse-sample conditions [19,20]. This framework has been successfully applied in mineral prospectivity prediction [21], but no systematic application precedent exists in the domain of tunnel geothermal hazard susceptibility assessment.

To address the foregoing challenges, the present study takes the Nige Tunnel on the Yunnan-Guizhou Plateau as an engineering case and proposes a three-stage geothermal hazard susceptibility assessment framework integrating multi-source data fusion with Monte Carlo uncertainty quantification. The framework takes field-measured hot spring survey data and ten multi-source conditioning factors from open-source datasets as inputs; constructs samples through a discharge-temperature-based differential weighting scheme; applies stochastic perturbation to input data via Gaussian noise injection and fractal buffer randomization of fault distance; trains an L2-regularized logistic regression model across 500 Monte Carlo iterations, with predictive performance evaluated using leave-one-out assessment (LOO); and ultimately performs ensemble aggregation in log-odds space. The standard deviation of log-odds values across iterations is adopted as a quantitative measure of predictive uncertainty, enabling the identification of spatial regions that are sensitive to parameter perturbations and thus exhibit comparatively lower prediction reliability.

2. Study Area Overview and Data

2.1. Study Area Overview

The project area is situated in the southwestern portion of the Yunnan–Guizhou Plateau, as shown in Figure 1a, with the terrain generally sloping from north to south. Under the influence of regional geological structures, the mountain ranges are predominantly oriented north–south and northeast, and the topography is characterized by low- to middle mountains, with elevations generally ranging from 1200 to 2500 m above sea level. The plateau surface exhibits undulating relief, with mountains, rivers, valleys, and fault-bounded basins arranged in alternating patterns, punctuated by numerous rift lake basins. The geomorphological types within the area are complex and diverse, dominated by montane landscapes shaped by tectonic erosion and dissolution, with karst landforms also extensively developed.

Figure 1. Geographical location and geological setting of the study area. (a) Topographic relief derived from digital elevation model showing fault systems and drainage network; (b) geological map illustrating the spatial distribution of lithological units and measured geothermal spring temperatures (°C).

In terms of regional tectonic setting, the study area lies within the southern segment of the Xianshuihe–Eastern Yunnan seismic belt, at the intersection of the north–south-trending Xiaojiang seismic belt and the northwest-trending Red River fault seismic belt, forming a pronounced conjugate X-shaped structural pattern. According to regional geological data, the tunnel site falls within the southeastern margin of the Sichuan–Yunnan platform anticline (Kang–Dian Axis) of the Yangtze paraplatform. The area lies at the confluence of the meridional, latitudinal, and Tethyan–Tibetan–Myanmar arcuate structural systems and is broadly controlled by the Red River Fault Zone to the south. Since the Paleozoic, the region has undergone multiple episodes of tectonic deformation superimposed upon one another, resulting in exceptionally complex geological structures.

Regional active fault systems commonly constitute preferential pathways for the upward transfer of deep-seated thermal energy. Heat reservoirs, including anomalous thermal sources in the upper mantle, radiogenic heat from radioactive element decay, and residual heat from recent magmatic activity, may transfer heat upward along active fault zones or drive deep meteoric water circulation, ultimately leading to moderate-to-high and high-temperature hydrothermal springs at the surface. The tunnel site is roughly 18 km away from the closest part of the Red River Fault. Two subsidiary faults, the Longchahe Fault and the Jiashahe Fault, both trending north-northeast, extend into the tunnel study zone. These faults serve as the main thermal pathways, contributing to the high geothermal gradient observed in the area. Three hot springs have been identified within a 5 km radius of the tunnel study area, with measured discharge temperatures ranging from 53.8 to 87.9 °C, classifying them as moderate-to-high and high-temperature hydrothermal springs. The lithological data are derived from the Soil and Terrain Database (SOTER) for China [22]. The study area is predominantly composed of clastic sedimentary rocks, granite, and metamorphic rocks, with locally distributed carbonate rocks, as shown in Figure 1b. The southern part is dominated by siltstone, mudstone, claystone, and basalt, with locally occurring limestone and other carbonate rocks; the northern and western parts are mainly composed of granite and granodiorite; the northeastern part is characterized by shale and pelitic sedimentary rocks.

2.2. Evaluation Factors

Based on the geological background, tectonic setting, and geothermal-related characteristics of the study area, ten conditioning factors were selected to construct the indicator system for geothermal hazard susceptibility assessment. These factors collectively reflect the geological conditions governing the occurrence and spatial distribution of geothermal resources. All datasets were resampled to a uniform spatial resolution of 1 km × 1 km, as shown in Figure 2. All conditioning factor datasets were standardized for spatial resolution, projected coordinate system, and data precision before analysis. This study employs the Generic Mapping Tools (GMT) to visualize ten key factors in geothermal resource assessment, combined with the Python 3.14.3 programming language for data preprocessing and result validation.

Figure 2. Spatial distribution maps of the ten geothermal conditioning factors used in the susceptibility assessment. (a) slope; (b) distance to faults; (c) terrestrial heat flow; (d) Moho depth; (e) peak ground acceleration; (f) river density; (g) aeromagnetic anomaly; (h) rainfall; (i) land surface temperature; (j) NDVI. The color bar represents increasing values from left to right.

2.2.1. Slope

Slope characterizes the relief and morphological variability of the land surface and was derived from digital elevation model (DEM) data, with values expressed in degrees (°). The elevation data were obtained from the Shuttle Radar Topography Mission (SRTM) global DEM developed by NASA, the data of which is distributed by the U.S. Geological Survey (USGS). Slope is closely associated with surface hydrothermal circulation and groundwater recharge and discharge dynamics, as it governs the direction and intensity of geothermal fluid migration. Low-slope areas favor groundwater convergence and may enhance geothermal fluid activity.

2.2.2. Fault Distance

Faults represent the primary structural control on geothermal resource distribution. Faults and fault zones represent brittle discontinuities in the crust characterized by enhanced permeability, serving as primary conduits for active geothermal fluid circulation. Regions proximal to faults typically exhibit more vigorous geothermal fluid flow and greater potential for geothermal resource development. Fault-related fracture systems significantly enhance geothermal gradients and create favorable conditions for rapid geothermal fluid ascent [23]. Fault data were sourced from the Institute of Geology, China Earthquake Administration [24]. Major fault traces within the study area were extracted, and the distance from each evaluation unit to the nearest fault was computed. Proximity to faults is generally associated with more active geothermal fluid circulation and greater development potential. A distance-decay model was applied to quantify the spatial relationship between fault proximity and geothermal favorability.

2.2.3. Terrestrial Heat Flow

Anomalously elevated surface heat flow indicates local crustal thinning and modification of lithospheric thermal structure, representing one of the most critical indicators for assessing geothermal resource potential. Higher heat flow values reflect steeper geothermal gradients and are closely associated with the presence of shallow magmatic heat sources [25]. Heat flow data for the study area were obtained from the fifth compilation of terrestrial heat flow in China, published by the Institute of Geology and Geophysics, Chinese Academy of Sciences [26].

2.2.4. Moho Depth

The Mohorovičić discontinuity (Moho) defines the boundary between the crust and upper mantle, and its depth reflects crustal thickness. Crustal thickness is intimately linked to lithospheric thermal structure and geothermal gradient; shallower Moho depths correspond to steeper geothermal gradients and greater geothermal resource potential. Moho depth data for the study area were derived from the CRUST1.0 global crustal model [27].

2.2.5. Peak Ground Acceleration

Peak ground acceleration (PGA) quantifies the intensity of ground motion during seismic events and serves as an indicator of crustal stress state and tectonic activity. Regions of high seismicity are often associated with active crustal deformation, which may indicate elevated geothermal activity. PGA data were obtained from the Global Seismic Hazard Map (version January 2023) [28]. PGA is employed here as a proxy for tectonic activity and its dynamic relationship with geothermal resources.

2.2.6. River Density

River density reflects the degree of development of the surface drainage network and is closely related to precipitation-driven recharge and groundwater supply conditions. High river density indicates abundant surface water and favorable groundwater recharge, both of which regulate geothermal fluid circulation. In precipitation-rich regions, fluvial systems serve not merely as surface water bodies but as preferential zones for groundwater recharge, where infiltrating water percolates to depth and participates in geothermal fluid circulation within deep reservoirs [29]. River density was derived from Landsat 9 OLI imagery. Areas with high river density are generally associated with superior recharge conditions for geothermal fluids.

2.2.7. Rainfall

Precipitation is the primary source of groundwater recharge and directly influences the intensity of circulation and the replenishment of geothermal fluids. Daily precipitation data were obtained from the CHIRPS dataset, covering ten years from 2016 to 2025, and the multi-year mean annual precipitation was used as the assessment value. Areas with abundant rainfall provide favorable groundwater recharge, promoting the formation and movement of geothermal fluids. Precipitation values were spatially interpolated to derive estimates for each grid cell, expressed in millimeters (mm).

2.2.8. Aeromagnetic Anomaly

Aeromagnetic anomalies reflect spatial variations in subsurface lithology and magnetic mineral content and are closely related to deep geological structures. Positive anomalies often correspond to high-susceptibility rocks such as magnetite and may indicate the presence of deep-seated heat sources. Aeromagnetic surveys provide an effective means of identifying and mapping geothermal anomaly zones by resolving high-susceptibility rock bodies and deep crustal structural features that characterize geothermal systems [30]. Aeromagnetic data were obtained from the EMAG2 model, which is compiled from the CHAMP satellite magnetic anomaly model MF5 (wavelength > 330 km) [31].

2.2.9. Land Surface Temperature

Land surface temperature (LST) directly reflects the thermal radiation characteristics of the Earth’s surface and is closely associated with subsurface heat flux and geothermal anomalies. Areas with anomalously elevated LST often coincide with geothermal manifestations and are therefore important indicators of geothermal resources [32,33]. LST data were retrieved from the thermal infrared bands of Landsat 8 satellite imagery using thermal infrared inversion, covering ten years from 2016 to 2025, with values expressed in degrees Celsius (°C).

2.2.10. Normalized Difference Vegetation Index

The normalized difference vegetation index (NDVI) is a remote sensing-derived measure of vegetation cover that reflects the vigor of surface vegetation. NDVI is closely coupled with surface hydrothermal conditions and can indirectly indicate surface moisture and temperature regimes, thereby linking vegetation patterns to geothermal manifestations [34]. NDVI was computed from Landsat 8 multispectral imagery. NDVI values range from −1 to 1, with high values indicating dense vegetation cover, which may reflect elevated surface moisture content or thermally anomalous conditions.

2.3. Geothermal Sampling Sites

To clarify the heat source responsible for the elevated temperatures in the study area, geologists conducted detailed in-situ investigations of three hot springs within the research region. The sampling work focused on three representative geothermal sites: the Nige hot spring, the Laohutan hot spring, and the Yashadi hot spring. These three springs are distributed along two river systems (the Longchahe River and the Jiashahe River) with dispersed geographical locations and strong representativeness. The field work comprised the following procedures: (1) precise recording of the location and elevation of each hot spring orifice; (2) in-situ temperature measurements and flow rate estimations; (3) field observations and documentation of geological characteristics and physical phenomena surrounding the spring orifices (such as mineral deposits and gas odors); and (4) sample collection with appropriate contamination prevention measures.

3. Method

The three-stage geothermal hazard susceptibility assessment framework proposed in this study is illustrated in Figure 3.

Figure 3. Workflow of the proposed geothermal hazard susceptibility assessment framework, incorporating stochastic data perturbation, Monte Carlo logistic regression, and ensemble uncertainty quantification.

3.1. Independence Analysis of Conditioning Factors

To assess the degree of multicollinearity among the ten conditioning factors, three diagnostic methods are employed: Pearson correlation coefficient, Spearman rank correlation coefficient, and variance inflation factor (VIF). The Pearson correlation coefficient measures the linear association between two variables. For variables x and y, it is defined as (Equation (1)):

$$r={\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n(x_i-\overline{x})(y_i-\overline{y})}}{\sqrt{{\displaystyle {\sum }_{i=1}^n{(x_i-\overline{x})}^2}}\sqrt{{\displaystyle {\sum }_{i=1}^n{(y_i-\overline{y})}^2}}}}$$

(1)

where x_i and y_i represent values of the i-th conditioning factor $\overline{x}$ and $\overline{y}$ are means, and n is the sample size. The correlation coefficient r ranges from [−1, 1], with absolute values closer to 1 indicating stronger correlation.

Spearman’s rank correlation coefficient captures monotonic relationships (including nonlinear relationships) between two variables by rank-transforming the data. It is calculated based on the Pearson correlation coefficient of the ranked data (Equation (2)):

$$\rho =1-{\displaystyle \frac{6{\displaystyle {\sum }_{i=1}^n{d}_i^2}}{n(n^2-1)}}$$

(2)

where d_i is the difference between the ranks of the two variables, and n is the sample size. Spearman’s coefficient likewise ranges from −1 to 1 and exhibits superior capability in detecting nonlinear monotonic relationships compared to Pearson’s coefficient.

The variance inflation factor quantifies the impact of multicollinearity on the variance of regression coefficients. For the j-th variable, VIF is defined as (Equation (3)):

$${\mathrm{VIF}}_j={\displaystyle \frac{1}{1-R_j^2}}$$

(3)

where $R_j^2$ is the coefficient of determination from an auxiliary regression model in which the j-th variable serves as the dependent variable, and all other variables serve as independent variables.

3.2. Data Preprocessing and Sample Construction

Positive samples were derived from field-verified hot spring locations, each recorded with geographic coordinates and measured discharge temperature. A temperature-weighting scheme was applied to assign differential sample weights, exploiting the discriminative capacity of spring temperature. The weight for each positive sample was calculated as (Equation (4)):

$$w_i={\displaystyle \frac{T_{\max }-T_{\min }}{T_i-T_{\min }}}\times (W_{\max }-W_{\min })+W_{\min }$$

(4)

where T_min and T_max are the minimum and maximum temperatures across all hot spring points, and W_min = 0.3 and W_max = 1.0 define the weight-mapping range. Higher-temperature springs, which exhibit more pronounced thermal anomalies, receive greater weights during model training, thereby enhancing the model’s sensitivity to intense geothermal anomalies.

Negative samples were generated using an exclusion buffer strategy. A buffer zone of 3 km radius was established around each positive sample pixel. Based on the spatial association characteristics of geothermal systems, this buffer radius effectively isolates the region directly controlled by the heat source, preventing transitional features of geothermal anomalies or far-field geothermal effects within the buffer zone from being misclassified as negative samples. Negative samples were drawn by random sampling without replacement exclusively from valid pixels outside these buffers, with the total number of negative samples set to ten times that of positive samples. Given the sparse distribution of positive samples, moderately increasing the number of negative samples enriches the representativeness of training data, enabling the model to adequately learn the feature space of negative samples and thereby enhance its capacity to discriminate between geothermal anomalies and background. All negative sample weights were fixed at 1.0 to maintain regularized processing.

3.3. Monte Carlo Parameter Perturbation

The Monte Carlo approach simulates input data uncertainty by randomly perturbing conditioning factors over 500 iterations. In each iteration, all ten factors are perturbed according to factor-specific schemes. Nine factors are generated from Gaussian normal distributions, while the fault distance factor is perturbed using uniform distributions within a fractal buffer weighting function. This is grounded in the physical understanding that fault control over geothermal fluid migration exhibits nonlinear spatial decay (Equation (5)).

$$w(d)=\left\{\begin{array}{l}1.0(d\le d_{\min })\\ C·d^{-\alpha }(d_{\min }<d<d_{\max })\\ 0.0(d\ge d_{\max })\end{array}\right\}$$

(5)

where d is the actual distance from each pixel to the nearest fault (in km), C = dα_min is a normalization constant, α = 1.5 is the fractal exponent governing the decay rate, and d_min and d_max are randomly sampled in each iteration from uniform distributions over [0.5,2.0] km and [6.0,10.0] km, respectively. For the remaining nine conditioning factors, Gaussian random noise perturbation is applied (Equation (6)):

$$X_{perturbed}=X_{original}+N(0,\sigma )$$

(6)

where σ = 0.05 × SD_layer, and SD_layer is the standard deviation of each factor computed over the entire study area. This formulation simulates the random measurement and model errors commonly present in remote sensing retrieval and geophysical interpretation.

3.4. Logistic Regression Model and Performance Evaluation

In each iteration, the perturbed data are standardized to zero mean and unit variance prior to training a binary logistic regression classifier. The model takes the form (Equation (7)):

$$P(\mathrm{Geothermal} \mathrm{Anomaly})={\displaystyle \frac{1}{1+e^{-({\beta }_0+{\displaystyle {\sum }_{j=1}^{10}{\beta }_j{x}_j})}}}$$

(7)

where X_j denotes the standardized value of the j-th conditioning factor, and β_j is its corresponding regression coefficient. Sample weights are incorporated into the training objective to amplify the contribution of positive samples, particularly high-temperature spring points. The model hyperparameters are set as follows: L2 regularization coefficient C = 1.0, solver algorithm lbfgs, and a maximum of 1000 iterations.

Model performance in each iteration is assessed using the leave-one-out area under the receiver operating characteristic curve (LOO-AUC), computed via Leave-One-Out (LOO) cross-validation. Specifically, for each of the 33 training samples, a logistic regression model is trained on the remaining 32 samples, and the held-out sample is used for testing. The probability predictions from all 33 leave-one-out evaluations are aggregated to compute the AUC-ROC score. This LOO-AUC provides an unbiased estimate of model generalization performance, which is particularly important for small sample sizes.

3.5. Susceptibility and Uncertainty Indices

The probability predictions from all 500 iterations are transformed into log-odds values to improve numerical stability (Equation (8)):

$${\mathrm{Log}\text{-}\mathrm{Odds}}_i=log({\displaystyle \frac{Pi}{1-Pi}})$$

(8)

The log-odds values are averaged across iterations and mapped back to the probability domain via the inverse logistic function to yield the integrated susceptibility index (Equation (9)):

$$\mathrm{Geothermal} \mathrm{Susceptibility}={\displaystyle \frac{1}{1+e^{-\mathrm{Log}\text{-}\mathrm{Odds}}}}$$

(9)

This index, ranging from 0 to 1, aggregates the results of 500 stochastic perturbation runs, with higher values indicating greater geothermal susceptibility. The uncertainty index is defined as the standard deviation of the log-odds values across iterations (Equation (10)):

$$\mathrm{Prediction} \mathrm{Uncertainty}=\mathrm{SD}\left(\mathrm{Log}\text{-}\mathrm{Odds}\right)$$

(10)

The uncertainty index quantifies the dispersion of susceptibility predictions. High uncertainty areas exhibit large inter-iteration variability, reflecting substantial sensitivity to parameter perturbation and thus greater prediction uncertainty, whereas low-risk areas yield stable and reliable estimates.

4. Results

4.1. Field Measurements and Observable Characteristics

As shown in Figure 4a, the Nige hot spring emerges on the left bank of the Longchahe River at the exit of the Nige Tunnel, with a measured discharge temperature of 67.9 °C, a flow rate of approximately 1.06 L/s, and a spring orifice elevation of 908 m. It is classified as an ascending spring, and the discharge vapor carries a faint odor of hydrogen sulfide. As shown in Figure 4b, the Laohutan hot spring emerges on the right bank of the Longchahe River at the exit of the Nige Tunnel, with a measured discharge temperature of 53.8 °C, a flow rate of approximately 1.24 L/s, and a spring orifice elevation of 762 m. It is likewise classified as an ascending spring; a small amount of yellowish material is observed on the walls of the spring orifice, and the discharge vapor carries a faint odor of hydrogen sulfide. The Yashadi hot spring emerges on the left bank of the Jiashahe River at the entrance of the Nige Tunnel, with a measured discharge temperature of 87.9 °C, a flow rate of approximately 2.20 L/s, and a spring orifice elevation of 940 m. It is also classified as an ascending spring; a small amount of yellowish material is present on the orifice walls, and the discharge vapor carries a faint odor of hydrogen sulfide.

Figure 4. Field photographs of hot spring temperature measurements. (a) Nige hot spring (67.9 °C); (b) Laohutan hot spring (53.8 °C); (c) Yashadi hot spring (87.9 °C) [35,36].

4.2. Independence Analysis Results

As shown in Figure 5, correlation analysis was conducted to assess the degree of multicollinearity among the ten conditioning factors, revealing several pairs of factors with notably high correlation coefficients. Magnetic anomaly and peak ground acceleration displayed a strong negative correlation, with Pearson and Spearman coefficients of −0.85 and −0.91, respectively. Although both factors reflect variations in the physical properties of the regional lithosphere, their underlying mechanisms are fundamentally distinct: magnetic anomalies serve as indicators of magmatic heat sources, whereas peak ground acceleration captures the capacity for tectonic stress release, such that their respective contributions to geothermal prediction operate through different physical pathways. Moho depth and rainfall likewise exhibited a notable negative correlation, with a Pearson correlation coefficient of −0.82, attributable to a spatial co-occurrence between deep crustal structure and surface climate patterns rather than to any shared physical process; the two factors therefore retain independent geophysical significance. Land surface temperature and NDVI showed a moderate, nonlinear negative correlation, with a Spearman’s rank correlation coefficient of −0.71, consistent with the well-established coupling between surface energy balance and vegetation dynamics.

Figure 5. Multicollinearity assessment of the ten geothermal conditioning factors. (a) Pearson correlation matrix; (b) Spearman correlation matrix; (c) variance inflation factor (VIF) values for each conditioning factor.

Notwithstanding the correlations identified above, the variance inflation factor for each conditioning factor remained below 5, satisfying the independence requirements for multivariate statistical modelling. Given that the correlated factor pairs differ substantially in their physical mechanisms and geothermal implications, and that no evidence of harmful multicollinearity was detected, all ten conditioning factors were retained in the modelling framework to maximize the information content extracted from the multi-source dataset.

4.3. Geothermal Hazard Susceptibility Evaluation

The integrated geothermal hazard susceptibility map, derived by averaging log-odds values across all 500 Monte Carlo iterations and transforming the ensemble mean back to the probability domain via the inverse logistic function, is presented in Figure 6. The resulting susceptibility index exhibits pronounced spatial heterogeneity across the study area, with its distribution closely governed by the underlying tectonic architecture and fault geometry.

Figure 6. Geothermal hazard susceptibility maps from representative Monte Carlo iterations illustrating ensemble convergence. (a) susceptibility map from iteration 1; (b) susceptibility map from iteration 100; (c) susceptibility map from iteration 500.

To enhance interpretability and practical engineering utility, the continuous susceptibility index was reclassified into five ordinal categories, namely Very Low, Low, Medium, High, and Very High, through an equal interval classification scheme. The spatial distribution and areal proportion statistics of each susceptibility class are illustrated in Figure 7a and Figure 7b, respectively. The resulting frequency distribution is markedly left-skewed, indicating predominantly low- to moderate geothermal favourability across the study domain, with susceptibility elevated only in localized zones. The Very Low class constitutes the largest proportion of the study area, covering 1533 km² and accounting for 48.1% of the total assessment domain, followed by the Low class at 736 km² (23.1%), the Medium class at 465 km² (14.6%), the High class at 315 km² (9.9%), and the Very High class representing the smallest fraction at 137 km² (4.3%). Although the High and Very High categories collectively encompass only approximately 14.2% of the study domain, their spatial clustering is strongly consistent with the region’s dense fault network, elevated terrestrial heat flow, and prevailing active tectonic regime, confirming concentrated rather than uniform spatial distribution of geothermal risk. Notably, the Nige Tunnel traverses zones predominantly classified as High to Very High susceptibility, highlighting substantial and localized geothermal risk that must be systematically addressed throughout the tunnel construction and operational phases.

Figure 7. Statistical distribution of geothermal hazard susceptibility classes. (a) Pie chart showing the areal proportion of each susceptibility class; (b) bar chart showing the pixel count and percentage of each susceptibility class.

4.4. Uncertainty

The spatial distribution of the uncertainty index is presented in Figure 8. The uncertainty index is quantified as the standard deviation of log-odds values across the 500 Monte Carlo iterations, thereby capturing the degree of prediction variability attributable to stochastic input perturbations. Uncertainty values range from approximately 0.5 to 2.5, with elevated values concentrated in transitional zones between adjacent susceptibility classes and in regions where the spatial variability of conditioning factors is pronounced or where observational data density is insufficient to reliably constrain predictions.

Figure 8. Spatial distribution of prediction uncertainty quantified as the standard deviation of log-odds values across 500 Monte Carlo iterations.

Zones classified in the Very High susceptibility category generally exhibit moderate to elevated uncertainty, reflecting the logistic regression model’s inherent sensitivity to stochastic perturbations in input parameters under conditions of intense geothermal activity. Conversely, areas assigned to the Very Low susceptibility class tend to exhibit comparatively low uncertainty, indicating that the model yields stable predictions in geothermally quiescent domains. The spatial coincidence of high susceptibility and elevated uncertainty delineates priority areas where targeted field investigation and supplementary geophysical data acquisition would most effectively reduce predictive ambiguity and improve the reliability of engineering risk assessments. Of particular significance, the Nige Tunnel alignment intersects several zones characterized simultaneously by high susceptibility and elevated uncertainty, reinforcing the need for continuous geothermal monitoring protocols and adaptive risk mitigation strategies throughout the construction and operational phases.

4.5. Model Evaluation

The predictive performance of the Monte Carlo logistic regression framework was rigorously assessed through leave-one-out cross-validation applied independently across all 500 stochastic iterations, with model discrimination quantified by the area under the receiver operating characteristic curve, as shown in Figure 9. The resulting distribution of LOO-AUC values is approximately normally distributed, concentrated within the range of 0.7 to 1.0, with a mean of 0.824 and a standard deviation of ±0.074.

Figure 9. Frequency histogram of leave-one-out area under the receiver operating characteristic curve (LOO-AUC) values from 500 Monte Carlo iterations, with the mean value (0.824) indicated by the pink dashed line and the ±1σ range (0.074) indicated by the orange dotted lines.

The comparatively narrow standard deviation of the AUC distribution reflects the robustness of the ensemble framework to stochastic input perturbations, demonstrating that predictive performance remains statistically stable across the full range of simulated data-uncertainty scenarios. The mean AUC of 0.824 substantially exceeds the 0.5 benchmark for uninformative random classification and is comparable to or surpasses performance metrics reported in analogous geothermal susceptibility assessments conducted in structurally complex geological settings.

4.6. Sensitivity Analysis

As shown in Figure 10a, mean LOO-AUC values were evaluated across noise perturbation ratios ranging from 0.025 to 0.150. Model performance remains stable across this range, with mean AUC consistently between 0.80 and 0.84. A marginal but progressive decline is observed as the noise ratio increases, suggesting that excessive stochastic perturbation gradually attenuates predictive accuracy.

Figure 10. Sensitivity analysis of the Monte Carlo logistic regression model to key hyperparameters evaluated by mean leave-one-out AUC (LOO-AUC). (a) effect of noise ratio on model performance; (b) effect of negative sample ratio on model performance; (c) effect of regularization parameter (C) on model performance. Shaded areas and error bars represent the standard deviation across 500 Monte Carlo iterations.

Figure 10b presents mean LOO-AUC values evaluated for negative sample ratios ranging from 5 to 18. Discriminative performance increases steadily as the ratio is elevated from low values, stabilizing at ratios of approximately 10 and above, beyond which further increments yield progressively diminishing improvements. The ratio of 10 employed in this study lies within this stable plateau regime, validating the adopted sample construction strategy.

The influence of the L2 regularization coefficient C was evaluated over a logarithmic range spanning 10⁻¹ to 10¹, as shown in Figure 10c. Mean LOO-AUC increases gradually from approximately 0.79 at C = 10⁻¹ to a stable value near 0.84 at C = 10⁰ and beyond, indicating that moderate to weak regularization is most appropriate for the current dataset. The value of C = 1.0 adopted in this study resides within the region of maximum and stable performance.

The correlation matrix presented in Figure 11 reveals several notable inter-factor relationships and their respective associations with geothermal susceptibility. Among all conditioning factors, fault distance exhibits the strongest positive correlation with susceptibility (0.60), underscoring the dominant structural control exerted by fault proximity on geothermal fluid pathways. Slope also shows a moderately positive correlation (r = 0.54), reflecting the influence of topographic relief on thermal gradients and fluid circulation patterns. NDVI shows a positive correlation of 0.41 with susceptibility, whereas river density exhibits the most pronounced negative correlation at −0.40, suggesting that densely drained areas are associated with reduced geothermal favorability within the study domain. Several pronounced inter-factor correlations are also evident, most notably between mag and pga at −0.85, between moho and rainfall at −0.82, and between lst and ndvi at −0.68, indicating multicollinearity among these predictor pairs. The overall pattern of factor-susceptibility correlations is geophysically consistent and supports the physical plausibility of the conditioning factor selection employed in this study.

Figure 11. Pearson correlation matrix between the ten geothermal conditioning factors and the final geothermal hazard susceptibility index, illustrating the pairwise linear relationships among all variables, including susceptibility.

5. Discussion

Treating all hot spring occurrences as equally weighted implicitly assumes that each spring is equally representative of the underlying geothermal system. This assumption is physically unjustified: spring temperature serves as a composite proxy for hydrothermal circulation depth and heat-flux intensity, with higher temperatures indicating deeper fluid sourcing and stronger thermal anomalies [37]. The three springs in the study area span a temperature range of 34.1 °C, and, given that only three positive samples exert disproportionate leverage on the logistic decision boundary, uniform weighting risks diluting the discriminative signal carried by high-temperature springs with that of lower-temperature occurrences, thereby systematically suppressing the model’s sensitivity to intense geothermal anomalies. The temperature-weighting scheme adopted in this study converts the binary presence signal into an ordinal representation of hydrothermal intensity, enabling the model to learn more from factor configurations associated with high-temperature hydrothermal environments.

The susceptibility pattern is characterised by a concentrated high-risk core in the central-northern portion of the study domain, from which elevated values extend along two oblique structural corridors oriented northwest–southeast and northeast–southwest before diminishing toward the domain periphery. This pattern cannot be attributed to fault proximity alone; rather, it reflects the spatial coincidence of fault intersection geometry, topographic convergence, and multi-factor thermal conditioning, collectively constituting the defining characteristics of a geothermal sweet spot as described in the exploration literature [38].

However, the strong predictive signal of fault distance reflects spatial correlation patterns derived from the statistical model rather than explicit mechanistic simulation of fluid dynamics processes. Although the model identifies structural corridors where geothermal fluids are likely to concentrate, it does not directly simulate the coupled thermo-hydrodynamic processes governing fluid migration rates, pressure gradients, and heat transfer efficiency within fault damage zones. Within the framework of regional-scale analysis, this study employs spatial coupling relationships among multi-source datasets to effectively delineate tectonic-topographic composite domains of preferential geothermal fluid accumulation. Built upon this spatial framework, subsequent investigations can deploy coupled thermo-hydrodynamic models at local scales (fault-to-pore scales) to explicitly solve the governing equations controlling fluid migration rates, pressure gradient evolution, and heat transfer efficiency.

The comparatively weak contributions of heat flow and Moho depth are closely related to the spatial resolution limitations of their source datasets. At the 1 km × 1 km spatial resolution employed in this study, the spatial gradients of these datasets are insufficiently resolved to effectively detect kilometre-scale thermal anomalies. This represents an inherent constraint when applying regional-scale geophysical products to site-scale susceptibility mapping [39] and should not be interpreted as evidence that deep thermal structure is geologically unimportant; the incorporation of high-resolution borehole temperature gradient data would be expected to substantially improve the predictive power of these factors.

Given these limitations, the dominant role of fault distance among all evaluated factors is consistent with the physical mechanics of fault-controlled hydrothermal systems: in tectonically active settings, cataclastic rocks and damage zones within fault corridors generate high-permeability fluid pathways that facilitate efficient upward transport of deep-seated hydrothermal fluids [37]. Notably, the predictive contribution of fault distance exceeds that of heat flow and Moho depth, both of which are theoretically more direct indicators of deep thermal energy supply, suggesting that the rate-limiting control on geothermal fluid accumulation in this region is not the magnitude of basal heat input but rather the structural permeability available for upward fluid migration. This implies that the efficacy of the geothermal system in this region is structurally, rather than thermically, limited.

As shown in Figure 12, the susceptibility map reveals spatially differentiated geothermal exposure geometries among the five tunnels traversing the study domain, with implications for risk-differentiated engineering design. The tunnel in the northern part of the central cluster intersects the highest-susceptibility pixels at its midpoint, indicating maximum thermal exposure at depth along its alignment. The two tunnels to the west and south of the core enter high-susceptibility zones only near their portal ends, with intermediate sections passing through comparatively lower-risk terrain, implying that geothermal hazard is concentrated at portal-proximal segments rather than distributed uniformly along the full alignment. The tunnel to the east runs broadly parallel to the southeastern susceptibility corridor, maintaining persistently elevated but sub-maximum susceptibility exposure along its entire length, which is consistent with the results of actual geothermal testing conducted in the Nige Tunnel [40]. These spatial contrasts indicate that geothermal mitigation measures, including thermal drainage design, real-time temperature monitoring, and emergency cooling capacity, need not be applied uniformly across all tunnel lengths, but should be prioritised at the specific alignment segments where susceptibility and predictive uncertainty are simultaneously at their highest.

Figure 12. Monte Carlo ensemble-based geothermal susceptibility map showing probability distribution and relative positions of five tunnel alignments (Dashidong, Douyancun, Tabaiyi, Nige, and Feigu tunnels).

It should be noted that although temporal variations have been incorporated in certain datasets—such as Rainfall and Land Surface Temperature (LST), which were represented by decadal average values—the proposed framework remains essentially static and does not incorporate temporal evolution, hydrothermal variability, or permeability changes associated with tectonic activity. Future investigations should consider integrating temporal scales into the framework to enable spatio-temporal evolution analysis.

6. Conclusions

This study takes the Nige Tunnel on the Yunnan–Guizhou Plateau as a representative engineering case to address the problem of geothermal hazard susceptibility assessment under conditions of extremely limited sample availability. A geothermal hazard susceptibility assessment framework that integrates multi-source data and Monte Carlo uncertainty quantification was developed, enabling a quantitative evaluation of the spatial distribution of regional geothermal hazards under limited observational data.

(1) A three-stage assessment framework was developed, incorporating temperature-weighted positive sample construction to convert the binary hot spring occurrence signal into an ordinal representation reflecting hydrothermal intensity. Monte Carlo stochastic perturbation was applied across 500 iterations of an L2-regularized logistic regression model, with ensemble uncertainty quantification enabling identification of spatial regions sensitive to parameter perturbations. This approach achieves robust predictive performance (mean LOO-AUC = 0.824) even under sparse-sample conditions.

(2) The susceptibility assessment reveals pronounced spatial heterogeneity in geothermal hazard. High and Very High susceptibility zones account for 14.2% of the study area, with strong spatial alignment to mapped fault traces and hydrothermal discharge locations, confirming geological plausibility. Notably, the Nige Tunnel traverses predominantly High to Very High susceptibility zones, indicating a substantial and localized geothermal risk requiring systematic mitigation during construction and operation.

(3) Fault distance emerges as the dominant predictive factor, surpassing terrestrial heat flow and Moho depth. This indicates that the rate-limiting control on geothermal fluid enrichment in this region is not the magnitude of basal heat input but rather the structural permeability available for efficient upward fluid migration through fault damage zones. This finding demonstrates that in fault-controlled systems, structural geology assessment should take primary precedence in susceptibility evaluation.