Introduction

In 2013, a 7.0-magnitude earthquake struck Lushan County, Ya’an City, China, with a focal depth of 13 km. This seismic event, occurring in the aftermath of the devastating Wenchuan earthquake, inflicted further damage upon the region. Lushan County is situated in the southern segment of the Longmenshan Fault Zone1 and is recognized as a typical region prone to frequent geological disasters following the Wenchuan event, characterized by distinct tectonic and seismic activity. The 2013 Lushan earthquake triggered strong seismic effects, leading to extensive rock mass fracturing and a significant decline in slope stability, which resulted in numerous potential landslide and collapse hazards. The region is also lithologically sensitive, with widespread interbedded Jurassic sandstone and mudstone formations. These rocks are weakly resistant to weathering and prone to forming soft interlayers, making them highly susceptible to earthquake-induced landslides. Moreover, multiple types of geological hazards coexist in the area, including landslides, rockfalls, and debris flows, making it an ideal site for testing the generalizability of susceptibility assessment models across different hazard mechanisms. Located in the transitional zone between the Sichuan Basin and the western Sichuan Plateau, Lushan County intersects fault zones associated with three major rivers, further intensifying its geological vulnerability. The occurrence of these two significant seismic events has exacerbated the region’s existing environmental challenges, leading to a surge in geological disasters. These hazards have severely hindered infrastructure development and economic growth in Lushan County, posing substantial risks to human life and property security.

In recent years, propelled by the rapid advancement of Geographic Information Systems (GIS), research on geological disaster early warning and prediction has yielded notable progress2. While some studies have explored landslide development and spatial distribution in Lushan County using GIS technology3,4,5, a comprehensive post-earthquake susceptibility assessment of geological disasters (including landslides, debris flows, and collapses) across the entirety of Lushan County necessitates further exploration. Such research endeavors hold promise in furnishing robust scientific underpinnings for disaster monitoring, early warning systems, and disaster mitigation strategies in post-earthquake regions like Lushan County.

Currently, the main research approach for susceptibility assessment of geological disasters revolves around integrating Geographic Information Systems (GIS) with statistical principles and mathematical models6. Among these, commonly employed quantitative assessment models encompass the logistic regression (LR)7, the information value (I) method8,9, the certain factor (CF) model10, the analytic hierarchy process (AHP)11, machine learning methods12, the evidence weight method13, the entropy method14, and the frequency ratio method15. For example, Li et al.16 assessed the susceptibility of landslide disasters in Qinghai Province using the frequency ratio method and machine learning method, with results indicating higher accuracy with the machine learning method. Chen et al.17 investigated the application of information value and logistic regression (LR) models for producing landslide susceptibility maps of the Zigui-Badong area near the Three Gorges Reservoir in China. Du et al.18 introduced an integrated model that combines the information value method and logistic regression for landslide susceptibility mapping in the highly landslide-prone Bailongjiang watershed in southern Gansu province, China. Myronidis et al.19 developed a landslide susceptibility model for a landslide-prone area in Cyprus, using a combination of the analytic hierarchy process and the frequency ratio method in GIS, achieving a 73.9% accuracy and providing insights for effective landslide risk mitigation. Some studies have also adopted disaster vulnerability function models to assess infrastructure losses under the influence of individual hazards such as earthquakes20, or under compound hazard scenarios such as earthquake–flood events21.

It is evident that different evaluation models yield varying susceptibility zoning results. Additionally, each model has its own advantages and disadvantages. The information value (I) model essentially evaluates and compares the amount of information each influencing factor contributes to the study object. By calculating the overall information provided by these factors, the model enables regional susceptibility prediction and classification8. The certain factor (CF) model, initially proposed by Shortliffe et al.22 and later improved by Oh et al.23, is a probabilistic function that measures the certainty of each evaluation factor by calculating the difference between conditional and prior probabilities, thereby assessing the susceptibility to geological hazards in a given area. However, single evaluation models have inherent limitations, such as the inability to determine the weights of influencing factors and to eliminate correlations among them. Although the machine learning method boasts higher accuracy, it poses challenges in model parameter tuning17,18. The information value method and certain factor model are widely used in susceptibility assessment of geological disasters due to their simplicity, strong operability, and ability to conduct rapid assessments. However, these two models fail to reflect the contribution of each evaluation factor to the occurrence of geological disasters and are significantly influenced by factor grading20.

To explore the impact of various mathematical models on the rationality of susceptibility assessment outcomes for geological disasters, a case study was conducted using post-earthquake disaster data from Lushan County, Ya’an City. Utilizing Geographic Information Systems (GIS), 12 evaluation factors closely linked to terrain, hydrological conditions, land cover, and other external factors were initially identified. The information value (I) model, the certain factor (CF) model, and coupling models such as the informative-logistic regression (I-LR) model and certain factor-logistic regression (CF-LR), alongside the machine learning-based random forest (RF) model. Subsequently, the susceptibility of post-earthquake disasters in Lushan County was assessed and delineated using these models, and their accuracy and validity were discussed. The research outcomes hold significant potential to guide the prevention, control, monitoring, and early warning efforts for geological disasters in post-earthquake regions like Lushan County.

Study area and data sources

Study area overview

Lushan County, situated at the western fringe of the mountainous terrain encircling the Sichuan Basin, lies in the northeastern precincts of Ya’an City, straddling the upper reaches of the Qingyi River. Geographically, it spans between longitudes 102° 52′ E and 103° 11′ E, and latitudes 30° 01′ N and 30° 49′ N, nestled within the southern expanse of the Longmenshan Fault Zone. Seismic activity ranges from VII to VIII, with peak ground accelerations registering between 0.10 g and 0.20 g. The topography is characterized by a north-south elevation gradient, with elevations ranging from 541 m to 5279 m. The western and northern sectors are dominated by rugged mountainous terrain and deep valleys, while the central and southeastern areas comprise lower mountains, hills, and river valleys. Geological formations predominantly include Cambrian, Ordovician, Silurian, Devonian, Permian, Triassic, Jurassic, and Cretaceous systems, featuring diverse rock types such as sandstone, mudstone, shale, conglomerate, and limestone. The hydrological network is extensive, with 556 rivers and streams converging into the Qingyi River and 11 rivers boasting drainage areas exceeding 30 km2. The geographical delineation of the study area is depicted in Fig. 1.

Fig. 1
Fig. 1
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Map of the study area with topography and distribution of disaster sites.

Data sources

Based on geological disaster data and field surveys in Lushan County, a total of 189 disaster sites of various types were documented following the earthquake, including 91 landslides, 55 collapses, 40 unstable slopes, and 3 debris flows, as depicted in Fig. 1.

The foundational data for assessing the susceptibility of geological disasters encompass: (1) A 30-meter resolution Digital Elevation Model (DEM) utilized for extracting slope, aspect, and hydrological characteristics; (2) Lushan County’s 1:500,000 geological map utilized for identifying rock types, faults, and other relevant geological features; (3) Landsat 8 Operational Land Imager (OLI) remote sensing imagery employed for computing the Normalized Difference Vegetation Index (NDVI).

Model evaluation framework

The model evaluation framework consists of five key aspects:

  1. (i)

    Construct a unified post-earthquake disaster list and 12 condition factors (189 disaster sites, including landslides, collapses, unstable slopes, and debris flows);

  2. (ii)

    Discretize the factors and perform multicollinearity diagnostics (VIF), including only those factors with acceptable multicollinearity for modeling;

  3. (iii)

    Systematically compare five representative models under the same factor set and classification strategy: Information Value (I) model, Certainty Factor (CF) model, Information Value-Logistic Regression coupling model (I-LR), Certainty Factor-Logistic Regression coupling model (CF-LR), and Random Forest (RF) model;

  4. (iv)

    Use a multi-indicator evaluation (frequency ratio, ROC-AUC, PR curve, and F1 score), rather than relying solely on AUC;

  5. (v)

    Conduct map validation and provide actionable policy interpretations using an external (cross-time) event list (e.g., the overlap rate of disaster points in high/extreme-risk areas).

Susceptibility assessment models

Information value (I) model

The information value (I) model stands as the prevailing model for assessing the susceptibility of geological disaster activity. Its procedural framework entails, initially, the statistical analysis of historical disaster data; subsequently, the computation of information values for each factor across different factor grades, grounded on the precipitating factors of geological disasters; and ultimately, the summation of information values across diverse factors to derive the total information value (I). The magnitude of I serves as a barometer of the contribution of a specific influencing factor within a designated grade interval to the occurrence of geological disasters. The formal expression for the information value model24 is as follows:

$$I=\sum\nolimits_{{i=1}}^{n} {I({x_i}} ,H)=\sum\nolimits_{{i=1}}^{n} {\ln \frac{{{N_i}/N}}{{{S_I}/S}}}$$
(1)

where I represents the total information value of the evaluation unit, n denotes the number of influencing factors, I (xi, H) signifies the information value contributed by evaluation factor xi to the occurrence of geological disaster event H, Ni represents the number of geological disasters distributed within the specific evaluation factor xi, N is the total number of geological disasters in the study area, Si denotes the area containing evaluation factor xi within the study area, and S represents the total area of the study area. The total information value I serves as a comprehensive indicator for assessing the susceptibility of geological disasters. A larger I indicates a higher likelihood of geological disasters, whereas a smaller value suggests a relatively lower likelihood of occurrence.

Certain factor (CF) model

The certain factor (CF) model, introduced by Shortliffe et al.22, is a probabilistic function method employed for analyzing the sensitivity of various evaluation factors in triggering geological disasters, thereby facilitating susceptibility assessment of disasters within the study area. The underlying premise of this model posits that the conditions for future geological disasters resemble those of past occurrences. Its computational formula is expressed as follows:

$$CF=\left\{ \begin{gathered} \frac{{{P_a} - {P_s}}}{{{P_S}(1 - {P_a})}},{P_a}<{P_s} \hfill \\ \frac{{{P_a} - {P_s}}}{{{P_a}(1 - {P_s})}},{P_a} \geqslant {P_s} \hfill \\ \end{gathered} \right.$$
(2)

where CF represents the certainty factor of geological disaster occurrence; Pa denotes the conditional probability of geological disasters occurring within the evaluation factor category a, which can be represented by the ratio of the area of geological disasters in category a to the total area of category a in the study; Ps represents the ratio of the total number of disaster points to the total area of the study area. Once the study area is determined, Ps represents the overall point density, which is generally a constant value; whereas Pa represents the local point density, which is a variable. After comparing the two, the respective formula is then applied for computation.

According to Eq. (2), CF ranges from − 1 to 1. A positive CF value indicates an increased certainty of disaster occurrence, with values closer to 1 suggesting a higher likelihood of disasters and a greater susceptibility of the evaluation unit to such events. Conversely, a negative CF value indicates a reduced certainty of disaster occurrence, with values closer to -1 indicating a lower likelihood of disasters and a decreased susceptibility of the evaluation unit to geological disasters.

Coupled model based on the principles of logistic regression

The logistic regression principle constitutes a statistical analytical method used to explore the relationship between binary classification outcomes and factors demonstrating no overt correlation with them. In the analysis of geological disaster issues, the independent variables encompass selected evaluation factors such as elevation, slope, lithology, etc. The dependent variable manifests as a binary variable conventionally denoted by 0 and 1, where 0 signifies the absence of geological disaster events, while 1 denotes their occurrence. The formula for this model is articulated as follows23:

$$\left\{ \begin{gathered} P(Y=1|X)=\frac{1}{{1+{e^{ - Z}}}} \hfill \\ Z={\beta _0}+{\beta _1}{x_1}+{\beta _2}{x_2}+...+{\beta _n}{x_n} \hfill \\ \end{gathered} \right.$$
(3)

Where x1, x2, x3, …, xn represent the independent variables; P denotes the probability of disaster occurrence, with values ranging from 0 to 1; 1, 2, 3, …, n represent the logistic regression coefficients.

Due to the inability of singular information value and certainty factor models to determine the relative importance of each evaluation factor, the absolute values of logistic regression coefficients can effectively reflect the contribution of factors to disaster occurrence. Consequently, coupling these two models with the logistic regression model resolves the challenge of assessing the relative importance among evaluation factors and mitigates the subjective influence inherent in a single model.

Informative-logistic regression (I-LR) model

The specific procedure for model coupling involves initially computing the information value for each evaluation factor under different grades as per Eq. (1). These computed results are then imported into SPSS software as independent variables for binary logistic regression, where regression equations are formulated and logistic regression operations are conducted to determine the logistic regression coefficients for each evaluation factor. Subsequently, in accordance with Eq. (3), each evaluation factor’s information value is assigned corresponding logistic regression coefficients before being aggregated. Utilizing the aggregated result, the I-LR model is established for susceptibility assessment of geological disasters.

Certain factor-logistic regression (CF-LR) model

The CF-LR coupling model, akin to the I-LR coupling model, follows a similar procedural approach. It entails computing the deterministic coefficient values for each evaluation factor under various grades as per Eq. (2). Subsequently, in accordance with Eq. (3), the information values of evaluation factors are assigned corresponding logistic regression coefficients. Ultimately, the CF-LR model can be established for the susceptibility assessment of geological disasters.

Random forest model

The Random Forest (RF) model introduces randomness through both bootstrap sampling and random feature selection. Bootstrap sampling with replacement ensures diversity in the training subsets, thereby enhancing the resolution of the feature space and facilitating the formation of more accurate and smoother decision boundaries. In RF, each decision tree is typically constructed using the Classification and Regression Tree (CART) algorithm. A large ensemble of trees is generated based on randomly selected subsets of samples and features to perform either classification or regression tasks. The process of applying the Random Forest model is illustrated in Fig. 2. In the Random Forest calculation, each sample point in the training set receives a probability value between 0 and 1 for each decision tree. The average probability across all decision trees reflects the likelihood of a disaster occurring at that sample point. The final disaster zonation map is constructed by dividing the probability range (0–1) into five categories: very high susceptibility areas (probability between 0.8 and 1.0), high susceptibility areas (probability between 0.6 and 0.8), moderate susceptibility areas (probability between 0.4 and 0.6), low susceptibility areas (probability between 0.2 and 0.4), and very low susceptibility areas (probability between 0.0 and 0.2).

Fig. 2
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Process and principles of applying the Random Forest model.

For classification, the final prediction is determined by majority voting across all trees, whereas for regression, the mean prediction is used. During the construction of classification trees, the Gini index is employed as the criterion for selecting the optimal split feature and split point. A smaller Gini index indicates a better partition. The Gini index is calculated as follows:

$$Gini\_index(D,a)=\sum\limits_{{v=1}}^{n} {\frac{{{D_v}}}{D}} Gini({D_v})$$
(4)
$$Gini({D_v})=1 - \sum\limits_{{k=1}}^{m} {{p_k}^{2}}$$
(5)

where D denotes the total number of samples; Dv represents the number of samples in the v-th branch node for feature a; \({p_k}=\frac{{{C_k}}}{D}\) and Ck is the number of samples belonging to class k.

Training and testing samples

Utilizing the subset feature function in ArcGIS 10.8, 159 disaster sites were extracted from the actual 189 disaster sites, combined with 741 randomly generated non-geological disaster sites, totaling 900 samples as training data to meet the spatial requirements of the logistic regression model. The distribution of disaster and non-disaster sites is illustrated in Fig. 3. The remaining 30 actual geological disaster sites were allocated as testing samples. During the susceptibility assessment of geological disasters, the allocation of training and testing samples in the I model, CF model, I-LR model, and CF-LR model is delineated in Table 1.

Fig. 3
Fig. 3
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Distribution of disaster sites.

Table 1 Number of disaster and non-disaster samples under different models.
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Selection and analysis of evaluation factors

The meticulous selection of evaluation factors profoundly influences the precision of geological disaster susceptibility assessment. Drawing from comprehensive survey data and scholarly references, various facets such as terrain, hydrological conditions, land cover, and external factors were scrutinized for their role in disaster predisposition. Subsequent analysis led to the identification of twelve key factors essential for assessing geological disaster susceptibility in Lushan County, encompassing elevation, slope, aspect, curvature, engineering geological lithology, distance to rivers, terrain ruggedness, PGA, distance to faults, distance to roads, NDVI, and surface cutting depth.

Fig. 4
Fig. 4Fig. 4
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Susceptibility assessment factors: (a) Elevation; (b) Slope; (c) Aspect; (d) Curvature; (e) Engineering geological lithology; (f) Distance to rivers; (g) Terrain ruggedness; (h) PGA; (i) Distance to faults; (j) Distance to roads; (k) NDVI; (l) Surface cutting depth.

The selection of the twelve evaluation factors was guided by three fundamental principles: dominance of geological processes, data availability, and indicator independence. These factors were classified into four categories: (1) Topographic and geomorphic factors, including elevation, slope, aspect, and curvature, which control slope stress distribution and surface runoff pathways25; (2) Geotectonic and lithological factors, comprising engineering geological units, surface relief, distance to faults, and peak ground acceleration (PGA); (3) Hydrological and anthropogenic factors, including distance to rivers, distance to roads, and surface incision depth; (4) Ecological surface factor, represented by the normalized difference vegetation index (NDVI), which reflects vegetation cover and its role in enhancing slope stability through root reinforcement. Importantly, PGA was selected as a substitute for traditional rainfall indicators, considering that post-earthquake landslides are primarily controlled by residual seismic stress rather than hydrological triggers26. Employing ArcGIS’s reclassification function, these chosen factors were categorized, as depicted in Fig. 4. Detailed grading criteria for each factor and the corresponding information regarding disaster points are meticulously documented in Table 2.

Table 2 The classification of evaluation factors and corresponding disaster sites.
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(1) Elevation.

Elevation plays a crucial role in shaping the landscape and influencing various environmental factors, including vegetation cover, biological activities, precipitation patterns, and temperature regimes27. Notably, the study area exhibits significant elevation disparities between its northern and southern regions, ranging from 541 to 5282 m, segmented into six intervals (Fig. 3a). Among these, elevations ranging from 1131 to 1623 m account for 55% of disaster occurrences. Notably, no disasters have been recorded above the elevation of 2833 m.

(2) Slope.

Slope gradient, indicative of the steepness of the terrain, is a pivotal factor influencing slope stability and landslide susceptibility16. Derived directly from Digital Elevation Model (DEM) data, slope gradients are categorized into seven intervals, as depicted in Fig. 3b. The majority of disaster sites in the study area are concentrated within the range of 0° to 40°, with the highest incidence observed within the 10° to 20° range, constituting 32% of the total.

(3) Aspect.

Aspect, or slope orientation, significantly affects microclimatic conditions and moisture regimes, thereby influencing slope stability and landslide occurrence28. In the study area, slopes oriented between 112.5° to 157.5° and 157.5° to 202.5° (southeast and south) exhibit notably higher disaster occurrence rates, accounting for 19% and 23%, respectively. These orientations are identified as predominant contributors to disaster occurrences. Consequently, the probability of landslides on sunlit slopes in Lushan County is considerably higher.

(4) Curvature.

Surface curvature, reflecting slope change rates, significantly influences surface runoff convergence29. Positive curvature indicates convex surfaces, while negative values indicate concave ones. Larger absolute curvature values denote steeper terrain. Within our study area, disaster sites are mainly clustered within a curvature range of -2 to 1, with the − 2 to -1 interval exhibiting the highest incidence at 21%.

(5) Engineering geological lithology.

Engineering geology lithology determines slope material composition and engineering properties, directly affecting deformation and stress distribution3. Based on detailed investigations, lithology in our study area is classified into eight categories (Fig. 3e). Shale and carbonate rock lithologies constitute a significant proportion of disaster sites (29% and 44%, respectively). This is primarily due to widespread carbonate rock lithology distribution in Lushan County, coupled with severe weathering erosion. Surface-weathered soils undergo increased bulk density and reduced shear strength under rainfall infiltration, leading to geological disasters.

(6) Distance to rivers.

Water bodies exert erosional effects on slopes adjacent to riverbanks, enlarging or forming free faces on slopes and potentially causing bank collapses and landslides30. Our results indicate that 75% of disaster sites are located within 400 m of the river center. This confirms that slopes closer to water bodies experience greater erosion effects, rendering them more susceptible to the formation of weak sliding zones.

(7) Terrain ruggedness.

Terrain ruggedness, denoting the disparity in elevation between the highest and lowest points within a defined area, stands as a macroscopic indicator delineating regional terrain features. It quantifies terrain morphology, facilitates landform classification, and reflects ground undulations and incision levels31. In our study area, disaster sites gravitate toward relief zones under 310 m, with only 19 sites surpassing this threshold. This discrepancy is ascribed to meticulous disaster documentation in human-inhabited locales, whereas occurrences in remote regions like high mountain gorges remain significantly underreported.

(8) Peak ground acceleration (PGA).

Peak ground acceleration (PGA), representing seismic attributes across various parameters, including amplitude, frequency, and duration, bears substantial influence on the genesis and activation of unstable rock masses. Seismic waves inflict damage on rock mass interiors, ultimately precipitating changes and failure32. PGA distribution in our study area is categorized into three tiers: 0.10 g, 0.15 g, and 0.20 g (Fig. 3h). The expansive coverage of 0.15 g PGA, spanning 905.5 km2, harbors a pronounced concentration of disaster sites, accounting for 85% of the total.

(9) Distance to faults.

The development of geological disasters is notably shaped by fault structures, exerting direct influence on primary fault planes and surrounding rock masses. This dynamic engenders ruptures, compositional shifts, and alterations in physical and mechanical properties33. Utilizing GIS analytics, fault proximity within the study area is stratified into nine intervals (Fig. 3i). Disaster sites predominantly cluster within intervals spanning less than 1000 m and exceeding 6000 m, constituting 21% and 36%, respectively.

(10) Distance to roads.

The distance to roads signifies the impact of human activities on geological disasters. Road construction inevitably involves activities such as slope cutting and top loading, which disrupt original terrain features and compromise the integrity of rock and soil structures34. Utilizing GIS, the distribution of major transportation corridors within the study area is stratified into seven intervals based on road distance (Fig. 3j). Notably, disaster sites within the 0–500 m range account for the largest proportion, constituting 38%. This indicates that slopes closer to roads experience greater anthropogenic disturbances, exhibiting more pronounced signs of soil instability, and are highly susceptible to disasters under external factors such as earthquakes or heavy rainfall.

(11) Normalized difference vegetation index (NDVI).

Forest vegetation effectively mitigates soil erosion on slopes by anchoring roots in the soil, enhancing soil erosion resistance and shear strength, and increasing slope stability35. NDVI quantitatively describes the vegetation cover index, with values ranging from − 1 to 1. Based on NDVI values calculated from remote sensing imagery, the study area is classified into six categories (Fig. 3k). Disaster sites predominantly cluster within the range of 0.45 to 0.65, indicating a propensity for disasters to occur in areas with moderate vegetation cover. Lower vegetation cover areas often correspond to terrain conditions in townships and are less prone to disasters. Conversely, higher vegetation cover areas exhibit closer vegetation-soil contact and less soil erosion, thereby enhancing slope stability.

(12) Surface cutting depth.

Surface cutting depth refers to the difference between average elevation and minimum elevation within a specific range, reflecting the extent of natural environmental erosion on the earth’s surface. It is commonly used to study soil erosion and surface erosion development36. Through GIS analysis, the surface cutting depth in Lushan County ranges from 7.9 to 464.8 m, divided into six intervals (Fig. 3l). Disaster sites predominantly occur in areas with a surface cutting depth below 198.9 m, with only three instances above this threshold. Thus, in the study area, greater surface cutting depth correlates with reduced susceptibility to geological disasters.

Geological hazard susceptibility assessment

Susceptibility assessment to geological hazards using I and CF models

Calculation results of I and CF values

Based on the distribution of disaster sites across various classification levels of each evaluation factor in the training samples, the I values and CF values were calculated using Eq. (1) and Eq. (2), respectively (Table 2). This illustrates the relative sensitivity of each classification level within the same evaluation factor and facilitates comparison among the classification levels of different evaluation factors.

Analysis of evaluation factor correlation

High correlation among evaluation factors can distort the model or impede accurate predictions. Therefore, it is imperative to assess multicollinearity among the 12 evaluation factors by computing the variance inflation factor (VIF) for each indicator, as shown in Table 3. If VIF > 10, it indicates severe multicollinearity among the factors. However, Table 3 indicates that the selected evaluation factors exhibit no severe multicollinearity, thus affirming that all 12 factors are suitable for inclusion in the model.

Table 3 Results of variance inflation factor calculation.
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Disaster susceptibility zoning under I and CF models

(1) Disaster susceptibility zoning under the I model.

Utilizing GIS’s raster calculator tool, the distribution map of geological disaster susceptibility in Lushan County is obtained by overlaying the information values of each evaluation factor’s classification level in the study area. Employing the natural breaks classification method, Lushan County is demarcated into 5 susceptibility level intervals: extremely high susceptibility zone, high susceptibility zone, moderate susceptibility zone, low susceptibility zone, and extremely low susceptibility zone (Fig. 5a). These zones encompass approximately 13.67%, 24.56%, 24.81%, 19.45%, and 17.51% of the total area, respectively. The areas characterized by extremely high and high susceptibility to geological disasters are predominantly situated in the low mountains and river valleys of the southern and central regions of the study area, exhibiting a plethora of water systems and notable river erosion. Moreover, frequent human activities such as road construction and bridge building are prevalent, contributing to substantial alterations and disturbances in the geological environment. Conversely, the extremely low and low susceptibility zones are primarily located in the high mountain gorges of the northern part of the study area, where human activities are minimal. Hence, human engineering endeavors within the study area exert a significant influence on the evolution of geological disasters.

Fig. 5
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Susceptibility assessment maps: (a) I model results; (b) CF model results.

(2) Disaster susceptibility zoning under the CF model.

The method for obtaining the distribution map of certain factor values for geological disasters in Lushan County follows the same procedure as for obtaining the distribution map of information values. Utilizing the natural break classification method, the distribution map of certain factor values is categorized into five susceptibility level intervals: extremely high susceptibility zone, high susceptibility zone, moderate susceptibility zone, low susceptibility zone, and extremely low susceptibility zone (Fig. 5b). These zones, respectively, cover 14.15%, 19.83%, 23.21%, 24.04%, and 18.77% of the total area. In comparison to the I model, the distribution pattern of susceptibility zones remains generally consistent, albeit with a notable increase in the proportion of low susceptibility zones by approximately 5% (62 km2).

Susceptibility assessment to geological hazards using I-LR and CF-LR models

Determination of regression coefficients for evaluation factors

The I and CF values of the 12 evaluation factors at the sample points were individually input into the SPSS software for binary logistic regression analysis. Here, the I and CF values of each evaluation factor at different classification levels served as independent variables, while the occurrence of geological disasters (with 1 representing geological disaster sample points and 0 representing non-geological disaster sample points) was considered the dependent variable. The logistic regression outcomes for both the I and CF models are summarized in Table 4.

Table 4 Results of logistic regression analysis.
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It is crucial to exercise restraint in the selection of evaluation factors, as their significance within the equation is determined by the Sig value. Only when the Sig value falls below 0.05 does it denote statistical significance. Examination of the regression results reveals that, for both models, the Sig values associated with six factors, including elevation, slope, engineering geological lithology, surface undulation, PGA, and distance to fault, all exceed 0.05. This indicates a lack of statistical significance based on significance testing and necessitates their exclusion from further analysis.

Subsequently, aspect, curvature, distance to river, distance to road, NDVI, and surface cutting depth were chosen for recalibration. The Sig values associated with these factors were found to be less than 0.05, underscoring their statistical significance, as detailed in Table 5. This affirms the reliability of the logistic regression results and the statistical significance of the selected evaluation factors. By substituting the regression coefficients into Eq. (3), the I-LR susceptibility evaluation model and the CF-LR susceptibility evaluation model were derived.

Table 5 Results of the logistic regression analysis after removing collinear factors.
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Hazard susceptibility zoning under I-LR and CF-LR models

(1) Susceptibility zoning under I-LR model.

By employing Eq. (3), the GIS raster calculator tool was utilized to assign corresponding regression coefficients to each information layer, enabling the generation of hazard susceptibility evaluation maps for the I-LR model. Employing the natural break method, Lushan County was stratified into 5 susceptibility level intervals: extremely high susceptibility area, high susceptibility area, moderate susceptibility area, low susceptibility area, and extremely low susceptibility area (Fig. 6a). These zones, respectively, account for 13.47%, 21.21%, 25.26%, 24.85%, and 15.21% of the total area. Compared to the standalone I model, there is a noticeable reduction in the proportion of extremely high and high susceptibility areas.

Fig. 6
Fig. 6
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Susceptibility assessment maps: (a) I-LR model results; (b) CF-LR model results.

(2) Susceptibility zoning under CF-LR model.

The approach for acquiring the geological hazard susceptibility assessment map under the CF-LR model mirrors that of the I-LR model. Following the overlay of each deterministic coefficient layer with its corresponding regression coefficients, Lushan County was delineated into five susceptibility level intervals using the natural break method: extremely high susceptibility area, high susceptibility area, moderate susceptibility area, low susceptibility area, and extremely low susceptibility area (Fig. 6b). These zones, respectively, encompass 13.01%, 20.39%, 24.94%, 26.47%, and 15.19% of the total area. The findings demonstrate a notable alignment between the CF-LR and I-LR coupled models, with the areas of susceptibility zones demonstrating close comparability.

Susceptibility assessment based on the RF model

The RF model was constructed using the same set of influencing factors as the IV model and implemented in IDLE (Python 3.12). The resulting susceptibility zoning map is shown in Fig. 7. By incorporating both sample and feature randomness, the RF model effectively reduces the impact of outliers on prediction results. In the Random Forest model calculation, each sample point in the training set receives a probability value between 0 and 1 for each decision tree. The average probability across all decision trees reflects the likelihood of a disaster occurring at that sample point. The final disaster zonation map is constructed by dividing the probability range (0–1) into five categories: very high susceptibility areas (probability between 0.8 and 1.0), high susceptibility areas (probability between 0.6 and 0.8), moderate susceptibility areas (probability between 0.4 and 0.6), low susceptibility areas (probability between 0.2 and 0.4), and very low susceptibility areas (probability between 0.0 and 0.2). As illustrated in Fig. 6, the areas classified as high and very high susceptibility zones are smaller in the RF model compared to those in the IV model. The proportions of the five susceptibility classes—very high, high, moderate, low, and very low—are 10.26%, 19.88%, 25.40%, 24.42%, and 20.04% of the total area, respectively.

Fig. 7
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Susceptibility zoning map based on the RF Model.

Validation and comparison

To validate the accuracy of the susceptibility assessment results for geological hazards in Lushan County generated by the four models, frequency ratio analysis and Receiver Operating Characteristic (ROC) curve analysis were employed.

Frequency ratio analysis

Frequency ratio analysis compares the proportion of test samples within each susceptibility zone to the proportion of zone area. Results (Table 6) show that across the four models, the area of extremely high susceptibility zones consistently comprises approximately 14% of the study area, yet encompasses over 40% of test sample points. This indicates a significantly higher susceptibility compared to other regions. Furthermore, frequency ratio values exhibit an increasing trend from zones of extremely low to extremely high susceptibility, indicating a notable rise in hazard susceptibility. These findings underscore the effectiveness of all models in assessing geological hazard susceptibility in Lushan County.

Table 6 Rationality test for geological hazard susceptibility zoning in Lushan County.
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ROC curve analysis

The ROC curve is a convenient and intuitive method widely employed to assess the relationship between specificity and sensitivity in geological hazard susceptibility evaluation19. It graphically represents the cumulative percentage of correct predictions for both disaster and non-disaster units. Specifically, the horizontal axis portrays specificity, reflecting the false positive rate, while the vertical axis represents sensitivity, reflecting the true positive rate26. The ROC curve systematically evaluates the model’s rationality, with a higher degree of convexity toward the upper left corner indicating greater accuracy, as measured by the area under the curve (AUC)37. AUC values range from 0 to 1, where AUC=[0.50, 0.70] suggests lower prediction accuracy, and AUC=[0.70, 0.90] indicates higher accuracy.

Fig. 8
Fig. 8
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ROC curve and AUC value: (a) Results for I, CF and RF model; (b) Results for LR-I, LR-CF and RF model.

The ROC analysis of the four models is depicted in Fig. 8. The results reveal AUC values of 0.816 for the I model, 0.815 for the CF model, 0.822 for the LR-I model, and 0.825 for the LR-CF model. Thus, all models effectively assess the geological hazard susceptibility of Lushan County. Notably, the I-LR and CF-LR models, which account for the relative importance of each evaluation factor, demonstrate superior evaluation performance compared to the individual I and CF models, exhibiting a slightly higher degree of alignment with actual results. However, the random forest model based on machine learning has an AUC value of 0.920 for evaluation accuracy, demonstrating the best performance.

F1 score analysis

The confusion matrix is a commonly used metric for evaluating classification models, as it summarizes the prediction results by comparing them with actual historical data19,20. It consists of four components: false negatives (FN), true positives (TP), true negatives (TN), and false positives (FP). FN refers to the number of positive instances incorrectly predicted as negative; TP refers to the number of correctly predicted positive instances; TN represents the number of correctly predicted negative instances; and FP refers to the number of negative instances incorrectly predicted as positive.

The Precision-Recall (PR) curve is another important evaluation tool, where precision (P) is the proportion of correctly predicted positive samples among all predicted positives, and recall (R) is the proportion of actual positives correctly identified by the model. The F1 score is the harmonic mean of precision and recall and is calculated as follows:

$${\text{F}}1 - score=2 \times \frac{{P \times R}}{{P+R}}$$
(6)

Figure 9 presents the PR curves and F1 scores for different models. The PR curves show that the I, CF, I-LR, and CF-LR models enclose similar areas under the curve, all of which are smaller than that of the machine learning-based Random Forest (RF) model, indicating the superior predictive performance of the RF model. In F1 score calculations, a threshold of 0.5 is typically used, where values below 0.5 indicate non-landslide cases and values above 0.5 indicate landslide occurrences38. As shown in Fig. 10, the F1 scores for the I, CF, I-LR, and CF-LR models are 0.76, 0.73, 0.77, and 0.75, respectively, with minimal differences. In contrast, the RF model achieves an F1 score exceeding 0.80, further demonstrating its superior prediction accuracy.

Fig. 9
Fig. 9
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Precision-Recall (PR) curves.

Fig. 10
Fig. 10
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Comparison of F1 Scores.

Discussion

Disaster susceptibility is not static but evolves over time in response to environmental factors such as rainfall, aftershocks, and progressive slope failures. A growing body of research recognizes the dynamic nature of post-earthquake hazards. For instance, Xu et al.39 reported that the combined effects of rainfall and aftershocks can gradually deform originally stable slopes in mountainous regions, causing a sustained increase in landslide susceptibility for months or even years after a seismic event. Progressive slope failures may further alter topography, thereby affecting both the probability and scale of future disasters.

In the present study, regional susceptibility was assessed using short-term post-earthquake data by comparing five models, including four traditional statistical methods and one machine learning approach—Random Forest (RF). Although the susceptibility zoning results were broadly consistent across the models, the RF model achieved the highest area under the ROC curve (AUC), indicating superior predictive accuracy. A survey of 20 disaster points (summarized in Table 7) reveals that 18 of them are located within the very high and high susceptibility zones, resulting in an overlap rate of 90%, while the remaining 2 points fall within the moderate susceptibility area, further validating the model’s effectiveness. This is consistent with the RF-based map (Fig. 11), where most disaster points recorded between 2013 and 2024 (as shown in Table 7) are located within high or very high susceptibility zones.

However, the current model does not explicitly incorporate the temporal evolution of susceptibility influenced by rainfall or aftershocks. This may be considered a limitation in terms of adaptability to dynamic hazard conditions. Future work should consider integrating real-time monitoring data and time-dependent modeling frameworks to more accurately track the progression of hazard susceptibility.

Table 7 Post-earthquake disaster events in Lushan County.
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Fig. 11
Fig. 11
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Post-earthquake geological hazard validation in Lushan County.

In addition to model structure, the selection and weighting of evaluation factors also significantly impact prediction accuracy. For example, Zhou et al.40 applied a combined weighting scheme to assess the risk of landslides affecting road networks and demonstrated improved model precision. Yan et al.41 integrated the Analytic Hierarchy Process (AHP) with the Evidence Weight model, highlighting the benefits of quantifying expert judgment to assign more scientifically grounded weights. These findings underscore the importance of selecting appropriate weighting strategies that reflect both data availability and geological complexity.

Nevertheless, including more variables does not necessarily improve model performance. High correlations among factors can introduce redundancy or bias, reducing predictive reliability. Therefore, multicollinearity diagnostics and correlation filtering are essential prior to model integration. Guo et al.42 further emphasized the need for hazard-specific susceptibility modeling in multi-hazard regions, suggesting that constructing tailored index systems for different hazard types can enhance the relevance and precision of risk assessments.

Moreover, variations in spatial resolution, dataset completeness, and model parameterization also affect the robustness of susceptibility assessments. High-resolution inputs, such as meter-level DEMs or sub-meter remote sensing imagery, can capture fine-scale geomorphological features and improve the delineation of high-risk zones. However, excessive resolution may lead to data redundancy and computational inefficiencies, particularly in large-scale regional analyses43.

Finally, the temporal completeness of disaster datasets remains critical. While long-term inventories contribute to model training and validation, the increasing frequency of extreme climate events necessitates greater emphasis on recent data. Time-sensitive and event-driven data can better reflect current hazard dynamics and improve the timeliness and accuracy of susceptibility predictions. Some studies have incorporated hyperparameter tuning to avoid overfitting, which improves the quality of the zonation map and prediction accuracy44,45. However, in this study, hyperparameter tuning was not applied for the following reasons: (i) under controlled sample size and scenario comparisons, excessive tuning might amplify variance and reduce the fairness and comparability between different models; (ii) the RF model uses random sampling of both samples and features, along with bootstrap sampling, which helps avoid overfitting.

The focus of this study is twofold: first, to compare and analyze the differences and accuracy of five mathematical models for post-earthquake disaster susceptibility evaluation in the same study area; and second, to generate a geological disaster susceptibility zonation map for Lushan County, providing technical references for disaster monitoring, early warning, and mitigation planning in the region. However, there are still the following limitations: (i) the improvement in AUC values under the ROC curve for traditional coupled models is small compared to single models. To assess whether there is a significant difference, statistical significance testing is needed. This would require expanding the sample size to obtain multiple sets of AUC values for a given model, along with the corresponding mean and standard deviation parameters; (ii) due to the limited availability of public pre- and post-earthquake event inventories and sufficient positive samples, no comparison was made with pre-earthquake disaster susceptibility; (iii) although dynamic influencing factors (such as rainfall and aftershocks) are mentioned in the study, the generated susceptibility maps are static.

Conclusion

In this study, geological hazard susceptibility assessments in Lushan County were performed using the I model, CF model, I-LR model, and CF-LR model based on GIS technology. The following conclusions can be drawn:

(1) Twelve factors were selected, including elevation, slope, aspect, curvature, engineering geological lithology, distance to rivers, terrain ruggedness, PGA, distance to faults, distance to roads, NDVI, and surface cutting depth. All these factors passed the collinearity test and were included in both the I and CF models. The ROC accuracies of these models were 0.816 and 0.815, respectively, indicating a relatively consistent correspondence between geological hazard susceptibility zoning and the actual situation in the study area.

(2) Through logistic regression analysis, only six factors (aspect, curvature, distance to rivers, distance to roads, NDVI, and surface cutting depth) had Sig values less than 0.05 and were thus included in the I-LR and CF-LR models. However, the ROC accuracies of these models were 0.822 and 0.825, respectively, surpassing those of the individual I and CF models and exhibiting better alignment with the actual situation in the study area. Therefore, the selection of evaluation factors should prioritize those that play a dominant role in the occurrence of geological hazards while ensuring that there is no strong correlation among the factors.

(3) The machine learning-based Random Forest (RF) model demonstrated the best overall performance, achieving the highest ROC AUC value of 0.920 among all evaluated models. Compared to traditional statistical models, including the I model, CF model, I-LR model, and CF-LR model, the RF model produced more refined susceptibility zoning with reduced areas classified as high and very high risk. This superiority was further supported by consistent results from Precision-Recall curves and F1-scores.