Machine Learning Prediction of Co-Seismic Landslide with Distance and Azimuth Instead of Peak Ground Acceleration

Abstract

Most machine learning (ML) studies on predicting co-seismic landslides have relied on Peak Ground Acceleration (PGA). The PGA of the ground strongly correlates with the relative position and azimuth of the seismogenic faults. Using the co-seismic landslide records of the 2008 Wenchuan earthquake, we show that the ML model using the distances and azimuths from the epicenter to sites performs better than the PGA model regarding accuracy and actual prediction results. The distances and azimuths are more accessible than the PGA because obtaining accurate and realistic large-scale PGAs is difficult. Considering their computational efficiency and cost-effectiveness, the ML models utilizing distances and azimuths from the epicenter to the sites as inputs could be an alternative to PGA-based models for evaluating the impact of co-seismic landslides. Notably, these models prove advantageous in near-real-time scenarios and settings requiring high spatial resolution, and provide favorable assistance in achieving the goal of sustainable development of society.

1. Introduction

Landslides are a natural hazard when earth, debris, and rocks slide down a slope due to gravity [1,2]. The ground shaking during earthquakes induces instability, leading to these gravitational movements [3]. Co-seismic landslides, as secondary hazards of earthquakes, can cause significant damage to human life, infrastructure, and the economy [1]. Moreover, the displacement of masses triggered by landslides can result in the formation of dammed lakes or floods, posing risks to downstream urban areas [4,5]. Consequently, the efficient and rapid assessment of the impact area of post-earthquake landslides is crucial, particularly in urban expansion.

Predicting landslides is a complex task due to the significant variability in ground materials and surface conditions, often observed over short distances [6]. There are many challenges in predicting co-seismic landslides, and one of the most important challenges is the uncertainty of the seismic characteristics. Previous studies have commonly employed empirical or numerical simulation methods to estimate landslide patterns. Empirical methods involve establishing statistical correlations between landslide occurrences and various factors, such as slope, rock type, and rainfall, to facilitate predictive modeling [6]. Malamud, et al. [3] introduced a landslide-event magnitude scale, which provides a valuable framework for understanding the frequency-area distribution of landslides in landslide research. Following the Wenchuan earthquake in the year 2008, Gorum, et al. [7] investigated the correlation between landslides and related conditioning factors. Hungr and McDougall [8] developed two numerical models to simulate landslide runouts. Traditional landslide hazard risk analysis has frequently relied on statistical approaches. Carrara et al. [9] utilized statistical models and stepwise discriminant analysis to evaluate landslide hazards in central Italy. Lee et al. [10] proposed a statistical approach to assess the susceptibility of earthquake-triggered landslides. Since around 2000, researchers have started to use logistic regression for landslide hazard assessment [11]. Xu et al. [12] compared six machine learning models to map landslides triggered by the 2008 Wenchuan earthquake, incorporating eleven geological and topographical factors.

In recent studies, machine learning has emerged as a widely adopted approach for landslide susceptibility assessment. For example, Tien Bui et al. [13] employed support vector machines, artificial neural networks, kernel logistic regression, and logistic tree models to predict landslide hazards in Vietnam. Dou et al. [14] applied Random Forest and decision tree models for landslide susceptibility mapping in Japan. Merghadi et al. [15] conducted a comprehensive analysis of various machine-learning methods and found that the Random Forest algorithm exhibited excellent performance in mapping landslide susceptibility. Consistent results were reported by Dou et al. [14], highlighting the rapid and accurate generation of landslide susceptibility maps by the Random Forest model. Fan et al. [16] achieved significant progress in the near-real-time prediction of co-seismic landslide distribution by leveraging a dataset of 0.3 million landslides and incorporating multiple geological and topographical information as inputs. Liu et al. [17] demonstrated satisfactory performance in mapping landslide susceptibility using convolutional neural network (CNN)-based models. Sun et al. [18] found that the SVM model using multiple landslide conditioning factors to map the susceptibility to geological hazards in the Changbai Mountain region affected by volcanic activity gave good results. Wang et al. [19] introduced swap noise as an unsupervised mechanism to improve the generalization performance and transferability of the model, reduce false alarms, and improve accuracy through supervised fine-tuning. Su et al. [20] used several models such as a Backpropagation Neural Network (BPNN), Residual Neural Network (ResNet), Convolutional Neural Network (CNN), and Visual Geometry Group-16 (VGG-16) for landslide hazard assessment, and the results showed that the Inception model performed the best in rainfall-induced landslide susceptibility assessment.

The occurrence of landslides resulting from earthquakes is highly complex, influenced by factors such as geomorphology, geology, and vegetation cover. However, the primary driver of co-seismic landslides is seismic dynamics. While several studies have explored the use of machine learning for predicting co-seismic landslides, many of them rely on seismic dynamic factors such as Peak Ground Acceleration (PGA), seismic intensity, distance from the epicenter, and distance from the probable seismogenic fault [7,16,21,22,23,24,25,26,27,28,29]. PGA is generally considered one of the most crucial factors contributing to co-seismic landslides [12,21,27,28,30,31]. In practical applications, PGA is often used as an input parameter for machine learning models due to limited information on near-source observations and the spatial distribution of seismic faults. However, there are difficulties in obtaining real PGAs on a large scale. Empirically regressed ground-motion prediction equations (GMPEs) are commonly employed to predict ground motion, including PGA and peak ground velocity (PGV), based on a simple hypothesis. The ground shaking estimated by these equations may differ from the actual ground shaking conditions due to problems associated with the ergodic assumption and the incomplete incorporation of spatial correlation and constraints in empirical GMPEs [32].

This study aims to use distances and azimuths from the epicenter to sites as inputs into machine learning instead of PGA to achieve a more concise, faster, and economical way to accomplish the prediction. For an earthquake (e.g., the 2008 Wenchuan earthquake we discuss in this work), the ground motion at the site is mainly affected by the propagation path of seismic waves from the earthquake fault to the site. These effects can be mainly clarified as two critical parameters: the azimuth and epicentral distance. As the seismic wave spreads and propagates in 3D space, its energy and amplitude decay with the distance from the source [33]. The epicentral distance is a primary parameter to evaluate ground motion intensity in GMPE. Another critical factor is the azimuth of the size referring to the earthquake fault. Note that the azimuth is not considered in the traditional GMPE method when evaluating ground motion, as the method implemented a homogeneous seismic wave propagation pattern [34,35]. However, ground motion distributions are highly heterogeneous in observations and forward simulations [36,37]. Compared to other models, this paper’s innovative contribution is the use of easily obtained distances and azimuths to replace the difficult-to-obtain and potentially error-prone PGAs as inputs to assess co-seismic landslides.

Predicting co-seismic landslides is crucial for assessing seismic hazards, and this method enhances machine learning algorithms for landslide prediction, aiding seismic hazard mitigation and prevention [38]. The methodology proposed in this paper can contribute to local and global sustainable development goals. The subsequent sections will outline our approach to forecasting co-seismic landslides in the study area. Furthermore, we will comprehensively compare four prediction models based on varying inputs. Finally, this paper discusses the significant role distance and azimuth play from the epicenter to the site in this study.

2. Methods and Data

2.1. Modeling Approach

The objective of our model is to estimate the distribution probability of co-seismic landslides. The overview presented in Figure 1 summarizes the main steps of estimation procedure. Initially, we collected the data of earthquake-triggered landslides and various factors (Step 1). This study’s 12 factors are derived from topographical, geological, and seismic data (Step 1). These factors include elevation, slope, aspect, Terrain Ruggedness Index (TRI), distance to faults and water lines, soil type, lithology, landform, peak ground acceleration (PGA), and the distance and azimuth from the epicenter to the site (Step 2). We joined these data with the same spatial position alongside the corresponding landslide or non-landslide status (Step 3). Subsequently, a machine learning model used these data to give the probability estimation of co-seismic landslides (Steps 4 and 5). The outputs generated by these models provide valuable feedback for further improvement (Step 5).

2.2. Model Performance Assessment

A confusion matrix is a table layout that allows the visualization of the performance of a predictive model [39]. In the confusion matrix, the true positive (TP) and the true negative (TN) are the numbers of correctly classified grids. Meanwhile, the false positive (FP) and the false negative (FN) are numbers of grids that are classified incorrectly.

Accuracy is the ratio of correctly predicted landslide grids and non-landslide grids (TP and TN) in all input data (TP + FP + FN + TN) in Equation (1) [39]. Accuracy reflects the model’s overall ability for binary classifications. Precision is a proportion of correctly predicted landslides grids (TP) in all predicted landslides grids (TP + FP) in Equation (2), and Recall means the proposition of correctly predicted landslides grids (TP) in all observation landslides grids (TP + FN) in Equation (3) [39]. Precision and Recall represent the model’s ability to identify landslides.

$$\mathit{Accuracy}={\displaystyle \frac{\mathit{TP}+\mathit{TN}}{\mathit{TP}+\mathit{FP}+\mathit{FN}+\mathit{TN}}}$$

(1)

$$\mathit{Precision}={\displaystyle \frac{\mathit{TP}}{\mathit{TP}+\mathit{FP}}}$$

(2)

$$\mathit{Recall}={\displaystyle \frac{\mathit{TP}}{\mathit{TP}+\mathit{FN}}}$$

(3)

Receiver operating characteristics (ROC) curves help visualize model performance and select classifiers [40]. The area under the ROC curve (AUC) is a single scalar value to measure the classifier’s performance [41].

2.3. Extremely Randomized Trees

The Extremely Randomized Trees (ERT) model is one of the best-suited models for decision-making in landslide susceptibility mapping, and exhibits superior performance compared to other models [15]. The ERT machine learning model can reduce overfitting and increase efficiency. ERT is similar to the Random Forest model. The core idea of the ERT model is to increase the stochasticity of the model, thereby reducing the variance of the model and improving generalization. ERT models split the tree nodes through random attribution and cut-point choices, and have a unrelated output structure from the learning samples [42]. Compared with the Random Forest model, ERT has better computational efficiency with a similar accuracy [42]. The ERT method has three steps: splitting nodes, picking a random split, and stopping splitting if the split is smaller than a specific size. The parameters $K$, $n_{min}$, and $M$ correspond to the three steps described above. The parameter $K$ stands for the number of random splits based on attribute differences. The $n_{min}$ is the number of samples required for splitting a node. The $M$ represents the number of trees in the ensemble. The ERT node splitting procedure starts by importing all selected independent variables into the ERT model and randomly selecting $K$ attributes. Then, the procedure will generate $K$ splits randomly and construct many extra trees with these splits. Those trees will finally establish the extra tree ensemble [43].

Table 1. A summary of key parameters for model training.

Classifer	Parameters
Extremely Randomized Trees (ERT)	bootstrap = False n_estimaters = 10 criterion = gini max_depth = None min_samples_split = 2 max_features = auto random_state = None min_impurity_split = None

concludes the key parameters of the training algorithm for this study. The model and kernel can be defined as [42]:

$${\widehat{y}}_t\left(x\right)={\sum }_{i=1}^N{y}^i{l}_t^T\left(x^i\right)l_t\left(x\right)$$

(4)

and

$${Kernel}_t\left(x,x^{\prime }\right)=l_t^T\left(x\right)l_t\left(x\right)$$

(5)

where $l_{S_N}=\left\{(x^i,y^i:i=1,\dots ,N)\right\}$ is a learning sample of size $N$, and $t$ is a tree structure with $l_t$ leaves. Therefore, $l_{t,i}\left(x\right)$ is the characteristic function of the $i^{th}$ leaf of $t$, by the number of learning samples $n_{t,i}$, such that $l_{t,i}\left(x\right)=1$, and we defined $l_t\left(x\right)$ as the vector of (normalized) characteristic functions of t [42]:

$$l_t\left(x\right)={({\displaystyle \frac{l_{t,1}\left(x\right)}{\sqrt{n_{t,1}}}},\dots ,{\displaystyle \frac{l_{t,l_t}\left(x\right)}{\sqrt{n_{t,l_t}}}})}^T$$

2.4. Study Area and Data

2.4.1. Overview of the Study Area

The M 7.9 Wenchuan earthquake occurred on 12 May 2008 in the marginal zone between Longmen Mountain and the Sichuan Basin. This event caused loss of life, with 69,227 fatalities, 17,923 individuals reported as missing, and 374,643 people injured. The earthquake also caused extensive destruction to countless infrastructures and civilian buildings [26]. Longmen Shan’s uplift resulted from the northward subduction of the Indian plate beneath the Eurasian plate. The eastward expansion of the Tibetan Plateau played a critical role in triggering the Wenchuan earthquake, as the Tibetan Plateau exerted pressure against the Sichuan Basin [44].

The study area is located within the earthquake-affected region of Sichuan province in southwestern China. It is a square region measuring approximately 110 km in length and width, spanning from 103° to 104° E longitude and 31° to 32° N latitude. The study area is near Chengdu city, as indicated by the blue frame in Figure 2. Figure 2 provides a historical overview of earthquake events in this area dating back to 1900. In the study area, co-seismic landslides are primarily concentrated in the complex mountainous terrain, encompassing numerous active faults. The precise epicenter of the Wenchuan earthquake is located at co-ordinates 31.002° N and 103.322° E, denoted by the red star in Figure 2 (USGS).

2.4.2. Landslide Data

Using high-resolution aerial photographs, Xu et al. [27] collected a comprehensive inventory of landslides triggered by the 2008 Wenchuan earthquake. This inventory consists of 197,481 polygons that accurately depict the sizes and geometries of each co-seismic landslide resulting from the earthquake. The total area of landslides in this inventory is approximately 1160 km². For our study, we utilize this landslide inventory to demonstrate the application of our proposed machine-learning model.

2.4.3. Environmental Factor Data

Empirical evidence suggests that co-seismic landslides are influenced by multiple factors, including elevation, slope, aspect, topographic relief index (TRI), soil type, lithology, landform, distance to faults, distances to hydrographic networks, distance and azimuth from the epicenter to the site, and peak ground acceleration (PGA). The factors, including the aspect, Terrain Ruggedness Index, distance to faults, distance to water, distance to the epicenter, and azimuth from the epicenter are calculated by QGis. Our research incorporates all the factors above to investigate the relationship between landslides and earthquakes. It is important to note that all the information used in this study is publicly available and accessible.

Table 2. Classification of the seismic, terrain, and geologic factors.

Factor Type	Factor	Classification
Seismic	Peak ground acceleration (PGA) (g)	<0.1; 0.1~0.2; 0.2~0.3; 0.3~0.4; 0.4~0.5; 0.5~0.6; 0.6~0.7; 0.7~0.8; 0.8~0.9; >0.9;
	Distance to fault (km)	<15; 15~30; 30~45; 45~60; 60~75; 75~90; 90~105; 105~120; 120~135; >135;
	Distance to epicenter (km)	<10; 10~20; 20~30; 30~40; 40~50; 50~60; 60~70; 70~80; 80~90; 90~100; 100~110; >110;
	Azimuth angle from epicenter (degree)	<30; 30~60; 60~90; 90~120; 120~150; 150~180; 180~210; 210~240; 240~270; 270~300; >300;
Terrain	Elevation (m)	<500; 500~1000; 1000~1500; 1500~2000; 2500~3000; 3000~3500; 3500~4000; 4000~4500; >4500;
	Slope angle (degree)	<10; 10~20; 20~30; 30~40; 40~50; 50~60; 60~70; 70~80; >80;
	Slope aspect (direction)	N; NE; E; SE; S; SW; W; NW;
	Distance to hydrographic networks (km)	<3; 3~6; 6~9; 9~12; 12~15; 15~18; 18~21; 21~24; >24;
	Terrain Ruggedness Index	<30; 30~60; 60~90; 90~120; 120~150; 150~180; 180~210; 210~240; >240;
	Landforms	High-gradient mountain (TM); medium-gradient hill (SH); high-gradient hill (TH); plain (LP);
Geologic	Soil	Haplic Alisols (ALh); Cumulic Anthrosols (ATc); Calcaric Cambisols (CMc); Dystric Cambisols (CMd); Gelic Cambisols (CMi); Eutric Fluvisols (FLe); Haplic Greyzems (GRh); Eutric Leptosols (LPe); Gelic Leptosols (LPi); Mollic Leptosols (LPm); Haplic Luvisols (LVh); Chromic Luvisols (LVx); Dystric Podzoluvisols (PDd); Calcaric Regosols (RGc); Eutric Regosols (RGe);
	Lithology	Granite (IA1); Basalt (IB2); Gneiss, migmatite (MA2); Slate, phyllite, pellitic rocks (MA3/MB1); Sandstone, greywacke, arkose (SC2); Siltstone, mudstone, claystone (SC3); Shale (SC4); Limestone, other carbonate rocks (SO1); Eolian unconsolidated rock (UE1); Fluvial (UF); Unconsolidated (UR1);

gives the classification of possible co-seismic landslide factors. Seismic factors include PGA, distance to faults, distance to the epicenter, and azimuth angle from the epicenter. As shown in Figure 3, most of the co-seismic landslide area is PGA 0.6~0.9 g (Figure 3A). The relationships between landslide and distance to faults and epicenter are shown in Figure 3B,C. More than 80% of the landslides were within 45 to 120 km of faults, and 10 to 90 km of the epicenter. About 60% of landslides have an azimuth angle from the epicenter within 30 to 60 degrees (Figure 3D).

Terrain factors include elevation, slope angle, slope aspect, distance to hydrographic networks, terrain ruggedness index (TRI), and landforms. Most landslides are between 1000 and 3500 m above sea level (Figure 3E) and have slopes between 20 and 50 degrees (Figure 3F). The landslides have the most east- (E) and southeast-oriented (SE) aspects (Figure 3G). Most landslides were within 10 km of the network (Figure 3H). A total of 70% of the landslides had a TRI of 30 to 90 (Figure 3I), and almost all landslides belonged to the high-gradient mountain class (TM) (Figure 3J).

Geologic factors are soil factors and rock factors. Geologic factors consist of soil factors and rock factors. More than 40% of the landslides in the study area are haplic luvisols (LVh) (Figure 3K). Meanwhile, slate, phyllite, and pellitic rock (MA3/MB1) account for most of the landslide area, followed by Eolian unconsolidated rocks (UE1) (Figure 3L).

2.5. Training, Validation, and Test Data

This study considers 13 distinct layers, including 12 conditioning factor maps and a landslide inventory map. These layers provide various information about the study area. To ensure uniformity in analysis, all layers were converted into a grid format with a resolution of 30 m by 30 m, allowing for consistent spatial co-ordinates across all layers. Each grid point represented a specific location and comprised data such as latitude, longitude, elevation, slope, aspect, topographic relief index (TRI), soil type, lithology, landform, peak ground acceleration (PGA), distance and azimuth from the epicenter to the site, distance to faults, distance to water lines, and a landslide or non-landslide status.

This study involves nearly 13 million points, with approximately 0.8 million points representing landslide occurrences and the remaining points representing non-landslide areas. Landslide points were assigned a value of “1”, while non-landslide points were assigned a value of “0”. To facilitate model development and evaluation, the collected data will be partitioned into training, validation, and testing datasets using a split ratio of 7:2:1. The training dataset will be used for constructing the model. In contrast, validation and testing datasets will be employed to assess the model’s performance and validate its results.

2.6. Different Model Construction Schemes

The study employed four machine-learning models, each utilizing different factors as inputs. The first model, ERT-A, utilized all 12 available factors to investigate the relationship between earthquakes and landslides. The second model, ERT-B, shared 11 factors with ERT-A, excluding peak ground acceleration (PGA) from its inputs. Similarly, the third model, ERT-C, leveraged ten factors from ERT-A but eliminated azimuth and distance variables to evaluate the impact of co-seismic landslides specifically. Lastly, the fourth model, ERT-D, employed the same factor inputs as ERT-A, excluding seismic factors. ERT-D focused on seven factors: elevation, slope, aspect, topographic relief index (TRI), soil type, lithology, and landform.

3. Results

3.1. Prediction Performance

The prediction results from four models are illustrated in

Table 3. Comparison of prediction results.

Index	ERT-A 1	ERT-B 2	ERT-C 3	ERT-D 4
Accuracy	0.904	0.902	0.897	0.855
Precision	0.832	0.829	0.822	0.769
Recall	0.892	0.890	0.879	0.808
AUC	0.963	0.963	0.958	0.929

¹ The ERT-A’s input factors: the elevation, slope, aspect, TRI, soil, lithology, landform, distance to faults, distance to hydrographic network, PGA, and the distance and azimuth from the epicenter to the site. ² The ERT-B’s input factors: the elevation, slope, aspect, TRI, soil, lithology, landform, distance to faults, distance to hydrographic network, and the distance and azimuth from the epicenter to the site. ³ The ERT-C’s input factors: the elevation, slope, aspect, TRI, soil, lithology, landform, distance to faults, distance to hydrographic network, and PGA. ⁴ The ERT-D’s input factors: the elevation, slope, aspect, TRI, soil, lithology, and landform.

. Except for ERT-D, all three models showed a similar performance in co-seismic landslide prediction and can had a good capacity for co-seismic landslide assessment.

The results in Table 3 show that the ERT-B model performed similarly to the ERT-A model. The ERT-A model used geological, topographic, and seismic factors to predict landslides. Meanwhile, the ERT-B model used the same input except PGA information. These two models’ accuracy, recall, and AUC scores were over 0.90, and the precision scores were over 0.825. For comparison, the ERT-C model, which has input factors similar to those of the ERT-A model except for the distance and azimuth from the epicenter to the site, scored slightly lower in all categories than ERT-A and ERT-B. Specifically, ERT-C had an accuracy of under 0.9, a precision of under 0.825, a recall of under 0.88, and an AUC of under 0.96. The ERT-D model, which had inputs without seismic factors, had the worst performance.

The results indicate that the seismic factors are critical in these models. Earthquake-related factors play a dominant role in co-seismic landslide assessment. Moreover, the distance and azimuth from the epicenter to the site can replace PGA to predict co-seismic landslides. The two epicenter-related factors capture the impact of earthquake energy on the earth’s surface. If complete and credible PGA data are obtained, no significant difference exists between the PGA and the distance and azimuth between the epicenter and the site. However, often, there are missing PGA observations, and missing PGA data may result in landslide underestimates or overestimates. The results also indicate that the main factor inducing landslides after an earthquake is the destabilization of the existing loose material on the ground surface caused by the propagation of seismic energy to the ground surface. This argument, however, still requires an explanation of physical processes.

3.2. Landslides Prediction Results

Figure 4 illustrates the comparison of four estimated landslide results from various inputs. Only selected areas have been illustrated here to facilitate the presentation.

Figure 4A–D are four estimated results from ERT-A, ERT-B, ERT-C, and ERT-D. The majority of the main characteristics of the spatial distribution of landslides and non-landslide areas have been captured in Figure 4A–C. The differences between the actual landslide extent and the predicted four outputs are relatively small. The predicted landslide clearly and accurately outlines the boundaries of the actual landslide.

The landslide prediction results in Figure 4A–C are noticeably better than those in Figure 4D. Figure 4A shows the output using all 12 factors. Figure 4B,C are the predicted landslide impact extent derived without the input of PGA and epicenter-related factors, respectively. Contrasting Region I in Figure 4B,C, the ERT-B model provides a more accurate prediction of the landslide area than the ERT-C model. This finding reflects that using epicenter correlation factors can more accurately characterize the landslide area than the PGA. Figure 4D shows the results obtained using the non-seismic factors. It needs a better prediction near Region II, III, and IV. Many non-landslide areas are misclassified as landslides. It indicates that seismic factors can play a significant role in predicting co-seismic landslide machine learning.

4. Discussion

Machine learning operations provide a valuable means to generate a landslide susceptibility map, enabling a more comprehensive understanding of landslide risk. Figure 5 presents a comparison of landslide susceptibilities obtained using different inputs.

Figure 5A–D depict the susceptibility results obtained from ERT-A, ERT-B, ERT-C, and ERT-D, respectively. These maps are divided into five categories based on the predicted landslide probabilities, ranging from 0 to 100%. The categories include Very low (0–10%), Low (10–30%), Moderate (30–70%), High (70–90%), and Very high (over 90%). Utilizing machine learning predictions, each point on the map is assigned to one of these categories. The red areas indicate the highest landslide risk, while the dark green areas represent locations with the lowest risk. The differences between the actual and predicted landslide areas are relatively small in Figure 5C. Notably, Figure 5B, utilizing ERT-B’s input factors, performs better in Region I than in Figure 5C. Conversely, Figure 5D, incorporating non-seismic factors, demonstrates a less accurate assessment of landslides in Regions II, III, and IV, compared to Figure 5A–C.

The details of co-seismic landslide estimation and susceptibility mapping are depicted in Figure 6. The figure illustrates the prediction of landslides along a line segment and compares it to the actual landslide area. The small colored squares represent the predicted results from ERT-B, corresponding to the probability line indicated by the blue dashed line in the diagram above. The predicted result, represented by the blue line, provides a reliable representation of the actual landslide area depicted in orange. It is important to note that, in the vicinity of the area with a 50% probability of prediction, indicated by the green dotted line, the predicted results exhibit slight deviations from the actual landslide area. These errors primarily arise from the limitations of the prediction’s resolution, which is set at 30 m.

The above discussion highlights the significant influence of seismic dynamic parameters on machine learning-based earthquake-induced landslide prediction. It was observed that utilizing distances and azimuths from the epicenter to sites as input factors in machine learning models yields better evaluation results than Peak Ground Accelerations (PGAs). This finding supports the notion that seismic energy is crucial in triggering seismic landslides. The complex geological conditions, surface structure, and various other factors contribute to the non-uniform propagation of seismic energy to the surface. Consequently, certain azimuths experience significantly more damage than others [47]. As a result, distance and azimuth from the epicenter to the site cannot be treated merely as co-ordinates, instead, they are essential seismodynamic parameters involved in the physical process of earthquake-induced landslides. Due to the difficulty of obtaining accurate and realistic large-scale PGAs, using distance and azimuth to replace PGAs to predict landslides is a more practical approach. The conclusions of this study can be used in assessing earthquake-induced disasters predicted by machine learning, such as earthquake-induced landslides or earthquake-induced economic losses.

We have used the co-seismic landslides of the 2008 Wenchuan earthquake as a machine-learning training set. In future studies, machine learning needs should be transferred to consider other earthquakes’ characteristics and co-seismic landslides’ factors when predicting co-seismic landslides in another region. The accuracy of predicting the Wenchuan earthquake landslides in this study using machine learning is 90.2% (Table 3), and further improvement may require measures such as optimizing the model and changing the sampling of inputs. Another way to obtain the accurate ground shaking distribution is the physics-based numerical simulation [48,49,50], which requires large-scale computing and means that the hazard study of earthquakes needs subsequent work.

5. Conclusions

PGAs are closely related to the distance and azimuth of the seismogenic fault. Due to the difficulty of obtaining accurate and realistic large-scale PGAs, this study used the co-seismic landslide records of the 2008 Wenchuan earthquake to train a machine learning model. It presents an alternative approach to assessing the spatial distribution of co-seismic landslides by utilizing distances and azimuths from the epicenter to sites as seismodynamic parameters instead of PGA. The results indicate that these factors effectively predict the spatial distribution of co-seismic landslides. The derived landslide susceptibility map accurately captures the spatial characteristics of landslide and non-landslide areas based on the distance and azimuth from the epicenter to the site. In addition, the authority can apply the conclusion of this study to near-real-time co-seismic landslide prediction. The model using distance and azimuth from the epicenter to the site simplifies the steps, improves the prediction efficiency, and reduces the data processing cost compared to the model relying on PGA. In real emergency rescue scenarios, the conclusions of this study can be used to more conveniently and quickly investigate the range affected by co-seismic landslides without first calculating the PGA. This conclusion will also help society reach the goal of long-lasting, safe, and sustainable development on a regional and global scale.

However, it is essential to acknowledge the limited understanding of the physical processes involved in landslide occurrence, which hampers the interpretation of machine learning methods in landslide prediction. Better seismodynamic factors exist beyond those investigated in this study that could improve co-seismic landslide prediction. The limitation of this study is the need for validation of co-seismic landslides in other parts of the globe. Future work should apply the findings of this study to other areas where co-seismic landslides occur to explore the applicability of this study more broadly.