Geological Hazard Identification and Susceptibility Assessment Based on MT-InSAR

Abstract

Geological hazards often occur in mountainous areas and are sudden and hidden, so it is important to identify and assess geological hazards. In this paper, the western mountainous area of Beijing was selected as the study area. We conducted research on landslides, collapses, and unstable slopes in the study area. The surface deformation of the study area was monitored by multi-temporal interferometric synthetic aperture radar (MT-InSAR), using a combination of multi-looking point selection and permanent scatterer (PS) point selection methods. Random forest (RF), support vector machine (SVM), convolutional neural network (CNN), and recurrent neural network (RNN) models were selected for the assessment of geological hazard susceptibility. Sixteen geological hazard-influencing factors were collected, and their information values were calculated using their features. Multicollinearity analysis with the relief-F method was used to calculate the correlation and importance of the factors for factor selection. The results show that the deformation rate along the line-of-sight (LOS) direction is between −44 mm/year and 28 mm/year. A total of 60 geological hazards were identified by combining surface deformation with optical imagery and other data, including 7 collapses, 25 unstable slopes, and 28 landslides. Forty-eight of the identified geological hazards are not recorded in the Beijing geological hazards list. The most effective model in the study area was RF. The percentage of geological hazard susceptibility zoning in the study area is as follows: very low susceptibility 27.40%, low susceptibility 28.06%, moderate susceptibility 21.19%, high susceptibility 13.80%, very high susceptibility 9.57%.

1. Introduction

The occurrence of geological hazards poses great danger; for example, landslides and debris flows have led to a large number of deaths and significant economic and property losses [1,2]. On steep slopes in mountainous areas, a series of geological hazards can be triggered by large-scale movements of water, sediments, and other materials [3]. The interferometric synthetic aperture radar (InSAR) technique can obtain surface deformation information and is an effective means to assist in the identification of geological hazards. Geological hazard susceptibility assessments can be used as a reference for relevant researchers and are an important part of geological hazard prevention and control [4].

InSAR is characterized by a wide spatial coverage, a high monitoring accuracy and all-weather monitoring, making it an important technology for geological hazard monitoring and identification [5,6,7,8]. Differential InSAR (D-InSAR) was extended from InSAR technology to allow for deformation monitoring [9]. MT-InSAR can overcome the effects of D-InSAR by spatial and temporal incoherence, as well as atmospheric effects, and acquires a long time series of deformation in the target area. Additionally, the monitoring accuracy technology has been able to reach millimeter level [10]. Geological hazards will be accompanied by a certain degree of surface deformation before and after the occurrence of geological hazards. Therefore, the identification, monitoring, and assessment of geological hazards can be carried out in conjunction with surface deformation monitoring using the MT-InSAR technology. Nowadays, MT-InSAR techniques, such as PS-InSAR [11], SBAS-InSAR [12], and SqueeSAR [13], are widely used in the monitoring and identification of geological hazards such as landslides, unstable slopes, and so on.

Geological hazard susceptibility assessment is an evaluation of the ease of occurrence of geological hazards in the study area [14]. The spatial distribution of geological hazards can follow complex patterns, depending on the spatial variability of a large number of predisposing factors. Geological hazard susceptibility assessment is the use of data or expert experience to find patterns in the distribution of geological hazards in a certain area [15]. Geological hazard susceptibility assessments can be mainly categorized into qualitative methods and quantitative methods [16,17]. Qualitative methods are mostly based on experience, such as the analytic hierarchy process (AHP) method [18], historical geological hazard inventory analysis [19], and expert scoring methods [20]. These methods are simple and cost-effective, but less objective and only suitable for the analysis of smaller study areas [21]. With the development of geographic information data and computer technology, quantitative methods have gradually become the mainstream method in the assessment of geological hazards [22]. Quantitative methods are able to utilize the relationship between data and geological hazards for susceptibility assessments, which is more objective and accurate than qualitative methods, as these mainly include statistical methods and artificial intelligence methods. There are many statistically based methods of susceptibility assessment, such as the information value method, the frequency ratio method, the coefficient of determination method, and the weights of evidence method [23,24,25]. Artificial intelligence methods can learn the deep features of geological hazards and reveal the nonlinear change characteristics of geological hazards: for example, machine learning methods such as logistic regressions [26], support vector machine [27], and random forest [28], and the deep learning methods such as deep neural network [29], convolutional neural network [30], and recurrent neural network [31]. There are now many reliable methods for assessing geological hazard susceptibility, so many researchers have studied the comparison of the effectiveness of different models. However, in different studies, different regions and data lead to different model effects, so it is necessary to select multiple models for comparison when conducting a geological hazard susceptibility study in a certain region.

This paper will focus on the MT-InSAR geological hazard identification study and the comparison of different geological hazard susceptibility assessment models. This study takes the western mountainous area of Beijing, where geological hazards are frequently developed, as the study area [32]. We will conduct research on landslides, collapses, and unstable slopes in the study area. Firstly, surface deformation information for the study area, from September 2016 to September 2022, was extracted using the MT-InSAR to identify geological hazards. Collecting geological hazard influencing factors was undertaken for the geological hazard susceptibility assessment, using identified and historical geohazards as samples. Finally, the geological hazard susceptibility was assessed using the RF, SVM, CNN, and RNN models, and the effectiveness of each model was compared, to achieve a reasonable and reliable geological hazard susceptibility assessment. This study provides a reference for the study of geological hazards in the mountainous areas of western Beijing, as well as for the study of susceptibility assessment model options.

2. Study Area and Datasets

2.1. Study Area

As shown in Figure 1a,c, the study area is in Fangshan District and Mentougou District, Beijing, China (115.561838°–115.999379°E and 39.700610°–40.020247°N) and covers an area of 1328 km². The area is located in the northeastern section of the Taihang Mountains, so the geomorphology is dominated by mountains and the elevation is mainly between 36 m and 2036 m. The age stratigraphy of the study area is fully developed. The diaphanous fold in which the study area is located is part of the Yanshan platform fold belt, and the geological and tectonic changes in the study area mainly occurred in the Indo-Chinese and Yanshan periods.

The main geological structures in the study area are folds, large fractures, and general fractures. The study area has a continental monsoon climate, the area below 1000 m is a warm temperate climate zone, and the area above 1000 m is a cold temperate climate zone, due to the influence of the topography. There is a large temperature difference between different areas at different times, with more precipitation in summer and less precipitation in winter, and overall uneven precipitation throughout.

The occurrence of geological hazards in the study area is mainly influenced by the complex topographic and geological conditions in the study area, the existence of fracture structures, the large amount of precipitation during the rainy season, and the frequent human engineering activities. The main types of geological hazards in the study area are collapses, landslides, and unstable slopes, the distributions of which are shown in Figure 1c. The characteristics of these geological hazards are as follows [33,34]:

• Collapses: Collapses are usually sudden in nature; some have no significant deformation in the InSAR deformation results. In optical images, the contour line of the collapse body is obvious; its color is related to the lithology, which is usually lighter in tone than the surrounding, as mostly gray or grayish white. The collapse body is piled up on the bottom of slopes with a bumpy surface. Sometimes huge boulders are visible. There is very poor vegetation cover.
• Unstable slopes: Unstable slopes are slopes with large deformation and they are often close to underground resource extraction areas.
• Landslides: The main types of landslides include rotational landslides, translational landslides, and debris flows. The deformation is evident, and a number of typical features can be easily distinguished, like the detachment and accumulation zones, crown, scarp, flank, main body, foot, and toe.

2.2. Datasets

In this study, a total of 80 views of descending track RADARSAT-2 SAR data, from September 2016 to September 2022, were used for MT-InSAR deformation monitoring. As Figure 1b shows, the SAR range fully covers the study area. The RADARSAT-2 SAR data are from a C-band synthetic aperture radar with a wavelength of 5.6 cm and a revisit period of 24 days. The data mode is the Extra Fine mode, offering a resolution of 5 m. The ALOS 12.5 m digital elevation model (DEM) from Japan Aerospace Exploration Agency (JAXA) and precise orbit data were used to remove the flat earth and topographic phases.

The geological hazard data are divided into two parts, one for geological hazards identified by combining surface deformation information, and one for historical geological hazards. The historical geological hazards data are from the geological hazards list for Beijing, published in 2022, including 1034 collapses (71% of the total), 260 unstable slopes (18% of the total) and 158 landslides (11% of the total). A good susceptibility assessment would require us to perform a separate assessment for each type of geological hazards, but also would need a large amount of training data. Therefore, we performed a susceptibility assessment with every type together, in order to have a large number of data; more refined assessments will be the objectives of future works.

Following a review of the relevant literature and considering the topography of the study area, geology, human activities, climate and other factors, 16 geological hazard-influencing factors were selected [35,36,37,38,39]. These included elevation, slope, aspect, plan curvature, profile curvature, topographic wetness index (TWI), topographic roughness index (TRI), slope length and slope angle factor (LS-factor) [40], precipitation, normalized difference vegetation index (NDVI), distance to rivers, distance to roads, landcover, distance to faults, stratigraphic unit, and distance to mine origin. The elevation was determined using 2.5 m resolution DEM data, collected by UAV in 2022 and provided by the Beijing Institute of Geological Hazard Prevention, and the slope, aspect, plan curvature, profile curvature, TWI, TRI, and LS-factor were all also calculated by this DEM. Precipitation was calculated using ERA5 1° resolution atmospheric reanalysis data. NDVI was calculated based on the GEE platform, using 30 m resolution Landsat8 data. The distance to rivers and distance to roads were calculated from road and river vector data, obtained from the OpenStreetMap website. Landcover data were from the ESA WorldCover 10 m resolution landcover data for 2020, released by ESA. Distance to faults and stratigraphic units were obtained from the 1:2,500,000 geological map vector data, 1:1,000,000 geological map vector data, and the 2021 China Mineral Properties Data vector data, respectively, released by the China Geoscientific Data Discovery Publishing System. The distances to the mine origin were obtained from 2021 China Mineral Properties Data vector data, and were defined as the mine origin in a place that had been mined, including both open pit and underground mines. Finally, all raster data with a resolution higher than 30 m were resampled to 30 m, and precipitation data with a resolution lower than 30 m were converted to 30 m by Kriging interpolation. The vector data were converted to 30 m resolution raster data. All data were integrated to construct the dataset.

3. Materials and Methods

3.1. Overview

Figure 2 illustrates the flowchart of this study. Firstly, we used MT-InSAR to obtain the surface deformation of the study area. We combined the PS point selection method and the multi-looking point selection method to select the interferometric points. Then, we used precision orbit data and DEM data for the differential interferometric calculations of surface deformation. The surface deformation consists of linear and nonlinear deformation. After calculating the surface deformation, the geological hazards in the study area were identified based on the rate of surface deformation. We collected geological hazard-influencing factors, combining identified geological hazards and historical geological hazards to create a geological hazards sample, then calculated the information value of the influencing factors. Next, the correlation between the factors was calculated by multiple covariance analysis, and the importance of the factors was calculated by the relief-F method for the selection of influencing factors. Finally, we used the RF, SVM, CNN, and RNN models to assess the geological hazard susceptibility, and compared and analyzed the performance of each model by multiple indicators.

3.2. MT-InSAR Processing

In this study, an interferometric point target analysis (IPTA) technique was used for surface deformation information extraction. IPTA technology is a MT-InSAR technique that allows the researcher the flexibility to perform baseline combinations, interferometric point selection, and other operations to conduct the study.

3.2.1. Interferometric Point Target Selection

In this study, the amplitude deviation threshold method and the multi-looking point selection method were used to select interferometric point target. The amplitude deviation threshold method is a commonly used method for selecting PS points in MT-InSAR. This method uses the amplitude stability of the image element instead of coherence. In general, the statistical characteristics of the amplitude can only be calculated correctly if the number of images is sufficiently large (≥25). Amplitude deviation $D_A$ can be calculated as follows [41]:

$$D_A=\frac{{\sigma }_A}{m_A}$$

(1)

where ${\sigma }_A$ is the mean of the amplitude and $m_A$ is the variance of the amplitude.

To increase the density of interferometric point targets, we performed multi-looking analysis on the data, with a 3:3 ratio for differential interference and selected all the pixels of the data, after having performed multi-looking, as candidate target points; this approach can reduce the impact of SAR data noise, and differential phases with high coherence can be obtained.

The points selected by the above two methods were fused as candidate coherent points, and these points were masked by a temporal coherence threshold and a standard deviation threshold to obtain the final point target.

3.2.2. Calculation of Linear Deformation

Due to the interference of the coherent point targets of the main image with the coherent point targets of other images, the flat earth phase and terrain phase were then removed by external DEM data. Assuming a total of K sets of interferometric pairs and n coherent point targets are selected, the phase value of point i (1 < i < n) on the kth (1 < k < K) amplitude differential interferogram can be expressed as follows [42]:

$${\phi }_i^k=wrap\left({\phi }_{i,def}^k+{\phi }_{i,atm}^k+{\phi }_{i,noise}^k+{\phi }_{i,restopo}^k\right)$$

(2)

where $wrap$ is the unwrapped phase with a value between $[-\pi ,\pi )$, ${\phi }_i^k$ is the phase value of the point target, ${\phi }_{i,def}^k$ is the deformation phase of the target point due to the change in LOS direction of the satellite during the two imaging sessions of SAR data, ${\phi }_{i,atm}^k$ is the phase of atmospheric delay due to different atmospheric delays when SAR data were imaged twice, ${\phi }_{i,noise}^k$ is the noise phase due to random noise in the radar imaging process, ${\phi }_{i,restopo}^k$ is the phase of DEM residuals due to insufficient aging or accuracy of the DEM used for differential interference. The phase of DEM residuals can be expressed in Equation (3) [42]:

$${\phi }_{i,restopo}^k=-\frac{4\pi }{\lambda }\frac{B_{i,\perp }^k}{r_i\sin {\theta }_i}\Delta h_i$$

(3)

where $\lambda$ is radar wavelength, $B_{i,\perp }^k$ is the vertical spatial baseline, $r_i$ is the distance between the radar and the target point, and $\Delta h_i$ is the DEM residuals.

The deformation phase can usually be divided into two parts, a part concerned with the linear deformation phase with time, and a part concerned with the nonlinear deformation phase. The deformation phase can be expressed in Equation (4) [42]:

$${\phi }_{i,def}^k=\frac{4\pi }{\lambda }{t}_i^{}·v_i+{\phi }_{i,nolinear}^k$$

(4)

where $t_i^{}$ is the time interval of the interference pair where the target point is located and $v_i$ is the linear deformation rate of the target point.

Errors such as an atmospheric delay phase in the differential interference phase of different interference pairs cannot be calculated using the phase of a single target point. These errors can be calculated at stable target points with high coherence, where the deformation is smaller and less affected by the atmosphere. The errors can be attenuated, and the deformation of the point target can be modeled and solved, by constructing a Delaunay triangular network to connect the high coherence points for quadratic differential calculations. The differential phase between adjacent points in the triangular network can be expressed as follows [42]:

$$\begin{array}{ll}\varphi \left(x_k,y_k;x_p,y_p;t_i\right)& =\frac{4\pi }{\lambda ·r_i·\sin {\theta }_i}·{\overline{B}}_{\perp }^k·\Delta h\left(x_k,y_k;x_p,y_p\right)+\\ & \frac{4\pi }{\lambda }{t}_i·\Delta v\left(x_k,y_k;x_p,y_p\right)+{\phi }_{res}^k\left(x_k,y_k;x_p,y_p;t_i\right)\end{array}$$

(5)

where $\Delta h\left(x_k,y_k;x_p,y_p\right)$ is the difference in elevation correction values between two target points, $\Delta v\left(x_k,y_k;x_p,y_p\right)$ is the difference in linear deformation rates between two target points, ${\phi }_{res}^k\left(x_k,y_k;x_p,y_p;t_i\right)$ is the phase residual, and the main components are nonlinear deformation rate, atmospheric delay phase, and noise phase. The closer the distance in space, the higher the atmospheric correlation, so the closer the target points are, and the more similar they are, the more they are affected by the atmosphere and the smaller the atmospheric phase in the differential phase is. In the Delaunay triangular network, the combined target points are limited to a 1 km horizontal distance in space, and the atmospheric phase in the differential phase of the two points is negligible. The linear deformation rate and elevation residuals of each target point are constant across the interference pairs and can be calculated as follows [42]:

$$\begin{array}{ll}{\varphi }_{\mathrm{model}}\left(x_k,y_k;x_p,y_p;t_i\right)& =\frac{4\pi }{\lambda ·r_i·\sin {\theta }_i}·{\overline{B}}_{\perp }^k·\Delta h_{\mathrm{model}}\left(x_k,y_k;x_p,y_p\right)\\ & +\frac{4\pi }{\lambda }{t}_i·\Delta v_{\mathrm{model}}\left(x_k,y_k;x_p,y_p\right)\\ \end{array}$$

(6)

From this equation, it can be seen that the relative elevation residuals between the vertical baseline and the two points are linearly related to the corresponding slope, and the time interval of the interference pair is linearly time related to the slope corresponding to the relative deformation velocity. In order to seek the optimal solution for the phase of elevation residuals and the phase of linear deformation, the coherent point targets in the Delaunay triangular network connected by reliable edges can be filtered according to the coherence, and the coherence function model is as follows [42]:

$$\begin{array}{ll}{\gamma }_{\mathrm{model}}\left(x_k,y_k;x_p,y_p;t_i\right)& =\frac{1}{K}·\left|{\displaystyle \sum _{i=0}^N\exp \left[j·\left(\begin{array}{l}\delta {\varphi }_{diff}\left(x_k,y_k;x_p,y_p;t_i\right)\\ -\delta {\varphi }_{\mathrm{model}}\left(x_k,y_k;x_p,y_p;t_i\right)\end{array}\right)\right]}\right|\\ & =\frac{1}{K}·\left|{\displaystyle \sum _{i=0}^N\exp \left[j·\delta {\varphi }_{res}\left(x_k,y_k;x_p,y_p;t_i\right)\right]}\right|\end{array}$$

(7)

where $j$ is an imaginary unit. The value of this function is one when the coherent point target is completely uncorrelated, and zero in the case of complete decoherence. After screening the coherent point targets with a good quality according to the coherence, a coherent point was selected as the reference point, to calculate the linear deformation phase, and elevation residuals were solved on each connected edge of the triangular network, as follows [42]:

$$\begin{array}{ll}v\left(x,y\right)& =\frac{1}{{\displaystyle \sum _m{\gamma }_{\mathrm{model}}\left(x,y,x_i,y_i\right)}}·{\displaystyle \sum _m\left[v\left(x_i,y_i\right)+\Delta v\left(x,y,x_i,y_i\right)\right]}\\ & ·{\gamma }_{\mathrm{model}}\left(x,y,x_i,y_i\right)\end{array}$$

(8)

where m is the number of points connected to the interference point target. The equation for calculating the elevation residuals is the same as this equation.

3.2.3. Calculation of Nonlinear Deformation

After calculating the linear deformation phase and the elevation residual phase in the differential interference phase of the coherent point target, the nonlinear deformation phase was also calculated. The nonlinear deformation phase is present in the phase residual of the coherent point target, which consists of the nonlinear deformation phase, the atmospheric delay phase, and the noise phase. The main components of the phase residuals are as follows [42]:

$${\phi }_{i,res}^k={\phi }_{i,noleaner}^k+{\phi }_{i,atm}^k+{\phi }_{i,noise}^k$$

(9)

The three components of the phase residuals have different spatial–temporal characteristics, and they can be extracted based on their spatial-temporal distribution characteristics. The influence of the troposphere is different at different moments, so the influence of atmospheric delay on the radar signal at different moments during interference is also different, causing the atmospheric delay phase to have a high correlation in space and be a low-frequency signal, but to be random in time and be a high-frequency signal. The nonlinear deformation is a low-frequency signal in time and a high-frequency signal with randomness in space. The phase noise is random in space and time.

The atmospheric phase of each view image affects each interference pair in which that view image is located. In order to calculate the atmospheric delay phase for each interferometric pair, the atmospheric phase of the main image needed to be calculated. The baseline combination chosen in this study was a multi-master image approach. Considering that each scene image is involved in several sets of differential interference, the time average of the interferometric atmospheric phase of multiple interferometric pairs can be regarded as an approximation of the atmospheric phase of the main image, as follows [42]:

$${\overline{\phi }}_{i,res}={\displaystyle \sum _{k=1}^K\frac{{\phi }_{i,atm}^k}{K}}$$

(10)

Then, the atmospheric phase in the differential interference phase of each interference pair can be calculated as follows [42]:

$${\phi }_{i,atm}^k=\mathrm{lp}\_\mathrm{space}\left(\mathrm{hp}\_\mathrm{time}\left({\phi }_{i,res}^k-{\overline{\phi }}_{i,res}\right)\right)+\mathrm{lp}\_\mathrm{space}\left({\overline{\phi }}_{i,res}\right)$$

(11)

where $\mathrm{lp}\_\mathrm{space}$ is a low-pass spatial filter, and $\mathrm{hp}\_\mathrm{time}$ is a high-pass time filter. ${\overline{\phi }}_{i,res}$ denotes the atmospheric delay phase of the point target in the main image, meaning that high-pass filtering ${\phi }_{i,res}^k-{\overline{\phi }}_{i,res}$ can eliminate the effect of nonlinear distortion and obtain the atmospheric delay phase with the noise phase in the slave image of the kth interference pair, and that low-pass filtering of the results will obtain the atmospheric phase of the slave image. The atmospheric phases of the master and slave image were then summed to give the complete atmospheric phase of the interference pair. Finally, the nonlinear deformation phase was obtained by removing the atmospheric phase in ${\phi }_{i,res}^k$, and low-pass filtering to remove the noise phase, as follows [42]:

$${\phi }_{i,nolinear}^k=\mathrm{l}\mathrm{p}\_\mathrm{space}\left({\phi }_{i,res}^k-{\phi }_{i,atm}^k\right)$$

(12)

Finally, the nonlinear deformation phase was added to the linear phase to achieve the complete deformation information of the target at the coherent point.

3.3. Geological Hazard Susceptibility Assessment Method

3.3.1. Influencing Factors Selection

• Information Value Model

The information value model can calculate the information value of the influencing factors using the spatial relationship between the geological hazards and the influencing factors. The information value can reflect the level of the contribution of the influencing factors to the occurrence of the hazards. In this study, the influencing factors were reclassified, and the information value of each classification of each influencing factor was used as the features of geological hazards, so as to improve the accuracy and efficiency of the geological hazard susceptibility evaluation model.

For geological hazard $B$, $X_{ij}$ is each classification of each influencing factor (i is the number of influencing factors, $j$ is the number of subclasses of each influencing factor). The information value can be expressed as in Equation (13) [15]:

$$I_{ij\to B}=\ln \frac{P(B/X_{ij})}{P(B)}(i=1,2,\dots n,j=1,2,\dots ,m)$$

(13)

where $P(B/X_{ij})$ is the probability of geological hazard occurrence in the area of $X_{ij}$, and $P(B)$ is the probability of geological hazard occurrence in the whole study area.

Since it was difficult to express the probability of the occurrence of geological hazards in this study, the probability was calculated based on the number of geological hazard grids as follows [15]:

$$I_{X_{ij}\to B}=\ln \frac{N_{ij}/S_{ij}}{N/S}$$

(14)

In Equation (14), $I_{X_{ij}\to B}$ is the information value of $X_{ij}$, $N_{ij}$ is the number of geological hazard grids in the area of $X_{ij}$, $S_{ij}$ is the number of grids in the area of $X_{ij}$. $N$ is the number of geological hazard grids in the whole study area, and $S$ is the number of grids in the whole study area.

2

Multicollinearity Analysis

Multicollinearity analysis can be used to calculate the correlation between influencing factors. Multicollinearity means that at least two influencing features are highly correlated linearly. In this study, tolerance level (TOL) and variance inflation factor (VIF) were used for the evaluation. For the independent variable data set, i.e., the influencing factors $X=\left\{X_1,X_2,\dots ,X_n\right\}$, the VIF value was calculated as follows [43]:

$$\mathrm{VIF}=1/\left(1-R_j^2\right)$$

(15)

where $R_j^2$ is the correlation coefficient of the regression equation, fitted with the influencing factor $X_j$ as the dependent variable, and the rest of the influencing factors are the independent variables.

The value of TOL is the reciprocal of VIF. In general, if VIF < 10 (TOL > 0.1), the influencing factors are considered to be independent of each other, they can all be used for geological hazard susceptibility evaluation, and there is no collinearity.

3

Relief-F

The relief feature selection (relief-F) method can be used to calculate the relative importance of the influencing factors to geological hazard occurrence. The relief-F algorithm evaluates the importance of a feature’s ability to discriminate in a classification task as an evaluation factor, by calculating the degree of difference between factors in the same class of nearest-neighbor samples and in different classes of nearest-neighbor samples. For the input sample set $D$, we randomly selected a sample $R$, then selected the same-category nearest-neighbor sample set $H$ and the non-category nearest-neighbor sample set $M$ of sample $R$. The weight of the influencing factor $X_i$ can be expressed as follows [44]:

$$\begin{array}{ll}{W}_i& =W_i-{\displaystyle \sum _{j=1}^k\frac{diff\left(X_i,R,H_i\right)}{mk}}+\\ & {\displaystyle \sum _{C\ne Class\left(R\right)}\left\{\frac{p\left(C\right)}{1-p\left[Class\left(R\right)\right]}{\displaystyle \sum _{j=1}^k\frac{diff\left[X_i,R,M_j\left(C\right)\right]}{mk}}\right\}}\end{array}$$

(16)

where $p(C)$ is the probability of the class $C$, $Class\left(R\right)$ is the class of $R$, $M_j\left(C\right)$ is the jth sample of class $C$, and $diff$ is the difference between different samples on an influencing factor. After repeating this process m times, the weights $W_i$ can be calculated.

3.3.2. Geological Hazard Susceptibility Assessment Models

• RF

Random forest (RF) is an algorithm that assembles multiple decision trees through an ensemble learning approach [45]. The random forest model consists of several decision trees and uses the Bagging model to take multiple independent samples from the total sample as the training dataset, which are then fed into the decision tree for classification. The Bagging method draws samples randomly and with put-back, as an independent training set, and builds a decision tree for each extracted training set separately. Finally, the decision results of each decision tree are combined for voting, resulting in the optimal classification result.

In this study, we used python to complete the RF model, based on the random forest classifier in the Scikit-learn framework.

2

SVM

The support vector machine (SVM) model is a supervised machine learning model. SVM takes the training error as the constraint of the optimization problem and minimizes the confidence interval as the optimization objective [46]. The basic principle of SVM is to map the sample data to a high-dimensional space and find the optimal hyperplane in that space to partition the different classes of data. In this process, the model finds a set of support vectors that are the closest data points to the hyperplane. This hyperplane separates the data points of the two categories and uses the maximum interval to improve the classification accuracy. Based on this principle, the SVM model is suitable for two-class classification problems such as geological hazard susceptibility evaluation where both positive and negative samples exist.

In this study, we used python to complete the SVM model based on the support vector machine classifier in the Scikit-learn framework.

3

CNN

Convolutional neural network (CNN) models are feedforward neural networks with a deep structure that can be computed by convolving data. In this study, 1D-CNN architectures were used. In addition to the input and output layers, as in a normal neural network, the network structure also includes two convolutional layers, one pooling layer, and two fully connected layers [47].

The convolution kernel in the convolution layer can be regarded as a regular shaped filter. The convolution window slides over the input data set and sums the inner product of its fixed weights with the data inside the window. The convolution kernel outputs convolutional features after completing one convolution operation on the entire input data, namely the primary features extracted by the convolution operation. The pooling layer is used to achieve the sampling of features, which can reduce the amount of data used while retaining useful information, preventing over-fitting, and improving the generalization ability of the model. The fully connected layer can map high-dimensional features extracted by convolution and pooling operations to a low-dimensional feature space. We extract the geological hazard features by convolution and pooling operations, and then reorganize them by a fully connected layer. Finally, we let the fully connected layer be connected to the output layer, which consists of two neurons representing geological hazards and non-geological hazards.

In this study, the CNN model was implemented in python under the Tensorflow framework, and included two convolutional layers, a maxpool layer, a flattened layer, two fully connected layers and a dropout layer between the fully connected layers.

4

RNN

A recurrent neural network (RNN) is a neural network that recurses the input sequence data in the direction of the data over the sequence and is able to chain all nodes together [48]. Unlike other neural networks, RNN can use serialized information, and it can capture dynamic information in serialized data by periodically connecting hidden layer nodes. Each unit in the RNN is associated with other units in the hidden layer at different time intervals, so that information can be passed from one layer to the next in the network. In 2020, Wang Yi et al. experimentally demonstrated that inputting the influencing factors into the RNN model according to their importance can effectively improve the performance of the RNN model for geological hazard susceptibility assessment [18]. Therefore, we ranked the importance of the factors according to the relief-f method, constructed the sequence data based on the importance ranking of the factors, and input them into the RNN model for the evaluation of geohazard susceptibility.

In this study, the RNN model was implemented in Python under the Tensorflow framework and included a simple RNN layer and a fully connected layer.

3.3.3. Model Evaluation

Five randomly selected training and validation sets were put into a 7:3 ratio for cross-validation. The training set is inputted into the geological hazard susceptibility assessment model for training, and the validation set is classified and evaluated for accuracy using the trained model receiver operating characteristic (ROC) curve, which can effectively indicate the predictive power of different geological hazard susceptibility assessments [49]. In this study, ROC curves were used to assess model effectiveness by calculating area under the curve (AUC) values, in order to compare different models’ predictive abilities. In addition, three indicators, namely the recall, F-score, and Matthews correlation coefficient (MCC), are used to compare different models’ accuracy [14]:

$$\mathrm{Recall}=\frac{TP}{TP+FN}$$

(17)

$$\mathrm{F}\text{-}\mathrm{score}=\frac{2\times TP}{2\times TP+FP+FN}$$

(18)

$$\mathrm{MCC}=\frac{TP\times TN-FP\times FN}{\sqrt{\left(TP+FP\right)\times \left(TP+FN\right)\times \left(TN+FP\right)\times \left(TN+FN\right)}}$$

(19)

4. Results

4.1. Deformation Results from MT-InSAR

In this study, the IPTA technique uses small baseline ideas for interferometric pair combining, in order to reduce the effect caused by spatial–temporal incoherence and improve the interferometric quality. Due to the time interval of the data being stabilized and the addition of precision orbital data, there is no spatial–temporal baseline threshold set during the combination of interferometric pairs, and the main image of the data of each view is combined with the data of the following two views, forming a total of 157 interferometric pairs, as shown in Figure 3a.

We set the amplitude deviation threshold to 1.25 for point selection, then combined it with the points selected by the multi-looking method, and finally calculated the temporal coherence of all the points, keeping the points with temporal coherence greater than 0.7 as monitoring points. A total of 1,418,107 points were finally selected. Figure 4a shows the annual average surface deformation rate along the radar line of direction of sight of the study area, from September 2016 to September 2022, acquired by the MT-InSAR technique mentioned in Section 3.2. The figure shows that most of the study area was in a stable state, and the maximum deformation rate was −44 mm/year. Figure 3b shows a histogram of the standard deviation for all points, with an average value of 1.33, which proves the reliability of the monitoring points.

4.2. Geological Hazard Identification

In this study, we combine InSAR deformation results, UAV imagery, and Google Earth data for geological hazard identification. The identified geological hazards were mainly classified into three categories: collapses, unstable slopes, and landslides. The principles for identifying geological hazards were as follows:

• Using 10 mm/year as the threshold [50], we selected the areas where deformation points with deformation greater than this threshold gathered, and considered these areas as deformation areas;
• Using orthophoto images generated by UAV, Google Earth, we considered the terrain, topography, and spectral, textural, topographical, and morphological features of the deformation area to confirm whether it was a geological hazard. Finally, we classified geological hazards [34];
• At this point, there were still geological hazards that could not be identified by deformation. Supplementary identification was carried out, based on optical images, topography, and the distribution of historical geological hazards.

As shown in Figure 4b, a total of 60 geological hazard areas were identified, with 7 collapses, 25 unstable slopes, and 28 landslides, of which 12 were on the geological hazards list as existing geological hazards. Several typical geological hazards in the study area are shown in Figure 5.

4.3. Geological Hazard Susceptibility Assessment

We combined the identified geological hazards and the geological hazards in the geological hazards list to create the sample of geological hazards. All the grids where the geological hazard samples were located were used as positive samples. We selected the same number of non-geological hazard grids as negative samples. The information value of each influencing factor was calculated, as shown in

Table A1. Information values of geological hazard-influencing factors.

Factor	Factor Class	No. of Grids	% of Grids	Geohazard Grids	Geohazard Grids(%)	Information Value
Elevation (m)	36–322	209,817	14.21%	1113	15.52%	0.088047
	323–607	493,627	33.43%	2121	29.57%	−0.122668
	608–893	458,644	31.06%	1642	22.89%	−0.305135
	894–1179	220,270	14.92%	1295	18.06%	0.190881
	1180–1465	70,910	4.80%	956	13.33%	1.020815
	1466–1750	17,422	1.18%	43	0.60%	−0.677065
	1751–2036	5779	0.39%	2	0.03%	−2.641615
Slope (rad)	0–0.27	250,062	16.94%	1132	15.78%	−0.070538
	0.28–0.54	540,151	36.58%	2909	40.56%	0.103146
	0.55–0.81	591,174	40.04%	2879	40.14%	0.002517
	0.82–1.08	90,736	6.15%	248	3.46%	−0.575096
	1.09–1.35	4288	0.29%	4	0.06%	−1.650096
Aspect	Flat (−1)	917	0.06%	0	0.00%	0
	North (337.5°–22.5°)	186,881	12.66%	644	8.98%	−0.382895
	Northeast (22.5°–67.5°)	193,637	13.11%	690	9.62%	−0.309825
	East (67.5°–112.5°)	198,927	13.47%	913	12.73%	−0.056733
	Southeast (112.5°–157.5°)	199,209	13.49%	913	12.73%	−0.05815
	South (157.5°–202.5°)	182,796	12.38%	1010	14.08%	0.128804
	Southwest (202.5°–247.5°)	169,656	11.49%	1077	15.02%	0.267631
	West (247.5°–292.5°)	167,063	11.32%	1081	15.07%	0.28674
	Northwest (292.5°–337.5°)	177,383	12.01%	844	11.77%	−0.02069
Plan Curvature	−0.027–0.0049	116,417	7.88%	412	5.74%	−0.316689
	−0.0048–−0.0014	330,995	22.42%	1701	23.72%	0.056334
	−0.0013–0.0015	561,709	38.04%	2940	40.99%	0.074647
	0.0016–0.005	331,235	22.43%	1628	22.70%	0.011746
	0.0051–0.026	136,108	9.22%	491	6.85%	−0.297538
Profile Curvature	−0.025–−0.005	109,963	7.45%	825	11.50%	0.434706
	−0.004–−0.002	332,736	22.54%	1957	27.29%	0.191285
	−0.001–0.001	611,892	41.44%	2869	40.00%	−0.035371
	0.002–0.005	317,488	21.50%	1292	18.01%	−0.177027
	0.006–0.071	104,385	7.07%	229	3.19%	−0.794898
TWI	1.7–5	733,943	49.71%	2972	41.44%	−0.181972
	2.1–6.9	458,604	31.06%	2734	38.12%	0.204803
	7–9.6	190,190	12.88%	846	11.80%	−0.088035
	9.7–13.8	73,221	4.96%	422	5.88%	0.170992
	13.9–24.3	20,510	1.39%	198	2.76%	0.686823
TRI	0–6.8	229,329	15.53%	1171	16.33%	0.049212
	6.9–12.7	533,731	36.15%	3036	42.33%	0.157161
	12.8–18.6	514,331	34.84%	2422	33.77%	−0.031761
	18.7–28.8	170,129	11.52%	483	6.73%	−0.537784
	28.9–107.9	27,898	1.89%	60	0.84%	−0.815454
LS-Factor	0–18.1	501,137	33.94%	2041	28.46%	−0.176255
	18.2–144.6	959,959	65.02%	4948	68.99%	0.059278
	144.7–488.1	13,703	0.93%	139	1.94%	0.736289
	488.2–1554.7	1512	0.10%	43	0.60%	1.767196
	1554.8–4609.9	99	0.01%	1	0.01%	0.732065
Precipitation (m)	0–100	117,012	7.93%	123	1.72%	−1.572805
	100–200	258,261	17.49%	1006	14.03%	−0.262946
	200–500	353,546	23.95%	1273	17.75%	−0.341595
	500–1000	335,283	22.71%	2284	31.85%	0.295996
	1000–2000	412,367	27.93%	2795	38.97%	0.290961
NDVI	−0.41–0.04	1329	0.09%	0	0.00%	0
	−0.03–0.19	37,393	2.53%	337	4.70%	0.618068
	0.2–0.32	64,701	4.38%	935	13.04%	1.090239
	0.33–0.41	219,242	14.85%	1365	19.03%	0.248202
	0.42–0.47	563,527	38.17%	2490	34.72%	−0.094708
	0.48–0.55	502,529	34.04%	1588	22.14%	−0.429954
	0.56–0.84	87,748	5.94%	457	6.37%	0.069683
Distance to Road (m)	0–100	189,712	12.85%	2167	30.21%	0.851954
	100–200	136,799	9.27%	422	5.88%	−0.457145
	200–500	307,285	20.81%	1082	15.09%	−0.324847
	500–1000	346,864	23.49%	2659	37.07%	0.453135
	1000–2000	349,585	23.68%	630	8.78%	−0.994665
	>2000	148,622	10.07%	246	3.43%	−1.079712
Distance to River (m)	0–100	58,036	3.93%	538	7.50%	0.646264
	100–200	54,507	3.69%	268	3.74%	0.012127
	200–500	143,741	9.74%	313	4.36%	−0.802341
	500–1000	196,071	13.28%	449	6.26%	−0.751985
	1000–2000	317,163	21.48%	1766	24.62%	0.136525
	>2000	706,951	47.88%	3838	53.51%	0.111214
Landcover	Tree cover	894,102	60.56%	3496	48.75%	−0.218287
	Shrubland	62	0.00%	0	0.00%	0
	Grassland	474,735	32.15%	2700	37.65%	0.158476
	Cropland	24,995	1.69%	72	1.00%	−0.51801
	Built-up	49,604	3.36%	404	5.63%	0.514295
	Bare	29,827	2.02%	500	6.97%	1.164069
	Water	2248	0.15%	0	0.00%	0
Stratigraphic Unit	C	207,927	14.08%	715	9.97%	−0.387618
	J	259,323	17.56%	470	6.55%	−1.028055
	Jx	582,921	39.48%	4786	66.73%	0.482686
	O	62,197	4.21%	302	4.21%	−0.042593
	P	71,121	4.82%	676	9.43%	0.629097
	Qb	161,641	10.95%	245	3.42%	−1.206833
	Qp	129,310	8.76%	287	4.00%	−0.825443
	∈	2029	0.14%	0	0.00%	0
Distance to Fault (m)	0–100	44,805	3.03%	311	4.34%	0.383891
	100–200	45,550	3.09%	268	3.74%	0.218595
	200–500	130,518	8.84%	922	12.86%	0.401452
	500–1000	199,420	13.51%	1464	20.41%	0.439933
	1000–2000	348,381	23.60%	1848	25.77%	0.114981
	>2000	707,827	47.94%	2359	32.89%	−0.349788
Distance to Mine Origin (m)	0–100	9670	0.65%	152	2.12%	1.201271
	100–200	25,462	1.72%	375	5.23%	1.136157
	200–500	120,030	8.13%	1146	15.98%	0.702709
	500–1000	251,046	17.00%	1528	21.31%	0.252497
	1000–2000	483,530	32.75%	2685	37.44%	0.160741
	>2000	627,062	42.47%	1286	17.93%	−0.835335

and Figure A1.

Table 1. Multicollinearity analysis results for landslide-influencing factors.

Influencing Factor	TOL	VIF	Influencing Factor	TOL	VIF
Elevation	0.796	1.256	Precipitation	0.760	1.315
Slope	0.501	1.995	NDVI	0.693	1.422
Aspect	0.918	1.090	Distance to Road	0.869	1.151
Plan Curvature	0.943	1.060	Distance to River	0.908	1.101
Profile Curvature	0.843	1.186	Landcover	0.736	1.359
TWI	0.773	1.293	Stratigraphic Unit	0.690	1.448
TRI	0.496	2.016	Distance to Fault	0.820	1.090
LS-Factor	0.792	1.263	Distance to Mine Origin	0.740	1.352

presents the analysis of covariance between the influencing factors. It can be observed that all correlation coefficients are below 0.7 and the VIF values of these factors are below five (TOL > 0:2). Figure A2 shows the correlations between the factors, all of which are less than 0.5. Therefore, all the factors are independent of each other and there is no covariance between them. Figure 6a shows the importance of each influencing factor, as calculated by the relief-F method, and it can be seen that the importance of the influencing factors is positive, i.e., all the influencing factors contribute to the occurrence of geological disasters to a certain extent. Among them, the stratigraphic unit factor and the road distance factor have a higher importance to the occurrence of geological hazards. In summary, all influencing factors can participate in the vulnerability assessment.

We inputted the influencing factors as the features, the information values as the features value, and whether or not the feature was a geological hazard as a label into the model for training and used the trained model to predict the probability of each grid being a geological hazard, which was then used as the susceptibility index for that grid. The models’ parameter settings are shown in

Table 2. Parameter settings of the models.

RF		SVM		CNN		RNN
n_estimators	10	C	100	Learning rate	0.001	Learning rate	0.001
max_depth	50	Gamma	0.0002	Epoch	512	Epoch	512
min_samples_split	10	Kernel function	rbf	Batch_size	256	Batch_size	256
min_samples_leaf	50			Activation function	sigmoid	Activation function	tanh

. Then, the susceptibility of all grids was reclassified into five classes, using the natural breaks method, as follows: very high susceptibility, high susceptibility, moderate susceptibility, low susceptibility, and very low susceptibility. Figure 7a–d shows the results of the susceptibility assessment of the four methods; as can be seen from the figure, the distribution and pattern of susceptibility zones derived from the four methods are relatively similar.

Table 3. Correlations of susceptibility across models.

Models Used to Compare	Pearson Correlation Coefficient	Models Used to Compare	Pearson Correlation Coefficient
RF and SVM	0.792	SVM and CNN	0.595
RF and CNN	0.692	SVM and RNN	0.783
RF and RNN	0.709	CNN and RNN	0.532

shows the correlation of geological hazard susceptibility derived from each model, from which it can be seen that there is a strong correlation between all models. The accuracy and runtime of the four models are shown in

Table 4. Performances of different models.

Evaluation Indicators	RF	SVM	CNN	RNN
Recall	0.753	0.747	0.861	0.708
F1_score	0.774	0.776	0.788	0.756
MCC	0.561	0.566	0.592	0.547
Runtime	6.4 s	561 s	555 s	506 s

and the ROC curves and AUC of the four models are shown in Figure 6b. All four models achieved good prediction accuracy, with the RF model having the highest AUC value and the shortest runtime.

We calculated statistics regarding the number of grids of geological hazard susceptibility zones derived from the four models, and regarding the number of grids of geological hazards in those susceptibility zones. As shown in Figure 8, most of the susceptibility zones derived from the four models were in the very low susceptibility and low susceptibility zones, and most of the geological hazard grids were within the very high susceptibility and high susceptibility zones. As can be seen in Figure 7e–h and Figure 8, the RF model zoning results had the lowest percentage of geological hazard grids within the low and very low susceptibility zones and the highest percentage of geological hazard grids within the high and very high susceptibility zones; the susceptibility zoning decreases in steps from low to high, which was mostly consistent with the distribution of geological hazard susceptibility [51]. Therefore, the RF model was considered to be the best model for the geological hazards susceptibility assessment in the study area, and the results were as follows: very low susceptibility 27.40%, low susceptibility 28.06%, moderate susceptibility 21.19%, high susceptibility 13.80%, and very high susceptibility 9.57%.

5. Discussion

In this study, we used MT-InSAR, combined with PS point selection and multi-looking point selection, to improve the density of the monitoring points. We also obtained denser monitoring points for surface deformation monitoring in the mountainous areas of western Beijing with high vegetation cover. We evaluated the accuracy using the statistical standard deviation, which proved the reliability of the method to improve the density of monitoring points.

From the identification results, MT-InSAR was more effective in identifying slow-moving geological hazards, such as landslides and unstable slopes, and less effective in identifying faster-moving geological hazards, such as collapses. Geological hazards in the study area were distributed in a regular pattern, with many points and small surfaces. Most of the geological hazards on the list were found by manual surveys, and they were distributed near roads, making it easier to find hazards related to human activities and those that were a greater threat to people’s lives and safety. MT-InSAR can be used to find hazards in more hidden areas that are difficult for surveyors to reach, such as valleys and mining areas. This proves the reliability of MT-InSAR technology for geological hazard identification, as it was more comprehensive than manual surveys.

Although there are differences in the triggering mechanisms and characteristics of different types of geological hazards, there are still common characteristics in their spatial distribution. The models in this study were assessed for multiple types of geological hazards and reliable results were obtained. This demonstrates that the models used in the study can all learn the common characteristics of multiple types of geological hazard. The occurrence process of geological hazards is more complicated, and there are many assessment methods. Many scholars have already compared different susceptibility assessment models to select the most suitable model for the study area [52,53]. The results show that all models can perform effective geological hazard susceptibility assessments. The RF model worked better than the other three models, yielding a less noisy and smoother susceptibility map with a more reasonable percentage of susceptibility partitions. Additionally, the RNN model was far quicker than other models in terms of runtime. Although the model accuracy of the CNN model was high, its zoning results were biased towards bipolarity, which was not in line with the geological hazard zoning rule. This is due to the variety of geological hazards in the geological hazard samples used, and in the sample added to the historical geological hazards, resulting in geological hazards of a large time span, which in turn resulted in noise in the data samples. Relative to the scope of the study area, the number of samples of geological hazards was small, and the deep learning model found it difficult to effectively learn the characteristics of geological hazards. The RF model, with the characteristics of multi-model decision-making, is very good at overcoming these problems.

6. Conclusions

In this paper, we mainly carried out geological hazard identification and susceptibility assessments, and effectiveness evaluations of different models in the western mountainous area of Beijing. Two main results were obtained, as follows:

First, a combination of multi-looking point selection and PS point selection was used to increase the density of MT-InSAR monitoring points and obtain surface deformation information about the study area, and the accuracy of this method was demonstrated by counting the standard deviation of the monitoring points. The study area was found to be essentially in a steady state, with a maximum deformation rate of −44 mm/year. Based on surface deformation information combined with optical images, 60 geological hazards were identified in the study area, with 7 collapses, 25 unstable slopes, and 28 landslides.

Second, the identified and historical geological hazards were combined as geological hazard samples, and the geological hazard influencing factors were collected. They were analyzed as the features of the geological hazards, and their information values were analyzed as the feature values. The factor selection was carried out, using multicollinearity analysis and the relief-F method. The results showed that 16 influence factors could all be used for the geological hazard susceptibility assessments; among these, roads and stratigraphic units had the greatest impact on geological hazards. Finally, the geological hazard susceptibility assessment results were obtained using different models for comparison. All models achieved reliable results, with the RF model performing best. This demonstrates the great advantage of RF models in learning multi-class and long time-span geological hazard characteristics. Additionally, the percentages of geological hazard susceptibility zoning in the study area were as follows: very low susceptibility 27.40%, low susceptibility 28.06%, moderate susceptibility 21.19%, high susceptibility 13.80%, and very high susceptibility 9.57%.

The research in this paper has significance for future research on surface deformation, the distribution of geological hazards, and the assessment of geological hazard susceptibility in the mountainous areas of western Beijing, and also provides a reference for the prevention and control of geological hazards in Beijing and the whole North China region. The methodology of this paper can also be used as a reference for MT-InSAR surface deformation monitoring or geological hazard susceptibility assessment model selection in similar study areas. Future research can be conducted regarding three aspects: (1) research on the automatic identification of geological hazards can be carried out based on optical images, deformation rates, and differential phases, and automatic geological hazard identification can improve the efficiency of geological hazard identification. (2) Dynamic assessment of geological hazard susceptibility, when combined with precipitation, soil moisture, seasons and other dynamic factors, can more accurately identify geological hazard-prone areas and provide references for geological hazard prevention and control. (3) Refined assessment of the susceptibility of different types of geological hazards, as their characteristics are not identical. A good susceptibility assessment requires that each type be assessed separately.