Applied Science and Innovative Research 

ISSN 2474-4972 (Print) ISSN 2474-4980 (Online) 

Vol. 9, No. 1, 2025 

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146 
 

Original Paper 

Satellite Remote Sensing Estimation of Ground Subsidence along 

Transmission and Transformation Lines Based on Multi-scale 

Geographically Weighted Regression 

Xiao Li1, Qingkun Yang1, Chen Cao1, Tie Jin1 & Xiguan An1 

1 College of Construction Engineering, Jilin University, Changchun 130012, Jilin, China 

 

Received: January 20, 2025    Accepted: February 22, 2025    Online Published: February 28, 2025 

doi:10.22158/asir.v9n1p146          URL: http://doi.org/10.22158/asir.v9n1p146 

 

Abstract 

In this paper, a 5km area along the 750kV Third passage project in Shaanxi Province is taken as the 

research area. Based on the analysis of the application and limitation of traditional two-dimensional 

regression model in land subsidence simulation, the advantages of multi-scale geographical weighted 

regression model in automatically calculating bandwidth and exploring spatial heterogeneity of impact 

factors are explored. Based on the geological environment of the region and the latest geological disaster 

data, seven influencing factors including slope, topographic relief, average annual rainfall, topographic 

humidity index (TWI), distance from river, distance from fault and distance from road were selected as 

dependent variables, and the SBAS-InSAR results covering the whole region were taken as independent 

variables. On the basis of evaluation factor analysis, The land subsidence results along the 750kV third 

passage project in northern Shaanxi and Guanzhong were simulated by ArcGIS platform. The evaluation 

results show that the fault distance and precipitation in the study area have great influence. 

Keywords  

Land subsidence multi-scale geographical weighted regression InSAR driving force analysis 

 

1. Introduction 

As the social electricity consumption in Shaanxi Province increases year by year, it is of great importance 

to improve the intelligent level of power grid, support cross-regional power trading and rural 

electrification, and ensure the safe construction and operation of line projects (Xie Huafei, 2011). 

Transmission lines have the characteristics of long distance and long span. At the same time, due to the 

complex and fragile engineering geological conditions, the monitoring of geological hazards in the 

transmission line area is particularly heavy (Liu Hujun, 2004). The main part of Shaanbei - Guanzhong 



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750kV third channel project is located in Weinan City, the east of Weihe Basin and the southern margin of 

the Loess Plateau. It has complex geological structure, large topographic relief and active fault 

movement (He Hongqian, 2011; Zhao Jingbo & Chen Yun, 1994). Loess is the main type of soil in the 

region, which has the characteristics of large porosity and high water content, and is prone to 

compression and settlement when the water content changes caused by external forces or rainfall factors 

(Zhang Maosheng & Li Tonglu, 2011; Zhang Puxuan, 2017). The groundwater resources in the study 

area are abundant. In the process of engineering construction or agricultural irrigation, a large amount of 

groundwater will be extracted, which will easily lead to ground settlement and subsidence funnel, 

threatening the stability of transmission line base (Yin Yueping, Zhang Zuochen, & Zhang Kaijun, 2005).  

Land subsidence is a kind of slow regional geological disaster caused by groundwater, mineral resource 

exploitation, crustal movement and other factors (F. Raspini, F. Caleca, M. Del Soldato, D. Festa, P. 

Confuorto, S. Bianchini, 2022). At present, in the study of land subsidence, in addition to the use of 

high-precision geometric leveling, telescopometer, global navigation satellite system or global 

positioning system network to detect it, satellite remote sensing means, especially synthetic aperture 

radar interferometry technology, are also used to study land subsidence (Fan Shan-Shan, Guo Hai-Peng, 

Zhu Ju-Yan, et al., 2013), and its effectiveness in this field has been repeatedly proved. 0Compared with 

the original methods, InSAR technology has great advantages in monitoring scope and monitoring cost, 

and is less affected by climate. The millimeter-level accuracy, wide area data coverage, high frequency 

data sampling, ability to track deformation history, and higher benefit/cost ratio compared to targeted 

ground monitoring activities have led to the increasing use of SAR interferometry in the field of land 

subsidence research. 

In order to predict land subsidence, and then plan and guide the key areas of deformation in the 

construction and operation of transmission lines, researchers choose to use regression analysis method to 

quantify the influence of variables and analyze the causal relationship between multiple independent 

variables (Li Li, 2014; Li Guangyu, Zhang Rui, Liu Guoxiang, et al., 2018; Xiong Q., 2023). Ordinary 

least squares (OLS) is the simplest regression analysis method, which can directly explain the average 

influence of each variable on the dependent variable. However, if the land subsidence in different regions 

is significantly affected by different factors, the OLS hypothesis is no longer applicable. On this basis, 

the consideration of spatial heterogeneity and optimal bandwidth is added, and a geographically 

weighted regression model (GWR) and a multi-scale geographically weighted regression model 

(MGWR) are gradually produced, among which the fitting error of the MGWR model is significantly 

smaller than that of GWR and OLS. Huang Shuangfei (2024) took Qingchuan County, Guangyuan City, 

Sichuan Province as the research object, and selected elevation, slope, slope direction, relief of terrain, 

rock, rainfall, distance from fault zone, distance from water system, distance from residential site, and 

vegetation cover type as independent variables to study landslide susceptibility. The results show that 

MGWR model can realize factor correlation and spatial non-stationary integration. Previous studies have 

shown that the reasonable use of multi-scale geographical weighted regression model can improve the 



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accuracy of regional land subsidence simulation. 

By allowing independent variables to function on different spatial scales, MGWR model structure is 

more flexible, and the most suitable spatial scale can be selected for different independent variables, thus 

improving the adaptability and flexibility of the model. It can more accurately reflect the influence of 

each independent variable in different regions, and improve the explanatory power and accuracy of the 

model; More local details and changes can be captured to better reflect complex spatial structures and 

relationships; Better adapt to the spatial changes of data, improve the fit degree and prediction accuracy 

of the model. This paper adopts the multi-scale geographical weighted regression method; The influence 

of different independent variables on different spatial scales, so as to improve the reliability and accuracy 

of ground settlement prediction of transmission lines. This study conducted field geological survey on 

route selection, combined with geotechnical investigation data in the region, and selected 7 independent 

variables including slope, topographic humidity index, distance from river, distance from road, distance 

from fault, average annual rainfall and topographic relief. Based on single-scale geographical regression 

analysis model and MGWR model, ArcGIS platform was adopted to analyze the results. The ground 

subsidence rate of transmission and transformation line selection was simulated to verify the accuracy of 

the simulation results, and the simulation results were compared in order to better understand the 

relationship between ground subsidence and its influencing factors, and at the same time to provide 

certain basis for line selection, power tower site selection and subsequent safe operation. 

 

2. Overview of the Research Area 

The main part of the Shaanbei - Guanzhong 750kV third passage project is located in Weinan City, 

Shaanxi Province, in the east of Weihe Basin. The geographical coordinates are 

34°15'20.42"~35°25'22.02" N, 109°26'29.56"~109°49'06.96" E, and the research area is 5km on both 

sides of the route. The length of the line is 2×161km, and the research area is 883.54km2. 

The northern section of the line is located on the edge of the Ordos block and in the transition area 

between the basin and the Loess Plateau. The middle section is located in the eastern section of Weihe 

Cenozoic faulted basin in Guanzhong Basin; The southern section is adjacent to the Qinling Mountains, 

which is the Qinling fold transition zone of the Weihe fault depression basin (Li Xianggen & Ran 

Yongkang, 1983). A series of active faults (Feng Xijie & Dai Wangqiang, 2004; Peng Jianbing, Su 

Shengrui, & Mi Fengshou, 1992) developed in and along the margin of the Weihe fault Basin, an area 

with frequent neotectonic activity along the line, which is manifested by large differences in block uplift 

and subsidence and frequent seismic activity at the junction of uplift and fault depression (Quan 

Xinchang, 2005; Peng Jianbing et al., 2012; Yue-fei Wang, 2023). The landforms are distributed in a 

banding pattern, from south to north, the landforms are successively mountainous, alluvial plain, alluvial 

plain, loess tableland and mountainous area. The thickest part of the Quaternary system is over 700m, 

which is located in the north of Linwei Area (Daniel Yuh Chao, 2019). The terrain is high in the north and 

south and low in the middle, with an elevation ranging from 340.0m to 1100.0m (S. Ye, Y. Xue, J. Wu, X. 



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Yan, & J. Yu, 2015). The study area belongs to the temperate semi-arid continental monsoon climate, 

with strong spatio-temporal difference of rainfall, which is concentrated in summer, and its spatial 

distribution is more in the north and south, less in the middle. Weihe River and Beiluo River are the most 

developed rivers in this region. 

 

Figure 1. Overview Map of the Study Area 

 

3. Study Method 

3.1 SBAS-InSAR Technique 

Small-baseline synthetic aperture radar interferometry (SBAS-InSAR) solves the problem of 

incoherence caused by too long spatial baseline of conventional InSAR technology, which can fully 

improve the resolution of data sampling time, monitor large areas and non-urban areas, and use the 

settled displacement rate and accumulated displacement as the ground settlement number (P. Berardino, 

G. Fornaro, R. Lanari, & E. Sansosti, 2002).  

The principle of SBAS-InSAR technology is as follows: suppose that N+1 radar data images are acquired 

in the study area within the time period of tN0~t, and certain time and space thresholds are set for them. 

After interference processing, M-amplitude differential interferography is obtained (H. Yu, A.S. 

Fotheringham, Z. Li, T. Oshan, W. Kang, L.J. Wolf, 2020). M satisfies the equation as follows: 

  
𝑁+1

2
< 𝑀 <

𝑁(𝑁+1)

2
                                        (1) 

ForA the phase j interferoBgram obtained from the main image and generated from the image at two time 

points tB and t (tA<t), the interference phase of any point in the diagram is:(𝑥, 𝑟) 

𝛿𝜙𝑗(𝑥, 𝑟) = 𝜙(𝑡𝐵, 𝑥, 𝑟) − 𝜙(𝑡𝐴, 𝑥, 𝑟) ≈ ∆𝜙𝑑𝑖𝑠𝑝 + ∆𝜙𝑡𝑜𝑝𝑜 + ∆𝜙𝑜𝑟𝑏 + ∆𝜙𝑎𝑡𝑚 + ∆𝜙𝑛𝑜𝑖𝑠𝑒    (2) 

In Formula 3-8, and represents the phase of the two images at the point; 

𝜙(𝑡𝐵, 𝑥, 𝑟)𝜙(𝑡𝐴, 𝑥, 𝑟)(𝑥, 𝑟)∆𝜙𝑑𝑖𝑠𝑝 Is the cumulative deformation ofAB the object along the line of sight of 

the satellite at time t0 and t relative to t; ∆𝜙𝑡𝑜𝑝𝑜, ∆𝜙𝑜𝑟𝑏, ∆𝜙𝑎𝑡𝑚𝑜,∆𝜙𝑛𝑜𝑖𝑠𝑒 Refers to the phase errors 



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caused by terrain, orbit, atmosphere and noise respectively. 

When the deformation error caused by the atmosphere, noise, terrain and track is removed, the phase 

change can be expressed as: 

𝛿𝜙𝑗(𝑥, 𝑟) = 𝜙(𝑡𝐵, 𝑥, 𝑟) − 𝜙(𝑡𝐴, 𝑥, 𝑟) ≈
4𝜋

𝜆
[𝑑(𝑡𝐵, 𝑥, 𝑟) − 𝑑(𝑡𝐴, 𝑥, 𝑟)]            (3) 

In formula (9), represents deformation. 𝑑 (𝑡𝐴, 𝑥, 𝑟)𝑑 (𝑡𝐵, 𝑥, 𝑟). Let the initial time deformation be 0, then 

the phase time series of the interferogram is: 

𝜙(𝑡𝑖 , 𝑥, 𝑟) =
4𝜋

𝜆
𝑑(𝑡𝑖 , 𝑥, 𝑟)(𝑖 = 1, . . . , 𝑁)                            (4) 

A point variable represented by a vector is: 

𝜙 = [𝜙(𝑡1), . . . , 𝜙(𝑡𝑁)]𝑥                                    (5) 

Then the vector composed of the interferogram phase, whose value is: 

  𝛿𝜙 = [𝛿𝜙1, . . . , 𝛿𝜙𝑀]𝑥                                      (6) 

𝛿𝜙𝑖(𝑖 = 1, . . . 𝑀) Is the phase value of each point relative to the reference point. For the master and slave 

images, the phase value can be expressed as: 

𝛿𝜙 = 𝐴𝜙                                             (7) 

A is a matrix of MN, where each row corresponds to an interference relative. ×When the phase solution 

is converted to the problem of the rate of phase change, equation (7) can be converted to: 

𝐵𝑣 = 𝛿𝜙                                             (8) 

In the formula, B is MN matrix, SVD processing of the matrix, the average velocity v can be obtained, 

and then the integral operation can solve the deformation information of each pixel of the 

interferogram.× 

3.3 K-means Cluster Analysis 

The K-Means method divides the data into several uniform clusters with similar features, initializes the 

center of the k-cluster with a random search in each iteration, and then measures the distance from the 

data point (Xij) to the center (Cj). The cluster k is assigned to the data point xij by minimizing the 

objective function specified by formula (9). Due to the large study area and large amount of InSAR 

deformation data, in order to shorten the calculation time of the model while preserving the data 

properties, the clustering analysis method is adopted. 

3.3 Single Scale Two-dimensional Regression Model 

The OLS model establishes the relationship between the dependent variable and one or more 

independent variables on a global scale by means of least square method. This relationship is also known 

as classical linear regression, and its equations are: 

𝑦𝑖 = 𝛽0 + ∑ 𝛽𝑘𝑥𝑖𝑘 + 휀𝑖
𝑚
𝑘=1                                  (9) 

Geographically weighted regression model (GWR model) is the regression coefficient of independent 

variables in the model changes at different local points, so as to contain local variation, which can depict 

a more accurate relationship between variables in the data, and calculate the local independent variable 

coefficient by weighted least square method in the form of independent matrix (H. Yu, H. Gong, B. Chen, 

K. Liu, M. Gao, 2020; L. Zhang, Y. Li, R. Li, 2023):  



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�̂�𝑖𝑘 = [𝑋𝑇𝑊𝑖𝑋]−1𝑋𝑇𝑊𝑖𝑌                                 (10) 

Its equation is as follows: 

𝑦𝑖 = 𝛽0(𝑢𝑖 , 𝑣𝑖) + ∑ 𝛽𝑘(𝑢𝑖 , 𝑣𝑖)𝑥𝑖𝑘 + 휀𝑖
𝑚
𝑘=1                           (11) 

3.4 Multi-scale Geographical Weighted Regression Model 

To better understand the drivers behind land subsidence, regression analysis of SBAS-InSAR results can 

be performed using machine learning methods. Combined with the land subsidence impact factor data, a 

land subsidence prediction model can be built. The ordinary least squares (OLS) method is the most basic 

global method in regression analysis, but it does not consider the scale factor. The GWR method solves 

the scaling problem by calculating the optimal bandwidth, taking into account the spatial heterogeneity to 

a certain extent, but each of its influencing factors is limited to the same scale. To overcome this 

limitation, the MGWR method allows to examine spatial heterogeneity by relaxing different influencing 

factors at different scales (A.S. Fotheringham, W. Yang, W. Kang, 2017). Its equation is as follows: 

𝑦𝑖 = 𝛽𝑏𝑤𝑜(𝑢𝑖 , 𝑣𝑖) + ∑ 𝛽𝑏𝑤𝑘(𝑢𝑖 , 𝑣𝑖)𝑥𝑖𝑘 + 휀𝑖
𝑚
𝑘=1                       (12) 

Where: is the longitude and latitude of the space position i. (𝑢𝑖 , 𝑣𝑖)𝛽𝑏𝑤𝑜(𝑢𝑖, 𝑣𝑖) Is the constant term, is 

the local coefficient estimate of the KTH independent variable; 𝛽𝑏𝑤𝑘(𝑢𝑖 , 𝑣𝑖)𝑦𝑖, m and are the same 

parameters as MGWR.𝑥𝑖𝑘휀𝑖 

3.5 Model Accuracy Verification Method 

The use of post-fit algorithms during calibration allows for iterative estimates of additive terms, which 

can improve the accuracy of the model. To capture the nonlinear relationship between the dependent and 

independent variables, the model should be converted to a generalized additive model form, as shown in 

the equation: 

�̂� = ∑ 𝑓�̂� + 휀̂𝑚
𝑘=1                                    (13) 

The convergence termination criterion is determined by the rate of change of the sum of squares of 

residuals (SOCRSS). The change in fraction between successive iterations can be expressed as follows: 

𝑆𝑂𝐶𝑅𝑆𝑆 = |
𝑅𝑆𝑆2−𝑅𝑆𝑆1

𝑅𝑆𝑆2
|                                (14) 

In the SM-GWR method, the spatial weight matrix is determined based on the 3D spatial distance 

between the calibration position and the adjacent position. The closer the adjacent position is to the 

calibration position, the stronger its effect. The double quadratic kernel function is used to calculate the 

spatial weight matrix, focusing only on the influence of nearby points on the bandwidth determination, 

and its formula is as follows: 

𝑤𝑖𝑗 = {[1 − (
𝑑𝑖𝑗

𝑏
)

2

]
2

, 𝑖𝑓|𝑑𝑖𝑗| < 𝑏

0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

                          (15) 

Where an indicator of the Euclidean distance separating the local calibration point i from its 

corresponding observation point j; 𝑑𝑖𝑗b represents the bandwidth parameter. This weight decreases as 

the distance between the two observations increases, and more if the distance is closer to the bandwidth 



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parameter. If the distance between the two observations is greater than the bandwidth parameter, the 

weight is set to zero. 

Bandwidth selection is usually performed using modified Akaike Information Criteria (AICc). This 

standard prevents the selection of smaller bandwidths, which can complicate the model. Therefore, this 

helps prevent overfitting and non-smooth fitting. The calculation formula used to select the optimal 

bandwidth for the AICc represents the following formula: 

𝐴𝐼𝐶𝑐 = 2𝑛 log𝑒 (
𝑅𝑆𝑆

𝑛
) + 𝑛 log𝑒 2𝜋 + 𝑛 {

𝑛+𝑡𝑟(𝑆)

𝑛−2−𝑡𝑟(𝑆)
}                     (16) 

Lower AICc and RSS values indicate an improved level of reproducibility of the independent variable. 

RSS is used to evaluate model accuracy 

𝑅𝑆𝑆 = ∑ (𝑦𝑝𝑟𝑒𝑑,𝑖 − 𝑦𝑜𝑏𝑠,𝑖)
2𝑛

𝑖=1                              (17) 

R2 is used to evaluate the fit of the model (Hu, B., Zhou, J., Wang, J., Chen, Z., Wang, D., & Xu, S., 2009)  

𝑅2 = 1 − 𝑅𝑆𝑆 ∑ (𝑦𝑜𝑏𝑠,𝑖 − �̅�𝑜𝑏𝑠)𝑛
𝑖=1⁄                           (18) 

Where denotes the predicted value, denotes the actual value, and denotes the average true value. 

𝑦𝑝𝑟𝑒𝑑𝑦𝑜𝑏𝑠𝑦
𝑜𝑏𝑠

 

T-value tests are used as partial tests to evaluate a model, and by validating individual parameter 

estimates, potential errors or inaccuracies in the model can be identified, and necessary adjustments can 

then be made. 

𝑡(𝑖,𝑗) =
�̂�(𝑖,𝑗)

𝑠𝑒(𝑖,𝑗)
                                       (19) 

 

Figure 2. Technology Roadmapping 



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4. Data Processing 

4.1 InSAR Data Processing 

In this paper, Sentinel-1A satellite is used to obtain synthetic aperture radar images of the study area, and 

70 scenes of descent orbit data are selected for processing. The oblique range resolution is 13.93 meters, 

and the image time is five years from February 4, 2018 to May 21, 2023. The polarization mode is VV 

polarization and the incidence Angle is 39.60°. In addition, the distance resolution is 2.33 meters and the 

azimuth syncline distance resolution is 14.01 meters. Table 1 presents the radar data series for the study 

area. 

 

Table 1. Sentinel-1A SAR Dataset 

Sn. Image time 
Serial 

number 
Image time 

Serial 

number 
Image time 

Serial 

number 
Image time 

1 20180204 21 20190530 41 20201015 61 20220502 

2 20180216 22 20190623 42 20201108 62 20220526 

3 20180312 23 20190717 43 20201226 63 20220806 

4 20180405 24 20190810 44 20210119 64 20221204 

5 20180429 25 20190927 45 20210212 65 20221228 

6 20180523 26 20191021 46 20210401 66 20230121 

7 20180616 27 20191114 47 20210425 67 20230226 

8 20180710 28 20191208 48 20210519 68 20230322 

9 20180803 29 20200101 49 20210706 69 20230427 

10 20180827 30 20200125 50 20210811 70 20230521 

11 20180920 31 20200218 51 20210904   

12 20181014 32 20200313 52 20210928   

13 20181107 33 20200406 53 20211022   

14 20181201 34 20200430 54 20211115   

15 20181225 35 20200524 55 20211209   

16 20190118 36 20200617 56 20220102   

17 20190211 37 20200711 57 20220126   

18 20190319 38 20200804 58 20220219   

19 20190412 39 20200828 59 20220315   

20 20190506 40 20200921 60 20220408   

 

The results show that the overall average deformation rate during the monitoring period is -19.19 ~ 6.42 

mm/y, and the whole study area presents uneven subsidence. The main subsidence areas exist in Linwei 

District, Pucheng County and Chengcheng County, and a relatively obvious continuous subsidence 



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phenomenon is formed, which has a wide influence area and a large subsidence rate, and the subsidence 

area is about 600 km2. In Linwei District, the surface uplift and subsidence existed simultaneously. The 

largest subsidence area is located in Tangshan Bay Ecological City. 

 

Figure 3. Technology Roadmapping 

 

 

Figure 4. Deformation Velocity Distribution Map 

 

4.2 Selection and Analysis of Independent Variables 

4.2.1 Slope 

Slope plays a strong controlling role in the development and occurrence of geological hazards, and 



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determines the stress state and stability of slope. At the same time, slope also has an impact on surface 

runoff and groundwater (Wang Zhiwang, Liao Yonglong, & Li Duanyou, 2006). In order to consider the 

impact of slope on geological hazards in the study area, a slope grid map was obtained based on the 

digital elevation model (DEM) of the study area and the slope analysis function of ArcGIS platform. 

According to the natural breakpoint classification method by ArcGIS platform, they were classified into 

5 categories: 0~4.24°, 4.24°~9.55°, 9.55°~16.98°, 16.98°~26.80° and 27.80°~67.66° (Figure 4a). 

4.2.2 Topographic Relief 

For the loess tableland and hilly landform contained in the study area (Zhao Wenwu, Fu Bojie, & Chen 

Liding, 2003), topographic relief is an important and typical influencing factor of land subsidence in the 

study area (Fadhillah, M.F., Achmad, A.R., & Lee, C., 2020). Topographic relief was calculated based on 

DEM in the study area, and it was divided into 5 groups, namely, 2-34, 34-69, 69-111, 111-179, and 

179-399 (Figure 4b). 

4.2.3 Distance from River 

In the study area, there are many rivers with different discharge, and some routes are selected near the 

riverbank and need to cross Luo River and other rivers repeatedly. According to the river vector data of 

the study area, six distance grade river buffers of 0~100m, 100~200m, 200~400m, 400~600m, 

600~800m, 800~1000m and >1000m were established through the multi-ring buffer function of ArcGIS 

platform (Figure 4c). 

4.2.4 Distance from the Road 

The traffic load on the road, especially the frequent passage of heavy vehicles, will have a dynamic effect 

on the soil growth period of the foundation near the road. This repeated load will lead to gradual 

compaction and deformation of the foundation soil, and eventually lead to ground settlement. The closer 

the area is to the road, the more obvious the impact of traffic loads (Wang, W., Wu, L., Gong, H., Fan, P., 

Wu, W., Zhou, Y., & Zhang, Z., 2019). By using the ArcGIS platform multi-ring buffer function, six 

distance levels of road buffer zones of 0~100m, 100~200m, 200~400m, 400~600m, 600~800m, 

800~1000m and >1000m are established (Figure 4d). 

4.2.5 Distance from Fault 

Geological structure is an important factor affecting the development of geological disasters. The rock 

mass in the complex structure area is broken, the weathering is serious, and the slope integrity is low. At 

the same time, precipitation seeps into the slope along the structural cracks, reducing the strength of the 

slope [34]. 0By using the ArcGIS platform's multi-ring buffer function, fault buffers were created, which 

were classified into 6 categories of 0~2000m, 2000~5000m, 5000~10000m, 10000~20000m, 

20000~40000m and >40000m (Figure 4e). 

4.2.6 Topographic Humidity Index 

Topography can affect the flow direction of groundwater and the secondary distribution of precipitation, 

thus affecting the spatial distribution of water and the strength of different rock and soil bodies on the 

surface. Therefore, topography has an important impact on the occurrence of land subsidence (Wang, J., 



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Wang, C., Zhang, H., Tang, Y., Duan, W., & Dong, L., 2021). In order to study the impact of topography 

on land subsidence in the study area, topographic humidity index (TWI) is introduced to express the 

spatial distribution of water in rock and soil mass. The formula is as follows: 

𝑇𝑊𝐼 = ln
𝛼

tan 𝛽
 

Where: is the catchment area; 𝛼𝛽Is slope. According to the digital elevation model (DEM) of the study 

area and the raster calculator function of ArcGIS platform, the raster map of terrain wetness index is 

obtained. Based on the natural breakpoint function of ArcGIS platform, It was reclassified into 5 

categories of 3.10~6.62, 6.62~8.29, 8.29~10.47, 10.47~13.73, 13.73~24.44 (Figure 4f). With the 

increase of TWI value, the density of geological hazard points showed a decreasing trend. 

4.2.7 Average Annual Rainfall 

Rainfall has a positive effect on land subsidence, and the occurrence of land subsidence usually has a 

strong correlation with rainfall in time. In this paper, the average annual rainfall from 2018 to 2023 is 

used as an independent variable, and the grid data of average annual precipitation in the study area is 

generated according to the obtained precipitation nc data, and based on the natural breakpoint function of 

ArcGIS platform. It was reclassified into 5 categories of 6268~6532, 6532~6831, 6831~7118, 

7118~7336 and 7336~7732 (Figure 4g). 

 

Table 2. Characteristics of Independent Variables in the Study Area 

Variables Code Range Unit 

Average annual settling rate Y -19.19-6.42 mm/a 

Slope SLOPE 0-67.44 ° 

Topographic relief TER_UNDU 2-399 - 

Distance from fault FAULT_DIST 0-4971.62 m 

Distance from road ROAD_DIST 0-723.90 m 

Rainfall RAIN 6268.6-7732.2 mm 

Topographic humidity index TWI 2.512-24.459 - 

Distance from river RIVER_DIST 0-20337.1 m 

 



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Figure 4. Independent Variables of Classification 

a. Distribution Map of Slope; b. Distribution Map of Topographic Relief; c. Distribution Map of Distance 

from Rivers; d. Distribution Map of Distance from Roads; e. Distribution Map of Distance from Faults; f. 

Distribution Map of Topographic Wetness Index; g. Distribution Map of Annual Average Precipitation 

 

The independent variables above were selected, and the annual deformation rate was taken as the 

dependent variable. The analysis was carried out through OLS, GWR and MGWR models, and the 

analysis results were compared respectively to obtain the most influential factors, and the accuracy of the 

three models in the analysis and calculation process was analyzed. 

 

 



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5. Model Results and Verification 

5.1 Three Model Results 

5.1.1 Analysis of Simulation Results 

GWR model and MGWR model were used to predict the deformation rate of the study area respectively, 

and the prediction results were shown in Figure 5. By comparing the distribution of the predicted 

deformation rate results with the calculated results of SBAS-InSAR, it can be seen that the predicted 

deformation distribution is consistent with the reality, and the average annual deformation rate calculated 

by the MGWR model ranges from -4.12-2.75mm/y. The average annual deformation rate calculated by 

the GWR model ranges from 0.319 to 0.859mm/y, and compared with the overall average deformation 

rate of -19.19 to 6.42 mm/y during the monitoring period, it can be seen that the prediction result of the 

MGWR model is more accurate. 

 

Figure 5. Estimated Annual Average Subsidence Rate of the Study Area 

 

 

 

 

 

 



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Table 3. Performance Table of Independent Variables of the MGWR Model in the Study Area 

Dependent variable Average annual settling rate 

Performance values Average Minimum Maximum T-value Alpha value 

Slope 0.033 -0.017 0.062 2.448 0.041 

Topographic relief 0.087 0.048 0.167 2.364 0.044 

Distance from fault -0.613 -6.203 3.063 3.748 0.010 

Distance from road 0.046 -2.679 1.662 3.756 0.009 

Rainfall -1.346 -1.543 -1.183 2.253 0.047 

Topographic humidity index 0.004 -0.049 0.039 2.545 0.038 

Distance from river -0.324 -0.734 0.051 2.086 0.049 

 

As can be seen from the table, the model shows good fitting performance for the non-uniform distribution 

of the average annual settlement rate and cumulative settlement value in the study area. T-values and α 

values in the table indicate that the selected independent variables maintain their statistical significance 

within 95% confidence interval when predicting the annual average settlement rate and cumulative 

settlement value. 

5.1.2 Independent Variable Analysis 

Through the calculation of the three models, the distribution diagram of the influence coefficient of the 

independent variables corresponding to different models was obtained, as shown in Figure 6, 7 and 8. 

 

 

Figure 6. The Results of the OLS Model 

 



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Figure 7. The Results of the GWR Model 

 

 

Figure 8. The Results of the MGWR Model 

 

After statistical comparison of the results of the three models, it is found that the distance from the fault 

has the greatest impact on the land subsidence in the region, followed by the average annual rainfall. Due 

to the complex geological structure conditions in the study area, which is located in the Loess Plateau 

area and is dominated by loose thick layer loess, it is easy to slip through faults or collapse to the fracture 

zone. Moreover, rainfall is not evenly distributed throughout the year and is mainly concentrated in 



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summer. Therefore, the distribution of faults plays a decisive role in the stability of loess region, and the 

distribution of rainfall plays a role in inducing settlement. 

5.2 Comparison of Model Results 

 

Table 4. Comparison Table of Model Performance in the Study Area 

Dependent variable Average annual settling rate   

Model OLS GWR MGWR 

Count 8386 8386 8386 

R2 0.084 0.702 0.726 

AICc -19174.5 -26419.1 13907.9 

RSS 48.799 12.924 2043.605 

Bandwidth - 84 44-3563 

 

The MGWR model is compared with the traditional model, the higher the R2, the better the fit; The lower 

the AICc and RSS values, the higher the independent variable reproducibility level. 

5.3 Model Accuracy 

The calculation results of GWR model and MGWR model were used to draw the error prediction error map 

of space points in the study area. The area with small prediction error indicates that the prediction model has 

better adaptability in this area. As shown in Figure 9, both models have good adaptability in the region. 

 

 

Figure 9. Fitting Residual Distribution in the Study Area 



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6. Conclusion and Discussion 

According to the deformation characteristics in the 750kV third passage project area of northern Shaanxi 

and Guanzhong and its geological environment, 7 indexes including slope, topographic humidity index, 

distance from river, distance from road, distance from fault, rainfall and topographic relief were selected 

as independent variables, and the land subsidence was predicted by combining MGWR model and GIS 

technology. The following conclusions can be obtained: 

(1) Based on the field investigation and InSAR results, this study used a spatial multi-scale geographical 

weighted regression model to predict the land subsidence along the 750kV third passage project in 

Shanbei and Guanzhong, Weinan City, Shaanxi Province. The model calculated the optimal bandwidth 

required by the simulation, and explored the spatial heterogeneity of different influencing factors. The 

influence of different factors in different regions of the route on land subsidence was quantitatively 

studied. 

(2) As can be seen from the frequency distribution diagram of the spatial variation coefficient, among the 

seven independent variables selected, the fault distance, followed by precipitation, has a greater impact 

on the land settlement in the line region. 

(3) From R2 of the average annual deformation rate in the study area, it can be seen that MGWR model 

can better fit the land subsidence reflected by satellite monitoring data. Compared with GWR and OLS 

models, MGWR model has higher prediction accuracy, which is improved by 1000%. Moreover, this 

model can overcome the shortcomings that InSAR results cannot directly derive continuous and compact 

settlement field, and the prediction error is small, which can provide important reference value for the 

prevention and control of the ground subsidence disaster of the line. 

 

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