Research on the Applicability of DInSAR, Stacking-InSAR and SBAS-InSAR for Mining Region Subsidence Detection in the Datong Coalfield

Abstract

Intensive and large-scale underground coal mining has caused geological disasters such as local ground subsidence, cracks and collapse in the Datong coalfield, China, inducing serious threats to local residents. Interferometric synthetic aperture radar (InSAR) has the capability of surface deformation detection with high precision in vast mountainous areas. DInSAR, stacking-InSAR and SBAS-InSAR are commonly used InSAR-related deformation analysis methods. They can provide effective support for mine ecological security monitoring and prevent disasters. We use the three methods to conduct the deformation observation experiments in the Datong coalfield. Sentinel-1A data from November 2020 to October 2021 are used. As a result, a total of 256 deformations in the Datong coalfield were successfully detected by the three methods, of which 218 are mining deformations, accounting for 85% of the total deformations. By comparing the results of the three methods, we found that DInSAR, stacking-InSAR, and SBAS-InSAR detected 130, 256, and 226 deformations in the Datong coalfield, respectively, while the deformations caused by coal mining were 128, 218, and 190. DInSAR results with long spatiotemporal baselines are seriously incoherent. SBAS-InSAR results of displacement rate are more precise than stacking-InSAR, and the mean standard deviation is 1.0 mm/a. However, for areas with lush vegetation or low coherence, SBAS-InSAR has poor performance. The detection deformation area results of DInSAR and SBAS-InSAR are subsets of stacking-InSAR. The displacement rates obtained by stacking-InSAR and SBAS-InSAR are consistent; the mean difference in the displacement rate between the two methods is 2.7 mm/a, and the standard deviation is 5.1 mm/a. The mining deformation locations and their shapes in the study area can be identified with high efficiency and power by stacking-InSAR. Therefore, with a comprehensive understanding of the advantages and limitations of the three methods, stacking-InSAR can be an effective and fast method to identify the level, location and range of mining deformation in lush mountainous areas.

1. Introduction

The Datong coalfield is the main coal production base in China, producing over 100 million tons of raw coal every year and playing a crucial role in the rapid growth of the national economy [1,2]. However, a series of problems, such as ground subsidence, landslides, soil erosion, and destruction of structures resulting from the mining and utilization of coal resources, have introduced a large negative effect on the lives and property of local residents [3]. Therefore, it is of great practical significance to monitor the surface deformation caused by coal mining [4,5,6,7,8,9,10].

Differential interferometric synthetic aperture radar (DInSAR), stacking-InSAR and small baseline subset InSAR (SBAS-InSAR) are popular methods for the monitoring of mining subsidence, permafrost-related subsidence, building subsidence and landslide. [11,12,13,14,15,16,17]. DInSAR, as an emerging Earth observation method, can measure surface deformation induced by underground mining activities with large spatial coverage, low cost, high accuracy, and all-weather observation capabilities [18]. It helps to locate and monitor underground mining subsidence in a wide area with low cost and high efficiency that conventional geophysical techniques, such as leveling [19], three-dimensional laser scanning [20], and the global navigation satellite system (GNSS) [21], are unlikely to do that [22]. However, the application of conventional DInSAR is mainly limited by spatiotemporal incoherence and atmospheric phase screening [23,24,25]. Wu et al. obtained the ground surface subsidence of the Kailuan mining area in Tangshan city, China from two ERS-1/2 images with a time span of half a year, using processed DInSAR and analyzing the expansion and evolution process of the subsidence, as well as the influence of spatiotemporal incoherence, atmospheric phase delay and DEM error on DInSAR results [26]. Ge et al. investigated the complementarity of DInSAR with GPS and GIS by utilizing multisource satellite SAR images over a mining site in southwest Sydney and found that longer wavelength SAR data are more robust in the incoherence area and more suitable for areas experiencing high rate ground deformation compared to short wavelengths, but they are not sensitive to slight mining subsidence [27]. Dong et al. adopted a DInSAR technique with acquired Envisat ASAR data to detect and measure surface deformation caused by underground coal mining in the Huainan coal mining field and indicated that the trends of both vertical deformation and horizontal extent all increased with time and the development of mining. On the other hand, it was found that some limitations, such as the requirements of the spatiotemporal baseline, weather information and DEM data resolution, hamper the precise analysis and validation of the results [28].

To meet the needs of long-term mining subsidence monitoring and weaken the effect of atmospheric phase screens, stacking-InSAR, a simple and effective method has been developed, in which the average line of sight (LOS) mining subsidence velocity is estimated by weighting and averaging a series of unwrapped interferograms according to the time span [17,29,30,31,32]. Qin et al. used stacking-InSAR and a finite difference method 3D model to monitor the ground deformation in the Fangzhuang coalfield during 2016 and found that ground deformation was mainly caused by mining activities and that the spatial pattern was controlled by geological faults in the study area [33]. Jiang et al. revealed the spatiotemporal information of land subsidence in areas affected by coal fires by applying stacking, persistent scatterers interferometry and two-pass DInSAR methods in the Wuda coalfield (northern China), and the results are consistent with GPS observations and coal fire data obtained by field investigations [34]. Zhu et al. identified 578 active landslides in the western part of Guizhou with dense vegetation and steep terrain using the stacking-InSAR method, in which natural landslides, reservoir landslides, and mining-induced landslides accounted for 2.4%, 4.2%, and 93.4%, respectively [35].

Although the results from the stacking-InSAR method can be more accurate than those from DInSAR in some cases, a more refined model is still needed to mitigate topographic error and obtain sequential subsidence results [36,37,38]. To improve the monitoring accuracy of the InSAR technique, Berardino et al. presented a small-baseline subset InSAR (SBAS-InSAR) technique, which is robust with respect to possible errors of the DEM used in the derivation of the differential interferograms and can effectively remove the atmospheric phase screen in the results [39]. However, SBAS-InSAR is only applied to pixels exhibiting a sufficiently high coherence degree [40,41,42,43,44,45]. Chen et al. accurately identified the location, range, spatiotemporal change trend, and basin edge subsidence information of subsidence mining in Shangdong Province, China using DInSAR and SBAS-InSAR, and verified and corrected the subsidence results using leveling [46]. Pawluszek-Filipiak et al. studied the mining subsidence of the Rydultowy coalfield in Poland by combining the advantages of both DInSAR and SBAS-InSAR techniques and found that the obtained results were in good agreement with leveling data [47]. Ghzala et al. detected active earthflows near a mining area of central Rwanda using 26 Sentinel-1 SAR images from 2014 to 2018, and the mean velocity was approximately −30 to −20 mm/year [48]. DInSAR, stacking-InSAR and SBAS-InSAR have attracted increasing attention and have been used in many mining subsidence areas. Moreover, the deformation results can be better estimated by stacking-InSAR and SBAS-InSAR using distributed scatterer and polarimetric optimization techniques [49,50,51,52]. However, the differences in performance and applicability of these three methods for mining subsidence identification in lush mountainous areas need to be further discussed and understood.

In this study, DInSAR, stacking-InSAR and SBAS-InSAR technologies are applied to process 28 Sentinel-1A images covering the Datong coalfield area and identify the mining subsidence of the study area by combining surface deformation information, optical remote sensing images, and geomorphic features. By comparatively analyzing the monitored results of the three methods, we were able to understand and identify the reasons for the different detection results and applicability of the three methods, which are significant for the further application of mining subsidence detection using InSAR methods.

2. Data and Methods

2.1. Satellite Data

Sentinel-1A is an earth observation satellite launched by the European Space Agency on April 3, 2014. The main purpose of the satellite is to continuously obtain C-band SAR data. Compared with other SAR data, Sentinel-1A data are openly accessible and have the advantages of a short regression period of 12 days, and the orbital tube radius is less than 50 m, which makes it widely used in the InSAR field [53,54]. For the monitoring of the location and deformation of coal mine subsidence and collapse in the Datong coalfield, a total of 28 Sentinel-1A terrain observation progressive scan (TOPS) mode images from November 2020 to October 2021 were used. The pixel spacing of the range is approximately 2.33 m, and the pixel spacing of the azimuth is approximately 13.96 m (

Table 1. Detailed parameters of the Sentinel-1A data.

Parameter	Value
Wavelength	5.6 cm
Central incidence angle	39.0851°
Polarization mode	VV
Orbital direction	Ascending
Azimuth/Rang pixel spacing	13.96/2.33 m

). In addition, optical remote sensing data with a resolution of 3 m in the study area were obtained. The high-resolution optical remote sensing image is mainly applied for the further interpretation of coal mining subsidence and InSAR monitoring results in the Datong mining area.

2.2. Methods

In this study, DInSAR, stacking-InSAR and SBAS-InSAR processing were performed using the GAMMA software. The specific process is shown in Figure 1 Assuming a set of N + 1 Sentinel-1A SAR images acquired at ordered time ($t_0,t_1,\cdots ,t_N$) that cover the study area, the first step was to generate and coregistered SLC images with external DEM data and precision orbit data. $M$ interferograms were achieved using the constraints on the perpendicular and temporal baselines (in the paper, $M=72$ and the combination of differential interferograms produced by data pairs characterized by a small spatiotemporal baseline is shown in Figure 2), and the flattening and topographic effects were removed with the SRTM DEM. Then, adaptive filtering and phase unwrapping were used to obtain a series of unwrapped differential interferograms. Because the study area is located in a mountainous area, a simple linear model was employed to remove the topography-dependent atmospheric phase. Finally, for an arbitrary pixel $(x,y)$ in interferogram $i$ (generated by SAR images acquired at time $t_1$ and $t_2$), the value can be expressed as

$${\varphi }_{diff}={\varphi }_{def}+{\varphi }_{topo\_res}+{\varphi }_{atm\_res}+{\varphi }_{noise},$$

(1)

where ${\varphi }_{def}$, ${\varphi }_{topo\_res}$, ${\varphi }_{atm\_res}$ and ${\varphi }_{noise}$ represent the phase of land deformation, topographic errors, residual atmospheric artifacts and decorrelation/thermal noise, respectively, along the radar LOS. After removing or weakening the other phase component, the unwrapped differential interferometric phases consist mainly of the deformation phase, and they can be converted into a surface displacement by multiplying a constant factor, i.e., the DInSAR result.

Stacking-InSAR is an enhanced technology that estimates the linear displacement using a set of unwrapped differential interferograms. It improves the deformation accuracy by minimizing residual atmospheric artifacts ${\varphi }_{atm\_res}$, noise phases ${\varphi }_{noise}$, and topographic errors ${\varphi }_{topo\_res}$ [30]. The average displacement rate and standard deviation of the average displacement rate can be estimated by the weight of the time interval on each interferogram as follows:

$$\overline{V}={\displaystyle \sum _{i=1}^M{d}_i·\Delta T_i}/{\displaystyle \sum _{i=1}^M\Delta T_i^2},$$

(2)

$${\sigma }^2(\overline{V})={\displaystyle \sum _{i=1}^M{(d_i-\overline{V}\Delta T_i)}^2}/\Delta T_i^2,$$

(3)

$$d_i=-\frac{\lambda }{4\pi }{\varphi }_{diff},$$

(4)

in which ${\varphi }_{diff}={\varphi }_{def}+{\varphi }_{topo\_res}+{\varphi }_{atm\_res}+{\varphi }_{noise}$ represents the unwrapped differential interferometric phase of pixel (x,y). $\overline{V}$ denotes the average displacement rate along the LOS. $\lambda$ is the radar wavelength. $\Delta T_i$ is the time interval of the i-th interferogram.

In a more realistic scenario, the DInSAR phase expression in (1) is important to reconsider and rewrite as follows, i.e., the SBAS-InSAR model is applied to pixels exhibiting a sufficiently high coherence degree:

$${\varphi }_{diff}(x,y)=\frac{4\pi }{\lambda }\left[d(t_2,x,y)-d(t_1,x,y)\right]+\frac{4\pi }{\lambda }·\frac{B_{\perp }}{r\sin \theta }\Delta Z(x,y)+{\varphi }_{atm\_res}(x,y)+{\varphi }_{noise}(x,y),$$

(5)

where $d(t_2,x,y)$ and $d(t_1,x,y)$ are the cumulative displacements along the LOS at times $t_2$ and $t_1$, respectively, with respect to reference time $t_0$, i.e., implying $d(t_0,x,y)=0$, $\forall (x,y)$. $\Delta Z(x,y)$ represents the DEM error used for the interferometric processing. It depends on the perpendicular baseline component $B_{\perp i}$ as well as on the sensor-target distance in the LOS direction $r$ and the look angle $\theta$. Assuming that $v_{j,j+1}$ is the deformation rate along the LOS between two adjacent SAR acquisition dates, the cumulative deformation from $t_1$ to $t_2$ can be modeled as

$${\varphi }_{def}=\frac{4\pi }{\lambda }{\displaystyle \sum _{j=1}^{C_i-1}{v}_{j,j+1}(t_{j+1}-t_j)},$$

(6)

where $C_i$ is the number of SLC acquisitions in the time sequence from $t_1$ to $t_2$. Then, the least squares or singular value decomposition method can be used to estimate the SBAS-InSAR time series deformation results.

Stacking-InSAR weights the data using the temporal baseline, thus reducing the influence of spatiotemporal incoherence, the residual atmospheric phase and the topographic error phase. However, compared with equal weighting, the temporal weighted method overestimates the displacement rate of the deformation point with positive acceleration and underestimates the displacement rate of the deformation point with negative acceleration. SBAS-InSAR models the deformation velocity considering the topographic error and the atmospheric phase error, and the results will be more reliable. SBAS-InSAR abandons points with low temporal coherence; therefore, the point density will be sparser compared to stacking-InSAR. The validated point distribution and the deformation rate values of stacking-InSAR and SBAS-InSAR may be inconsistent in continuously accelerated deformation areas.

3. Study Area

The southeastern part of Datong is a basin, and the elevation is generally between 950 and 1050 m, while the main topography of the northwest is mountainous, and the elevation is mainly between 1500 and 2100 m. The Datong coalfield is located northwest of Datong city, spanning Datong, Huairen, Shanyin, Zuoyun and Youyu counties (Figure 3). It is a multitemporal coalfield, including the Carboniferous-Permian coalfield and Jurassic coalfield. The Jurassic coalfield has an area of 772 km², and the Carboniferous-Permian has an area of 1739 km² [1]. As an important economic pillar of Datong city, the coal industry promotes rapid economic development. At the same time, perennial coal mining has also caused geological disasters such as surface subsidence, landslides, and ground fissures, which have caused serious damage to residents and infrastructure around the mining area.

4. Results and Analysis

4.1. Analysis of DInSAR Results

The DInSAR method has unique advantages in nonlinear deformation monitoring, but it is not suitable for long-term deformation monitoring. To better explore the impact of errors other than spatiotemporal incoherence on the DInSAR results, two images with a time baseline of 12 days and a spatial baseline of 9 m were selected for DInSAR processing. Figure 4a shows the monitoring results of the small spatiotemporal baseline. The coherence of the entire region is high, and the deformation region is obvious. It can be seen from section line AB that the deformation line graph is smoother than the results of the long spatiotemporal baseline. The deformation value of the area without subsidence at both ends of the line is almost 0 mm. However, at the same time, we can see that some areas are obviously affected by atmospheric phase screen and DEM errors, and the number of detected deformation regions is small due to the short time. Coal mining is a long-term process, so long-term and effective monitoring is essential to predict and respond to the geological disasters caused by mining subsidence. Figure 4b shows the DInSAR monitored results of the long-term baseline. The number of deformation regions is significantly greater than the results of the short-time baseline. However, an excessively long-time baseline leads the DInSAR results to serious incoherence, the subsidence gradient is greater than the threshold of deformation ambiguity, the monitoring results are seriously affected by noise, and the deformation range is blurred. Figure 4 shows that there are many noise points in the study area, the section line fluctuates severely, and the maximum deformation along the LOS direction is only −127 mm in the whole study area. Nevertheless, the location and number of deformation regions in the long-term DInSAR results are still useful. Based on the DInSAR results, a total of 130 deformation areas were identified, of which 128 were caused by coal mining, accounting for 99% of the total.

4.2. Analysis of the Stacking-InSAR Results

The monitoring results of the stacking-InSAR method are shown in Figure 5. A total of 256 deformation areas are found, of which 218 are caused by underground coal mining, accounting for 85% of the total. The determination of the subsiding underground coal mines not only needs to rely on the deformation displacement but also needs to be combined with optical remote sensing images and DEM for comprehensive analysis and judgment. Judging from the optical images, whether there are corresponding coal mining facilities and mining traces in the deformed area and using DEM terrain data and deformation morphology to exclude the possibility of other deformations such as landslides, it is determined that the deformation area is caused by coal mining. For the convenience of research, the whole research area is divided into three zones, as shown in Figure 5b–d. The mining deformation in zone b is mainly distributed on both banks of the Shili River (at present, the river has dried up, and most of the riverbed areas are residential areas), and the number of deformations is 35, of which 34 are caused by underground coal mining. The mining deformations in zone c are densely distributed, the displacement rate is generally higher than that in zones b and d, and there are 79 deformation areas, of which 64 are mining deformations. The largest number of mining deformation areas is 142 in zone d, of which 120 are mining deformations, but their displacement rate is generally smaller. The maximum displacement rate in zone c obtained by stacking-InSAR is also the maximum displacement rate in the entire study area. It is located near Silaogou, as shown in Figure 5c, and is −460 mm/a. The maximum displacement rates of zones b and d are located near Yungang town (Figure 5b) and Louzigou (Figure 5d), which are −365 mm/a and −269 mm/a, respectively.

Most of the deformation morphology in the study area is a typical settlement funnel shape, but there is also some special deformation morphology. In Figure 5e, the subsidence areas e1 and e3 extend a long strip shape deformation, which may be caused by small face mining of coal or subsidence of the old goaf. In addition, the deformation at e1 and e2 tends to rise, which may be caused by the look angle $\theta$ of the satellite. The relationship between the monitored deformation of the LOS direction and the downslope displacement can be summarized as shown in Figure 6. When the slope faces the sensor and the slope angle is smaller than the look angle, the landslide displacement will make the ground approach the sensor along the LOS direction, resulting in a monitored result of the ground rise; when the slope angle is equal to the look angle, the sensor cannot capture the landslide displacement; when the slope angle is greater than the look angle, the landslide displacement will make the ground move away from the sensor along the LOS direction; when the slope faces away from the sensor and the slope angle is less than or equal to ${(90-\theta )}^{\circ }$, the landslide displacement will cause the ground to move away from the sensor along the LOS direction, and the slope angle is greater than ${(90-\theta )}^{\circ }$, hill shade will be generated, and the sensor cannot capture the landslide displacement.

4.3. Analysis of the SBAS-InSAR Results

The monitoring results of the SBAS-InSAR method are shown in Figure 7. A total of 226 subsidence areas were detected, of which 190 deformations were caused by mining. To compare the stacking-InSAR and SBAS-InSAR, the three zones of the SBAS results are also enlarged and displayed, as shown in Figure 7b–d. SBAS-InSAR detected a total of 35 deformation areas in zone b, of which 34 were caused by coal mining, while 75 and 116 deformation areas were detected in zones c and d, of which mining deformation accounted for 81% and 82%, respectively. The maximum displacement rate of the LOS direction in zone b detected by SBAS-InSAR is located in Yungang town, which is −373 mm/a, the maximum displacement rate in zone c is −355 mm/a located in Silaogou, and the maximum displacement rate in zone d is −373 mm/a located in Louzigou (see

Table 2. Maximum displacement rate results monitored by stacking-InSAR and SBAS-InSAR.

Zone	Location	Deformation Rate
		Stacking-InSAR	SBAS-InSAR
b	Yungang Town	−365 mm/a	−373 mm/a
c	Silaogou	−460 mm/a	−355 mm/a
d	Louzigou	−269 mm/a	−265 mm/a

). SBAS-InSAR can only monitor subsidence with highly coherent points. Therefore, the number of subsidence areas monitored by SBAS-InSAR is less than that monitored by stacking-InSAR, especially in the lush d zone. By the same token, the position of the deformation region where the maximum subsidence of the three study zones is detected by SBAS-InSAR is consistent with the stacking-InSAR results, but the maximum displacement rate of the deformation cannot be detected by SBAS-InSAR, which makes the maximum displacement rate result of SBAS near Silaogou in zone c smaller than that of stacking-InSAR. There are high coherence points at the maximum displacement rate of the subsidence area near Yungang town and Louzigou in zones b and d, so the monitored displacement rate of stacking-InSAR is close to the SBAS-InSAR results.

In addition to obtaining the deformation rate, we also use the SBAS-InSAR method to obtain the time-series cumulative deformation of the Datong coalfield. Compared with the stacking-InSAR method, this is a unique advantage. We took the monitored results on 5 November 2020 as the reference image and obtained the sequential accumulated SBAS-InSAR results from 5 November 2020 to 31 October 2021 (Figure 8). With the development of underground coal mining exploitation, the magnitude and range of mining subsidence in the study area have gradually increased. The maximum cumulative subsidence of zones b-d in the whole study period are located in Yungang town, Silaogou and Louzigou, and the corresponding deformation is −356 mm, −318 mm and −242 mm, respectively. Although the largest deformation in the study area is located in zone b, the development of deformation space ranges in zone c is most significant, and the influence range of deformation is also the largest, followed by zone b. In zone d, small deformation is dominant.

5. Discussion

When using the SBAS-InSAR model, the coherence point selection algorithm, (e.g., the amplitude dispersion index, coherence stability, signal-to-clutter ratio, etc.), is necessary to select high coherence points. These selected points can be high coherence maintained over a certain time span. The Datong coalfield is located in a mountainous area with lush vegetation, which makes some areas on the interferogram seriously incoherent, and excessive mining subsidence will also cause incoherence. Therefore, the number of deformation areas detected using SBAS-InSAR is less than the result of stacking-InSAR (

Table 3. Statistical results and applicability analysis of DInSAR, stacking-InSAR and SBAS-InSAR.

Category	Method	Count	Mining Deformation	Applicability
1	Identified by three methods	256	218	-
2	Stacking-InSAR	256	218	Low coherence Less images required Less time consuming
3	SBAS-InSAR	226	190	Influenced by atmosphere phase and DEM error Cumulative time-series deformation
4	DInSAR	130	128	Small spatiotemporal baseline Nonlinear deformation Low technical requirements

) and is a subset of stacking-InSAR. As shown in Figure 9, we zoomed in on three typical deformation areas. The magnitude of mining deformation in the first area is small (Figure 9a,d,g,j), which prevents the deformation from being detected by DInSAR with a short spatiotemporal baseline, while there is poor coherence of DInSAR with a long spatiotemporal baseline. However, it can be identified by both stacking-InSAR and SBAS-InSAR. The second area is lush with vegetation (Figure 9b,e,h,k), which means that the results of both DInSAR with a long spatiotemporal baseline and SBAS-InSAR poor coherence and useful deformation information cannot be obtained. There is deformation with large magnitude and high coherence in the third area (Figure 9c,f,i,l), which can be detected by all methods, but the level of deformation is too large for the number and location of the subsidence basin center and cannot be determined by SBAS-InSAR and DInSAR with a long spatiotemporal baseline.

As shown in Figure 10, we selected two typical subsidence areas near Jiangjiawan and Nanhewan from the study area for a comparative analysis and uniformly set the color bar of the SBAS-InSAR and stacking-InSAR monitoring results [55]. The maximum deformation rate of the LOS direction monitored by stacking-InSAR is −150 mm/a (Figure 10a). Due to the lack of high coherence points in the deformation center, the maximum deformation rate of the LOS direction monitored by SBAS-InSAR is less than the result of stacking-InSAR, which is −135 mm/a (Figure 10b). In Figure 10e,f, the loss of high coherence points caused by the lush vegetation on the slope almost makes the SBAS-InSAR results of the whole subsidence area missing, and the subsidence is monitored only at the edge of the area without vegetation. The stacking-InSAR model calculates the linear displacement rate through weighted unwrapped differential interferograms and does not involve the selection of coherent points. Therefore, compared with SBAS-InSAR, it is more suitable for the detection of underground coal mining deformation with lush vegetation on the ground.

To further illustrate the above phenomenon, we extracted the profiles of two regions across the subsidence center, AB and CD in Figure 10. Figure 10a–c shows that the deformation ranges of the SBAS-InSAR monitored result are larger than those of stacking-InSAR (same starting unwrapped point). There is an offset between the two results (Figure 10g), because the deformation acceleration is negative, the stacking-InSAR method underestimates the deformation velocity. In addition, due to the excessive subsidence rate, the deformation center area lacks highly coherent points, which means that its subsidence value cannot be detected by SBAS-InSAR. It can be seen from the line graphs that located in Nanhewan with lush vegetation and coupled with the large settlement rate of the settlement center, the broken line diagram of SBAS-InSAR results is discontinuous, and the deformation center results are missed (Figure 10h). Stacking-InSAR can completely monitor the deformation area, but the serious incoherence makes the deformation broken line of stacking-InSAR fluctuate greatly in the vegetated area.

Figure 11 shows the standard deviation of the displacement rate monitored by stacking-InSAR and SBAS-InSAR. On the one hand, the standard deviation of the displacement rate can reflect the precision of the result calculated by the stacking-InSAR and SBAS-InSAR methods; on the other hand, it also shows the applicability of the models. The hypothesis of the stacking-InSAR model is that the deformation is linear during the study period, and it will have model error in the solution of nonlinear deformation. SBAS-InSAR can obtain the accumulative time-series deformation of the entire study span, but it can only detect the linear velocity between time-adjacent acquisitions, and the average displacement rate needs to be fitted. It can be seen from the standard deviation figure that some deformation regions have larger standard deviations, which indicates that these regions are greatly affected by noise or that the deformation in the region is nonlinear. Combined with the displacement rate results, we can further infer that they are mining areas with nonlinear deformation (Figure 11c,d). Due to the existence of the topographic error phase, the standard deviation of stacking-InSAR is significantly larger (Figure 11a). The deformation rate standard deviation of SBAS-InSAR (Figure 11b), except for some mining deformation regions, is closer to the value of 0 mm/a. The maximum value of the SBAS-InSAR standard deviation in the study area is 18 mm/a, and the average value is 1 mm/a, while the maximum value of the stacking-InSAR standard deviation is 54 mm/a, and the mean is 13 mm/a. SBAS-InSAR models the deformation rate and DEM error and uses filtering to separate the components of the atmospheric phase screen, nonlinear deformation and noise, which reduces the influence of the atmospheric phase screen, DEM errors, etc., on the deformation rate, so the deformation rate standard deviation of SBAS-InSAR results in these areas is less than that of stacking-InSAR, and the displacement rate estimated by SBAS-InSAR is more precise.

As seen in Figure 12a, the correlation coefficient between the stacking-InSAR results and SBAS-InSAR results in the Datong coalfield is 0.91, and the monitoring results of the two methods are consistent. However, due to the different methods of the two methods in obtaining the deformation rate, the SBAS-InSAR results are smaller in the area with positive deformation acceleration. There are more points below the black line, meaning that many points are overestimated by stacking-InSAR. Thus, the deformation acceleration is positive, and the coal mining regions are changing quickly and threatening. According to Figure 12b, the maximum difference in the deformation rate between stacking-InSAR and SBAS-InSAR is 58 mm/a. The difference in the deformation rate between the same point pairs of the two methods less than 10 mm/a accounts for 90.7% of the total number of points, and less than 20 mm/a accounts for 99.9%. The mean difference in the deformation rate obtained by SBAS-InSAR and stacking-InSAR is 2.7 mm/a, the RMSE is 5.8 mm/a, and the standard deviation is 5.1 mm/a.

The time-series accumulative deformation obtained by SBAS-InSAR can more intuitively reveal the time-series changes in the subsidence basin. We selected the section lines AB and CD (Figure 13a,b) to analyze the temporal evolution of the subsidence basin, but due to poor coherence, some results of accumulative deformation on the section line are missing. According to the time-series cumulative deformation of the section line (Figure 13c,d), the maximum cumulative settlement on section line AB during the study period reached −163 mm/a, and the displacement rate from point A to point B increased. The maximum cumulative subsidence on profile line CD is 336 mm/a, and the subsidence magnitude of the subsidence basin from point C to point D is symmetrical as a whole. The time-series subsidence results on the two section lines show approximately uniform subsidence.

Through analysis of the three algorithms, we can obtain the advantages and applicability of DInSAR, stacking-InSAR and SBAS-InSAR. However, the model complexity and elapsed processing time of the three algorithms also need to be considered in practical applications. With the same computer configuration (RAM: 64 GB, CPU: Intel (R) Xeon (R) gold 5118 CPU @ 2.30 GHz), the DInSAR model is the simplest and has the shortest elapsed time. The stacking-InSAR and SBAS-InSAR algorithms need to be based on unwrapped differential interferograms. The stacking-InSAR method requires weighted short baseline data sets to calculate the linear displacement rate, and the elapsed time is 106 s (from unwrapped difference interferograms to the final displacement results), while the SBAS-InSAR model is the most complex, and the elapsed time is the longest, which is 19.6 min.

6. Conclusions

Taking the Datong coalfield in China as the study area, using 28 Sentinel-1A data, we detected 256 deformation areas. Combined with deformation morphology, DEM and optical remote sensing data, 218 coal mining subsidence areas were identified. Comparing the results of DInSAR, stacking-InSAR and SBAS-InSAR, we can draw the following conclusions:

(1) We identified 256 and 226 deformations using the stacking-InSAR and SBAS-InSAR methods, respectively, on the Datong coalfield, while the identified deformations caused by coal mining were 218 and 190, respectively. Poor coherence caused by a long spatiotemporal baseline means that the DInSAR method identifies only 130 deformation areas, of which mining deformation accounted for 128. The stacking-InSAR method detects all deformation areas efficiently and quickly, which shows a great advantage for determining the deformation of mining areas in lush mountainous areas with poor coherence. Due to the lush vegetation in the study area, 30 deformation areas cannot be determined using SBAS-InSAR. The detection deformation results of DInSAR and SBAS-InSAR are subsets of the stacking-InSAR results. (2) The DInSAR method plays a crucial role in nonlinear deformation monitoring over a short time span. The displacement rate obtained by stacking-InSAR has good consistency with SBAS-InSAR, and it has far less elapsed time. In high coherence areas, the displacement rate estimated by SBAS-InSAR is more precise than that estimated by stacking-InSAR, and the time-series accumulative deformation obtained by SBAS-InSAR can more intuitively reveal the time-series changes in the subsidence basin. (3) Stacking-InSAR has an advantage for detecting the deformation area range and morphology, and it is helpful for determining the type of deformation. (4) Underground coal mining not only caused deformation along the LOS direction away from the sensor but also caused landslides, which made the deformation of some areas close to the sensor along the LOS direction.