Land Subsidence Monitoring Method in Regions of Variable Radar Reflection Characteristics by Integrating PS-InSAR and SBAS-InSAR Techniques

Abstract

In the InSAR solution, the uneven distribution of permanent scatterer candidates (PSCs) or slowly decoherent filtering phase (SDFP) pixel density in a region of variable radar reflection feature can cause local low accuracy in single interferometry. PSCs with higher-order coherence in Permanent Scatter InSAR (PS-InSAR) are generally distributed in those point targets of urban built-up areas, and SDFP pixels in Small Baseline Subset InSAR (SBAS-InSAR) are generally distributed in those distributed targets of countryside vegetation areas. According to the respective reliability of PS-InSAR and SBAS-InSAR for different radar reflection features, a new land subsidence monitoring method is proposed, which combines PS-SBAS InSAR by data fusion of different interferometry in different radar reflection regions. Density-based spatial clustering of applications with noise (DBSCAN) clustering analysis is carried out on the density of PSCs with higher-order coherence in PS-InSAR processing to zone the region of variable radar reflection features for acquiring the boundary of data fusion. The vector monitoring data of PS-InSAR is retained in the dense region of PSCs with higher-order coherence, and the vector monitoring data of SBAS-InSAR is used in the sparse region of PSCs with higher-order coherence. The vertical displacements from PS-InSAR and SBAS-InSAR are integrated to obtain the optimal land subsidence. The verification case of 38 SAR images acquired by the Sentinel-1A in Suzhou city indicates that the proposed method can automatically choose a matched interferometry technique according to the variability of radar reflection features in the region and improve the accuracy of using a single interferometry method. The integrated method of the combined field is more representative of overall subsidence characteristics than the PS-InSAR-only or SBAS-InSAR-only results, and it is better suited for the assessment of the impact of land subsidence over the study area. The research results of this paper can provide a useful comprehensive reference for city planning and help decrease land subsidence in Suzhou.

1. Introduction

As an effective method to measure land subsidence, interferometric synthetic aperture radar (InSAR) can study the past by exploring data archives and is a powerful technology for extracting information related to land subsidence with day-and-night and all-weather imaging capabilities, broad spatial coverage, high spatial and temporal resolution, and it can acquire data remotely [1,2]. It has been proved to be a powerful geodetic tool to monitor land subsidence caused by anthropogenic and natural processes for instance underground water resources recharge and discharge, mine subsidence, volcanic eruptions and deflation, landslides, and earthquakes [3,4,5,6,7,8]. Over-exploitation of underground water often causes surface subsidence and gradually develops from low subsidence in a small area to large subsidence in a wide area, on the basis of the vegetation coverage, geological conditions, and urban development condition. Therefore, it is crucial to choose a reasonably applicable monitoring method.

Time-series InSAR techniques, such as the persistent scatterer interferometry (PS-InSAR) [9,10,11] and small baseline subset interferometry (SBAS-InSAR) [12,13,14,15,16,17,18,19,20], have been proposed and widely employed in land subsidence monitoring. InSAR measurements are affected by various errors and noise sources. The PS-InSAR technique is based on the SAR data stack in the same district, which is generally composed of several datasets. From this stack, one single master acquisition is selected, considering temporal and spatial baselines in a certain way to guarantee high coherence of those persistent scatterers in all interferograms formed over the stack [21,22]. If those persistent scatterers are building structures and city underlying surfaces, the phase and amplitude of them can maintain stability over a long time series, and PS-InSAR has high reliability and accuracy incoherence. Otherwise, in nonmetropolitan areas, those persistent scatterers with high coherence are relatively sparse, resulting in the accuracy of PS-InSAR being decreased. The SBAS-InSAR technique is one of the most widely used methods, which utilizes interferogram networks from which temporal and perpendicular baselines are constrained in length and time to reduce the influences of geometric decorrelation [23,24]. This also combines a method of connecting multiple SBASs that leads to an increase in temporal and spatial sampling. SBAS-InSAR generally needs two-dimensional phase unwrapping by the minimum cost flow method or the branch cutting method. The fringe of interferograms in the urban areas will give rise to the difficulty of two-dimensional phase unwrapping. Therefore, due to the differences in scattering characteristics in different areas of variable radar reflection regions, whether it is sparse persistent scatterers with high coherence or the interferometric fringe, this will make the single traditional interferometry methods, such as PS-InSAR or SBAS-InSAR, have limitations. At present, some studies [25,26,27,28] have only simply superimposed the two techniques and failed to consider the advantages and disadvantages of each of them. Experience with using PS-InSAR and SBAS-InSAR has shown that PSCs with higher-order coherence in PS-InsSAR are generally distributed in those point targets of urban built-up areas, and SDFP pixels in SABS-InSAR are generally distributed in those distributed targets of countryside vegetation areas, which causes PS-InSAR to have better accuracy in urban built-up areas, and SABS-InSAR has better accuracy in countryside vegetation areas. Therefore, this paper makes use of the distinctive advantages of PS-InSAR and SBAS-InSAR to effectively fuse the measurement data for common land subsidence challenges in urban and suburban areas.

In this study, we address the problem of the local low accuracy of the single interferometry in a region of variable radar reflection features. According to the respective reliability of PS-InSAR and SBAS-InSAR to different radar reflection features, we propose a new land subsidence monitoring method of integrating PS-InSAR and SBAS-InSAR by data fusion of different interferometry in different radar reflection regions. In the datasets of Sentinel-1A 38 SAR, Suzhou city will be used as an application to verify the validity of the proposed method in those regions of variable radar reflection characteristics.

2. Methodology

2.1. Proposed Method

The core idea of the proposed land subsidence monitoring method is to fuse the data of PS-InSAR and SBAS-InSAR according to differences in radar reflection characteristics. PS-InSAR processing is used for the high-density zone of PSCs with higher-order coherence, and SBAS-InSAR processing is utilized for the low-density zone of PSCs with higher-order coherence or the high-density zone of SDFP pixels. Cluster analysis is used to acquire the boundary of data fusion by zoning some sub-regions of land subsidence monitoring following the density of PSCs with higher-order coherence.

The processing of the proposed methodology is divided into seven main steps, and the flowchart is illustrated in Figure 1.

Step 1: N SAR images are obtained to form the SAR images set, where N is greater than or equal to 20, and the SAR images set is referred to as the same observation scene and registered together.

Step 2: A SAR image set obtained in Step 1 is processed by PS-InSAR to solve the ground subsidence monitoring. The PSCs satisfying the coherence threshold C are screened, and C is greater than or equal to 0.9.

Step 3: The longitude and latitude coordinates (x, y) of all the PSCs and their corresponding higher-order coherence C are sorted out to form a database for cluster analysis, and the barycentric coordinate G (a, b) of the spatial distribution of PSCs is obtained by the barycentric method.

Step 4: The barycentric coordinate G (a, b) is regarded as the initial center point of the Kernel-based DBSCAN algorithm. The longitude and latitude coordinates (x, y) of all PSCs are analyzed by cluster analysis, and the spatial distribution of all PSCs is zoned into two sub-regions according to the distribution density of all PSCs.

Step 5: The minimum geometric boundary L of two sub-regions is obtained by establishing the irregular triangular mesh of the discrete PSCs in two sub-regions, calculating the edge length of the triangle unit on the smallest convex edge of the irregular triangular mesh of the discrete PSCs. Based on the constraint that the minimum convex edge is less than 4000~5000 m, the minimum convex edge is gradually trimmed by using ArcGIS.

Step 6: A SAR image set obtained in Step 1 is processed by SBAS-InSAR to solve the land subsidence monitoring, and the raster data of SBAS-InSAR results are converted into vector data.

Step 7: According to the minimum geometric boundary L, the land subsidence monitoring of PS-InSAR remains in the sub-region of the high-density zone of PSCs with higher-order coherence. The vector data of the SBAS-InSAR are substituted for the land subsidence monitoring of PS-InSAR in the low-density zone of PSCs with higher-order coherence.

2.2. Time Series InSAR Analysis Method

For the PS-InSAR technique [29], the master images are preferably selected so that they approximately minimize spatial and temporal decorrelation actions. For all selected persistent scatterer candidates (PSCs), $p_i$, the interferometric phase of the flattened differential interferogram, N, is written as a combination of different contributions, as follows:

$$\Delta {\varphi }_{s,k}\left(p_i\right)=\Delta {\varphi }_{{}_{s,k}}^{\mathrm{height}}\left(p_i\right)+\Delta {\varphi }_{{}_{s,k}}^{\mathrm{disp}}\left(p_i\right)+\Delta {\varphi }_{{}_{s,k}}^{\mathrm{atm}}\left(p_i\right)+\Delta {\eta }_{s,k}\left(p_i\right)$$

(1)

where s and k represent the interferometric pairs, in which k is the master image and s is the slave image. Due to the inaccuracy of the external DEM, $\Delta {\varphi }_{{}_{s,k}}^{\mathrm{height}}\left(p_i\right)$ corresponds to DEM error; $\Delta {\varphi }_{{}_{s,k}}^{\mathrm{disp}}\left(p_i\right)$ corresponds to the linear deformation rate. $\Delta {\varphi }_{{}_{s,k}}^{\mathrm{atm}}\left(p_i\right)$ denotes the atmospheric phase delay, and $\Delta {\eta }_{s,k}\left(p_i\right)$ indicates the temporal and geometrical de-correlation noises. The benchmark for selecting the PSCs of stable pixels for PS-InSAR analysis is based on the use of the Amplitude Dispersion Index (ADI) on a stack of single master interferograms [10]. The ADI considers pixels with lower values of changes in amplitude of SAR images as candidates for PS-InSAR analysis, namely, regarding the PSCs. Consequently, a high mean coherence or low ADI value corresponds to a better phase quality. The ADI of one certain indicated pixel can be presented as:

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

(2)

where ${\sigma }_A$ and ${\mu }_A$ are the standard deviation and mean of a series of amplitude values, respectively.

For the SBAS-InSAR technique [30,31], the processing of SBAS-InSAR consists of four steps [32]:

Step 1: Selecting small baseline subsets;

Step 2: Interference processing based on the given baseline sets;

Step 3: Retrieving the unwrap deformation phase with a 3D phase unwrapping algorithm;

Step 4: Separating the error components of the unwrapping phase to grain the real deformation. The equations of SBAS-InSAR are listed as follows [33]:

$$\frac{N+1}{2}⩽M⩽N\left(\frac{N+1}{2}\right)$$

(3)

$${\varphi }_j\left(x,r\right)=\varphi \left(t_B,x,r\right)-\varphi \left(t_A,x,r\right)\approx \Delta {\varphi }_{\mathrm{disp}}+\Delta {\varphi }_{\mathrm{topo}}+\Delta {\varphi }_{\mathrm{atm}}+\Delta {\varphi }_{\mathrm{noise}}$$

(4)

Equation (3) denotes the quantity range of M differential interferograms generated by $N+1$ SAR images at the same area with ordered time $(t_0,t_1,\cdots ,t_N)$. Equation (4) indicates the composition of the interferometric phase of the interferogram j (generated by two images at $t_B$ and $t_A$) in the pixel $(x,r)$, where x and r are the azimuth and the range coordinate, respectively. Phase $(x,r)$ is caused by the variation in the distance along the line of sight (LOS) between target and radar. For each PS or SBAS, a measurement of the displacement rate (mm/yr) along the line of sight (LOS) and time series of the deformation during the collection period is available. When considering the direction of the movement, the LOS of radar sensors along the ascending orbit is more appropriate, thus allowing for a more reliable measurement of actual displacement. In this case, the displacements recorded by the PS are characterized by negative values. Moreover, phases $\Delta {\varphi }_{\mathrm{topo}}$, $\Delta {\varphi }_{\mathrm{orb}}$, $\Delta {\varphi }_{\mathrm{atm}}$ and $\Delta {\varphi }_{\mathrm{noise}}$ are generated by the topography, satellite orbit error, atmosphere effect, and other noises, respectively. The deformation phase is obtained by SBAS-InSAR removing the residual component from the interferometric phase. Subsequently, a series of M equations with N unknowns can be established as the following matrix:

$$\begin{array}{cc}\hfill & \mathrm{A}\varphi =\delta \varphi \hfill \\ \hfill & \varphi ={\left[\varphi \left({\mathrm{t}}_1\right),\varphi \left({\mathrm{t}}_2\right),\cdots ,\varphi \left({\mathrm{t}}_{\mathrm{N}}\right)\right]}^{\mathrm{T}}\hfill \\ \hfill & \delta \varphi ={\left[\delta \varphi \left({\mathrm{t}}_1\right),\delta \varphi \left({\mathrm{t}}_2\right),\cdots ,\delta \varphi \left({\mathrm{t}}_{\mathrm{N}}\right)\right]}^{\mathrm{T}}\hfill \end{array}$$

(5)

where A represents the $M\times N$ coefficient matrix. $\varphi$ is the $N\times 1$ vector of unknown deformation phase values with measurement points, and $\delta \varphi$ is the $N\times 1$ vector of unwrapped phase values.

3. Study Area and SAR Datasets

3.1. Study Area

The study area is located in Suzhou City, Anhui Province, in the middle of Huaibei plain, covering a rectangular range of $20\times 20$ km² around the center. It is located from ${33}^{\circ }30’$ to ${33}^{\circ }42’$ N latitude and ${116}^{\circ }49’$ to ${117}^{\circ }2’$ E longitude, as shown in Figure 2. The overburden layer of the study area is the Cenozoic loose layer with a thickness of 228.40~233.72 m, which can be divided into four aquifers and three water-retaining layers from top to bottom. There are four water plants and 110 wells located within the scope of the groundwater source region in this study area. Due to the long-term extraction of groundwater, the groundwater in the water source area has been seriously excessive-extracted, which has caused a continuous and increasing land subsidence.

3.2. SAR Datasets

Archived Sentinel-1A (2017–2020) datasets and the ancillary data of ALOS World 3D with 30 m resolution are analyzed to monitor the land subsidence. These include 38 images in interference wide-swath mode, a single look complex of image pairs, and the VV channel, which comes from https://scihub.esa.int/ (accessed on 16 February 2020).

Table 1. Main parameters of satellite system.

Satellite Sensor	Orbit	Revisit Period/d	Wave Band	Wavelength/cm	Incident Angle/°	Resolution Ratio/m
Sentinel-1A	Sun synchronous satellite	12	C	5.6	38.9	5 × 20

summarizes the main parameters of the satellite system.

By comparing Sentinel-1A data in the study area from 2015 to 2020, it is found that the satellite changed its orbit in a certain period from April 2017 to May 2017, and the shooting angle of Sentinel-1A data is stable after June 2017. Therefore, 38 images of Sentinel-1A data in this study area from June 2017 to July 2020 are selected for PS-InSAR and SBAS-InSAR process by SARscape software. To meet the processing requirements of the PS-InSAR and SBAS-InSAR at the same time, the time baseline and spatial baseline of the InSAR data source should be as small as possible. After viewing the orbital distribution of each image, one phase of SAR images monthly is selected for the experiment, and the experimental data correspond to the following

Table 2. The date of Sentinel-1A 38 SAR images acquired from 2017 to 2020.

		Month	1	2	3	4	5	6	7	8	9	10	11	12
	Day
Year
2017			/	/	/	/	/	25	19	24	17	23	28	22
2018			27	20	28	21	27	20	26	19	24	18	23	29
2019			22	27	23	28	22	27	21	26	19	25	30	24
2020			17	22	29	22	28	21	27	/	/	/	/	/

.

4. Comparison of Single Interferometry

4.1. Result of PS-InSAR Processing

In the PS-InSAR procedure, the master image is acquired from the two-dimensional space center consisting of a spatial baseline and temporal baseline (22 January 2019). Ascending 37 sentinel-1 images are then co-registered concerning the master images, and a total of 37 interferograms are generated from datasets using interference processing. The spatial baseline is mainly distributed between −130 m and 110 m, and the longest spatial baseline is 128.756 m with a time range of −576 d to 552 d (Figure 3).

For the first differential processing of the 37 interferograms, the reference ellipsoidal phase is calculated using the precision orbital of Sentinel-1A datasets and deduced from the initial interferometric phase. The topographic phase is simulated using ALOS World 3D data, and the topographic phase is deduced from the first differential interferometric phase to obtain the interferometric phase images after two differential interference phases. Combining the amplitude images of 38 Sentinel-1A datasets with the coherence coefficient images obtained from the interference processing, the minimum coherence threshold is set to 0.75 using the amplitude departure index method to identify the stable scattering targets in the study area. The average deformation rate of the candidate points and DEM correction coefficient are estimated, the atmospheric phases for PS candidate points are removed and the final average displacement rate and cumulative surface deformation are obtained, and the results are shown in Figure 4.

4.2. Result of SBAS-InSAR Processing

The 19 August 2018 images are selected as the main master images in the SBAS-InSAR technique processing and setting the spatial and temporal baseline threshold was set after resampling all SLC image registration (Figure 5). The time span of this experiment is long (approximately 38 months); to reduce the adverse effects of topography, atmospheric delay, and orbital deviation on the generation of interferometric datasets, the time baseline length of the interferometric datasets is limited to 270 d, which will generate 272 interferometric pairs.

The coherence calculating, flatting, filtering, and minimum phase unwrapping based on minimum cost flow (MCF) [34,35,36] are carried out for 272 interferometric pairs. Orbital refinement and residual phase removal are performed on the unwrapping results, and the GCP points are used to accurately estimate the orbital parameters and deduct the residual flat phase and orbit errors. Combined with the calculated high coherence points, the modeling solution is carried out to establish the equations matrix; then, the linear deformation rate and elevation error are estimated using the matrix singular value decomposition (SVD) method. The participating phases are separated, the atmospheric phase component in the residual phase is estimated, and it is deducted from the residual phase. The decorrelation noise phase involved in the phase is removed using a filtering method to obtain the nonlinear deformation phase. Finally, the linear deformation phase and the nonlinear deformation phase are superimposed to acquire the final accurate deformation result, as shown in Figure 6.

4.3. Results Comparison of PS-InSAR and SBAS-InSAR

The PS-InSAR monitoring results showed that the annual average deformation rate in the study area ranged from −35.35 to 10.39 mm a⁻¹, and the subsidence areas are primarily located in the west, south, and southeast of the main urban area. The SBAS-InSAR monitoring results show that the annual average deformation rate in the study area ranges from −43.17 to 4.37 mm a⁻¹.

Comparing Figure 5 and Figure 6, the common results show that both techniques have a consistent spatial distribution, especially in the three subsidence funnel areas in the west, south, and southeast of the main urban area, which are highly consistent in deformation range and magnitude. The different results show that the selections of PS points in the processes of PS-InSAR are mainly distributed on houses, roads, and other artificial buildings, while the denser vegetation cover is less distributed in the field, and there is no PS point distribution in rivers, lakes, and other water areas, while there is a large amount of spatial and temporal decoherence phenomena in the PS-InSAR monitoring results so that the monitoring result is empty. On the contrary, the SBAS-InSAR technique overcomes the spatial-temporal decoherence in this area and obtains more data, and the center area of the funnel is monitored near Zhoujia between West Third Ring Road, Suyong Road, Suwo Road, and Jingtai Expressway, where the sedimentation rates range from −43.2 to −30.0 mm/a.

The red dots a-e are the feature points in Figure 7.The characteristic points near three subsidence funnel areas (corresponding to red dots a, b, and c in Figure 7, respectively) and other characteristic points far away from three subsidence funnel areas (corresponding to red dots d, suburb, and red dots d, urban center, in Figure 7) are selected to more intuitively compare the changes in cumulative subsidence with time by different single interferometry.

The temporal variations of cumulative settlement at each point are shown in Figure 8, and the calculated results are shown in

Table 3. Detailed cumulative time series analysis and deviations results.

Point	PS-InSAR Cumulative Settlement Monitoring Value/mm	SBAS-InSAR Cumulative Settlement Monitoring Value/mm	Cumulative Settlement Monitoring Value Deviation/mm	Average Annual Subsidence Rate Deviation/(mm·a ${}^{-1}$)
a	−69.5	−61.4	−8.1	−2.5
b	−53.1	−59.2	6.1	1.9
c	−38.5	−37.5	−1.1	−0.3
d	−31.5	−49.4	17.9	5.7
e	−40.8	−34.6	−6.2	−1.9

. In the proximity of wells 98, 48, and 15, the deviation value of the accumulated settlement of the two techniques is less than 10 mm, except for the feature point d. The maximum deviation is 8.1 mm, and the maximum deviation of the annual average settlement rate is 2.5 mm/a, which is within a reasonable range of error. However, there is a large deviation in the cumulative settlement monitoring values near the feature point d in the suburban area for both techniques, reaching 17.9 mm, and the deviation of the annual average settlement rate is 5.7 mm/a, which is approximately two or three times higher than that of other feature points.

It can be seen that the monitoring results of the two techniques have less deviation in the urban center and more deviation in the suburban areas. A difference is observed in Figure 8d, which is correlated with the feature points distribution and well location. It can be noticed that the feature point d is somewhat far away from the well group and in a location with high vegetation density. When the PS point density decreases, removing the atmospheric phase will produce a large error. After the linear deformation rate is estimated using the matrix singular value decomposition (SVD) method in SBAS-InSAR processing, the effect of atmospheric delay is removed using a low-pass filter with a certain time domain length to separate the non-linear deformation rate. Therefore, for the settling region of feature point d, when the PS point density is reduced, it can be considered that the SBAS-InSAR processing results are closer to the actual measured values.

To investigate the differences in precision between PS-InSAR and SBAS-InSAR monitoring results, the subsidence funnel area in the southwest of the urban center is selected as the study area, and the monitoring results of the two techniques are superimposed using ArcGIS software, as shown in Figure 9. The distributed continuous area in the figure is SBAS-InSAR monitoring data, while the PS points are discrete, and the area with a consistent subsidence rate shows no discrete points. The SBAS-InSAR monitoring results showed that the large deformation within the area of the black dashed box in Figure 9 has been smoothed, while the PS-InSAR monitoring results are relatively independent points with significant settlement differences between the building structure and the pavement. The results indicate that the PS-InSAR technique can display more details from smaller scales when performing subsidence monitoring in areas with complex urban features.

In conclusion, the numerical deviation of the monitoring results of the two techniques is large in the weak area of surface feature scattering in suburban areas, and the deviation of the annual SDFP subsidence rate reaches 5.7 mm/a, which is about 2 to 3 times higher than that of other areas. In the strong area of the surface feature scattering in the urban center, SBAS-InSAR has lower spatial resolution due to multi-view processing and phase unwrapping, and the difference in the settlement between buildings and their surroundings is smoothed with lower accuracy than PS-InSAR. By comparison, PS-InSAR is more suitable to research the settlement differences between building structures and their surroundings in central urban areas, while SBAS-InSAR is more suitable for studying large-scale deformation trends with lower resolution in suburban areas.

5. Fusion of PS-InSAR and SBAS-InSAR

5.1. Kernel-DBSCAN Clustering

Clustering analysis is performed by a Kernel-based DBSCAN (Density-Based Spatial Clustering of Application with Noise) algorithm, which is a density-based clustering non-parametric algorithm: given a set of points in some space, it groups together points that are closely packed together (points with many nearby neighbors), marking as outliers point that lie alone in low-density regions (whose nearest neighbors are too far away). Kernel density estimation is a useful statistical tool with an intimidating name, the implementation process of the method is as follows.

Supposing the independent distribution F contains $x_1,x_2,\cdots ,x_n$ sample points with probability density function f, the kernel density is estimated as follows:

$${\widehat{f}}_h\left(x\right)=\frac{1}{n}\sum _{i=1}^n{K}_h\left(x-x_i\right)=\frac{1}{nh}\sum _{i=1}^{n}K\left(\frac{x-x_i}{h}\right)$$

(6)

where h represents the bandwidth, and $K\left(x\right)$ denotes the kernel function.

The selection of bandwidth is often difficult, and different bandwidths will lead to significant differences in the fitted results. Generally, in cluster analysis, the mean squared integral error function ($MISE$) is usually chosen to optimize the bandwidth. It is defined as follows:

$$MISE\left(h\right)=E\int {\left(\widehat{f}\left(x\right)-f\left(x\right)\right)}^{2}dx$$

(7)

assuming:

$$\begin{array}{c}\hfill MISE\left(h\right)=\mathrm{AMISE}\left(h\right)+o\left(\frac{1}{nh}+h^4\right)\end{array}$$

(8)

$$\begin{array}{c}\hfill \mathrm{AMISE}\left(h\right)=\frac{R\left(K\right)}{nh}+\frac{1}{4}{m}_2{\left(K\right)}^2{h}^{4}R\left(f^{″}\right)\end{array}$$

(9)

where:

$$\begin{array}{c}\hfill R\left(K\right)=\int K{\left(x\right)}^{2}dx>0\end{array}$$

(10)

$$\begin{array}{c}\hfill m_2\left(K\right)=\int x^{2}K\left(x\right)dx>0\end{array}$$

(11)

Minimization $MISE$(h) is equivalent to minimization AMISE(h), and finding the partial derivative and making the derivative equal to 0:

$$\begin{array}{c}\hfill \frac{\partial }{\partial h}\mathrm{AMISE}\left(h\right)=-\frac{R\left(K\right)}{n{h}^2}+m_2{\left(K\right)}^2{h}^{3}R\left(f^{″}\right)=0\end{array}$$

(12)

$$\begin{array}{c}\hfill h_{\mathrm{AMISE}}=\frac{R{\left(K\right)}^{\frac{1}{5}}}{m_2{\left(K\right)}^{\frac{2}{5}}R{\left(f^{″}\right)}^{\frac{1}{5}}{n}^{\frac{1}{5}}}\end{array}$$

(13)

According to the estimated value range of Eps, a mathematical expectation method is adopted to calculate a reasonable interval of MinPts in the given dataset based on the example distance Dist; the formula is as follows:

$$MinPts=\frac{1}{n}\sum _{i=1}^n{P}_i$$

(14)

where $Pi$ indicates the number of samples contained in the Eps neighborhood of object i.

5.2. Statistics of Coherence Coefficient

More stable PS points can be calculated on the surfaces of artificial buildings during PS-InSAR interference processing. Highly coherent PS points may exist in both urban centers and suburban areas, but there is a difference in the distribution density of the PS points between urban centers and suburban areas because of the denser artificial buildings in urban centers, shown as in Figure 10.

The study area is mainly distributed in four land types: urban land, agricultural land, rural residential land, and dry land. Among them, PS points are mainly distributed in urban land and rural residential land, with less distribution in paddy fields and dry land areas. The study area is divided into urban land and non-urban land, and the PS points with different coherence coefficients are statistically analyzed. The coherence coefficients are classified and counted at 0.01 intervals for all PS points, and the ratio of the number of PS points in non-urban land and urban land areas is calculated for each interval. The results show that when the coherence coefficient is greater than 0.9, the ratio of the number of PS points in non-urban land and urban land areas decreases abruptly from 0.31 to 0.21 (Figure 11). It can be considered that the density difference between the distribution of PS points in urban central areas and urban suburban areas changes the most at this time.

All PS points are screened with a coherence coefficient of 0.9 as the threshold, and the screening results are shown in Figure 12. The results of the filtered PS points show a strong correlation between artificial buildings and PS points. The artificial buildings are relatively dense in the urban centers, and PS points show a dense cluster structure, while in the non-urban area, they are mainly distributed near the highway sections, and the density is much lower than that of the urban centers, showing a discrete cluster structure.

5.3. Clustering Analysis

The DBSCAN algorithm is used to cluster all PS points in MATLAB to obtain the dasymetric map of PS points. The values of clustering parameters will directly affect the quality of clustering results. Kernel-DBSCAN based on the non-parametric kernel density estimation theory is used for clustering analysis of the PS point datasets. Firstly, the spatial distance datasets among all PS points are calculated, and then this dataset is substituted into Equations (6) to (14) to calculate the neighborhood radius (Eps) and the minimum number of core objects (MinPts). This process is implemented based on the MATLAB programming language, and the kernel density estimation curve of the spatial distance datasets is shown in Figure 13.

The kernel density estimation cannot directly find the optimal parameter in the example, and the peak of the density curve can not only characterize the distribution characteristics of a single cluster in the distance but also the distribution characteristics of the distance between clusters. As shown in Figure 13, where the horizontal axis represents the distance between object points in space, and the vertical axis expresses the closeness of the object points in the vicinity of the distance, which has been subjected to dimensionless normalization. There is only one peak in the density curve, and the peak point corresponds to a distance of 4286.9 m, which indicates that the number of points with a distance between them of about 4286.9 m is the largest; thus, only a unique central cluster exists in the dataset. Then, the results of the clustering analysis are plotted in Figure 14. The yellow PS points are represented as urban center clusters. Since the urbanization development in the study area is concentrated in the northeast quadrant, it can be considered that the best clustering effect of urban center clusters can be guaranteed when the clustering radius is 4286.9 m. The finalized input parameters for Kernel-DBSCAN are Eps = 4286.9 and MinPts = 1983. It is well-known that the peak values of the density curve can characterize both the distribution of a single cluster in terms of distance and the distribution between clusters in terms of distance. When there are multiple urbanization centers, the kernel density curve will accordingly have multiple peaks; at this time, the first peak indicates the closeness between objects in a single cluster space, and the second peak indicates the closeness between objects in different cluster spaces. At this point, the distance value corresponding to the first peak is selected as the best effect.

5.4. Boundaries Fusion

The minimum convex surface of the urban center cluster is drawn using ArcGIS, and all PS points within the minimum convex surface are used as nodes to create a triangular mesh. The following calculation is performed on the triangle mesh; if any side of any triangle is greater than the maximum side length D, the triangle will be erased. Traversing the triangles from the outside to the inside of the triangular mesh. If the edge of the boundary triangle is less than the maximum edge length in the current iteration, the traversal will stop. Firstly, by calculating the maximum edge length of the external range of the triangular mesh, the maximum edge is eliminated in turn, and the area of the urban central cluster corresponding to the boundary correction is calculated. Equation (15) is used to calculate the overlap ratio ($\omega$) between the urban center cluster area and the townland area as an index to measure the accuracy of boundary correction.

$$\omega =\frac{\mathrm{S}1\cap \mathrm{S}2}{\mathrm{S}1\cup \mathrm{S}2}$$

(15)

where S1 represents the townland area of the current land use data, S2 expresses the area of the urban center area, and $\omega$ indicates the overlap rate.

The boundary extraction of urban center clusters is extracted as shown in Figure 15.

Table 4. Eliminate the largest edge of the outer contour of the triangle mesh.

	Maximum Side	$\mathit{S}1\cap \mathit{S}2$	$\mathit{S}1\cup \mathit{S}2$	Overlap Rate
1	–	115,403,348.94	138,519,186.10	83.31%
2	6350.65	115,339,728.74	138,042,118.69	83.55%
3	6046.70	115,128,944.82	136,211,030.91	84.52%
4	4604.77	114,453,742.01	135,250,500.18	84.62%
5	3727.83	111,474,879.95	132,154,035.59	84.35%

shows that without boundary correction, the overlap rate between the urban center cluster area and the townland area of the current land use data is 83.31%, and the overlap rate reaches the maximum value when the maximum side length is 4604.77 m, at which time the boundary correction accuracy can be considered as optimal.

5.5. Data Fusion Results

The division accuracy of the urban central and suburban areas is improved by adjusting the maximum side length of the triangular mesh. Using all PS points on the corrected boundary for zoning, all low-quality and low-density PS points in the suburban areas are removed and updated to SBAS-InSAR solution results. The final obtained settlement results are shown in Figure 16. This data fusion method is effective in merging the PS and SBAS-derived results. The integrated field better represents the overall subsidence pattern, provides more subsidence details, and agrees better with the engineering practice result than the single interferometric sources. This integrated method of the PS-InSAR and SBAS-InSAR can increase the density of PS points from the original 375/km² to 858/km², increasing by 128.8% in the built-up area. Furthermore, the monitoring point density increases from the original 348/km² to 1261/km², which is increasing up to 262.3% in the non-built-up area.

6. Discussion

The land subsidence of the abundant groundwater area was investigated by integrating PS-InSAR and SBAS-InSAR monitoring datasets both spatially and temporally. The integrated results are utilized to acquire correlation relationships between groundwater level influences and vertical land subsidence for the entire Suzhou city. Based on the correlations, an integrated PS-SBAS method of land subsidence monitoring is proposed in this study.

The monitoring area of PS-InSAR is 128.59 km², and a total of 110,308 PS points are reserved in the urban central area, with a density of 858 PS points per square kilometer, covering important infrastructures such as Suzhou Railway Station. The total number of PS points detects in suburban areas is only 47,054, while the number of SBAS grid points detects by SBAS technology in the same area is 170,469, which is about 3.6 times the total number of PS points in the same area, and it can provide more continuous data when monitoring regional ground subsidence near roads and bridges. Therefore, the proposed method can provide more monitoring points than any single interferometry.

We generated a comprehensive distribution map of the Suzhou urban and suburban areas through the integration of Sentinel-1 and ALOS SAR images based on the proposed procedure. A total of 915 active landslides were detected and mapped over an area of approximately 81,667.6 km², of which 69 landslides were in close vicinity of the Jinsha River. These landslides pose a risk of blocking the river, threatening the safety of hydropower stations if a failure occurs; the situation, therefore, demands widespread attention and should be monitored by in situ facilities such as GNSS. We concluded that InSAR measurements can play a significant role in the detection of active landslides and the accurate delineation of the boundaries of slope activity in the Jinsha River corridor. Furthermore, the proposed method is of greatly applicable significance for detecting and mapping landslides in geomorphologically complex areas.

Although the PS-SBAS fusion results in this paper are promising, there are still large errors exceeding 1 cm/year over certain regions in the study area. These large errors may be reduced by the results of setting up continuous GPS stations placed in these areas. The idea is to simulate atmospheric delays from continuous GPS measurements and then use the GPS measurements to correct for atmospheric effects in radar interferograms.

7. Conclusions

Based on the respective dependability of PS-InSAR and SBAS-InSAR for different radar reflection features, a new method of land subsidence monitoring by integrating PS-InSAR and SBAS-InSAR by data fusion of different interferometry in different radar reflection regions is proposed. This proposed method solves the problem of the local low accuracy of the single interferometry in a region of variable radar reflection feature. Additionally, the newly proposed method implements the technique of automatically selecting different interferometric data for different areas within the same survey area based on the scattering characteristics of ground objects. This integrated PS-SBAS method explores the correlation of scatterer types and their coherence coefficients, determines the correlation threshold, and screens out the clusters of high-coherence PS points. Then, the DBSCAN algorithm is utilized to extract the urban center clusters in built-up areas and delineate the boundaries of built-up and non-built-up areas.

By the use of 38 SAR images, Sentinel-1A time series, the comparison of the monitoring results of land subsidence in Suzhou city is discussed using PS-InSAR and SBAS-InSAR, respectively, and the effectiveness of the integrated method is verified in the study area with variable radar reflection characteristics. The results indicate that PS-InSAR and SBAS-InSAR have an obvious deviation facing different radar reflection characteristics. PS-InSAR is more suitable for studying the settlement differences between building structures and the surroundings in the central urban area, while SBAS-InSAR is more suitable for investigating the large-scale deformation trends with lower resolution in the suburban area.

Through the analysis of different InSAR technologies to assess their relative accuracy in estimating the land subsidence in Suzhou city, it can be known that the proposed method can synthesize the advantages of PS-InSAR and SBAS-InSAR to improve the quality and quantity of monitoring data for achieving more accurate monitoring of land subsidence than any single interferometry.