2.1.

Regional Overview

Beijing is located in the North China Plain to the northwest Loess Plateau, Nei Monggol Gaoyuan transition Zone. The geographical coordinate of Beijing is within east longitude 115°25′ to 117°35′ and north latitude 39°28′ to 41°05′, with the total area of $16422.78{\mathrm{km}}^2$ and altitude between 10 to 2309 m. Mountain area of Beijing accounts for 62%, lying in the northwest, southeast of low elevation.¹ The Mesozoic Yanshan movement formed the basic terrain skeleton of Beijing and the three geomorphic units of western mountainous area, northern mountainous region, and southeast plain. The area is a temperate continental monsoon climate, with the annual average temperature of 10°C to 12°C, annual average rainfall of more than 440 to 670 mm. Remote sensing image is shown in Fig. 1.

Fig. 1

Remote sensing image map of Beijing.

2.2.

Present Situation of Ground Subsidence in Research Area

The ground subsidence in Beijing is mainly caused by the lower part of the central alluvial belt, which is related to the Genesis type, lithology thickness, and structural, physical, and mechanical characteristics of the fourth basement, and the groundwater overexploitation is the main cause of ground subsidence.¹¹ Ground subsidence was first found in 1935, mainly from Xidan to the area of Dongdan, the local maximum cumulative settlement reached 52 mm by 1952. In the 5 or 6 years, with the rapid development of the local electronic industry, textile industry, and so on, the ground subsidence center occurred in the east eight Li–Li industrial zone and the Jiuxianqiao electronic industry area, the cumulative ground subsidence of the two settlement areas was 58 and 30 mm, respectively, and the total area of the settlement area was about $400{\mathrm{km}}^2$. From the 70s to the early 80s, the subsidence area was more than $600{\mathrm{km}}^2$.¹⁰ From 1982 to 1999, the east suburb of Beijing was formed on the basis of the original depression settlement, Changping District Shahe Eight village, Daxing City, One Elm Fort, Shunyi District Ping Village, and other new ground subsidence centers.⁹ Since 2000, the ground subsidence in Beijing plain area is still in the rapid development stage, as of the end of 2015, the ground subsidence amount of Beijing is more than 50 mm, which reaches 5317.12 km, and the area above 100 mm reaches $3815.29{\mathrm{km}}^2$. The ground subsidence destroys the municipal infrastructure, threatens the safety of major projects such as intercity railways, and some of the planned new towns have become one of the main geological disasters in the Beijing plain.^8,12

4.1.

SAR Image Registration and Interference Graph Generation

Before interference measurement, SAR primary and secondary images must be matched to ensure the good coherence. SAR image registration includes coarse registration and fine registration, and the coarse registration of the satellite position vector on the five points of the data imaging period in the header file of SLC data is matched. To ensure better interference quality, the registration error is controlled at the end of one-eighth pixels.¹⁶

To improve the spatial resolution of the monitoring, the interference resolution of the main and auxiliary single image complex images is 4 m and the distance resolution is 20 m. The registration and interference processing of SAR image is mainly carried out under the radar reference system of the main image and after obtaining the result of the deformation of the time series, to compare with other data (level data, GPS monitoring data, engineering geology, hydrogeological data, etc.), the geophysical characteristics related to ground subsidence are further revealed, and the deformation data under the radar reference system need to be converted to the geocentric coordinate system or the plane coordinate system. At the same time, the data obtained by external means, such as DEM and atmospheric delay, should be converted to the radar coordinate system to carry out geometric operations with the phase components of the difference interference results. This part of the work is implemented based on Doris Open source software written by Kampes and other people of the Netherlands Delft University. ASAR data from April 2012 to September 2015, the results of differential interference processing for each interference pair are shown in Fig. 3. (September 7, 2015, image is public main image.)

Fig. 3

The ASAR data difference interference result sequence diagram

In all the interference images, the results show that the interference in the urban area of Beijing is better and maintains high coherence, the longest time baseline of ASAR interference data concentration is 1190 days. In summer, the Beijing area is in the rainy period and affected by the atmospheric delay effect of interference effect of poor stripes is not obvious, such as the main image with the August 2014 interferogram. The interference effect of other interference is good, the result shows that the spatial distribution mode of the phase of interference deformation in autumn and winter, and its deformation amplitude are less affected by the atmospheric error.¹⁷

The most serious subsidence of urban land is Chaoyang District Beijing ground subsidence main Chaoyang, in the eastern suburbs such as Changping and Shunyi, some phase change information can be observed on the interferogram, and the interference of the various factors such as the D-InSAR of ground objects cannot form obvious interference fringes in the suburbs, and the surface subsidence is not easy to be detected on the interferogram.

4.2.

Principle of Interference Measurement for Permanent Scattering

PS technology improves the traditional D-InSAR technology by evaluating the accuracy of the deformation results (shape variables and velocities) of the atmospheric, and eliminating orbital and DEM errors (relative to the ground specific points).¹⁸ Reference to the permanent scattering point within the study area, and all ground velocity measurements are referenced at that point. Based on this, it is very important to refer to the permanent scattering body without deformation. Furthermore, the reference scattering body should be selected at the center of the research area as far as possible because the precision of the scattering body velocity measurement is proportional to the distance from the reference scattering body. Optimization of PS algorithm technical flow is shown in Fig. 4.

Fig. 4

Flowchart of interference technology for permanent scattering body.

Main processing steps for PS-InSAR are as follows:

In this equation, $\phi$ def for the eye upward deformation phase, $\phi$ topo for DEM introduced terrain error phase, $\phi$ atm for the atmosphere caused by the delay phase, $\phi$ orbit for orbital uncertainties caused by residual phase components, and $\phi$ noise for noise error components.

Among them, the ${\sigma }_v$ represents the phase standard difference, $m_A$ indicates the sequential amplitude mean, $D_A$ indicates the amplitude deviation index, therefore selects the PS point by the phase deviation index of this value method.

4.3.

Stamps Algorithm

In 2004, Hoope proposed a new method of interferometric measurement stamps, which selects PS points based on the discrete spatial correlation features of amplitude and phase characteristics, then uses three-dimensional (3-D) phase unwrapping.¹⁵ This method first selects PS point based on the amplitude discrete characteristic, then, the PS point is selected again based on the spatial coherence of phase, and stamps does not use the time transform function model to identify the PS point. Because of this advantage, although in the suburbs of this area, stamps can also well identify the PS point, to a certain extent, improve the accuracy of coherent interference, increase the number of interference image pairs, and improve the interference time resolution.¹⁷

In this paper, the stamps algorithm is used for PS-InSAR processing, the main steps of the algorithm are as follows.

First, the difference interference is obtained using the known external DEM data to obtain the differential interferogram, and the phase I of the difference interference and $x$ pixels can be considered as the following five parts

The average of the phase values of all primary PS points in the circle with pixel $x$ as center and $L$ radius can be obtained as

The mean value bar represents the phase mean of the search area, ${\overline{Ø}}_n$ means the average of $\mathrm{\Delta }{Ø}_{ϵ}+{Ø}_n$, assuming that the value is very small, the Eqs. (3) and (4) are subtracted from Eq. (5)

Because the residual phase error of DEM is proportional to the vertical baseline of each interference, the $K_{ϵ}$ is the proportional coefficient. If the value of ${\overline{\grave{Ø}}}_{n,x,i}$ is very small, $N$-amplitude difference interferogram can be obtained, and the least squares method can be used to evaluate $K_{ϵ}$. Customizable functions

5.1.

Data Reading and Clipping

First, read the header file and data body information and orbital information of the primary image, with east longitude of 116°60′ and north latitude of 40°06′ as the central point cut to obtain coverage of the city center in Beijing 21,000 rows and 4800 column image range, image coverage area of about $8503.24{\mathrm{km}}^2$, the specific range and location as shown in Fig. 5. Then, read into the auxiliary image of the header file and data body information and orbital information, the secondary image cutting center unchanged, the clipping range to 24,000 rows and 5000 columns.

Fig. 5

Map of range and location of PS-InSAR processing area.

5.2.

Results of Permanent Scattering Process

Use ASAR data from the year 2012 to 2015, the SRTM 90-m resolution DEM data, and the precision orbit ODR data to carry out the differential interference processing. On this foundation, the traditional PS method based on amplitude is adopted to select the PS point, then according to the phase space correlation, the phase unwrapping and the component appraisal, the time series of the deformation information (Fig. 6) are obtained. Using the new PS algorithm (StamPS), 30 images of ASAR have been applied in Beijing area. The area of study is about $8503.24{\mathrm{km}}^2$. In the ASAR interference dataset, a total of 574,887 radar target points were identified (averaging 68 PS dots $\mathrm{per}{\mathrm{km}}^2$), which remained phase-dependent during the 3-year period. In the center of the city, PS point density is $280/{\mathrm{km}}^2$, in the rural suburbs such as Tongzhou regional the permanent scattering density is $120/{\mathrm{km}}^2$, compared with the traditional PS technology it has a great improvement. The analysis results show that PS-InSAR technology can be applied in urban subsidence monitoring in Beijing.

Fig. 6

Beijing PS point selection result map.

Compare the PS point with the Google Earth high-resolution image overlay (Fig. 6), it is found that the permanent scattering body is mostly located on the roof of the building, the intersection of the road (or sidewalk), the vertical structure (and the wall of the building adjacent to the road, in which the direction of the road is parallel to the satellite descending orbit). No or less permanent scattering is identified in urban green space or other vegetation-covered areas.

The definition of interference measurement is relative, so the determination of settlement requires the correction and initial integration of one or more ground control points of the elevation and movement information. The stable region is usually selected as the reference point when the solution is entangled, assuming that these regions are almost zero-deformed. This paper selects the northern mountainous region as the reference area and then evaluates and removes topographic errors (Fig. 7), atmospheric and orbital errors, and obtains interferometric measurements of the time series in the study area (Fig. 8). With the December 14, 2013, image as the reference datum, the positive value in Fig. 9 indicates the relative main image settlement, the negative value indicates the relative main image rise, and the deformation results of time series shows that the surface deformation has obvious seasonal fluctuation characteristics, and shows the nonuniform deformation characteristics. By analyzing the results of time-series deformation in Beijing area, it is helpful to study the deformation characteristics of each point in Beijing ground subsidence deformation field. The method of PS interferometry to obtain the deformation results of long time series can help to analyze the linear and nonlinear characteristics of deformation in the research area.

Fig. 7

PS-InSAR winding phase diagram.

Fig. 8

Topographic residual error phase diagram and phase diagram of atmospheric and orbital residual errors.

Fig. 9

Deformation results of PS-InSAR time series.

On the basis of the deformation results, the annual average settlement rate of ground subsidence is calculated. In Fig. 10, each color point corresponds to a permanent scattering body, and the negative value represents the rise of the sedimentation positive, and the settlement trend is indicated by the hue change, and the red area in Fig. 10 represents the high settlement rate area of Beijing. The variation of color difference is large, whereas the settlement gradient is relatively large.

Fig. 10

Annual average settlement rate of ground subsidence.

5.3.

Results and Verification of Ground Subsidence Monitoring

The PS-InSAR monitoring results show that the ground subsidence in the Beijing urban area is still in the rapid development stage in 2012 to 2015, and the maximum annual settling rate reaches 140.01 mm. Several discrete subsidence funnels have formed a large settlement center in the Beijing urban area, and the settlement area is enlarged; the coverage involves the Chaoyang, Changping, Shunyi, Tongzhou, and other districts; the settlement center has the eastward movement trend (Fig. 11). There is no settlement in the central urban area, and the cumulative settlement of the serious subsidence areas, such as Chaoyang District and Changping District, is increasing every year, the spatial distribution range of the settlement area expands rapidly from the center of the city, the trend of the eastward shift is obvious, and the settlement center appears in the Pinggu County. The settlement range and settling rate of the study area vary with time. Among them, in the east five rings, the northeast five ring and the periphery curved zone for the subsidence fast development area, from the North Court, Jiuxianqiao, Dongba, Fu to the Fort head along the average annual deformation rate of $12\mathrm{cm}/\text{year}$, the maximum cumulative deformation reached 38 cm (2012 to 2015). Sedimentation rate of Shahe sedimentation area in Changping district is below $40\mathrm{cm}/\text{year}$. Compared with the historical settlement results (2010 to 2011), the urban land subsidence area of Beijing city is rapidly expanding.

Fig. 11

The map of the trend of ground subsidence in the city of Beijing from 2012 to 2015.

The annual average settlement rate (2012 to 2015) and equal-level measurement are calculated to obtain the cumulative settlement of 2012 to 2015 year based on the time-series deformation information (Fig. 12), and it is found that the level of Settlement Center is in good agreement with the PS-InSAR monitoring Settlement Center. This preliminary verifies the correctness of the PS-InSAR technology monitoring results.

Fig. 12

2012 to 2015 cumulative sedimentation isoline and 2010 to 2015 settlement trend comparison.

To detect the reliability of InSAR monitoring results, this paper compares and verifies the external level data of the same period. In the entire Beijing survey area, 23 available levels were selected, using the InSAR monitoring results to interpolate the settling rate at the level point, the PS points of the InSAR are not coincident with the level points, and then the results of interpolation are compared with the settling rate of the leveling points, and the measured value of the precision level is used as the truth, and the unbiased estimation of the standard deviation is used to verify the result of InSAR monitoring. The following is a comparison between the level results and InSAR results of the selected level points. As shown in Fig. 13, the two trends are basically consistent, the total settlement in the time period of 40 to 50 mm, the density of the level monitoring data is much smaller than the P-InSAR monitoring results, the results of the level monitoring floating in the P-InSAR results up and down 5 mm, thus confirming the P-InSAR technology used to detect surface deformation reliability.

Fig. 13

Statistic chart of verification of InSAR monitoring results.

5.4.

Temporal and Spatial Development Trend of Ground Subsidence and Its Cause Analysis

In this paper, the time-series settlement of PS points with 100-m radius at the center of five settlements is analyzed, and the settlement characteristics of five settlement areas are found to be different. The most serious subsidence areas in 2012 to 2015 were the Chaoyang–Tongzhou descending area and the Haiding–Chengdong settlement, and the settlement of the settlement center was up to 150 mm, and the fluctuation was decreased in a certain range, in which the settlement rate was the highest in 2013. The settlement rate of Haiding–Chengdong subsidence area was higher in 2014 and 2015, and the subsidence trend in Beijing was strengthened. From 2013 to 2015, the settlement rate of the Changping subsidence area increased, the settlement in 2014 subsidence area was up to 130 mm, the fluctuation in a certain range increased, and a rebound was evident in 2013, the rebound amount was up to 35 mm, and then there was a slight slowdown. From 2012 to 2015, the settlement rate of the Shunyi subsidence area was stable, and in 2015, the ground subsidence in local area rebounded, and the maximum rebound value was 15 mm. From 2014 to 2015, the subsidence rate of Daxing subsidence area increased, and the settlement of local area exceeded 60 mm. The east of ground subsidence in Beijing and the extension trend of southeast direction are slowly strengthened. Overall, the settlement rate has decreased in recent years, but some regions still have a large rebound (Fig. 14).

Fig. 14

The analysis of the ground settlement rate of the Beijing municipal city in 2012 to 2015.

Combined with the data of subsidence and groundwater level in 2012 to 2015, it is found that there is a high correlation between the decline of groundwater level and the occurrence of subsidence. The groundwater level distribution in Beijing in the 2012 was compared with the main groundwater funnel in Chaoyang–Tongzhou and Daxing subsidence area, and the groundwater funnel was in agreement with the subsidence area. From 2012 to 2015, Beijing city construction and rapid population growth, urban living water, industrial and agricultural water, increased groundwater mining level (Fig. 15), until 2015, the groundwater level has been formed a number of funnel areas such as Chaoyang–Tongzhou District, Daxing District, and Changping District, groundwater level is lower than the surrounding area, and settlement area of the spatial position is more consistent. Although there is no groundwater funnel in the east area of Haiding, it can be found that the groundwater level in the settlement funnel area is more convex, and the groundwater level in this area is obviously lower than the surrounding area.

Fig. 15

Comparison between underground water level and ground subsidence area (a) 2012 and (b) 2015.

With the large-scale construction of cities, the effect of land use on land subsidence is prominent. This paper compares the land use status of the typical district of Beijing with the monitoring data of the ground subsidence in different periods (Fig. 16) and finds that the ground subsidence is positively correlated with the land of urban industrial and mining residents. That is, with the rapid growth of construction land with industry and residence as the main purpose, the speed of ground subsidence is also accelerating. Among them, Changping area, Chaoyang–Tongzhou area, Daxing area, and Shunyi area are more obvious. Therefore, the effective use of groundwater maintains the total area of farmland, green space, a high degree of urban and mining residents land caused by ground subsidence, to curb the ground subsidence further. This provides an important reference for the prevention and control of urban land subsidence in Beijing, the rational formulation of urban future construction plan, and the improvement of social and economic sustainable development ability.

Fig. 16

The map of Beijing land use type in (a) 2012, (b) 2013, (c) 2014, and (d) 2015.

On the whole, the decrease in groundwater and the occurrence of ground subsidence have high spatial correlation. Urban water use, urban construction, and overexploitation of groundwater and mineral resources are the main reasons for the acceleration of urban land subsidence in Beijing, so it is necessary to rationally plan urban construction and resource exploitation in Beijing and to alleviate the shortage of water supply in Beijing city using the north–south project.