Monitoring, Analyzing, and Modeling for Single Subsidence Basin in Coal Mining Areas Based on SAR Interferometry with L-Band Data

Excessive exploitation of underground mine resources has caused serious land subsidence in China. -is paper focused on monitoring and modeling the single subsidence basin in coal mining area based on SAR interferometry (InSAR). -e optimum InSAR processing strategy to monitor the mining subsidence was built to obtain the land subsidence with large deformation. And a method of three-dimensional mathematical modeling of single subsidence basin based on InSAR measurements was presented. Using Jining Coalfield (China) as the study area, we acquired 7 L-band PALSAR images from January 2008 to February 2010 to monitor the land subsidence in Jining Coalfield. -e deformation maps in Jining Coalfield in different periods were obtained. Taking the Geting Coal Mine within the Jining coalfield as an example, we finely analyzed and interpreted the deformation maps. Compared with the simultaneous filed measurements, the precision of deformation measurement using D-InSAR in mining area was analyzed.-e root mean square error was 1.37 cm.-emethod of fine interpretation and analysis for a single subsidence basin was established. -e experiments have proved that InSAR technique with L-band InSAR data is suitable for monitoring mining subsidence with large deformation. And the 3D mathematical modeling method could be used for the single subsidence basin in coal mining area.


Introduction
Monitoring the land subsidence over mining regions is one of the most important tasks in monitoring the geographical conditions. Excessive exploitation of underground mine resources has caused serious land subsidence and ruined farmland and some water pit collapse in China [1,2]. It has become one of the most serious problems in restricting the environmental, social, and economic sustainable development in coal mining area. So, it is urgent to obtain the information about the land subsidence in coal mining area. e traditional monitoring methods mainly include the leveling, Global Positioning System (GPS), and total station [2,3]. ese methods have some limitations such as needing much field work, being time consuming and laborious, and having high cost [1], and the observation points are difficult to preserve. In addition, the update period is too long and the measuring data is discrete. So, we should seek a new monitoring method with low cost, short production period, and continuous data in monitoring the land subsidence over mining regions. e space-borne Interferometric Synthetic Aperture Radar (InSAR) is a new technique for Earth observation in the late 1900s [4][5][6][7]. It provides a new method to monitor the Earth surface deformation. It can quickly get the largearea surface deformation with high precision. And InSAR can identify some previously unknown land subsidence areas. It has been turned out to be an effective technique for land subsidence measurement due to its precision, spatial coverage, and resolution [8,9]. e capability of InSAR for surface deformation mapping has been demonstrated in many applications, such as earthquake activity [10], volcanic activity [11,12], the land subsidence in the city caused by groundwater over exploitation [13,14], landslide [15], and glacier movement [16].
InSAR technique has been applied to monitor the land subsidence in coal mining area [17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Ji et al. [18] demonstrated InSAR's ability to cost-effectively monitor illegal mining activities. A DInSAR-based illegal-mining detection system (DIMDS) was proposed to exploit the geometric, spatial, and temporal characteristics of those subsidence patterns [19]. Zheng et al. [20] analyzed land subsidence induced by coal mining in a 200 km 2 area in the Ordos Basin for the time period 2006-2015 using SBAS InSAR and D-InSAR. Hayman et al. [21] investigated the performance of the three satellite missions (Radarsat-2, Sentinel-1, and ALOS-2) with different imaging modes for mapping longwall mine subsidence. Yang et al. [22] presented a novel space-based method for locating and defining the underground goaf caused by coal extraction using Interferometric Synthetic Aperture Radar (InSAR) techniques. Xia and Wang [23] proposed a method that relied on the principle of the probability integration method (PIM) and on synthetic aperture radar interferometry (InSAR) to retrieve the location of an underground goaf. Du et al. [24] proposed a feature-points-based method for the efficient location of mining goafs based on D-InSAR. Chen et al. [25] employed the small baseline subset interferometry synthetic aperture radar (SBAS-InSAR) technology to obtain the time-series residual surface deformation based on the 40 Sentinel-1A images acquired from 14th February 2017 to 17th May 2020.
Although InSAR technique has been applied to monitor the land subsidence over mining regions, the special surface environment in mining area and the characteristics of mining subsidence restrict the application of InSAR technique in coal mining area on a large scale. ere have been some problems and difficulties in monitoring the land subsidence in mine area. For example, too large deformation will exceed the maximum deformation gradient [31] that InSAR can measure; the coherence caused by high vegetation land cover is poor; and the reliability and accuracy of InSAR monitoring are low. ese increase the difficulty in monitoring the land subsidence with InSAR technique.
According to the problems about obtaining the mining subsidence information, we carried out some studies to obtain the land subsidence based on InSAR technique. We will explore a suitable and feasible method and technical process related to the InSAR data processing. In this paper, the major objective is to provide an effective solution to obtain accurate and critical information on the land subsidence in coal mining area. is paper is organized as follows. e study area and SAR data are presented in Section 2. Section 3 describes the method and data processing strategy for monitoring the surface deformation with InSAR technique. And a method of three-dimensional mathematical modeling of subsidence basin based on InSAR measurements is presented. In Section 4, taking the Jining Coalfield (China) as study area, we obtain the land subsidence using InSAR technique with PALSAR data. And we analyze and interpret the results of mining subsidence based on InSAR technique. Finally, some valuable conclusions drawn from this study are given in Section 5.

Study Area.
e study area is located in the Jining City, which is the west-south part of the Shandong Province, North China. e region extends from 116.36°E to 116.94°E and from 35.32°N to 35.54°N (see Figure 1). ere have been more than 20 coal mines, such as Liangbaosi Coal Mine, Geting Coal Mine, Tangkou Coal Mine, Daizhuang Coal Mine, Xuchang Coal Mine, Nantun Coal Mine, Dongtan Coal Mine, and Gucheng Coal Mine. It caused serious surface collapse because of long-term and high-intensitive coal mining.

Data.
In order to monitor the mining-induced land subsidence with large deformation in coal mining area, the ALOS PALSAR data, which are L band (the wavelength is 23.6 cm), were used. Its central frequency is 1270 MHz. is means it has greater penetration.
We used a total of 7 L-band ALOS PALSAR images acquired from January 2008 to February 2010 over the Jining coalfield from an ascending orbit, as listed in Table 1. All PALSAR data were Fine Beam Single Polarization (FBS) imaging mode (single-look complex images, CEOS (Committee for Earth Observing Satellites) standard format and Level 1.1 products) and in HH polarization with the 34.3°i ncidence angle. e ALOS PALSAR data has a swath of about 70 km and a spatial resolution of about 7 m. e satellite repeat period of ALOS is 46 days.
From the optical remote sensing image, we can see that there are mostly farmlands in the study area and the vegetation is rich and well grown. is increases the difficulty in monitoring the land subsidence with InSAR technique.
In addition, the SRTM DEM in this region was used to remove the flat Earth phase in InSAR data processing and to geocode some products. It can also be used to do SAR simulating processing to remove the phase due to the topography [6,7,26].

Methods
SAR interferometry can provide the mining subsidence information and spatial-temporal evolution about the surface deformation based on time series radar data. e following is a brief introduction of the basic principle and process of InSAR about monitoring the mining deformation.

e Basic Principle for Monitoring the Land Subsidence
Using InSAR Technique. In fact, the phase of interferogram consists of 5 parts as follows [6,7]: where φ topography is the phase due to the topography; φ displacement is the phase due to the surface deformation at line of sight (LOS) of radar; φ atmosphere is the phase due to the atmospheric effects; φ flat is the flat Earth phase due to the special imaging geometry, side looking imaging; φ noise is the phase noises from the speckle due to coherence imaging, system noise, and radar shadow.
For monitoring the surface deformation with InSAR technique, there are three methods, named as two-pass method, three-pass method, and four-pass method [4,6,7,10]. e basic principle of InSAR can be found in the literatures [6,7,10]. Two-pass approach differential interferometry is more suitable for monitoring the land subsidence with large deformation [23,26]. It needs two sets of radar data acquired from the similar orbit and the DEM with high precision.

e Optimum InSAR Processing Strategy to Monitor the Mining Subsidence.
e procedures of two-pass D-InSAR include the interferogram generation, the SAR simulation based on DEM, the differential processing between the real interferogram and the simulated interferogram, the phase unwrapping, the transformation from the phase to deformation, the geocoding, and so on [6,7]. e methods and flowchart of data processing can be seen in [6,7,10]. Figure 2 is the technical flowchart for monitoring the mining subsidence with InSAR technique in our study.
When the coherence of InSAR pair is low, for example, in the densely vegetated area, a prefilter (including the  spectral shift filter and Doppler filter) is necessary in InSAR data processing [6]. e spectra of master and slave acquisitions are not completely overlapping. e spectral shift filter is intended to remove the part of the master and slave spectra which are not overlapping. e Doppler filter can remove the portion of the azimuth spectra, which are not common between master and slave image. e prefilter can obviously improve the coherence of interferogram and therefore improve the reliability and accuracy of InSAR measuring.
In addition, we also proposed an optimum strategy from coarseness to fine in InSAR processing. e specific method was as follows. Firstly, it carries out the coarse differential interferometric processing for the whole image. e number of looks in range direction was selected bigger in multilooking processing now. For example, the multilook of ALOS PALSAR data is 4 : 10 in the range direction and azimuth direction, respectively.
e differential interferogram should not carry out the subsequent data processing, such as the phase unwrapping and the transformation from phase to deformation. We can find several settlement regions according to the differential interferogram. en, we subset the radar data to several parts according to the locations of settlement regions, which include one or two coal mines. At last, it carries out the fine differential interferometric processing and subsequent data processing for every part. e number of looks in the range direction should be as small as possible in multilooking processing now. For example, the multilook of ALOS PALSAR data is 1 : 2 in the range direction and azimuth direction, respectively. is strategy can not only accelerate the speed of data processing, but also ensure the accuracy of monitoring results. Especially for the phase unwrapping, it can obtain more reliable result in small region.

e Method of ree-Dimensional Modeling for Subsidence Basin Based on InSAR Measurements.
After underground coal mining, a series of subsidence basins will form in the mining area. Based on analyzing a large number of interferograms using SAR interferometry in coal mine area, we found that they are usually manifested as a series of concentric circles or concentric ellipses with similar shapes for the single subsidence basin in the InSAR interferograms [32]. In order to conduct quantitative analysis of single subsidence basin, the InSAR monitoring results can be used to establish the mathematical model of the single subsidence basin. rough a series of experimental verifications, especially the analysis of the morphology of the horizontal section and vertical section of the subsidence basin, the mathematical model of the subsidence basin in the mining area can be established: where h is the settlement; (x, y) is the plane coordinates of settlement points; (x 0 , y 0 ) is the position of maximum subsidence center; a is the influence of the subsidence factor; b and c are the semimajor axis and semiminor axis of an elliptic equation, respectively. at is to say, 5 parameters of the mathematical model should be needed to solve: x 0 , y 0 , a, b, c. e parameters x 0 and y 0 determine subsidence basin the location of the maximum settlement. e parameter a determines the size of the ground settlement shape. e parameters b and c determine the geometric shapes of subsidence basin. ese five parameters will determine the position and form of subsidence basin in space.
Parameter a is obtained directly according to the maximum settlement amount of the subsidence basin monitored by InSAR. Parameters x 0 and y 0 are determined by the position of the maximum settlement amount of the subsidence basin. e maximum settlement amount and its position are detected and recorded through two-dimensional search in the deformation map. e other two parameters, b and c, determine the shape of the ellipse. And the solutions can be obtained by means of least square fitting based on some InSAR measurements at settlement points.

4.1.
e Differential Interferogram in Jining Coalfield. In order to monitor the land subsidence in Jining coalfield in detail, we carried out the differential InSAR processing for the 7 PALSAR radar data. We built 6 optimum interferometric pairs according to the parameters of the time of data acquisition and the baselines. e information about the InSAR pairs can be seen in Table 2.
We carried out the interferometric data processing for all InSAR pairs according to the processing flowchart in Figure 2.
e InSAR complex data registration adopted the  automatic search technique based on window. e phase noise was filtered using the modified Goldstein Radar Interferogram Filter [33,34]. e phase unwrapping process becomes difficult due to the presence of large areas of low coherence. In this case, the minimum cost flow (MCF) algorithm [35] enables obtaining better results than other methods. e ratio of multilooking is 1 : 2. e pixel size in range direction is 7.49 m, and the pixel size in azimuth direction is 6.15 m for the differential interferograms. It is necessary to carry out the processing of resampling because the pixel size is not the same in range direction and in azimuth direction. In order to further analyze the subsidence of deformation map, geocoding the differential interferograms is in need. ey are the results of geocoded differential interferograms as shown in Figure 3.

e Mining-Induced Land Deformation Fields in Jining
CoalField.
en, we can obtain the land deformation maps for every InSAR pairs after the conversion from the phase to deformation. e deformation maps have carried out some data processing procedures, such as the residual phase correction, the conversion from phase to deformation, and geocoding the products. ey have absolute geographical coordinates. According to the amount of deformation, the settlement is classified with different colors (see Figure 4). rough experiment, we also found that the InSAR pairs with too long interval or with too long perpendicular baseline cannot generate distinct interferometric fringes.
We also calculated the area of the land subsidence for the several important coal mines in different time intervals. ey include Liaobaosi Coal Mine, Geting Coal Mine, Yunhe Coal Mine, Tangkou Coal Mine, and Daizhuang Coal Mine. e areas of land subsidence are listed in Table 3. From Table 3, we can find that the land subsidence is very serious due to excessive exploitation of underground mine resources. e land subsidence of these 6 coal mines within Jining coalfield exceeds 6 km 2 .
A magnitude of 94.4 cm was firstly monitored by L-band InSAR in Jining coalfield. It appeared around the Dongtan Coal Mine in time interval from 10th January to 25th February, 2009. e radius of this subsidence basin is about 350 m and the major influence radius of this subsidence basin is about 256 m.

Accuracy Verification.
In order to verify and evaluate the accuracy of settlement monitoring in InSAR mining area, precise leveling observation was carried out simultaneously in the study area. e comparison of monitoring results between InSAR technique and leveling is shown in Figure 5. According to Figure 5, the deformation trend of InSAR monitoring results and leveling monitoring results is basically consistent, and the root mean square error was 1.37 cm. e root mean square error was relatively large. is was mainly caused by the inconsistency of observation time and space. Firstly, the time period of InSAR technique and leveling monitoring was not completely consistent. e time period of InSAR monitoring was from 13th January to 28th February, 2010, while the time period of leveling was from 11th January to 26th February, 2010. ey were not completely consistent. Secondly, leveling observation monitors the deformation information on a "point," while InSAR technique deals with the deformation information on a "surface" (i.e., pixel). In fact, it is the comparison between "point" and "surface," so they cannot correspond exactly.

Fine Analysis and Interpretation for Single Subsidence
Basin. It is very important to analyze the subsidence conditions of single coal mine. In the following, we take the interferometric pair with the time interval from 8th January to 23rd February, 2008 in Geting Coal Mine within Jining coalfield as an example to illustrate the fine analysis for the mining subsidence. We can generate the geocoded deformation map, the deformation contours, the subsidence profile, and three-dimensional deformation map for the single coal mine. Figure 6 is the results of fine analysis for single coal mine, taking the Geting Coal Mine as an example. en, the subsidence area can be counted based on the deformation map. Table 4 is the statistics of subsidence area of Geting Coal Mine. e maximum land subsidence in this time interval is 39.3 cm. e area which the settlement exceeds 5 cm reached 0.24 km 2 . And the remaining settlement areas statistics are shown in Table 4.

Modeling of Subsidence Basin Based on InSAR
Measurements. Taking Geting Coal Mine as an example, 46 points are selected to participate in the calculation. And the fitting model parameters can be obtained by calculating according to the least square method. In the image coordinate system, b � 36.13 and c � 34.17.
us, the three-dimensional model of the subsidence basin of Geting Coal Mine can be established as follows: In view of the transformation of image coordinate system to geographic coordinate system, pixel size and geographic coordinate system need to be considered. Figure 7 is the 3D display of the established model. From Figure 7, it can be seen that the 3D model is very consistent with the subsidence basin monitored by InSAR. erefore,

Conclusions
In this paper, the land subsidence in coal mining area was monitored using InSAR technique. Using 7 scenes of L-band PALSAR data from January 2008 to February 2010, we successfully obtained the mining subsidence deformation maps in the Jining Coal Mine during different periods based on an optimum InSAR data processing flowchart and strategy.
rough this study, we got some valuable conclusions in monitoring the land subsidence in coal mining area with InSAR technique.
(1) In the Jining coalfield, some subsidence basins with the radius of tens of meters to one hundred or several hundreds were formed. Generally, the maximum deformation of the subsidence basin ranges from 30 cm to 50 cm. e land subsidence of 6 coal mines within Jining coalfield exceeds 6 km 2 . (2) e magnitude of the land subsidence in the coal mine is larger. For the larger deformation, it is easier to monitor the land subsidence using SAR interferometry with L-band data. erefore, SAR interferometry with L-band data is an effective technique for mapping the land subsidence in mining area. In particular, SAR interferometry can detect some unknown subsidence basins. (3) Compared with the simultaneous filed measurements, the precision of deformation measurement using D-InSAR in mining area was analyzed. e root mean square error was 1.37 cm. It can meet the needs of monitoring the mining subsidence. (4) e method of three-dimensional mathematical modeling based on InSAR measurements is suitable for the single subsidence basin in the coal mine. e mathematical model can be used to quantitative analysis and simulation and early warning in the coal mine. In addition, for some interrupted or confused interferometric fringes caused by phase noise, the three-dimensional model of subsidence basin constructed in this paper can also be used to solve these problems, so that InSAR technology can be better applied to monitor the land subsidence in mining areas with large deformations.
When adequate SAR data are available, InSAR can partially replace the traditional leveling method for monitoring mining-induced subsidence. erefore, InSAR technique can provide an efficient technique in monitoring the land subsidence in coal mining area.
With regard to monitoring the land subsidence in mining area, it should be noted that radar data can be used to obtain not only the quantitative ground subsidence but also the information about the land cover and the land change. In the future, we will focus on mining the surface coverage and surface changes using multitemporal SAR data.

Data Availability
e SRTM DEM data used to support the findings of this study are included within the article.

Conflicts of Interest
e authors declare no conflicts of interest.