remote sensing Article Sequential InSAR Time Series Deformation Monitoring of Land Subsidence and Rebound in Xi’an, China Baohang Wang, Chaoying Zhao *, Qin Zhang and Mimi Peng School of Geology Engineering and Geomatics, Chang’an University, Xi’an 710054, China; [email protected] (B.W.); [email protected] (Q.Z.); [email protected] (M.P.) * Correspondence: [email protected]; Tel.: +86-29-8233-9251 Received: 7 October 2019; Accepted: 29 November 2019; Published: 1 December 2019 Abstract: Interferometric synthetic aperture radar (InSAR) time series deformation monitoring plays an important role in revealing historical displacement of the Earth’s surface. Xi’an, China, has suffered from severe land subsidence along with ground fissure development since the 1960s, which has threatened and will continue to threaten the stability of urban artificial constructions. In addition, some local areas in Xi’an suffered from uplifting for some specific period. Time series deformation derived from multi-temporal InSAR techniques makes it possible to obtain the temporal evolution of land subsidence and rebound in Xi’an. In this paper, we used the sequential InSAR time series estimation method to map the ground subsidence and rebound in Xi’an with Sentinel-1A data during 2015 to 2019, allowing estimation of surface deformation dynamically and quickly. From 20 June 2015 to 17 July 2019, two areas subsided continuously (Sanyaocun-Fengqiyuan and Qujiang New District), while Xi’an City Wall area uplifted with a maximum deformation rate of 12 mm/year. Furthermore, Yuhuazhai subsided from 20 June 2015 to 14 October 2018, and rebound occurred from 14 October 2018 to 17 July 2019, which can be explained as the response to artificial water injection. In the process of artificial water injection, the rebound pattern can be further divided into immediate elastic recovery deformation and time-dependent visco-elastic recovery deformation. Keywords: sequential estimation; InSAR time series; groundwater; land subsidence and rebound 1. Introduction The interferometric synthetic aperture radar (InSAR) is a remote sensing technique, which has been commonly used in the investigation of large-scale ground deformation. Land subsidence in urban areas has been investigated by the InSAR technique in Las Vegas, USA [1], Houston–Galveston, USA [2], Mexico City, Mexico [3], northeast Iran [4], West Thessaly Basin, Greece [5], Pisa urban area, Italy [6], Rome metropolitan area, Italy [7], Beijing [8], Tianjin [9], Taiyuan [10] and Datong, China [11]. Xi’an, China, has suffered from severe land subsidence and ground fissure hazards since the 1960s [12–14]. During the progress of economic development and urbanization, groundwater was over-exploited for more than 50 years [15]. Consequently, it caused the formation of fourteen ground fissures accompanying land subsidence throughout the city [14,15]. The maximum land subsidence rate reached 300 mm/year in 1996, and the maximum cumulative subsidence reached approximately 3 m over the past 60 years [16]. In order to alleviate the land subsidence and ground fissures caused by over-extraction of groundwater, artificial water injection and limitation of pumpage are two effective measures. In 1996, a policy of limiting the over-pumping of groundwater was issued, and the deformation rate began to decrease [17]. When an aquifer water level rises during artificial water injection, the rebound can Remote Sens. 2019, 11, 2854; doi:10.3390/rs11232854 www.mdpi.com/journal/remotesensing Remote Sens. 2019, 11, 2854 2 of 17 Remote Sens. 2019, 11, x FOR PEER REVIEW 2 of 17 be divided into short-term elastic recovery and time-dependent visco-elastic recovery [18]. Previous studystudy revealed revealed the the uplift uplift phenomena phenomena at at Jixiangcun Jixiangcun (point (point D D in in Figure Figure 4) 4) in in Xi’an Xi’an from from 2012 2012 to to 2018 2018 [19 ]. In this[19]. study,In this study, we used we used the sequential the sequential estimation estimation method method to to map map thethe surface surface deformation deformation between between 20152015 and and 2019 2019 in in Xi’an Xi’an with with 83 83 Sentinel-1A Sentinel-1A SARSAR images in in terrain terrain observation observation with with progressive progressive scans scans (TOPS) mode. Results show that some areas, such as Sanyaocun-Fengqiyuan and Qujiang New (TOPS) mode. Results show that some areas, such as Sanyaocun-Fengqiyuan and Qujiang New District, District, subsided continuously, areas such as Xi’an City Wall uplifted slowly, and areas such as subsided continuously, areas such as Xi’an City Wall uplifted slowly, and areas such as Yuhuazhai Yuhuazhai rebounded after long-term subsidence, during the analyzed period. rebounded after long-term subsidence, during the analyzed period. This paper is organized as follows: Section 2 describes the sequential InSAR time series This paper is organized as follows: Section2 describes the sequential InSAR time series estimation estimation method. Section 3 shows the study area and data. Section 4 shows three different surface method.deformation Section phenomena,3 shows the including study area continuous and data. land Section subsidence,4 shows uplift three and di ff rebounderent surface after long-term deformation phenomena,subsidence. including Finally, a continuousdiscussion on land rebound subsidence, deformation uplift and and conclusions rebound afterare given long-term in Section subsidence. 5 and Finally,Section a discussion 6, respectively. on rebound deformation and conclusions are given in Sections5 and6, respectively. 2. Methodology2. Methodology TheThe flow flow chart chart of data data processing processing is shown is shown in Figure in Figure 1, which1, includes which includes three core three steps: coreselection steps: selectionof coherent of coherent pixels, pixels, three-dimensional three-dimensional (3D) (3D)phase phase unwrapping unwrapping and andsequential sequential estimation estimation of of deformationdeformation parameters. parameters. FigureFigure 1. 1.Flow Flow chart chart ofof sequentialsequential InSAR time time series series estimation. estimation. 2.1.2.1. Selection Selection of of Coherent Coherent Pixels Pixels ToTo mitigate mitigate the the effects effects of decorrelation of decorrelation and retrieveand retrieve large-gradient large-gradient deformation, deformation, the small the small baseline subsetbaseline (SBAS) subset InSAR (SBAS) method InSAR wasmethod proposed was proposed based based on the on interferograms the interferograms with with short short spatial spatial and temporaland temporal baselines baselines [20]. In [20]. this In paper, this paper, we use we the use temporal the temporal coherence coherence to select to select coherent coherent pixels pixels [21,22 ], which[21,22], is defined which is in defined Equation in Equation (1) for one (1) generic for one pixelgenericx: pixel x: 1 N N u X exp{1( _u )} (1) x1 xixi,,,, xi γx = N i1 exp p 1( x,i ex,i Dφ ,x,i) (1) N − − − θ i=1 where N is the number of interferograms, represents the flattened and topographically corrected where N is the number of interferograms, represents the flattened and topographicallyu corrected interferogram, represents the spatially correlated phase component, _andu represents the interferogram, e represents the spatially correlated phase component, and φθ represents the spatially Remote Sens. 2019, 11, 2854 3 of 17 uncorrelated phase component (look-angle error phase). A more detailed introduction is provided in [21,22]. Followed by the phase unwrapping, the 3D phase unwrapping method was employed to mitigate the closed-loop discontinuities error in two-dimensional (2D) phase unwrapping [23]. It was used to explore the spatial and temporal relationships within the multi-interferograms, i.e., involving the computation of two Delaunay triangulations, which are usually referred to as “temporal” and “spatial” triangulations, respectively [24,25]. 2.2. Sequential InSAR Time Series Estimation After the atmospheric phase, orbital and digital elevation model (DEM) errors were removed from the interferograms, and we estimated the time series deformation phases by using the following function model: 2 32 3 2 3 6 1 1 0 ::: 0 0 0 76 '1 7 6 unw1 7 6 − 76 7 6 7 6 1 0 1 0 0 0 76 ' 7 6 unw 7 6 76 2 7 6 2 7 6 .− . .··· . 76 . 7 = 6 . 7 (2) 6 . 76 . 7 6 . 7 6 . 76 . 7 6 . 7 46 5746 57 46 57 0 0 0 0 1 1 'N unwM ··· − Ag Xg gL where ' (i = 1, , N) denotes the deformation phase at the different synthetic aperture radar (SAR) i ··· acquisition date and N is the number of SAR images. Note the deformation at the first SAR acquisition date is set to zero, i.e., '0 = 0. To estimate the deformation time series, the archived SAR data are modeled as: V = A X(1) L , P 1 1 − 1 1 (1) T 1 T X = (A1 P1A1)− A1 P1L1 (3) 1 T − QX(1) = (A1 P1A1) (1) where L1 is archived SAR data with design matrix A1 and weight matrix P1. X indicates the first estimation of parameter X, and QX(1) is its cofactor matrix. The superscript T stands for the transposition of a matrix. When we acquire a new SAR image, unlike conventional SBAS InSAR, to estimate deformation time series for all SAR images again we use the sequential estimation to update dynamically the deformation time series by only considering the unwrapped interferograms related to the new SAR image. Assuming the new measurements L2 are the unwrapped interferograms related to the (N + 2) th new SAR acquisition, the weight matrix is P , the design matrixes are A and B, and − 2 2 parameters are X and Y, we can write its observational equation as follows: " # h i X(2) V = A B L , P (4) 2 2 Y − 2 2 According to the principle of least squares (LS) Bayesian estimation [26], it holds that: T (2) (1) T 1 (2) (1) V P V + (X X ) Q− (X X ) = min (5) 2 2 2 − X(1) − Remote Sens.