Surface Deformation Monitoring and Spatiotemporal Evolution Analysis of Open-Pit Mines Using Small-Baseline Subset and Distributed-Scatterer InSAR to Support Sustainable Mine Operations

Abstract

Open-pit mining often induces geological hazards such as slope instability, surface subsidence, and ground fissures. To support sustainable mine operations and safety, high-resolution monitoring and mechanism-based interpretation are essential tools for early warning, risk management, and compliant reclamation. This study focuses on the Baorixile open-pit coal mine in Inner Mongolia, China, where 48 Sentinel-1 images acquired between 3 March 2017 and 23 April 2021 were processed using the Small-Baseline Subset and Distributed-Scatterer Interferometric Synthetic Aperture Radar (SBAS-DS-InSAR) technique to obtain dense and reliable time-series deformation. Furthermore, a Trend–Periodic–Residual Subspace-Constrained Regression (TPRSCR) method was developed to decompose the deformation signals into long-term trends, seasonal and annual components, and residual anomalies. By introducing Distributed-Scatterer (DS) phase optimization, the monitoring density in low-coherence regions increased from 1055 to 338,555 points (approximately 321-fold increase). Deformation measurements at common points showed high consistency ($R^2$ = 0.97, regression slope = 0.88; mean rate difference = −0.093 mm/yr, standard deviation = 3.28 mm/yr), confirming the reliability of the results. Two major deformation zones were identified: one linked to ground compaction caused by transportation activities, and the other associated with minor subsidence from pre-mining site preparation. In addition, the deformation field exhibits a superimposed pattern of persistent subsidence and pronounced seasonality. TPRSCR results indicate that long-term trend rates range from −14.03 to 14.22 mm/yr, with a maximum periodic amplitude of 40 mm. Compared with the Seasonal-Trend decomposition using LOESS (STL), TPRSCR effectively suppressed “periodic leakage into trend” and reduced RMSEs of total, trend, and periodic components by 48.96%, 93.33%, and 89.71%, respectively. Correlation analysis with meteorological data revealed that periodic deformation is strongly controlled by precipitation and temperature, with an approximately 34-day lag relative to the temperature cycle. The proposed “monitoring–decomposition–interpretation” framework turns InSAR-derived deformation into sustainability indicators that enhance deformation characterization and guide early warning, targeted upkeep, climate-aware drainage, and reclamation. These metrics reduce downtime and resource-intensive repairs and inform integrated risk management in open-pit mining.

1. Introduction

Underground mineral resources are a cornerstone of national economic and social development worldwide. With the rapid advancement of industrialization and urbanization, the rising demand for infrastructure and energy has markedly heightened reliance on mineral resources [1,2,3]. Among various modes of mineral extraction, open-pit mining has been widely adopted for the extraction of coal, non-ferrous metals, and non-metallic minerals, due to its high production efficiency, low unit cost, and relatively simple operational procedures [4]. However, the removal of overburden and excavation of ore bodies during open-pit mining can drastically alter surface topography, weaken slope stability, and disturb in-situ stress equilibrium. These changes, in turn, can trigger various geological hazards, such as slope failures, ground subsidence, collapses, and surface fissures [5,6,7,8]. These hazards can not only pose severe threats to mining safety but can also have detrimental impacts on nearby residential areas, transportation infrastructure, and ecological environments. Therefore, it is important to perform timely and accurate monitoring of surface deformation in open-pit mines, as well as to elucidate its spatiotemporal evolution patterns, for early warning and prevention of geological disasters [9,10].

Traditional deformation monitoring techniques, including leveling surveys, Global Positioning System (GPS) measurements, Unmanned Aerial Vehicle (UAV), and terrestrial laser scanning (TLS), have been widely applied in open-pit mine deformation monitoring [11,12,13]. Leveling surveys can provide highly accurate measurements, but require the installation of high-density monitoring stations, resulting in low operational efficiency and high labor intensity, and are therefore unsuitable for large-scale or topographically complex areas [14]. GPS technology offers high positioning accuracy and a high degree of automation, but its monitoring coverage is limited by the spatial distribution of observation points, and construction and maintenance costs remain relatively high [15]. UAV and TLS can rapidly acquire high-resolution surface deformation, but they are highly sensitive to meteorological conditions, and their data processing workflows are complex and costly [16,17]. In general, these methods suffer from limitations such as high cost, low efficiency, limited spatial coverage, and the inability to achieve high-frequency monitoring, which restricts their long-term and large-scale application in open-pit mine deformation monitoring [18,19]. In contrast, Interferometric Synthetic Aperture Radar (InSAR), with its all-weather and all-day acquisition capability, wide-area coverage, and high-precision monitoring, has become an important tool for deformation monitoring in mining areas, effectively compensating for the limitations of traditional monitoring techniques [20,21].

In recent years, with the continuous advancement of InSAR technology, it has been widely applied to deformation monitoring in open-pit mines. G. Herrera et al. [22] applied the differential InSAR (D-InSAR) technique to monitor non-linear deformation in open-pit mines, demonstrating its effectiveness while emphasizing the importance of acquisition geometry, detection thresholds, and temporal sampling for deformation monitoring. He et al. [23] integrated D-InSAR-based Small-Baseline Subset (D-InSAR-SBAS) and Multiple-Aperture InSAR-based Small-Baseline Subset (MAI-SBAS) techniques to retrieve vertical and north-south displacement fields for large open-pit mine slopes, demonstrating high accuracy and effectiveness for large-scale landslide bi-directional deformation monitoring. Zhang et al. [24] integrated multisource remote sensing data (GF-2 optical imagery, Radarsat-2, and Sentinel-1A SAR) with D-InSAR and DS-InSAR (Distributed-Scatterer InSAR) techniques to perform spatiotemporal monitoring and causal analysis of the collapse and dump slopes in the Xinjing open-pit mine. Bai et al. [25] used SBAS-InSAR and DS-InSAR to monitor seven years of deformation at the Shengli West No. 2 mine, showing that DS-InSAR offers higher precision in areas of low coherence and reveals the significant influence of mining activities on deformation evolution. Gül et al. [26] compared surface deformation monitoring in open-pit mines using Sentinel-1A and TerraSAR-X, showing that the two SAR datasets differ in accuracy and deformation mapping, with TerraSAR-X offering higher spatial resolution and better small-scale detail capture, while Sentinel-1A provides advantages in large-area monitoring and data accessibility.

Beyond monitoring, understanding the driving mechanisms of deformation is important for prediction and risk assessment. A widely used paradigm is to decompose displacement time-series into trend, periodic, and anomalous/residual components. However, from the perspectives of mechanistic interpretation and early warning, achieving a clean separation and quantitative attribution of these components remains challenging. Wavelet transforms, empirical mode decomposition (EMD), and seasonal-trend decomposition using LOESS (STL) approaches either depend on predefined bases and are prone to energy leakage or suffer from mode mixing and end effects, thereby hindering the separation of stable components in low-coherence or large-deformation gradient settings [27,28]. Although Variational Mode Decomposition (VMD) mitigates mode mixing via variational constraints, its performance is sensitive to parameterization, and it often struggles to represent slowly varying seasonal amplitudes [29]. Moreover, many existing studies emphasize long-term trends and their spatial patterns, while the independent separation and causal diagnosis of periodic behavior and short-term anomalies (often linked to environmental forcing) remain limited [30,31]. Furthermore, it remains difficult to ensure high spatiotemporal continuity and precision in rainforests, dense vegetation, or high-deformation gradient scenarios [32,33].

To this end, the SBAS-DS-InSAR method was employed with Sentinel-1 images to derive high-quality line-of-sight (LOS) deformation time-series over the open-pit mine. Based on these data, this study focuses on time-series decomposition of InSAR displacement—separating the trend, periodic, and residual components within a single LOS geometry—and proposes a trend–periodic–residual subspace-constrained regression (TPRSCR) method. The TPRSCR method integrates polynomial trend modeling with multiharmonic (Fourier) decomposition and introduces a slow seasonal-amplitude drift model to suppress the phenomenon of “periodic leakage.” Furthermore, the characteristics of spatial distribution and the underlying causes of long-term trend deformation were investigated, while the driving factors of periodic deformation were analyzed against the temperature and precipitation data. These results demonstrate that the proposed method provides valuable technical support for slope stability assessment, mining impact assessment, and geological hazard prevention in open-pit mines, while also offering methodological insights for the broader application of InSAR technology in mine safety monitoring.

2. Methods

2.1. Small-Baseline Subset and Distributed-Scatterer Interferometric Synthetic Aperture Radar

Time-series surface deformation was obtained using the SBAS-DS-InSAR approach (small-baseline subset fused with Distributed-Scatterer processing), which leverages the strengths of both SBAS-InSAR and DS-InSAR. In the SBAS-InSAR technique, multimaster interferograms were constructed using small-baseline subset thresholds, effectively mitigating the impact of temporal and spatial decorrelation on interferogram quality and enhancing data utilization through redundant observations [34]. In the DS-InSAR process, Distributed-Scatterer pixels were optimized, allowing more high-quality monitoring points to be identified and extracted in low-coherence regions [35]. All InSAR processing—image co-registration, interferogram formation, topographic phase removal, phase unwrapping, and SBAS and SBAS-DS-InSAR inversion is performed with the GAMMA 2017 software, and the DS-phase optimization is implemented in MATLAB 2024. Through the integration of these two approaches, the monitoring performance and data utilization were significantly improved. The SBAS-DS-InSAR processing chain is summarized in Figure 1.

The detailed steps are outlined as follows.

Interferogram formation: Assume that in the study area, N SAR image acquisitions are available at times $(t_1,t_2,\cdots ,t_N)$. One of the images is selected as the reference (used solely for co-registration), and all remaining images are co-registered to this reference to ensure a common geometry. Then a small-baseline network is constructed according to the prescribed temporal and spatial baseline thresholds $(B_t^{max},B_s^{max})$, from which M interferograms ($N-1\le M\le {\displaystyle \frac{N·(N-1)}{2}}$) are generated. The relationship between the interferometric phase ${\varphi }_m$ and the time-series phase ${\phi }_n$ can be expressed as [36]:

$$\underset{\varphi }{\left[\begin{array}{c}{\varphi }_1\\ {\varphi }_2\\ {\varphi }_3\\ ⋮\\ {\varphi }_{M-1}\\ {\varphi }_M\end{array}\right]}=\underset{\mathbf{B}}{\left[\begin{array}{ccccc}1& -1& 0& \cdots & 0\\ 1& 0& -1& \cdots & 0\\ 0& 1& \ddots & -1& 0\\ ⋮& ⋮& \ddots & ⋮& ⋮\\ 0& 0& 0& \cdots & 0\\ 0& \cdots & 0& 1& -1\end{array}\right]}\underset{\phi }{\left[\begin{array}{c}{\phi }_1\\ {\phi }_2\\ {\phi }_3\\ ⋮\\ {\phi }_{N-1}\\ {\phi }_N\end{array}\right]}$$

(1)

where $\mathbf{B}$ is the coefficient matrix with dimensions $M\times N$, whose columns correspond to the SAR images and rows correspond to the interferograms. The structure of B is determined by the configuration of the interferometric network. The elements of B take values only in $-1, 0, 1$, where −1 indicates that the acquisition is used as the secondary image in the interferometric pair, 1 indicates the reference image in that pair, and 0 denotes that the acquisition is not involved in the formation of that interferogram.

Phase optimization: A phase optimization method based on the decomposition of homogeneous-pixel time-series phase matrices [35] was employed to enhance interferogram quality and increase the density of high-quality monitoring points. The Homogeneous Target Coherence Index (HTCI) algorithm [37] was first applied to identify statistically homogeneous pixels (SHPs), which were then classified into persistent scatterers (PS) and distributed scatterers (DS). For each identified DS target, a homogeneous-pixel time-series phase matrix was constructed and subsequently subjected to singular value decomposition (SVD). Following a principal component analysis (PCA) approach [38], and under the homogeneity assumption, the rank-1 SVD approximation (first principal component) was retained to reconstruct the denoised interferometric phase. This procedure was applied to all DS targets, and then the resulting optimized phases were used to generate the optimized interferograms.

Subsequently, coherence is estimated from the SAR data, and the DS pixels are merged via coherence-weighted averaging to obtain the final DS-optimized interferometric phase, which is expressed as [35]:

$${\phi }_{\mathrm{ref}}={\displaystyle \frac{{\sum }_{i=1}^n{\phi }_i·{\mathrm{Coh}}_i}{{\sum }_{i=1}^n{\mathrm{Coh}}_i}}$$

(2)

where ${\phi }_{\mathrm{ref}}$ denotes the phase of the reference pixel, ${\phi }_i$ denotes the phase of the i-th homogeneous pixel, and ${\mathrm{Coh}}_i$ is the estimated coherence value.

Deformation phase retrieval. Based on the optimized time-series interferograms, high-quality monitoring points are first selected. When the number of interferograms satisfies $M\ge N$, the time-series phase vector $\mathit{\phi }$ is estimated via least squares [39,40]. If the system is underdetermined ($M<N$), the Moore–Penrose pseudoinverse computed by singular value decomposition (SVD) is employed instead [41]. Finally, the estimated time-series phase matrix is integrated over time to obtain the cumulative deformation for the corresponding interval.

2.2. Trend-Periodic-Residual-Subspace-Constrained Regression Method

Surface deformation at open pits arises from several drivers, including mining operations, slope unloading, rainfall infiltration, and thermo-elastic effects [42,43,44,45]. These processes generate a composite signal characterized by a slow, long-term trend superimposed with annual and seasonal periodic variations and abrupt noise components [46]. Signals from different sources may obscure one another, potentially leading to biased mechanism interpretation and ineffective early warning. Therefore, it is essential to decouple the trend, periodic, and residual components to separately extract long-term subsidence induced by mining operations, periodic responses driven by environmental factors, and anomalous residuals associated with sudden events. To this end, a Trend-Periodic-Residual Subspace-Constrained Regression (TPRSCR) method is proposed here to decompose deformation components from time-series observations. Unlike STL and other smoothing-based decompositions, TPRSCR (i) combines a polynomial trend with multiharmonic (Fourier) terms, (ii) explicitly models a slowly drifting seasonal amplitude, and (iii) jointly estimates all components in a coupled subspace, thereby suppressing seasonal-to-trend (“periodic”) leakage. The proposed TPRSCR algorithm, together with time-series decomposition, statistical analyses, and figure generation, was implemented in MATLAB 2024.

To rigorously decompose the three-dimensional time-series deformation data into three mutually independent components—trend, periodic, and residual—each pixel $(i,j)$ is represented in the time domain as [47]:

$$de{f}_{ij}\left(t_n\right)=T_{ij}\left(t_n\right)+S_{ij}\left(t_n\right)+R_{ij}\left(t_n\right),\hspace{1em}n=1,2,\dots ,T$$

(3)

where $de{f}_{ij}$ denotes the total surface deformation, $T_{ij}$ denotes the trend component, $S_{ij}$ denotes the periodic component, and $R_{ij}$ denotes the residual component. To improve numerical conditioning and eliminate dimensional effects, the time variable is normalized to ${\tau }_n\in [-1,1]$ as [48]:

$${\tau }_n={\displaystyle \frac{2(t_n-1)}{T-1}}-1$$

(4)

where $t_n$ denotes the n-th observation epoch and T is the total number of observation epochs. The trend component is modeled using a polynomial of degree at most d (where $d=1$ corresponds to a linear trend and $d=2$ represents a quadratic trend) [49]:

$$T_{ij}\left(t_n\right)=\sum _{r=0}^d{\beta }_{r,ij}{\tau }_n^r$$

(5)

where ${\beta }_{r,ij}$ is the coefficient of the r-th order polynomial term at pixel $(i,j)$. The periodic component accommodates multiple base periods and their harmonics. Given a set of base periods ${\left\{P_m\right\}}_{m=1}^{M_0}$ and the corresponding harmonic orders $\left\{H_m\right\}$, the periodic component is expressed as [50]:

$$S_{ij}\left(t_n\right)=\sum _{m=1}^{M_0}\sum _{h=1}^{H_m}\left[a_{mh,ij}sin\left({\displaystyle \frac{2\pi h}{P_m}}{t}_n\right)+b_{mh,ij}cos\left({\displaystyle \frac{2\pi h}{P_m}}{t}_n\right)\right]$$

(6)

where $a_{mh,ij}$ and $b_{mh,ij}$ denote, respectively, the sine and cosine coefficients of the h-th harmonic of the m-th base period at pixel $(i,j)$. If a slow seasonal-amplitude drift is present, a first-order drift term $S_{ij}^{\left(\mathrm{drift}\right)}$ may optionally be introduced to prevent these variations from being absorbed into the trend component [50]:

$$S_{ij}^{\left(\mathrm{drift}\right)}\left(t_n\right)=\sum _{m,h}\left[c_{mh,ij}{\tau }_n\right.sin\left({\displaystyle \frac{2\pi h}{P_m}}{t}_n\right)+d_{mh,ij}{\tau }_n\left.cos\left({\displaystyle \frac{2\pi h}{P_m}}{t}_n\right)\right]$$

(7)

where $c_{mh,ij}$ and $d_{mh,ij}$ denote the drift coefficients of the h-th harmonic of the m-th base period at pixel $(i,j)$.

To simplify notation, the pixel index $(i,j)$ is flattened into a single pixel index p. The time-series deformation of pixel p is represented as ${\mathbf{def}}_p={[de{f}_p\left(t_1\right),de{f}_p\left(t_2\right),\dots ,de{f}_p\left(t_T\right)]}^{\top }$. The trend design matrix ${\mathbf{X}}_{\mathrm{tr}}\in {\mathbb{R}}^{T\times (d+1)}$ and the seasonal design matrix ${\mathbf{X}}_{\mathrm{se}}\in {\mathbb{R}}^{T\times K_s}$ are constructed, where ${\mathbf{X}}_{\mathrm{se}}$ contains all sine and cosine terms (and, if drift is enabled, the $\tau sin(·)$/$\tau cos(·)$ terms). The complete design matrix $\mathbf{X}$ is obtained by horizontal concatenation [51], i.e., $\mathbf{X}=\left[{\mathbf{X}}_{\mathrm{tr}}{\mathbf{X}}_{\mathrm{se}}\right]\in {\mathbb{R}}^{T\times K}$. The joint linear model for each pixel is then [49]:

$${\mathbf{def}}_p=\mathbf{X}{\theta }_p+{\epsilon }_p,\hspace{1em}{\theta }_p={\left[\begin{array}{cccc}{\beta }_p^{\top },& {\mathbf{a}}_p^{\top },& {\mathbf{b}}_p^{\top },& ({\mathbf{c}}_p^{\top },{\mathbf{d}}_p^{\top })\end{array}\right]}^{\top }$$

(8)

where ${\mathbf{def}}_p$ is the time-series displacement vector of pixel p. $\mathbf{X}$ denotes the complete design matrix that combines trend and seasonal terms. ${\theta }_p$ represents the parameter vector including the polynomial coefficients (${\beta }_p$), sine coefficients (${\mathit{a}}_p$), cosine coefficients (${\mathit{b}}_p$), and optional drift coefficients (${\mathit{c}}_p$, ${\mathit{d}}_p$). ${\epsilon }_p$ is the residual deformation vector.

When there are no significant outliers or ill-conditioning issues, the parameters ${\widehat{\theta }}_p$ are estimated using least squares. If the number of samples is small, the number of harmonics is large, or the period configuration induces strong column collinearity, the SVD-based Moore–Penrose pseudoinverse is recommended. If outliers are present, the Huber loss-based iteratively reweighted least squares (IRLS) is employed, using the weight function $w\left(u\right)=min1,,c/\left|u\right|$ (where u is the standardized residual and $c\approx 1.345$) [52]:

$${\widehat{\theta }}_p^{(k+1)}=arg\underset{\theta }{min}{∥{\mathbf{W}}_p^{1/2}({\mathbf{def}}_p-\mathbf{X}\theta )∥}_2^2$$

(9)

where ${\mathbf{W}}_p$ is the diagonal weight matrix, i.e., ${\mathbf{W}}_p=\mathrm{diag}\left(w(r_{p,n}/s_p)\right)$, where $r_{p,n}$ denotes the residual of the n-th observation at pixel p, and $s_p$ represents the robust scale estimate. After parameter estimation, the trend and seasonal components are reconstructed [49]:

$${\widehat{\mathbf{T}}}_p={\mathbf{X}}_{\mathrm{tr}}{\widehat{\beta }}_p,\hspace{1em}{\widehat{\mathbf{S}}}_p={\mathbf{X}}_{\mathrm{se}}{\widehat{\gamma }}_p$$

(10)

where ${\widehat{\gamma }}_p$ collects all seasonal coefficients. The residual component is then obtained as [49]:

$${\widehat{\mathbf{R}}}_p={\mathbf{def}}_p-{\widehat{\mathbf{T}}}_p-{\widehat{\mathbf{S}}}_p$$

(11)

where ${\widehat{\mathbf{T}}}_p$, ${\widehat{\mathbf{S}}}_p$, and ${\widehat{\mathbf{R}}}_p$ represent the estimated trend, seasonal, and residual components, respectively.

3. Study Area and Dataset

The study area is the Baorixile open-pit coal mine, located in Chen Barag Banner, Hulunbuir City, Inner Mongolia, China, with approximate geographic coordinates approximately $49.{35}^{\circ }$ N ∼$49.{44}^{\circ }$ N and $119.{63}^{\circ }$ E ∼$119.{79}^{\circ }$ E (Figure 2). The mining area covers 43.7151 km², with total proven reserves of approximately 1.622 billion tonnes, an annual production capacity of 35 million tons, and an average stripping ratio of 3.22 m³/t, ranking it among the largest modern open-pit coal mines in China. Mining activities have caused significant surface disturbances, exerting substantial impacts on the surrounding hydrogeological and ecological systems, including groundwater level decline, the formation of erosion gullies in drainage areas, and the degradation of grassland vegetation [53]. The surface is predominantly covered by natural grasslands and exposed soil, with few man-made structures, indicating that DS targets dominate the scattering characteristics. Consequently, the DS-InSAR technique is employed to optimize DS targets and enhance phase stability, while the SBAS-InSAR technique is integrated to suppress temporal and spatial decorrelation and increase redundant observations, thereby ensuring the reliability of the deformation monitoring results.

Sentinel-1, developed under the Copernicus Programme (formerly GMES) of the European Space Agency (ESA), is an Earth observation satellite equipped with a C-band synthetic aperture radar capable of acquiring continuous imagery in all-weather, day and night conditions [54]. The satellite employs orbit maintenance with controlled separation, ensuring precise ground-track repeatability and short InSAR baselines. The Terrain Observation with Progressive Scans (TOPS) mode enables the acquisition of high-quality imagery while preserving pixel resolution [55].

48 Sentinel-1 images acquired between 3 March 2017 and 23 April 2021 were used to derive surface deformation in the study area, with acquisition parameters listed in

Table 1. Detailed parameters of the acquired SAR datasets.

Parameter	Value
Path	149
Frame	428
Azimuth angle	194.80 (degrees)
Incidence angle	39.21 (degrees)
Pixel spacing in slant range	2.33 (m)
Pixel spacing in azimuth	13.90 (m)
Wavelength	5.55 (cm)
Acquisition time	22:09 UTC

. The SAR imagery was downloaded from the National Aeronautics and Space Administration (NASA) [56], while the corresponding precise orbit data were obtained from the European Space Agency [57] to correct orbital errors. The external reference DEM was the Shuttle Radar Topography Mission (SRTM) dataset [58,59] with a resolution of 30 m, used to remove topographic and flat-earth phases. In the SBAS-InSAR process, interferograms were formed using spatial and temporal baseline thresholds of 200 m and 120 days, yielding 182 interferograms in total, as shown in Figure 3. In the SBAS-DS-InSAR workflow, an SHP-count threshold of 15 was adopted to separate PS and DS, and the DS pixels were then processed using DS-phase optimization.

4. Results and Discussion

4.1. Time-Series Deformation Monitoring Results

In this study, both SBAS-InSAR and SBAS-DS-InSAR techniques were used to derive ground deformation in the study area (Figure 4). As shown in Figure 4a, the SBAS-InSAR results comprise only 1055 monitoring points, with deformation rates ranging from −18.33 to 34.50 mm/year. Most of these points are located on man-made structures such as roads and buildings, whereas bare land and farmland areas contain few valid measurements. This indicates that although SBAS-InSAR, by constructing a small spatial-temporal baseline network, can partially suppress spatial and temporal decorrelation by constructing a small spatiotemporal baseline network, it remains limited in low-coherence areas and cannot provide complete surface deformation coverage in the mining area.

In contrast, SBAS-DS-InSAR incorporates a DS-phase optimization approach based on SBAS-InSAR, substantially increasing the spatial density of monitoring points. A total of 338,555 points were obtained, an ≈321-fold increase over SBAS-InSAR (Figure 4b), with deformation rates ranging from −12.96 to 7.52 mm/year. As evident in Figure 4a, the points with high deformation rates detected by SBAS-InSAR tend to be spatially isolated, indicating a higher likelihood of phase unwrapping errors and lower reliability. Fortunately, SBAS-DS-InSAR produces a more spatially uniform distribution without pronounced isolated points, indicating greater stability and reliability.

To further assess the consistency between the two techniques, a correlation analysis was performed using the common high-quality monitoring points, i.e., all SBAS-InSAR points (Figure 5). As shown in Figure 5a, the results show a strong correlation, with a correlation coefficient of 0.97. Linear regression analysis yields a slope of 0.88, slightly below unity, indicating generally consistent measurements at the same locations from both methods. The distribution of deformation-rate differences for the same monitoring points (Figure 5b) shows a mean of −0.093 mm/yr and a standard deviation of 3.28 mm/yr, implying no systematic bias between the two techniques and supporting their consistency, thus further confirming the validity of both results. Importantly, the accuracy of SBAS-InSAR has been extensively demonstrated in previous studies [34], so using all SBAS points as the common set ensures both the representativeness and reliability of the comparison. Overall, SBAS-DS-InSAR achieves a substantial increase in monitoring point density while maintaining accuracy, greatly enhancing the spatial coverage and reliability of deformation monitoring. This capability is of significant value for dynamic monitoring and early warning in open pits.

From the deformation results derived by SBAS-DS-InSAR, two major deformation zones were delineated (Figure 6). In Area I, the spatial extent of subsidence, as interpreted from optical imagery, closely follows the alignment of transportation routes. Although there is no formally constructed road on the northern side of this area, distinct vehicle tracks are visible in the optical images (indicated by the blue line in Area I), suggesting that repeated vehicular traffic has left clear surface traces. These observations suggest that subsidence here is primarily attributable to ground compaction from frequent vehicle traffic. During the monitoring period, no significant mining activity was observed in Area II; however, excavation began afterward. This suggests that preliminary site preparation—such as topsoil removal, temporary road construction, or site leveling—may have been carried out prior to active mining, resulting in a slight subsidence. Overall, these results demonstrate that most subsidence within the study area is directly or indirectly associated with open-pit mining activities, including active excavation, mining-related transportation, and pre-excavation site preparation.

4.2. Time-Series Deformation Decomposition Results

Figure 7 shows the trend rate, periodic amplitude, and residual from the proposed TPRSCR across all SBAS-DS-InSAR monitoring points. From Figure 7a, the long-term trend deformation rates range from −14.03 to 14.22 mm/year and exhibit an approximately normal distribution, indicating that the extents of subsidence and uplift areas are generally comparable. The spatial distribution of long-term subsidence closely matches the SBAS-DS-InSAR results, suggesting that the long-term trend is strongly influenced by transportation activities associated with open-pit mining. As highlighted by the blue circles in Figure 7b, the periodic deformation amplitudes are markedly higher along pit slopes, dumping sites, and along the edges of local subsidence basins. These periodic signals are likely driven by environmental factors such as seasonal freeze-thaw cycles that cause soil expansion and contraction, rainfall infiltration that leads to groundwater level fluctuations, and soil softening. In the northern part of the mining area, periodic amplitudes are superimposed on the long-term subsidence trend, resulting in areas that experience sustained subsidence and pronounced seasonal deformation, which can increase the risk of slope instability and pose engineering-safety risks. Regarding the residual component, the spatial map at the final epoch (i.e., 23 April 2021), as shown in Figure 7c, is largely near zero and spatially patchy, indicating noise-dominated behavior in most areas. However, several localized anomalies, highlighted by the orange circle, occur near slope benches and to the south of the mine. These features are likely associated with lower coherence and geometric distortions (e.g., layover/foreshortening). Consistently, as shown in Figure 7d, the residuals aggregated across all epochs have a mean of 0.00 mm and a standard deviation of 6.61 mm, approximating a zero-centered normal distribution. This supports the interpretation that the residual component is primarily random noise. In addition, as Areas A and B of Figure 7a, the long-term trend deformation is significantly greater than that measured by SBAS-DS-InSAR, whereas the opposite pattern is observed in Area C.

For further insight, decomposition was performed for P3–P5 (Areas A–C) and P1– P2 in the northern mining area (Figure 8). As shown in Figure 8, P1 within the mining-affected zone shows a pronounced subsidence trend, while P2, weakly impacted by mining, exhibits a minor uplift. P3 and P4 have near-zero linear trends, but display large periodic deformation amplitudes that gradually decrease over time. This suggests that, during the early monitoring stage when mining activities were limited, the soils were more susceptible to periodic deformation induced by expansion–contraction and groundwater level fluctuations. As mining and vehicular activities increased, soil compaction reduced the influence of periodic factors. P5 exhibits a persistent subsidence trend, the cause of which has been previously discussed.

As illustrated in Figure 8b, amplitudes differ across locations, but the periods and profiles are almost identical, implying a uniform source of periodic deformation throughout the area. These results demonstrate that the proposed TPRSCR method can effectively separate the individual components of time-series deformation, thereby providing clearer insights into the underlying deformation mechanisms and their causes.

4.3. Correlation Analysis Between Periodic Deformation and Precipitation

The maximum periodic deformation amplitude in this area reaches up to 40 mm (Figure 7b). This indicates that understanding the drivers of periodic deformation is important for interpreting surface deformation mechanisms and issuing early warnings for mining-induced deformation. Therefore, the monthly averaged skin temperature and the monthly averaged precipitation during the monitoring period were obtained covering April 2017 to July 2020 from the Copernicus Climate Data Store (https://cds.climate.copernicus.eu), with a spatial resolution of 0.1°. The relationships between periodic deformation, monthly averaged skin temperature, monthly averaged precipitation, and monthly averaged soil moisture are shown in Figure 9.

From Figure 9, it is evident that periodic deformation is correlated with precipitation, air temperature, and soil moisture at multiple depths. Specifically, rainfall pulses are followed by rapid increases in 0∼7 cm and 7∼28 cm soil moisture and coincide with short-term surface uplift, as shown in Figure 9b, indicating precipitation-driven near-surface swelling that amplifies seasonal amplitudes. In contrast, the 28∼100 cm soil-moisture series exhibits a delayed, lower-magnitude response relative to the surface layers. Consequently, its contribution to the observed deformation is minor. The skin temperature remains strongly periodic and leads to deformation by ∼34 days, consistent with slower thermo-elastic responses of the ground column. These results demonstrate that precipitation, near-surface soil moisture, and temperature are the dominant drivers of periodic deformation in the study area, and their combined effects significantly influence the temporal patterns and amplitude of surface deformation.

4.4. Comparison with Existing Methods

As ground-based observations were unavailable during the study period, we assessed the performance of the proposed TPRSCR by conducting a comparison with STL on the same LOS time-series deformation and by performing a controlled simulation experiment. The STL method was applied to the same time-series deformation data from the study area, and the decomposition results for representative monitoring points P1-P5 are presented in Figure 10. The STL method can separate the long-term trend and periodic deformation components to some extent. However, owing to the complex periodic behavior of the deformation, seasonal energy leaks into the trend component, as shown in Figure 10b. In contrast, the proposed TPRSCR algorithm integrates polynomial trend modeling with multiharmonic (Fourier) decomposition and introduces a slow seasonal-amplitude drift model, effectively suppressing the leakage of periodic components. These results demonstrate the superior applicability, robustness, and interpretability of the proposed method for decomposing surface deformation in open-pit mining environments.

Furthermore, a simulation experiment was conducted to quantitatively compare the performance of TPRSCR and STL. Specifically, a linear function was used to simulate the long-term trend, a sine–cosine superposition model was adopted to represent periodic deformation, and 20 mm of additive random noise was added. As shown in Figure 11, the STL algorithm exhibits significant “periodic leakage”, while TPRSCR effectively suppresses this effect. As shown in

Table 2. Comparison of component RMSEs for different methods (mm).

Method	Total	Trend	Periodic	Residual
TPRSCR	4.9	0.65	12.9	1.35
STL	9.6	9.74	12.54	9.37

, the root mean square errors (RMSE) of the total, trend, and periodic component of TPRSCR are 4.90 mm, 0.65 mm, and 1.29 mm, respectively, outperforming the corresponding STL values of 9.60 mm, 9.74 mm, and 12.54 mm, representing improvements of 48.96%, 93.33%, and 89.71%, respectively. These results confirm that the TPRSCR algorithm substantially improves the precision and robustness of time-series deformation decomposition in complex mining environments and provides a more reliable technical basis for deformation mechanism analysis and risk assessment in mining areas.

4.5. Sensitivity Analysis

To assess how observation noise and periodic deformation amplitude affect the decomposition accuracy of the proposed TPRSCR, we generated a synthetic LOS deformation time-series by combining (i) a linear trend (slope = 0.5 m), (ii) a sine–cosine superposition model to represent periodic deformation with randomly perturbed drift, and (iii) zero-mean Gaussian noise. For the noise experiment, the noise standard deviation $\sigma$ was varied from 0 to 1 m in increments of 0.01 m. For the periodic-amplitude experiment, the periodic amplitude increased from 0 to 5 m in increments of 0.05 m while the noise was fixed at $\sigma$ = 0.2 m. For each setting, we applied TPRSCR to recover the trend, periodic, and residual components and computed the component-wise RMSEs against the corresponding simulated (ground-truth) components.

Figure 12 shows an approximately linear relationship between the observation-noise level and the RMSEs of the three recovered components. Linear regressions yield slopes of 0.4014 (trend), 0.5314 (periodic), and 0.6815 (residual). On average, the RMSEs of the trend, periodic, and residual components correspond to about 16.39%, 25.35%, and 31.20% of the input-noise RMSE, respectively. This indicates an accuracy ranking of trend > periodic > residual and highlights that observation noise is the primary factor governing the decomposition accuracy.

Figure 13 shows sensitivity to periodic amplitude (noise fixed at $\sigma$ = 0.2 m). Although the periodic amplitude increases, the RMSEs of the trend, periodic, and residual components exhibit only modest fluctuations without systematic degradation. Thus, increasing the periodic amplitude does not materially degrade the accuracy of the TPRSCR. The average component RMSEs are 0.0715 m (trend), 0.1124 m (periodic), and 0.1376 m (residual), corresponding to 15.83%, 24.92%, and 30.49% of the observation-noise level, respectively—values that closely match those from the noise experiment, thus corroborating its conclusions.

Across a wide range of noise levels and periodic amplitudes, TPRSCR maintains low cross-component leakage and stable component estimates, with performance degrading gracefully only as noise increases. These results confirm that observation noise dominates the error budget, whereas periodic-amplitude variability has a limited impact on decomposition accuracy.

5. Conclusions

In this study, SBAS-DS-InSAR and TPRSCR were integrated to monitor and interpret surface deformation at the Baorixile open-pit coal mine. High-quality line-of-sight (LOS) deformation was derived using SBAS-DS-InSAR throughout the mine, and the time-series was subsequently decomposed with TPRSCR into long-term trend, seasonal variability, and residual components for mechanism-oriented analysis.

Operationally, DS-phase optimization increased the number of high-quality monitoring points from 1055 (SBAS-InSAR) to 338,555 (≈321-fold), greatly improving spatial coverage in low-coherence areas. The deformation rates at the common points showed strong consistency between SBAS-InSAR and SBAS-DS-InSAR ($R^2$ = 0.97), supporting the reliability of the SBAS-DS-InSAR results. Methodologically, TPRSCR—combining a polynomial trend with multiharmonic terms (Fourier) and an explicitly modeled, slowly drifting seasonal amplitude—suppresses seasonal-to-trend leakage observed with STL. In simulation tests, TPRSCR achieves lower RMSEs for the total, trend, and periodic components (4.90, 0.65, 1.29 mm) than STL (9.60, 9.74, 12.54 mm), corresponding to improvements of 48.96%, 93.33%, and 89.71%, respectively. These results translate into cleaner components and more defensible interpretations for real monitoring points.

The deformation field is jointly controlled by mining operations and environmental forcing. The study area exhibits a superimposed pattern of persistent subsidence and strong seasonality. Two major subsidence zones were identified: one linked to ground compaction from transportation activities and the other associated with pre-mining site preparation. The periodic amplitudes show strong correlations with precipitation and temperature, with an approximately 34-day lag relative to the temperature cycle. This indicates that precipitation directly drives near-surface soil swelling, while temperature regulates soil behavior over longer timescales through thermo-elastic effects.

This study establishes an integrated “monitoring–decomposition–interpretation” framework, enhancing the precision and interpretability of deformation monitoring in open-pit mines. It provides operational support for slope stability assessment, transportation management, and early warning of hazards. However, two limitations remain. First, the analysis is limited to the LOS deformation, and the full 3D deformation was not recovered. Second, ground-based validation (e.g., leveling/GNSS) was not available during the study period. Future work will integrate ascending-descending SAR data with GNSS/leveling to obtain high-precision 3D deformation. Higher-resolution DEMs (e.g., UAV-LiDAR) and additional hydrothermal indicators (e.g., freeze-thaw metrics) will be explored to further reduce residuals and refine attribution.