SBAS-InSAR-Based Monitoring and Hierarchical Spatiotemporal Deep Learning for Subsidence Monitoring and Prediction in Active Mining Areas: A Case Study of the Dexing Copper Mine

Highlights

What are the main findings?

• Surface subsidence exhibits marked spatial heterogeneity and pronounced temporal nonlinearity, with the most severe deformation localized within active open-pit mining zones and waste rock dumps, with the maximum subsidence rate reaching −126.121 mm/yr. Precipitation and soil moisture serve as the dominant driving factors—exhibiting statistically significant lagged effects, whereas temperature acts mainly as a modulating variable.
• The integrated framework, combining SBAS-InSAR-derived surface displacement time series with the hierarchical spatiotemporal dependency graph neural network (HSDGNN), achieves millimeter-level predictive accuracy, evidenced by a maximum R² of 0.995.

What are the implications of the main findings?

• The integration of SBAS-InSAR-derived displacement time series with the hierarchical spatiotemporal dependency graph neural network (HSDGNN) establishes a scalable, high-precision framework for large-area subsidence monitoring and forecasting in complex mining environments, thereby substantially enhancing spatiotemporal modeling fidelity under heterogeneous geological and hydrological conditions.
• By explicitly quantifying the dominant influence of hydrological drivers (precipitation and soil moisture) and delivering robust short-to-medium-term forecasts, the framework enables data-informed risk assessment and proactive early warning for mining-induced ground instability. Its methodological architecture is also transferable to other geomechanical hazards.

Abstract

Intensive mining over recent decades has caused severe ground subsidence in mining regions, threatening safety and long-term sustainability. High-precision, continuous monitoring and prediction of subsidence are therefore urgently needed. Traditional methods—terrestrial surveying and GPS—offer limited coverage, sparse measurement points, high costs, and poor scalability, making them unsuitable for large-scale, long-term surface deformation monitoring. InSAR is widely used for ground deformation monitoring due to its wide-area coverage, long-term sampling, high spatial resolution, and millimeter-scale precision. However, conventional InSAR often fails in vegetated areas and under steep deformation gradients—common in mining zones. To overcome these limitations, this study applied SBAS-InSAR, a method better suited for large-magnitude, continuous subsidence monitoring in mining areas. This study proposed an enhanced hierarchical spatiotemporal dependency graph neural network (HSDGNN) integrated with a Long Short-Term Memory (LSTM) module to improve temporal feature representation. Using this model, this study predicted surface subsidence at the Dexing Copper Mine under environmental drivers. Key findings are as follows: (1) Surface subsidence exhibited pronounced spatial heterogeneity and strong temporal nonlinearity; major subsidence zones were localized in open-pit excavation areas and waste rock dumps, with peak subsidence rates reaching −126.121 mm/yr. (2) Precipitation and soil moisture emerged as the dominant environmental controls on subsidence, displaying distinct seasonal modulation and quantifiable lagged responses—up to several months—relative to subsidence onset. (3) The HSDGNN model achieved high predictive accuracy for both Mine 1 and Mine 2, attaining R² values of up to 0.9950. This work establishes a robust, scalable, and operationally viable framework for high-precision subsidence monitoring and forecasting in geologically and anthropogenically complex mining environments.

1. Introduction

With the ongoing intensification of global mineral resource extraction, mining-induced ground subsidence has emerged as a critical geological hazard, posing significant threats to mining safety, regional ecological integrity, and infrastructure resilience [1,2,3]. In large-scale open-pit and underground mining zones, surface deformation typically manifests through prolonged temporal accumulation, marked spatial heterogeneity, and nonlinear evolutionary patterns over time—factors that may precipitate secondary hazards, including structural damage to engineered facilities [4,5]. Consequently, sustained monitoring and high-accuracy prediction of surface subsidence are essential for safeguarding operational safety in mining activities and enabling proactive, science-based geological hazard risk mitigation [6].

Conventional surface deformation monitoring primarily depends on terrestrial surveying techniques—including precise leveling, theodolite-based angular measurements, and total station observations—to acquire in situ deformation data within designated monitoring networks [7,8]. Periodic surveys are typically conducted using trigonometric leveling and horizontal/vertical angle measurements, with deformation parameters subsequently derived through rigorous post-processing and geodetic adjustment [9]. While these methods deliver high point-wise measurement accuracy, they suffer from significant operational constraints: labor-intensive fieldwork, low temporal efficiency, and inherently limited spatial sampling density, rendering them unsuitable for sustained, regional-scale ground subsidence monitoring [10,11].

Prior studies have utilized Differential Interferometric Synthetic Aperture Radar (D-InSAR) to extract surface deformation signals via two-pass interferometric analysis and subsequent geodetic inversion [12]. However, conventional D-InSAR remains constrained by several inherent limitations, including temporal and spatial decorrelation, atmospheric phase delay, and errors in the digital elevation model (DEM) used for topographic phase removal [10]. In contrast, Persistent Scatterer InSAR (PS-InSAR) enables stable, continuous, millimeter-scale monitoring of slow surface deformation across extensive regions, while substantially mitigating temporal decorrelation and atmospheric artifacts [13]. Integrated with in situ geodetic observations, PS-InSAR has been extensively applied to urban subsidence monitoring [14]. Nonetheless, its performance is critically dependent on the presence of spatially persistent radar scatterers; consequently, it often yields sparse spatial sampling and diminished deformation characterization fidelity, particularly in non-urban, low-coherence, or heavily vegetated terrains [15].

Small Baseline Subset Interferometric Synthetic Aperture Radar (SBAS-InSAR) is a well-established InSAR method for large-scale, high-precision surface deformation monitoring, especially in mining areas [16]. It uses small temporal and spatial baselines to suppress coherence loss, geometric decorrelation, orbital errors, and atmospheric phase delay [17]. This enables reliable retrieval of continuous deformation velocity fields and cumulative subsidence time series [18]. Unlike many InSAR techniques, SBAS-InSAR works well over vegetated terrain, exposed bedrock, and waste rock piles, requiring no dense, stable scatterers [19,20,21]. Its robustness across heterogeneous, dynamically changing surfaces makes it ideal for subsidence monitoring, mechanism analysis, environmental coupling studies, and deep learning-based prediction [22].

In addition, traditional empirical and physics-based models work well for subsidence in simple geological settings, but their reliance on rigid assumptions and fixed parameters limits applicability in complex, dynamic mining environments [23]. Machine learning and deep learning methods better capture nonlinearities and temporal evolution in InSAR-derived subsidence time series [24]. XGBoost (eXtreme Gradient Boosting) is a scalable, tree-based ensemble learning algorithm grounded in gradient-boosted decision trees [25]. It has been widely adopted for regression and time-series forecasting in environmental science and geoscience applications. XGBoost effectively captures nonlinear relationships, accommodates high-dimensional and heterogeneous datasets, and produces temporally and spatially continuous predictions [26]. These capabilities render it especially suitable for reconstructing multi-depth soil temperature and moisture fields, enabling environmental drivers to align closely with the temporal and spatial patterns of surface subsidence [27]. Consequently, XGBoost significantly improves the accuracy of subsidence prediction models and strengthens comprehensive mining monitoring capabilities [28]. Yet most studies still model only single points, ignoring spatial dependencies among monitoring locations [29]. Environmental drivers—precipitation, soil moisture, and temperature—strongly affect subsidence evolution, but integrating them is hindered by incompatible, incomplete, and heterogeneous data. Consequently, models lack generalization ability and stability in real-world mining conditions [30,31]. A unified predictive framework is needed: one that jointly models spatiotemporal subsidence patterns and fuses environmental data, directly tackling weak spatial representation and accuracy loss from environment-driven nonlinearity.

This study addresses three key challenges: (1) conventional interferometric methods struggle to deliver continuous, high-fidelity deformation data in complex mining environments; (2) multi-source environmental datasets suffer from mismatched spatiotemporal resolutions and missing values; and (3) existing models fail to capture dynamic spatial dependencies among monitoring points or integrate environment-driven nonlinear subsidence responses. This research includes: (1) applying SBAS-InSAR to quantify subsidence rates and reconstruct time-resolved deformation trajectories at the Dexing Copper Mine; (2) integrated precipitation, air temperature, and multi-depth soil moisture and temperature, using XGBoost-enhanced spatiotemporal interpolation to fill missing soil thermo-hydrological data for driver analysis and response pattern identification; and (3) proposed a Hierarchical Spatiotemporal Dependency Graph Neural Network (HSDGNN) that jointly models spatial topology and temporal dynamics to improve the prediction accuracy and physical interpretability of mining-induced subsidence.

2. Materials and Methods

2.1. Study Area

The Dexing Copper Mine (Figure 1) lies in the northeastern Huaiyu Mountains, Jiangxi Province, China [32]. Its terrain is highly dissected, dominated by low mountains and hills, with elevation changing sharply over short distances. The area has a subtropical humid monsoon climate: mean annual temperature 17–18 °C; precipitation 1800–2000 mm, concentrated April–September. Temperature varies markedly both year-to-year and within each year. Geologically, it sits at the tectonically active Yangtze–Cathaysia suture zone, marked by widespread faulting and rock mass disruption [33]. The bedrock consists mainly of granite, porphyry, and hydrothermally altered variants, locally covered by Quaternary sediments. Decades of open-pit mining have substantially degraded the structural integrity of the mine slope, rendering it highly susceptible to gravity-driven subsidence and deformation induced by rainfall infiltration and thermal cycling.

The stratigraphy of the mining area comprises several distinct lithological units, arranged vertically from surficial to deep (Figure 2). The uppermost unit consists of quaternary unconsolidated deposits—typically thin, loose, and highly compressible. Underlying this is a weathered rock zone, characterized by pervasive fracturing and localized brecciation. At greater depth lies a massive granite unit exhibiting high uniaxial compressive strength; however, it is intersected by fault zones that induce stress concentrations and generate interconnected fracture networks. As indicated by red dashed lines in the figure, these fault zones delineate the complex structural architecture of the ore body, serving as critical pathways for deep stress redistribution triggered by mining activities, and thereby contributing to surface subsidence.

2.2. Data Sources and Processing

2.2.1. Sentinel-1 Data

Sentinel-1 is an ESA Earth observation satellite launched in April 2014 (

Table 1. Parameters of the Sentinel-1 data.

Parameter	Value
Radar band	C-band
Acquisition period	6 January 2022–21 December 2024
Orbit direction	Ascending
Revisit cycle	12 days
Spatial resolution	5 × 20 m
Polarization	VV
Imaging mode	Interferometric Wide Swath (IW)
Number of images	100
Temporal baseline threshold	180 d

). It carries a C-band SAR sensor that operates day and night, regardless of clouds, rain, or darkness, with a spatial resolution of up to 5 m. Its sun-synchronous orbit provides 12-day revisit over mid-latitudes—ideal for monitoring surface change over time. Compared to optical sensors, Sentinel-1 excels in geohazard assessment, millimeter-scale deformation mapping, and long-term environmental monitoring. It supports multiple imaging modes, including Stripmap (SM), Interferometric Wide Swath (IW), and Extra Wide Swath (EW)—as well as multiple polarization configurations, such as vertical transmit–vertical receive (VV) and vertical transmit–horizontal receive (VH), enabling both wide-area coverage and high-resolution analysis. Its precise orbits and stable imaging geometry make it well suited for SBAS-InSAR, which is widely used for detecting earthquakes, landslides, subsidence, and volcanic activity. This study utilized 100 ascending-orbit Sentinel-1A SLC images, including 64 images from Path 142 and 36 images from Path 40, covering Dexing City, acquired from 6 January 2022 to 21 December 2024. All data were downloaded from the European Space Agency (ESA) Copernicus Open Access Hub through the Alaska Satellite Facility (ASF) Vertex search interface (https://search.asf.alaska.edu/).

2.2.2. Precise Orbit Data

Precise Orbit Ephemerides (POE) provide high-accuracy satellite position and velocity data to correct orbit-induced phase errors in InSAR processing. Because InSAR phase is sensitive to path length changes, even sub-centimeter orbit errors can bias deformation measurements, making millimeter-level orbital precision essential. This study uses ESA’s Precise Orbit Determination (POD) products to refine the orbital metadata of all Sentinel-1A SAR images prior to interferogram formation. The POE files—accurate to better than 5 cm in 3D position—were downloaded from the ASF Sentinel-1 Quality Control Archive (https://sentinels.copernicus.eu).

2.2.3. DEM Data

The Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Global Digital Elevation Model (GDEM), jointly developed by National Aeronautics and Space Administration (NASA) and Japan Aerospace Exploration Agency (JAXA), provides global 30 m resolution elevation data (https://earthdata.nasa.gov/). It is generated from stereo optical and thermal infrared imagery acquired by the ASTER sensor on NASA’s Terra satellite. Validated across diverse terrain types, GDEM has a vertical accuracy of ±20 m (LE90). Its global coverage, consistent georeferencing, and 30 m resolution make it widely used for geomorphology, hazard assessment, land use planning, hydrology, and slope analysis. In InSAR, it is commonly applied to remove topographic phase, especially when higher-resolution DEMs are unavailable.

2.2.4. Multi-Source Environmental Factor Data

To enable accurate construction of a predictive model for surface subsidence in mining areas, this study collected and reconstructed multi-source environmental factor data, including precipitation, surface air temperature, soil temperature, and volumetric soil moisture. Precipitation and surface air temperature data were obtained from the National Oceanic and Atmospheric Administration (NOAA, https://www.noaa.gov/), covering the period from January 2022 to December 2024, with monthly temporal resolution and broad spatial coverage across the study region. Soil temperature and volumetric soil moisture data at 0–40 cm depth were acquired from the Land Data Assimilation System jointly maintained by NASA and FEWS NET (FLDAS, https://ldas.gsfc.nasa.gov), providing gridded, depth-resolved hydrometeorological observations with high spatial and temporal resolution.

3. Research Methods

Figure 3 illustrates the methodological workflow of this study, encompassing sequential phases: data acquisition, preprocessing, and deep learning-driven predictive modeling.

3.1. SBAS-InSAR Technique

SBAS-InSAR is a multi-temporal InSAR method for estimating surface displacement at millimeter-scale accuracy over time. It selects SAR image pairs with small temporal (≤120 days) and perpendicular (≤400 m) baselines to minimize decorrelation and noise. After co-registration, differential interferogram generation, and phase unwrapping, the phase data are inverted using Singular Value Decomposition (SVD) or least-squares estimation to separate deformation from atmospheric delay, orbital errors, and topographic residuals, yielding ground velocity maps and displacement time series. Based on its high precision, dense temporal sampling, and robustness to decorrelation, SBAS-InSAR is widely used for urban subsidence, landslide motion, coseismic/postseismic deformation, and infrastructure stability monitoring. Baseline thresholds are set based on coherence in the study area. Deformation is extracted primarily from unwrapped interferometric phases, and the final inversion provides both velocity and full displacement time series.

Assuming that N + 1 SAR images are acquired over the same area with a specific observation time sequence of $T_0,T_1,\dots ,T_n$. After applying the spatiotemporal baseline threshold constraints, $M$ interferometric pairs are generated through interferometric processing. The number of interferometric pairs $M$ satisfies the following relationship.

$${\displaystyle \frac{(N+1)}{2}}\le M\le {\displaystyle \frac{N(N+1)}{2}}$$

(1)

For the M interferometric pairs, the phase differences in the corresponding pixels are calculated to obtain the differential interferometric phases $\delta {\varphi }_k(k=1,2,3,\dots ,M)$. If all interferograms satisfy the required quality conditions and are correctly phase-unwrapped, and if the effects of atmospheric delay, topographic variation, and surface deformation are neglected, the differential phase of any pixel $(x,r)$ in the $k$-th interferogram can be expressed as:

$$\delta {\varphi }_K(x,r)=\varphi (t_B,x,r)-\varphi (t_A,x,r)\approx {\displaystyle \frac{4\pi }{\lambda }}\left[d(t_B,x,r)-d(t_A,x,r)\right]$$

(2)

where $\lambda$ denotes the radar wavelength $d(t_A,x,r)$, and $d(t_B,x,r)$ represent the line-of-sight (LOS) surface deformation of pixel $(x,r)$ at acquisition times $t_A$ and $t_B$, respectively, relative to the reference epoch $t_0$.

Assume that the master image sequence $I_E=\left[I_{E1},\dots ,I_{\mathrm{EM}}\right]$ and the slave image sequence $I_S=\left[I_{S1},\dots ,I_{\mathrm{SM}}\right]$ have been arranged according to their acquisition times, the observation equations for the $M$ differential interferograms can be expressed as follows:

$${\mathit{IE}}_k>{\mathit{IS}}_k,\forall k=1,\dots ,M$$

(3)

$$I\delta {\varphi }_k=\varphi (t_{{\mathit{IE}}_K})-\varphi (t_{{\mathit{IS}}_K}),\forall k=1,\dots ,M$$

(4)

Equation (4) represents a system of $M$ observation equations with N unknown variables, which can be expressed as follows.

$$\delta \varphi =A\varphi$$

(5)

When $R(A)<N$, the rank of the corresponding normal equation coefficient matrix $A^{T}A$ becomes deficient. In this formulation, the linear system is SVD, a numerically stable least-squares method widely adopted in multi-temporal InSAR inversion for its robustness to ill-conditioning and noise.

This study utilized a total of 100 Sentinel-1 SAR images acquired over the study area. An interferometric network was established based on a temporal baseline threshold of 180 days to ensure sufficient coherence for reliable phase estimation. To enhance the signal-to-noise ratio (SNR) of the interferometric phase, multi-looking was applied with an azimuth-to-range sampling ratio of 4:1. Geocoding was performed using the ASTER GDEM, with all outputs referenced to the World Geodetic System 1984 (WGS84) coordinate system. Pixel-wise estimates of mean vertical subsidence velocity and cumulative displacement time series were subsequently derived.

3.2. XGBoost Model

XGBoost is a scalable, regularized gradient boosting framework built upon the gradient boosting decision tree (GBDT) paradigm [34]. It enhances predictive accuracy and generalization through second-order Taylor expansion of the loss function, L2-regularized objective, learning-rate shrinkage, and column subsampling—features that collectively mitigate overfitting and improve robustness to noise and feature redundancy. In this study, XGBoost was implemented to develop a hierarchical cascading model for estimating soil temperature and volumetric water content at depths of 0–40 cm. The objective function of XGBoost consists of two components: the empirical loss term, which measures the discrepancy between predicted and observed values, and the regularization term, which controls model complexity. The objective function can be expressed as follows:

$$(\theta )={\displaystyle {\displaystyle \sum _{i=1}^n}l(y_i,{\hat{y}}_i)}+{\displaystyle {\displaystyle \sum _{k=1}^k}\Omega (f_k)}$$

(6)

where $l(·)$ denotes a differentiable loss function, $f_k$ represents the $k$ regression tree, and $\Omega (f_k)$ is the regularization term of the tree structure, which is used to control model complexity and prevent overfitting. This regularization term incorporates components such as the number of terminal nodes and the squared L2 norm of leaf scores, thereby penalizing model complexity. It is formally defined as:

$$\Omega (f_k)=\gamma {\rm T}+{\displaystyle \frac{1}{2}}\lambda {\displaystyle \sum _{j=1}^{{\rm T}}{w}_j^2}$$

(7)

where $\Omega (f_k)$ denotes the regularization term of the $k$ decision tree; $T$ represents the total number of leaf nodes in the tree; $\gamma$ is the penalty coefficient controlling the complexity of the tree structure, which is used to suppress excessive node splitting; $\lambda$ denotes the L2 regularization coefficient applied to leaf node weights; and $w_j$ represents the weight value of the $j$ leaf node.

To improve computational efficiency, XGBoost applies a second-order Taylor expansion to the objective function. Consequently, the optimization form of the objective function at the $t$ iteration can be written as:

$$L^{(t)}\simeq {\displaystyle \sum _{i=1}^n\left[g_i{f}_t(x_i)+\frac{1}{2}{h}_i{f}_t^2(x_i)\right]+}\Omega (f_t)$$

(8)

where $L^{(t)}$ denotes the objective function of the model at the $t$ iteration; $n$ represents the total number of training samples; $g_i$ denotes the first-order gradient of the loss function with respect to the prediction of sample $i$; $h_i$ represents the second-order gradient (Hessian) of the loss function; $f_t(x_i)$ denotes the prediction output of the $t$ decision tree for sample $x_i$; and $\Omega (f_t)$ represents the regularization term used to control the complexity of the tree model and prevent overfitting.

$$g_i={\displaystyle \frac{\partial l(y_i,{\hat{y}}_i^{(t-1)})}{\partial {\hat{y}}_i}},h_i={\displaystyle \frac{{\partial }^{2}l(y_i,{\hat{y}}_i^{(t-1)})}{\partial {\hat{y}}_i^2}}$$

(9)

where $g_i$ and $h_i$ denote the first-order and second-order gradients of the loss function $l(·)$ with respect to the prediction ${\hat{y}}_i^{(t-1)}$ at iteration $t-1$, respectively. Here, $x_i$ is the feature vector of the $i$ training instance, $f_t(x_i)$ represents the output of the $t$ regression tree for $x_i$, and $\Omega f_t$ is the regularization term controlling the complexity of the tree.

If the set of leaf nodes in the tree is denoted by $J$, the optimal weight of each leaf node can be calculated as:

$$w_j^{*}=-{\displaystyle \frac{{\displaystyle {\sum }_{i\in I_j}{g}_i}}{{\displaystyle {\sum }_{i\in I_j}{h}_i+\lambda }}}$$

(10)

The corresponding optimal split gain can be expressed as:

$$L_{\mathit{split}}={\displaystyle \frac{1}{2}}\left[{\displaystyle \frac{{\left({\displaystyle {\sum }_{i\in I_L}{g}_i}\right)}^2}{{\displaystyle {\sum }_{i\in I_L}{h}_i+\lambda }}}+{\displaystyle \frac{{\left({\displaystyle {\sum }_{i\in I_R}{g}_i}\right)}^2}{{\displaystyle {\sum }_{i\in I_R}{h}_i+\lambda }}}-{\displaystyle \frac{{\left({\displaystyle {\sum }_{i\in I}{g}_i}\right)}^2}{{\displaystyle {\sum }_{i\in I}{h}_i+\lambda }}}\right]-\gamma$$

(11)

where $L_{\mathit{split}}$ denotes the gain of a candidate split in the decision tree; $I_L$ and $I_R$ represent the sample sets of the left and right child nodes after splitting, respectively; $g_i$ denotes the first-order gradient of the loss function with respect to the prediction of sample $i$; $h_i$ represents the second-order gradient (Hessian) of the loss function; $\lambda$ is the regularization parameter used to control model complexity and prevent overfitting; and $\gamma$ denotes the minimum loss reduction required for node splitting. This gain metric quantifies the improvement in objective function reduction conferred by a candidate split and serves as XGBoost’s primary splitting criterion. The input features fall into the following categories:

(1) Temporal features

To represent seasonal periodicity, the temporal information is encoded using sine–cosine transformations, which can effectively capture cyclical patterns in time-series data:

$$\sin ({\displaystyle \frac{2\pi m}{12}}),\cos ({\displaystyle \frac{2\pi m}{12}})$$

(12)

where $m$ represents the month index.

(2) Depth-dependent temperature gradient features

$$T_{\mathit{gradient}}=T_{10\mathrm{cm}}-T_{40\mathrm{cm}}$$

(13)

These features are designed to characterize the vertical variation in soil temperature, thereby capturing the depth-dependent thermal structure of the soil profile.

(3) Lag features

$$T_{0\mathrm{cm}}(t-1),T_{10\mathrm{cm}}(t-1)$$

(14)

These features are introduced to capture the short-term dynamic variations in the time series.

(4) Cascade features

When predicting soil temperature at deeper depths (e.g., 20–40 cm), the model incorporates the predicted temperature from the immediately preceding depth as an input variable.

$${\hat{T}}_z(t)=f_z^{(\mathit{XGB})}(x_t,{\hat{T}}_{z-\Delta z}(t),{\hat{T}}_z(t-1)$$

(15)

where $z$ (in cm) denotes the soil depth of the target layer, $\Delta z$ represents the depth interval between adjacent soil layers, and $f_z^{((XGB))}$ corresponds to the XGBoost model trained specifically for the soil layer at depth $z$. In this formulation, the model predicts the current soil temperature ${\widehat{T}}_z^{((t))}$ by incorporating the features vector $x$, the predicted temperature of the immediately preceding shallower layer ${\widehat{T}}_{z-\Delta z}^{(t)}$, and the predicted temperature of the same layer from the previous time step ${\widehat{T}}_z^{(t-1)}$, thereby capturing both vertical thermal dependencies and short-term temporal dynamics.

3.3. HSDGNN Model

To address coexisting and time-varying spatial dependencies among variables and attribute-level dependencies within variables, this study adopted and improved the HSDGNN model [35]. It represents multivariate time series as a two-level graph: an outer graph where each variable is a node (capturing inter-variable spatial dependencies), and an inner subgraph where attributes of each variable are sub-nodes (modeling intra-variable attribute dependencies). This structure explicitly encodes both inter-variable interactions and intra-attribute correlations. Temporal evolution of the graph topology is also encoded to improve spatiotemporal feature representation [36]. Building upon the original hierarchical spatiotemporal dependency graph neural network (HSDGNN) framework, this study introduced several adaptive architectural enhancements specifically designed to address key characteristics of mining-induced subsidence time series, including strong nonlinearity, long-term temporal dependencies, and dynamically evolving spatial correlations. Specifically, in the temporal modeling module, a Long Short-Term Memory (LSTM) network replaced the original single-layer Gated Recurrent Unit (GRU), thereby improving the model’s capacity to capture long-term settlement evolution patterns. Concurrently, the dynamic graph generation mechanism was tightly coupled with the spatial feature propagation process to explicitly encode time-varying spatial correlations among monitoring points, enhancing the model’s ability to represent complex spatiotemporal coupling structures inherent in mining subsidence prediction (Figure 4).

Given the observations from the past $T$ time steps:

$$X=(X_{-T+1},X_{-T+2},\dots ,X_0)$$

(16)

where $X_t=(X_{t,1},\dots ,X_{t,N})$, and each variable $X_{t,j}\in {ℝ}^c$ contains $C$ attributes. This study also includes temporal information as an attribute.

The objective of the model is to predict the primary attribute for the next $\tau$ future time steps, which can be formulated as:

$${(\hat{y}}_0,{\hat{y}}_1,\dots ,{\hat{y}}_{\tau })=f(X \left| G\right.,g_s)$$

(17)

where the outer graph $G=(V,E,A)$ represents the relationships among variables, in which $V$ denotes the set of variable nodes, $E$ represents the edges describing interactions between variables, and $A$ is the corresponding adjacency matrix.

Within each variable node, an attribute-level subgraph $G_S=(V_f,E_f,A_f)$ is constructed to represent the correlations among attributes, where $V_f$ denotes the set of attribute nodes, $E_f$ represents the connections between attributes, and $A_f$ is the corresponding adjacency matrix describing attribute-level dependencies.

The HSDGNN model first performs embedding on the attribute vectors at each time step to map the original feature space into a higher-dimensional representation space:

$$E=\sigma (W_I,X_t+b_I)$$

(18)

where $E$ denotes the embedded attribute feature representation; $W_I$ represents the learnable weight matrix used for feature transformation; $X_t$ denotes the input attribute feature vector at time step $t$; $b_t$ is the bias term; and $\sigma (·)$ denotes the nonlinear activation function.

$$R=\mathit{ReLU}({\mathit{EE}}^T)$$

(19)

where $R$ denotes the dynamic dependency matrix among attribute nodes, which is used to characterize the correlation strength between different attributes; $E$ represents the embedded attribute feature matrix obtained after feature embedding; $E^T$ denotes the transpose of matrix $E$; and $\mathit{ReLU}(·)$ is the Rectified Linear Unit activation function, introduced to retain positive correlations while suppressing negative responses. Through the matrix multiplication ${\mathit{EE}}^T$, the model measures pairwise similarity among attribute representations, thereby constructing the dynamic adjacency structure for attribute-level dependency learning.

$$F=(I_f+D^{-{\displaystyle \frac{1}{2}}}{\mathit{AD}}^{-{\displaystyle \frac{1}{2}}})X{\Theta }_I=(I_f+R)X{\Theta }_I$$

(20)

where $F$ denotes the attribute-fused feature matrix obtained after graph convolution; ${\Theta }_f$ represents the learnable weight matrix of the graph convolution layer; $I$ is the identity matrix introduced to preserve self-node features through self-connections; $A$ denotes the adjacency matrix of the attribute-level subgraph, describing the correlations among attribute nodes; $D$ represents the degree matrix corresponding to $A$, whose diagonal elements indicate the connection strength of each node; $D^{-1/2}{\mathit{AD}}^{-1/2}$ denotes the symmetrically normalized adjacency matrix, which improves the numerical stability of feature propagation; and $X$ is the input attribute feature matrix.

$$h_t^{L1}=\mathit{LSTM}(W_1{F}_t+b_1,h_{t-1}^{L1},c_{t-1}^{L1})$$

(21)

where $h_t^{L1}$ denotes the hidden state output of the first-layer LSTM at time step (t), (L1) represents the first temporal dependency learning layer, $F_t$ denotes the attribute-fused feature vector at time step (t), $W_1$ and $b_1$ are the learnable weight matrix and bias vector of the linear transformation, respectively, $h_{t-1}^{L1}$ represents the hidden state from the previous time step, and $c_{t-1}^{L1}$ denotes the cell state from the previous time step.

To capture the time-varying relationships among variables, the HSDGNN introduces a dynamic graph generation module decoupled from temporal modeling. Specifically, a node embedding matrix $M_e\in {ℝ}^{N\times E}$ and a temporal embedding matrix $T_e\in {ℝ}^{f_c\times E}$ are initialized. According to the time index, the corresponding temporal embedding is retrieved and combined with the node embedding to obtain an enhanced node representation: $N_e=M_e\odot T_e(X)$ where $\odot$ denotes the element-wise multiplication operation.

Subsequently, the temporal fusion information is projected into a fusion embedding space, which is used to construct the dynamic graph topology:

$$M=\sigma (W_{D}T+b_D)$$

(22)

where $M$ denotes the fused dynamic embedding representation used for dynamic graph construction; $W_D$ represents the learnable weight matrix for temporal feature transformation; $T$ denotes the temporal fusion feature matrix obtained from previous temporal dependency learning; $b_D$ is the bias term; and $\sigma (·)$ represents the nonlinear activation function. The node similarity is then computed to obtain the dynamic state transition matrix, which serves as an approximation of the dynamic graph topology.

$$G=\mathit{ReLU}(\mathit{tanh}(M\odot N_e)\cdot \mathit{tanh}{(M\odot N_e)}^T)$$

(23)

where $G$ denotes the dynamically generated adjacency matrix representing time-varying spatial correlations among monitoring nodes; $M$ represents the fused temporal embedding feature matrix; $N_e$ denotes the learnable node embedding matrix used to characterize the latent properties of different nodes; $\mathit{tanh}(·)$ is the hyperbolic tangent activation function for nonlinear feature transformation; ${(·)}^T$ denotes matrix transpose; and $\mathit{ReLU}(·)$ is the Rectified Linear Unit activation function used to retain positive correlations while suppressing negative connections. Through the similarity computation between embedded node representations, the model dynamically constructs the spatial topology structure, thereby capturing evolving spatiotemporal dependencies among monitoring points. The resulting matrix $G$ is treated as a time-varying adjacency (or transition) structure, which serves as the underlying topology for spatial information propagation in subsequent diffusion convolution operations.

For spatial dependency learning, the HSDGNN employs diffusion convolution to aggregate information among variables. The basic formulation can be expressed as:

$$Z={\displaystyle \sum _{k=0}^K{G}^k\cdot T\cdot {\Theta }_s^k}$$

(24)

where $Z_s$ denotes the spatial dependency feature representation obtained through diffusion graph convolution; $G^k$ represents the $k$ order diffusion matrix derived from the dynamic adjacency matrix $G$, which describes multi-hop spatial information propagation among nodes; $T$ denotes the temporal feature representation learned from the temporal dependency module; ${\Theta }_K$ represents the learnable parameter matrix corresponding to the $k$ diffusion order; and $K$ denotes the maximum diffusion step.

Furthermore, node-adaptive parameter learning enhances model flexibility by combining shared parameters with node embeddings, enabling node-specific transformations while preserving global parameter sharing.

$$Z={\displaystyle \sum _{k=0}^K{G}^k\cdot T\cdot M_e\cdot W_s^k}+M_e\cdot b_s^k$$

(25)

where $Z_s$ denotes the spatial feature representation after adaptive graph diffusion convolution; $G^k$ represents the $k$ order diffusion matrix derived from the dynamic graph structure; $T$ denotes the temporal feature representation obtained from temporal dependency learning; $M_e$ represents the node-adaptive embedding matrix used to characterize latent node-specific properties; $W_k$ denotes the learnable weight matrix corresponding to the $k$ diffusion order; $b_k$ represents the bias term associated with the $k$ diffusion operation; and $K$ denotes the maximum diffusion step.

To explicitly model the spatiotemporal coupling induced by temporal evolution of the graph topology, the diffused graph signals are fed into a second Gated Recurrent Unit (GRU) to capture temporal dependencies.

$$h_t^{G2}={\mathit{GRU}}_2(D(Z),h_{t-1}^{G2}\left|W_{G2})\right.$$

(26)

where $h_t^{G2}$ represents the spatial dependency features after diffusion graph convolution and feature transformation; $h_{t-1}^{G2}$ denotes the hidden state from the previous time step; and $W_2$ represents the learnable parameters of the GRU module. The diffused graph signals are fed into the second GRU to capture the spatiotemporal coupling induced by the dynamic graph topology, yielding an enhanced spatiotemporal representation. Through recurrent temporal updating, the GRU further captures long-term spatiotemporal dependencies and dynamic evolution patterns in mining subsidence sequences, thereby improving the temporal representation capability of the model.

4. Results

4.1. InSAR-Derived Deformation Results

A total of 100 Sentinel-1A SAR images acquired from the ascending orbit over the Dexing Copper Mine area between January 2022 and December 2024 were processed using the SBAS-InSAR technique to quantify surface deformation. The inversion yielded spatially resolved estimates of the annual mean deformation rate across the study region.

Figure 5 presents the spatial distribution of the annual mean subsidence rate across the study area. All deformation measurements are reported in the radar line-of-sight (LOS) direction, with positive values denoting upward displacement (uplift) and negative values indicating downward displacement (subsidence). Spatial analysis revealed pronounced heterogeneity in deformation patterns across the mining area. Distinct subsidence zones were predominantly localized within active open-pit excavation sites and waste rock disposal areas, where they coalesced into multiple characteristic subsidence funnels. The maximum observed subsidence rate was −126.121 mm/yr. Conversely, isolated uplift signals were detected at several locations, reaching a peak magnitude of +92.6334 mm/yr (Figure 5).

Nine representative monitoring points were selected based on the spatial distribution of deformation rates and intensity gradients within subsiding zones, to support time-series analysis and subsidence prediction. Points P1–P4 were situated in Mine 1, and points P5–P9 in Mine 2—each capturing distinct yet representative subsidence behaviors. Their precise geographic coordinates are listed in

Table 2. Coordinates of representative subsidence monitoring points.

Point ID	Location
P1	117°42′6.624″E	29°0′16.432″N
P2	117°42′50.899″E	29°0′10.245″N
P3	117°42′14.484″E	28°59′52.602″N
P4	117°42′55.876″E	28°59′36.792″N
P5	117°45′28.61″E	28°59′15.939″N
P6	117°45′1.626″E	28°59′5.168″N
P7	117°45′11.843″E	28°58′55.085″N
P8	117°44′54.553″E	28°58′51.876″N
P9	117°45′10.796″E	28°58′41.792″N

. These points constituted the primary observational targets for subsequent temporal modeling and deep learning–based subsidence forecasting.

4.2. Accuracy Validation

To assess the accuracy and robustness of the SBAS-InSAR–derived surface deformation measurements, two independent stacks of ascending Sentinel-1A SAR data—acquired along orbital Path 40 (n = 36 scenes) and Path 142 (n = 64 scenes) over the period January 2022 to December 2024—were separately processed using the SBAS-InSAR technique (Figure 6). The datasets acquired from the two ascending orbits were subjected to cross-validation. During accuracy validation, SBAS-InSAR processing was applied to both Sentinel-1A ascending tracks. Following geocoding, 200 spatially collocated subsidence measurement points—sharing identical latitude and longitude coordinates across both tracks—were identified. Cumulative subsidence values at these points were extracted for inter-track comparison. Pearson correlation analysis was conducted to quantify the linear agreement between the two datasets, and the corresponding coefficient of determination (R²) was computed. The analysis yielded an R² value of 0.9494, indicating a strong linear agreement between the two independently derived subsidence estimates (Figure 7). This high degree of inter-track consistency corroborated the repeatability, repeatability and methodological stability of the SBAS-InSAR for quantitative subsidence monitoring in the Dexing Copper Mine area.

4.3. XGBoost-Based Data Interpolation

To mitigate spatial sampling inconsistencies between mine subsidence observations and meteorological-hydrological datasets, an XGBoost-based spatial interpolation method was employed to reconstruct and harmonize the environmental variables. As illustrated in Figure 8, the reconstructed volumetric soil moisture values ranged from 0.35 to 0.43 m³/m³, and soil temperature values ranged from 7 to 27 °C. The majority of data points clustered tightly around the 1:1 reference line, indicating high predictive accuracy and minimal systematic bias between the modeled and observed values. Notably, no substantial increase in prediction dispersion or consistent overestimation or underestimation was observed across the extreme ranges: specifically, for volumetric soil moisture below 0.37 m³/m³ or above 0.41 m³/m³, and for soil temperature below 10 °C or above 23 °C.

As shown in

Table 3. Parameters of soil moisture interpolation model.

Depth Layer	RMSE (m3/m3)	MAE (m3/m3)	R2
0 cm	0.00380	0.00276	0.9631
5 cm	0.00347	0.00276	0.9693
10 cm	0.00347	0.00276	0.9693
15 cm	0.00306	0.00291	0.9652
20 cm	0.00355	0.00280	0.9669
25 cm	0.00334	0.00268	0.9699
30 cm	0.00335	0.00265	0.9697
35 cm	0.00345	0.00264	0.9671
40 cm	0.00344	0.00266	0.9668
Average	0.00350	0.00273	0.9675

and

Table 4. Parameters of soil temperature interpolation model.

Depth Layer	RMSE (°C)	MAE (°C)	R2
0 cm	1.6885	1.2790	0.9430
5 cm	1.6038	1.1705	0.9486
10 cm	1.6038	1.1705	0.9486
15 cm	1.5224	1.1063	0.9498
20 cm	1.3622	0.9956	0.9564
25 cm	1.2725	0.9942	0.9585
30 cm	0.7461	0.6708	0.9844
35 cm	0.6180	0.5094	0.9883
40 cm	0.4104	0.3429	0.9943
Average	1.2031	0.9155	0.9635

, the soil temperature interpolation model yielded RMSE values ranging from 0.4104 to 1.6885 °C (mean: 1.2031 °C) and MAE values from 0.3429 to 1.2790 °C (mean: 0.9155 °C). The corresponding R² values ranged from 0.9430 to 0.9943, with a mean of 0.9635. For volumetric soil moisture, the model achieved RMSE values between 0.00334 and 0.00380 m³/m³ (mean: 0.00350 m³/m³) and MAE values between 0.00264 and 0.00291 m³/m³ (mean: 0.00273 m³/m³), while R² values ranged from 0.9631 to 0.9699 (mean: 0.9675). Collectively, both models demonstrated high predictive accuracy and strong explanatory power across spatial locations.

Volumetric soil moisture time series at 0–10 cm and 10–40 cm depths exhibited pronounced seasonal periodicity. Overall, the values ranged from 0.23 to 0.43 m³/m³, with peak moisture (0.39–0.43 m³/m³) occurring during June–September—coinciding with the regional precipitation maximum—and minimum values (0.23–0.30 m³/m³) observed from October to December, consistent with the seasonal decline in rainfall. Relative to the 10–40 cm layer, the 0–10 cm layer displayed greater temporal variability, faster response dynamics to meteorological forcing, and higher annual amplitude. In contrast, deeper soil layers showed attenuated fluctuations, phase-lagged peaks (delayed by approximately 3–4 weeks), and reduced annual amplitude—indicative of thermal and hydraulic damping with depth (Figure 9).

Soil temperature time series likewise demonstrated systematic depth-dependent behavior. At 0–10 cm, temperatures varied between 6 and 27 °C, yielding an annual amplitude exceeding 20 °C and closely tracking atmospheric seasonal cycles. At 10–40 cm, the range narrowed to 7–25 °C, with progressive amplitude reduction and a phase delay of ~3–4 weeks relative to the surface layer; correspondingly, the variation profile became increasingly smoothed and less responsive to short-term atmospheric forcing (Figure 9).

As illustrates in Figure 10, volumetric soil moisture and temperature profiled from the 0–10 cm and 10–40 cm layers were integrated into a representative 0–40 cm column time series using depth-weighted averaging. Relative to the individual-layer records, the integrated series exhibited enhanced temporal continuity and attenuated high-frequency variability, thereby offering a more robust characterization of integrated near-surface hydrothermal conditions. The aggregated 0–40 cm soil moisture ranged from 0.26 to 0.42 m³/m³, with maxima (0.39–0.42 m³/m³) observed during June–September and minima (0.26–0.32 m³/m³) during October–December, preserving a well-defined seasonal cycle aligned with regional precipitation dynamics. The integrated soil temperature varied between 7 and 25 °C, peaking in July–August and reaching minima in December–January. Compared to the 0–10 cm layer, the column-integrated series displayed a reduced annual amplitude and a phase delay of approximately 2–3 weeks in peak timing.

As illustrates in Figure 11, volumetric soil moisture exhibited a distinct seasonal pattern: monthly averaged remained elevated during May–September, ranging from 0.39 to 0.42 m³/m³ in the 0–10 cm layer and 0.38 to 0.41 m³/m³ in the 10–40 cm layer, establishing a consistent vertical gradient that decreases with depth. From October to December, moisture declined to 0.30–0.34 m³/m³ across both layers, with proportionally greater reductions in the shallow (0–10 cm) zone. Notably, minimum values in the 20–40 cm layer lag those at the surface by approximately one month, reflecting downward moisture propagation delay. Soil temperature likewise displayed pronounced vertical and temporal structure. During July–August, the 0–10 cm layer reached peak values of 25–27 °C, whereas temperatures at 40 cm depth remain comparatively stable at 23–24 °C. In contrast, during December–January, surface temperatures declined to 7–9 °C, while deeper layers maintain milder conditions (8–10 °C). Thermal signal propagation from the surface to 40 cm depth was characterized by a phase lag of approximately 3–4 weeks, consistent with conductive heat transfer dynamics in unsaturated soils.

4.4. Analysis of Influencing Factors on Mining Subsidence

4.4.1. Impact of Precipitation on Mining Subsidence

Monthly precipitation (2022–2024) was aligned with InSAR-derived subsidence time series to assess its influence on mining-induced subsidence (Figure 12). June 2022 rainfall (25.52 mm) exceeded that of June 2023 (20.52 mm) and June 2024 (17.89 mm). Average June subsidence across nine monitoring points was −1.38 mm (2022), −1.27 mm (2023), and −1.58 mm (2024). During the rainy season (June–August), Points P3 and P9 subsided at −10.27 mm/month and −12.72 mm/month, higher than their dry-season (September–May) rates of −8.66 mm/month and −7.31 mm/month. Regionally, the rainy-season average was −8.20 mm/month versus −7.87 mm/month in the dry season. These patterns confirmed that subsidence rate increased during wet periods. Rainfall likely triggered this by raising pore water pressure and weakening overburden strength.

Precipitation influenced subsidence through two primary hydro-mechanical mechanisms: (1) infiltration-driven pore pressure buildup and (2) runoff-induced slope destabilization. First, sustained rainfall infiltrates loose overburden deposits and waste rock piles adjacent to mining pits, elevating pore water pressure. This reduces effective stress and inter-particle shear resistance, promoting plastic deformation of the soil matrix and progressive surface subsidence. Second, intense rainfall generated surface runoff that erodes pit slopes, redistributed near-surface stress, and initiated localized failures, including shallow collapses and translational slope movements.

4.4.2. Impact of Air Temperature on Mining Subsidence

Air temperature variations influenced mining-induced subsidence evolution through thermally induced stress changes in near-surface materials. Specifically, diurnal and seasonal thermal cycling induced reversible expansion and contraction of rock and soil matrices, thereby modulating surface stress state and affecting the stability of shallow overburden. At the Dexing Copper Mine, air temperatures ranged from approximately −2 °C to 35 °C annually. During high-temperature periods, thermal expansion contributed to stress redistribution and micro-crack closure, whereas low-temperature periods were associated with contraction, tensile stress accumulation, and potential desiccation-induced weakening—processes that collectively influence subsidence evolution.

Monthly air temperature data (2022–2024) were divided into high-temperature phases (≥30 °C) and low-temperature phases (≤5 °C) to assess thermal effects on mining subsidence (Figure 13). During high-temperature phases, subsidence across nine sites ranged from −4.2 to −8.6 mm/month; regional average: −6.5 mm/month. During low-temperature phases, it ranged from −10.6 to −14.9 mm/month; regional average: −11.2 mm/month. In January 2023 and 2024 (<5 °C), P3, P7, and P9 subsided > −12 mm/month; in July (≥30 °C), all three points subsided < −8 mm/month. Overall, low-temperature subsidence averaged 72% higher than high-temperature subsidence, confirming an inverse temperature–subsidence relationship.

4.4.3. Impact of Soil Moisture on Mining Subsidence

Volumetric soil moisture effected on mining subsidence are assessed by aligning InSAR-derived subsidence time series (Points P1–P9) with depth-resolved moisture data. Volumetric soil moisture in the 0–10 cm layer showed pronounced seasonal variability from 2022 to 2024, ranging from 0.32 to 0.45 m³/m³ (Figure 14). During high-moisture period (June–August), subsidence rates accelerated markedly across most monitoring points—evidenced by steeper slopes in cumulative subsidence time series. When surface moisture exceeded 0.42 m³/m³, the nine-point average subsidence rate was −9 to −12 mm/month; below 0.35 m³/m³, the average subsidence rate declined to −6 to −8 mm/month. These consistent inverse correlations confirmed that elevated near-surface soil moisture promoted enhanced subsidence magnitude and rate.

In comparison, soil moisture in the 10–40 cm layer showed less seasonally variability (0.34–0.43 m³/m³) than at the surface, with monthly changes in only 0.01–0.02 m³/m³—about half of the surface range (Figure 15). Moisture peaks lagged behind surface peaks by 20–35 days (mean: 28 days). High soil moisture (≥0.40 m³/m³) lasted 60–90 days at depth versus 20–40 days at the surface. When the mid-layer soil moisture exceeded 0.40 m³/m³, subsidence rates rose slightly (<0.5 mm/day), but cumulative subsidence increased by 15–25% over the next 2–3 months compared to low-moisture conditions (≤0.38 m³/m³). The peak correlation with subsidence rate occurred at a 1–2 month lag (R² = 0.69), far stronger than the synchronous correlation (R² = 0.40), confirming a delayed, cumulative effect.

Collectively, surface soil moisture functioned primarily as a short-term trigger: a monthly induced exceeding 0.05 m³/m³ induce transient acceleration in subsidence rates. In contrast, mid-layer soil moisture served as a sustained modulator, prolonging pore water pressure dissipation, delaying soil strength recovery, and facilitating progressive effective stress redistribution, thereby sustaining elevated subsidence rates over extended periods.

4.4.4. Impact of Soil Temperature on Mining Subsidence

Analysis of co-located soil temperature and subsidence time series (2022–2024) revealed consistent, phase-dependent correlations between thermal conditions and subsidence rates across all nine monitoring points (P1–P9). Surface soil temperature (0–10 cm) varied from 3.2 to 30.1 °C, and mid-layer soil temperature (10–40 cm) varied from 5.1 to 26.4 °C (Figure 16 and Figure 17). During high-temperature periods (>28.0 °C), subsidence rates ranged from −5.0 to −8.3 mm/month (mean: −6.4 mm/month); during low-temperature periods (<6.0 °C), subsidence rates increased markedly to −10.2 to −15.1 mm/month (mean: −12.1 mm/month)—an 89.1% rise relative to the high-temperature baseline. Site-specific responses were robust: at P3 and P7, low-temperature rates (−12.0 and −14.0 mm/month) were approximately double their high-temperature counterparts (−6.2 and −6.8 mm/month).

During July–August 2023, when surface temperatures peaked annually at 29.4–30.0 °C, subsidence time series exhibited transient fluctuations but no sustained acceleration in deformation rates. In contrast, during December 2023–January 2024, when surface temperatures remained below 5 °C, cumulative subsidence curves steepened markedly, indicating accelerated subsidence. Delayed thermal propagation resulted in mid-layer (10–40 cm) temperature peaked lagging surface peaks by 3–4 weeks, with attenuated amplitudes and reduced temporal variability. Critically, sustained mid-layer cooling (<8 °C) was followed within one month by a statistically discernible increase in subsidence rate, demonstrating a thermally mediated, delayed response mechanism.

Long-term monitoring (2022–2024) showed that subsidence intensified when near-surface temperatures were low and attenuates when high, a robust inverse temperature–subsidence relationship. Cryogenic contraction and enhanced overburden stress transfer drive acceleration during cooling; thermal expansion during warming partially counteracts subsidence accumulation.

4.5. Prediction of Mining-Induced Subsidence

4.5.1. Mine Subsidence Prediction Based on HSDGNN

This study introduced and applied the Hierarchical Spatiotemporal Dependency Graph Neural Network (HSDGNN), a novel graph neural network architecture explicitly designed for multivariate spatiotemporal forecasting of mining-induced surface subsidence.

Table 5. Hyperparameters of the HSDGNN Model.

Parameter Name	Notation	Value	Description
Input length	T	6 months	-
Prediction horizon	τ	3 months	-
Number of nodes	N	9	-
Diffusion convolution order	K	2	-
GRU hidden size	M	128	-
Training epochs	E	200	With early stopping based on validation loss
Learning rate	R	0.001	With scheduler decay to 0.0005 after 50 epochs
Batch size	S	32
Embedding dimension	D	64	For both node and temporal features

shows the specific parameters. By jointly encoding four environmental drivers (air temperature, precipitation, soil temperature, and soil moisture) and historical subsidence time series, HSDGNN explicitly models hierarchical spatial correlations among monitoring points and captured nonlinear temporal evolution patterns.

In the prediction task, the HSDGNN model adopted an input time window of length T = 6 months—i.e., historical observations from the preceding six months—and a prediction horizon of τ = 3 months, forecasting settlement values for the subsequent three months. Consequently, each supervised training sample was formulated in a sequence-to-sequence manner, mapping a 6-month historical input sequence to a 3-month future settlement output sequence. The prediction dataset was temporally partitioned into training, validation, and test subsets in a strict chronological order (70%/10%/20%) prior to sliding-window sample generation. Normalization parameters were estimated solely from the training subset to prevent data leakage and ensure that model evaluation emulates real-world forecasting conditions. Separate models were trained for Mine 1 (four monitoring points) and Mine 2 (five monitoring points).

Figure 18 presents the predictive performance of the HSDGNN model across both mining areas (Mine 1 and Mine 2), showing scatter plots of predicted versus observed subsidence values alongside corresponding boxplot distributions of residuals. For Mine 1, predictions aligned closely with observations—evidenced by tight clustering of points near the 1:1 line—with an R² of 0.9950, MAE of 3.8845 mm, and RMSE of 5.5566 mm. For Mine 2, the model achieved robust performance with R² = 0.9738, MAE = 6.1699 mm, and RMSE = 7.4906 mm. All residual magnitudes remained below 8 mm, confirming consistent sub-centimeter prediction fidelity across heterogeneous mining settings.

Figure 19 presents point-wise predictive performance across nine representative monitoring locations (P1–P9). Scatter plots of predicted versus observed subsidence were accompanied by boxplots of absolute prediction errors. In Mine 1, R² values ranged from 0.905 (P3) to 0.952 (P4), with all points exceeding 0.924. In Mine 2, R² spanned 0.870 (P8) to 0.945 (P9); while P6 (0.820) and P8 (0.870) represent the lowest-performing sites, their residuals remained centered near zero with no systematic bias or nonlinear distortion, indicating reliable linear predictability despite moderate correlation strength.

Figure 20 displays the predicted versus observed cumulative subsidence time series for all nine monitoring points (P1–P9). Prediction errors—defined as the difference between modeled and measured cumulative subsidence increments—remained bounded within ±5 to ±10 mm across the entire observation period. Critically, no temporal drift, trend reversal, or progressive error accumulation was evident across varying subsidence magnitudes, confirming the model’s temporal robustness and long-term predictive stability.

4.5.2. Comparison of Subsidence Prediction Models

To rigorously evaluate the effectiveness and robustness of the proposed HSDGNN model for mining-induced subsidence prediction, two established baseline models—Random Forest (RF) and LSTM networks—were selected for comparative benchmarking. All models were trained and tested under identical data partitioning, preprocessing, and evaluation protocols to ensure methodological fairness.

Table 6. Prediction accuracy comparison of different models.

	RMSE	MAE	R2
RF (Mine 1)	11.5754	8.8655	0.7582
RF (Mine 2)	14.1846	9.9792	0.6895
LSTM (Mine 1)	9.2181	7.5549	0.8495
LSTM (Mine 2)	10.7294	7.9145	0.7728
HSDGNN (Mine 1)	5.5566	3.8845	0.9950
HSDGNN (Mine 2)	7.4906	6.1699	0.9738

reports RMSE, MAE, and R² metrics across all representative monitoring points (P1–P9), enabling direct, cross-model performance assessment (Table 6).

Comparative results showed that the RF model—despite its interpretability—exhibited limited predictive capability for mining-induced subsidence, achieving only R² = 0.7582, RMSE = 11.5754, and MAE = 8.8655 for Mine 1, and R² = 0.6895, RMSE = 14.1846, and MAE = 9.9792 for Mine 2. This limitation stemmed from the intrinsic characteristics of random forests as a static, memoryless regression algorithm—specifically, its inability to model temporal persistence or nonlinear temporal evolution in subsidence dynamics. In contrast, LSTM network explicitly models sequential dependency through gated memory mechanisms, resulting in superior predictive performance: for Mine 1, R² = 0.8495, RMSE = 9.22, and MAE = 7.55; for Mine 2, R² = 0.7728, RMSE = 10.73, and MAE = 7.91. However, LSTM network processed each monitoring point independently, thereby neglecting inter-point spatial correlations—a critical limitation in geologically heterogeneous mining areas, where subsidence patterns exhibit strong spatial coherence. The proposed HSDGNN overcame this by jointly encoding both graph-structured spatial relationships among monitoring points and multivariate environmental drivers (precipitation, air temperature, soil moisture, soil temperature), thereby achieving superior accuracy: Mine 1 obtained R² = 0.9950, RMSE = 5.5566, MAE = 3.8845, and Mine 2 achieved R² = 0.9738, RMSE = 7.4906, MAE = 6.1699. Quantitatively, HSDGNN for Mine 1 achieved a 39.7% reduction in RMSE (−3.6615 mm), a 48.6% reduction in MAE (−3.6704 mm), and a +0.1455 increase in R² relative to LSTM; for Mine 2, HSDGNN yielded an 18.7% RMSE reduction (−1.2388 mm), an 18.3% MAE reduction (−1.7441 mm), and a +0.2010 increase in R². These consistent improvements—particularly the substantial error reduction in Mine 1—demonstrated the framework’s enhanced capability to capture complex spatiotemporal dependencies inherent in mining-induced subsidence.

5. Discussion

5.1. Multi-Factor Driving Mechanism of Mining Subsidence

InSAR-derived subsidence maps reveal pronounced spatial heterogeneity and nonlinear temporal evolution across the Dexing Copper Mine area. Major subsidence zones align with active open-pit and waste rock sites, confirming mining as the primary cause of surface deformation. Environmental factors (e.g., precipitation, temperature, soil moisture) modulate subsidence rates, especially during seasonal hydrological cycles.

Precipitation and soil moisture exhibit strong seasonal coherence with subsidence dynamics, confirming hydrological forcing as the primary accelerator of mining-induced surface deformation. Sustained rainfall increases pore-water pressure in unconsolidated overburden, thereby reducing effective stress and promoting time-dependent soil compression and particle rearrangement—processes that directly amplify both the magnitude and rate of subsidence. Depth-resolved soil moisture responses further reveal a two-phase hydromechanical mechanism: rapid near-surface infiltration drives short-term subsidence fluctuations, whereas slower moisture migration at intermediate depths governs long-term, consolidation-driven subsidence evolution.

In contrast, air temperature and soil temperature act as secondary seasonal modulators, exerting indirect control over subsidence through thermally induced expansion and contraction of near-surface materials, thereby altering local stress states and reducing rock mass stability. Critically, these thermal effects do not initiate subsidence; rather, they modulate its magnitude and temporal evolution. This reinforces the primacy of hydrological drivers—as the dominant control on mining-induced subsidence at the study scale—over temperature-mediated mechanisms.

5.2. Reconstruction of Multi-Source Environmental Driving Factors Based on XGBoost

Spatiotemporal resolution mismatches between multi-source environmental variables (e.g., soil moisture and soil temperature at multiple depths) and InSAR-derived subsidence time series critically compromise model input integrity. To ensure temporal consistency, this study applied XGBoost to interpolate and reconstruct these environmental fields at the InSAR observation frequency [37].

As a nonparametric, gradient-boosted tree ensemble, XGBoost robustly models nonlinear, non-stationary temporal–depth dependencies in environmental variables—without requiring stationarity or linearity assumptions [38]. This capability is particularly advantageous for mining subsidence systems, which exhibit strong non-stationarity due to coupled anthropogenic and hydrological forcing. Validation against ground-truth measurements confirms high reconstruction fidelity: predicted values align closely with observations (R² ≥ 0.91), residuals are tightly distributed around zero, and systematic bias is negligible. Moreover, feature subsampling during training ensures reconstruction stability across diverse hydrological regimes, yielding temporally consistent, physically coherent environmental inputs essential for HSDGNN-based spatiotemporal dependency modeling.

5.3. Improvement of Subsidence Prediction Accuracy

Mining-induced subsidence exhibits strong temporal dependencies and pronounced inter-point spatial correlations. Conventional machine learning models lack the capacity to encode long-term temporal memory in subsidence evolution [39]. While LSTM-based architectures effectively model nonlinear temporal dynamics, they inherently treat monitoring points as independent time series, thus neglecting spatial interactions critical to capturing regional subsidence patterns [40].

The HSDGNN model explicitly encodes spatial dependencies among subsidence monitoring points via a hierarchical graph architecture and incorporates a dynamic graph mechanism to track the temporal evolution of spatiotemporal coupling effects. This design directly reflects three intrinsic characteristics of mining-induced subsidence: multi-point kinematic coordination, spatially diffusive deformation propagation, and time-integrated deformation accumulation [41]. Consequently, HSDGNN delivers consistently high prediction accuracy across diverse mining sites and monitoring configurations, demonstrating robust generalization ability and operational readiness for engineering deployment.

5.4. Limitations and Future Work

While the proposed subsidence monitoring and prediction framework demonstrates strong performance in the study area, several limitations warrant consideration. First, the model omits groundwater level dynamics and key mining parameters (e.g., extraction rate, stope geometry, backfill properties), limiting mechanistic insight into subsidence drivers. Second, the HSDGNN graph relies solely on data—without incorporating geological or mining domain knowledge (e.g., faults, strata, mine layouts)—so it cannot encode physically realistic spatial constraint conditions.

Future work will integrate multi-source InSAR observations data, underground mining parameters (e.g., pillar stability, goaf geometry, ventilation-induced stress redistribution), and physics-informed graph structure learning, thereby strengthening model interpretability and enabling robust cross-regional generalization.

6. Conclusions

This study processed Sentinel-1 SAR acquisitions over the Dexing Copper Mine using SBAS-InSAR to derive high-resolution, time-series surface deformation data. An XGBoost-based temporal interpolation scheme reconciles spatial resolution mismatched between meteorological–hydrological datasets and InSAR observation data, enabling consistent reconstruction of soil moisture and soil temperature profiles across the InSAR acquisition timeline. To enhance subsidence prediction accuracy, this study developed an integrated framework that fuses multi-source environmental drivers with deep learning methods—specifically, HSDGNN.

Results revealed pronounced spatial heterogeneity and nonlinear temporal evolution in Dexing Copper Mine subsidence, with peak rates reaching −126.121 mm/yr. The XGBoost-based hierarchical cascade interpolation model reconstructed soil moisture and soil temperature profiles with high fidelity (R² > 0.96). Leveraging a hierarchical graph architecture, HSDGNN jointly encoded inter-point spatial dependencies and intra-attribute temporal dynamics, enabling physics-aware dynamic subsidence modeling. Quantitative evaluation showed that HSDGNN achieved R² = 0.995 and RMSE = 5.5566 for Mine 1, and R² = 0.9738 and RMSE = 7.4906 for Mine 2, sustaining millimeter-level accuracy. Relative to the RF and LSTM baseline models, HSDGNN reduced RMSE by 52.0% and 39.7% for Mine 1, and by 47.2% and 18.7% for Mine 2, respectively, while improving R² by 0.2368 and 0.1455 for Mine 1 and by 0.2843 and 0.2010 for Mine 2, demonstrating the superior capability of hierarchical spatiotemporal dependency modeling in capturing complex mining-induced subsidence dynamics. Future work will integrate underground mining parameters (e.g., pillar stability, goaf geometry), multi-source InSAR stacks, and physics-informed adaptive graph learning methods to strengthen cross-regional generalization ability and operational robustness.