A Missing Data Imputation Method for Waste Dump Landslide Deformation Monitoring Based on a Seq2Seq LSTM–Posterior Correction Model

Abstract

Surface deformation monitoring is essential for controlling instability processes such as urban infrastructure deformation, mining-induced subsidence, and landslide deformation. However, missing data often disrupt the continuity of the various deformation time series and compromise the reliability of monitoring results. This issue is particularly critical in long-term landslide studies, where conventional missing data imputation methods often neglect the nonlinear characteristics of slope deformation and fail to account for external influences under complex environmental conditions. To address these limitations, this study proposes a deep learning-based imputation method that integrates multi-source monitoring data. A Seq2Seq LSTM (sequence-to-sequence long short-term memory) model is constructed to reconstruct missing deformation values, and a posterior correction module is integrated to optimize the preliminary outputs, thereby enhancing imputation accuracy. The proposed approach is validated using a case study of the southern dump slope landslide at the Hesigewula South Open-Pit Coal Mine in Inner Mongolia, China. Experimental results on the test set demonstrate that the Seq2Seq LSTM–Posterior Correction model significantly outperforms traditional methods such as linear regression and baseline LSTM models. This method offers an effective solution to data gaps in landslide deformation monitoring, demonstrating strong potential for accurate nonlinear imputation in complex environments and providing a practical approach for long-term InSAR-based landslide studies in areas affected by missing SAR data.

1. Introduction

Natural resource exploration and exploitation form a critical foundation for human development and industrial progress [1]. In recent years, rising energy demand has intensified mineral resource extraction, with open-pit mining adopted as a primary method for coal production worldwide due to its high production efficiency, low operating costs, and efficient resource recovery [2]. This trend has resulted in a significant increase in both the number and distribution of open-pit mine slopes. On 22 February 2023, a disastrous landslide at the Xinjing Open-Pit Coal Mine in Inner Mongolia, China, resulted in 53 fatalities and significant infrastructure damage [3]. Such events highlight the critical importance of effective slope deformation monitoring to support early warning and risk mitigation in open-pit mining areas. Landslide deformation monitoring provides a critical foundation for forecasting, early warning, and disaster risk reduction [4]. Remote sensing technologies such as InSAR (Interferometric Synthetic Aperture Radar), GNSS (Global Navigation Satellite System), and UAV (Unmanned Aerial Vehicle) photogrammetry have been extensively applied and are now regarded as indispensable tools for landslide surveillance and geological hazard assessment [5,6,7,8,9,10]. These techniques enable the effective detection of surface displacement and facilitate the analysis of spatiotemporal evolution patterns, susceptibility zones, and rainfall-induced triggering mechanisms [11,12,13,14,15]. However, InSAR-based landslide monitoring is subject to substantial limitations. Influenced by both external and internal factors—such as phase decorrelation, atmospheric disturbances, and sensor malfunctions—InSAR time-series data often suffer from frequent data gaps. These missing values significantly compromise the continuity and interpretability of long-term landslide deformation monitoring, thereby constraining the advancement of landslide-related research [16,17,18].

Currently, mainstream approaches to imputing missing data can be broadly classified into three categories: (1) linear interpolation and conventional statistical time-series models such as ARIMA and spline interpolation; (2) machine learning algorithms including KNN (k-nearest neighbors) and random forests; and (3) deep learning architectures such as LSTM (long short-term memory) and transformer networks [19,20,21]. Although linear interpolation and conventional statistical time-series models offer computational efficiency and ease of implementation, they are generally limited in capturing dynamic patterns over extended gap periods. As such, they are more appropriate for handling short-term, high-frequency data gaps [22]. Machine learning models, characterized by structural transparency, fast training speed, and strong interpretability, are well-suited for imputing missing data over short- to medium-term time scales. However, their performance in more complex tasks is often limited by their insufficient capacity for modeling temporal dynamics [23]. Deep learning models demonstrate strong capabilities in capturing nonlinear patterns in time-series data. Architectures such as LSTM, CNN (Convolutional Neural Network), and RNN (Recurrent Neural Network) have been widely applied to tasks including time-series forecasting and missing data imputation [24,25,26] and have exhibited robust performance in various domains such as traffic flow prediction [27], power load estimation [28], and rainfall–runoff modeling [29]. Although shallow deep learning architectures are effective in capturing nonlinear trends, their structural simplicity often limits their effectiveness in modeling complex systems such as landslide deformation. Models with more complex architectures, such as Seq2Seq LSTM (sequence-to-sequence long short-term memory) [30], STGCN (Spatio-Temporal Graph Convolutional Network) [31], and SAITS (Self-Attention-based Imputation for Time Series) [32], have demonstrated superior performance in both missing data imputation and time-series forecasting. These models not only better capture nonlinear variation patterns but also significantly outperform their shallow counterparts when applied to tasks involving complex systems such as landslide deformation [33]. Li, M. et al. proposed a landslide multivariate displacement prediction method based on Seq2Seq LSTM, which exhibited enhanced capability in capturing local peaks and produced prediction curves that better matched the actual deformation patterns [34].

In landslide deformation data imputation, long-term dependencies—such as the influence of historical deformation on missing segments—are critically important. However, due to gradient-related issues, encoders often struggle to capture such dependencies, leading to poor retention of early sequence information and excessive sensitivity to more recent inputs [35]. In the absence of ground-truth constraints, error accumulation can lead to severe distribution shift, resulting in a dramatic decline in imputation accuracy [36,37,38]. Integrating deep learning with posterior correction offers an effective solution to the distribution shift caused by error accumulation. This multi-method fusion strategy combines the nonlinear modeling capacity of complex deep neural networks with the error suppression and trend alignment advantages of posterior correction [39], thereby enhancing the effectiveness of missing data imputation. Cascade-based approaches that model and correct the prediction errors of LSTM outputs have been successfully employed in time-series forecasting, resulting in significant improvements in prediction accuracy [40]. The integrated model conducts imputation of missing values in time-series monitoring data through a three-stage framework comprising data preprocessing, sequence learning–based reconstruction, and posterior correction. It exhibits strong capability in trend representation learning and delivers high imputation accuracy. In this framework, the Seq2Seq LSTM module captures nonlinear deformation trends and generates preliminary imputation results. The posterior correction module adjusts for accumulated errors through residual modeling, improving the accuracy of long-term landslide deformation reconstruction.

In this case, studying the southern dump slope landslide of the Hesigewula South Open-Pit Coal Mine in Inner Mongolia, we address an extensive data gap between December 2021 and March 2023. A Seq2Seq LSTM–Posterior Correction model is then employed for missing data imputation by fusing Sentinel-1B imagery from the European Space Agency with GNSS observations supplied by the mine operator. Compared with conventional imputation methods, our approach demonstrates superior capability in capturing complex nonlinear relationships between external factors and landslide kinematics. In comparative experiments involving multiple methods, the proposed approach achieved lower MSE (mean squared error) and MAE (Mean Absolute Error), along with higher PCC (Pearson Correlation Coefficients) on the test set, highlighting its superior performance in missing data imputation. The consistency between field-based engineering geological investigations and the imputed results further supports the reliability of the proposed method. This study offers a feasible solution for enabling long-term landslide deformation monitoring in areas affected by SAR data gaps.

2. Study Area

The Hesigewula South Open-Pit Coal Mine, as shown in Figure 1, is located in Xilingol League, Inner Mongolia Autonomous Region, along the southern ridge of the Greater Khingan Mountains, where marshland geomorphology is widely developed. The regional stratigraphy is primarily composed of the Upper Jurassic Manketouebo, Manitu, and Baiyingaolao Formations, the Lower Cretaceous Damoguaihe Formation, and Quaternary deposits. The regional tectonic structure is characterized by an asymmetrical, broad syncline, with a gently dipping western limb and a steeply dipping eastern limb. The region exhibits a typical continental climate, with annual temperature variations ranging from −42.1 °C in winter to 35.3 °C in summer. Most precipitation falls between June and August, accounting for approximately 70% of the yearly total.

The southern dump slope landslide at the Hesigewula South Open-Pit Coal Mine has a height of 69 m and a slope angle of 5.93°. The landslide extends from an altitude of approximately 915 m at the toe to 980 m at the crown. The landslide mass is primarily composed of waste soil dumped above the bedrock. The material is loosely structured with low cohesion and contains mudstone that undergoes a rapid loss of strength upon water infiltration, resulting in overall low slope stability. Historically, multiple minor deformation events have occurred at the southern dump slope landslide during the thawing period from April to May and in the months following heavy rainfall, particularly from August to October.

3. Data and Methods

In this study, we propose a Seq2Seq LSTM–Posterior Correction model for imputing missing data in long-term SAR deformation time series. By integrating Sentinel-1 SAR imagery with GNSS displacement measurements, the model leverages multi-source monitoring data to achieve high-accuracy reconstruction of deformation signals. The overall modeling workflow is shown in Figure 2.

3.1. Data

The dataset used in this study includes 79 descending C-band SAR scenes acquired by the European Space Agency’s Sentinel-1B satellite from 15 April 2018 to 7 December 2021. The Copernicus DEM with a spatial resolution of 8 m was employed for image co-registration and topographic phase removal. In addition, three-dimensional displacement data from 21 March to 17 May 2023 were obtained from nine GNSS stations deployed across the southern dump slope landslide area (Figure 3a), and the vertical displacement component was used in this study for analysis.

The SAR dataset for this area ends on 7 December 2021, due to the decommissioning of the Sentinel-1B satellite, resulting in a series of extended data gaps from December 2021 to March 2023. This interval severely compromises the continuity and reliability of a long-term deformation analysis for the landslide.

3.2. InSAR Processing

The SBAS-InSAR technique was applied to multi-temporal SAR imagery under small baseline constraints. Redundant differential interferograms were generated and analyzed using time series methods to effectively separate atmospheric delays, residual topography, and noise. This process enabled millimeter-level retrieval of surface deformation [41].

3.3. Data Preprocessing

The core processing steps include geocoding, image co-registration with a master image, differential interferometry, adaptive filtering, minimum-cost flow phase unwrapping, GACOS atmospheric correction, and phase-to-deformation conversion, followed by final geocoding [42]. This technique is particularly well-suited for time-series deformation monitoring. The use of redundant interferograms helps suppress errors and increases temporal sampling, resulting in high-density surface deformation measurements.

To ensure that the model effectively captures temporal patterns and to reduce interference from long-term trends, the original InSAR deformation time series was subjected to a series of preprocessing steps prior to imputation.

3.3.1. Uniformization of the Time Series Step Length

We performed temporal alignment and Gaussian interpolation on the original InSAR deformation series to unify the time-step intervals and improve the sequence continuity. This step was necessary to accommodate the input requirements of the Seq2Seq–Posterior Correction model, which relies on evenly sampled time series for effective learning.

A unified time index set, T = {t₁, t₂, …, t_n}, was constructed to resample the original time series of each monitoring point to a consistent daily temporal resolution. For any time point t_k with missing observations, the corresponding value was estimated using a temporal linear regression approach as follows:

$${\widehat{x}}_{t_k}=x_{t_i}+{\displaystyle \frac{x_{t_j}-x_{t_i}}{t_j-t_i}}\cdot (t_k-t_i),t_i<t_k<t_j$$

(1)

where $x_{t_i}$ and $x_{t_j}$ denote the nearest available observations before and after the missing time point, respectively. To avoid residual gaps at the tail of the time series following the regression-based interpolation, a forward-filling strategy was additionally implemented.

3.3.2. Trend Decomposition and Normalization

After interpolation, we conducted trend decomposition and normalization to further preprocess the InSAR time series data. To isolate the underlying trend, we applied linear regression to the training sequences and decomposed the original series X_t into a long-term trend component T_t and a short-term residual component R_t, as shown below:

$$X_t=T_t+R_t$$

(2)

where T_t is estimated through linear fitting, and R_t is further normalized as follows:

$${\tilde{R}}_t={\displaystyle \frac{R_t-\mu }{\sigma }}$$

(3)

The normalized residual series was segmented into paired input–output samples (X, Y) using a sliding window strategy. Upon the completion of model training, we restored the predicted deformation values to their original physical scale through inverse normalization and trend reconstruction, yielding the final reconstructed deformation time series.

3.4. Imputation Model for Landslide Deformation Monitoring Data

Given the frequent occurrence of missing data within the InSAR deformation time series in long-term landslide deformation monitoring, we propose a hybrid missing data imputation model that integrates a sequence-to-sequence (Seq2Seq) long short-term memory (LSTM) network with a posterior correction module based on trend inversion and residual adjustment. The proposed model performs missing data imputation for time-series monitoring data through a three-stage framework consisting of trend decomposition and normalization, sequence-based imputation, and posterior trend correction. It leverages multi-source monitoring data to reconstruct complete historical deformation records and demonstrates strong capabilities in trend learning and imputation accuracy.

3.4.1. Seq2Seq LSTM Module

To enable multi-step missing data imputation while preserving temporal continuity in the deformation time series, we adopt a Seq2Seq architecture based on long short-term memory networks [43].

The overall model consists of three main components. First, the encoder processes a normalized input sequence of dimension D through a stack of L LSTM layers, extracting temporal features and encoding them into the final hidden and cell states (h_T, c_T). Second, the decoder initializes its internal state using these encoded vectors and iteratively generates the target sequence in an autoregressive manner. Finally, a linear output layer maps the decoder outputs at each time step back to the original feature space. To enhance training stability and accelerate convergence, we employ teacher forcing [44] with a scheduled sampling mechanism. This approach enables a smooth transition from fully supervised learning to autoregressive inference during training. The teacher forcing ratio r decayed exponentially over training epochs, following the recursive formulation below:

$$r_{t+1}=\max (r_t\cdot \gamma ,r_{\min }),\gamma =0.95$$

(4)

This mechanism initially relies on InSAR deformation results to stabilize training and gradually transitions toward autonomous sequence generation—facilitating effective imputation without external guidance.

The model incorporates a multi-objective loss function during training, aiming to maintain continuity between imputed and historical segments by balancing missing data imputation accuracy and boundary smoothness. The total loss is defined as follows:

$${\mathcal{L}}_{\mathrm{total}}={\mathcal{L}}_{\mathrm{main}}+\lambda \cdot {\mathcal{L}}_{\mathrm{cont}}$$

(5)

Specifically, $\mathcal{L}$_main represents the MSE between the imputed and ground truth sequences, while $\mathcal{L}$_cont introduces a penalty for discontinuity between the final time step of the input sequence and the initial point of the imputed segment. The balancing coefficient λ is empirically set to balance the two terms. This loss design effectively alleviates boundary artifacts and enhances consistency in both trend and amplitude between the imputed and original sequences. The AdamW optimizer is employed for model training, with early stopping (patience = 5) applied to avoid overfitting. The dataset was split chronologically into training, validation, and test sets in an 8:1:1 ratio.

3.4.2. Posterior Correction Module

Although the Seq2Seq LSTM model can effectively capture temporal trends in InSAR deformation time series, it inevitably suffers from error accumulation during extended imputations, often resulting in trend drift and deviations from the InSAR deformation time series. To improve the trend fidelity of the imputed segments, we introduce GNSS displacement records as external references and develop a posterior correction strategy based on deformation rate differences. Specifically, linear regression is applied over a time window preceding the imputation start point to estimate the slope of the actual deformation trend from GNSS data, which is then used to guide the correction of the predicted trajectory.

Let ${\widehat{y}}_t$ denote the imputed InSAR time series and gt the GNSS displacement series. To quantify trend deviation, we perform linear regression on the GNSS data over a T_m-day window preceding the imputation start to estimate the reference slope β_GNSS. Similarly, the slope of the imputed segment, β_imp, is obtained by fitting the tail of the predicted sequence. The trend offset is then defined as the difference between these two slopes:

$$\Delta \beta ={\beta }_{\mathrm{GNSS}}-{\beta }_{\mathrm{imp}}$$

(6)

A linear correction term is then applied to each time step t at the tail of the imputed segment to realign its trend with the reference slope:

$${\tilde{y}}_t={\widehat{y}}_t+\Delta \beta \cdot \left({\displaystyle \frac{t-t_s}{t_e-t_s}}\right)\cdot \eta$$

(7)

The variables tₛ and tₑ represent the start and end of the imputed interval, respectively, while η $\in$(0, 1) is a smoothing coefficient that governs the strength of correction. The adjustment is applied in a linearly increasing manner, allowing the imputed sequence to gradually align with the GNSS-derived trend. This progressive correction effectively mitigates cumulative prediction errors and suppresses trend drift over time.

3.5. Evaluation Metrics for Model Performance

To evaluate the model’s missing data imputation performance, we applied three commonly used error metrics on the test set: MSE, MAE, and PCC. MSE and MAE quantify the deviation between the imputed deformation and the original InSAR deformation time series, which are defined as follows:

$$\mathrm{MSE}={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{\left({\widehat{y}}_i-y_i\right)}^2}$$

(8)

$$\mathrm{MAE}={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\left|{\widehat{y}}_i-y_i\right|}$$

(9)

The PCC is used to assess the linear relationship between the imputed values and the original InSAR deformation time series, with a particular focus on capturing overall trends. The PCC is defined as follows:

$$\mathrm{PCC}={\displaystyle \frac{{\displaystyle \sum _{i=1}^n({\widehat{y}}_i-\overline{\widehat{y}})}(y_i-\overline{y})}{\sqrt{{\displaystyle \sum _{i=1}^n{({\widehat{y}}_i-\overline{\widehat{y}})}^2}}\cdot \sqrt{{\displaystyle \sum _{i=1}^n{(y_i-\overline{y})}^2}}}}$$

(10)

The terms ${\widehat{y}}_i$ and $\overline{y}$ represent the mean values of the imputed results and the original InSAR deformation time series, respectively. All metrics are computed independently at each monitoring point, and the results are organized into structured tables to facilitate further comparative analysis and error visualization.

4. Results

4.1. SBAS-InSAR Deformation Results

Following InSAR processing, the results were decomposed, and the vertical displacement component was used for subsequent analysis. Consequently, we obtained the average deformation rate and cumulative displacement of the landslide in the vertical direction from 15 April 2018 to 7 December 2021, which were subsequently used for time-series deformation analysis.

Figure 3a illustrates the spatial distribution of average deformation rates for the southern dump slope landslide, with vertical surface displacements ranging from −47 mm/year to 28 mm/year. The head of the landslide exhibits relatively high subsidence rates, while most of the central area shows a slow downward movement. Notably, uplift is observed at the boundary between the head and central area, as well as at the toe. The surface fractures and displaced drainage infrastructure identified at the landslide head during field surveys (Figure 3b,c) correspond well with the high deformation rates indicated by the InSAR analysis, thereby corroborating the reliability of the InSAR results.

To capture both regional and site-specific deformation dynamics, we utilized six cumulative InSAR deformation maps acquired between 2018 and 2021 (Figure 4), alongside three representative monitoring points—P078, P117, and P477—located at the landslide’s toe, central body, and head scarp, respectively (Figure 5). These locations, each coinciding with a GNSS station (NP03, NC32, and NC30), were examined across the full observation span from 15 April 2018 to 17 May 2023 to characterize long-term spatiotemporal deformation patterns. The results indicate that the Hesigewula southern dump slope landslide has undergone sustained deformation over the observation period, with both displacement magnitude and spatial extent progressively increasing year by year. The displacement magnitude in the subsidence direction is greater at the main scarp of the landslide, while most areas of the central body exhibit smaller deformations. A slight uplift is observed in some localized zones within the main body and at the toe.

Representative monitoring points P078 and P117 exhibited a relatively steady subsidence trend from April to October 2018, with a low and nearly linear deformation rate, indicative of slow, uniform movement. Between October 2018 and November 2019, displacement fluctuated but remained limited in magnitude, suggesting a state of quasi-stability. In November 2019, deformation accelerated noticeably, followed by a gradual reduction in displacement rate through April 2021, transitioning into a slower but persistent subsidence phase. On 8 May 2023, during the GNSS monitoring period, P117 experienced a sharp displacement surge, indicating the occurrence of a landslide event accompanied by significant structural failure at the main scarp. Meanwhile, P078 showed no significant displacement during the same period. The representative monitoring point P477 exhibited relatively minor deformation during the InSAR monitoring period, following a slow and near-linear subsidence trend. On 15 May 2023, during the GNSS monitoring phase, a moderate uplift was detected.

Figure 5 shows that the deformation at the three representative points is temporally correlated with external factors. During the 2018–2021 InSAR monitoring period, deformation acceleration typically occurs 3–10 days after the annual maximum 12-day average rainfall, indicating a strong coupling between landslide activity and peak precipitation events. Similarly, around April of each year, when surface temperatures rise and remain above 0 °C—marking the thawing period—the deformation rates at the monitoring points also increase steadily, often producing secondary displacement peaks in certain years.

4.2. Missing Data Imputation in Landslide Deformation Monitoring

Following the preprocessing of the original InSAR deformation time series as outlined in the methodology, the Seq2Seq LSTM–Posterior Correction model was applied to reconstruct the missing deformation intervals.

Specifically, the model is configured to take a 90-day historical deformation sequence as input and predict a 30-day missing segment. During training, input–output pairs are generated using a sliding window strategy, ensuring complete coverage of the available time series for learning.

Table 1. Hyperparameters of the Seq2Seq LSTM model.

Hyperparameters	Parameter
LSTM hidden size	128
Number of LSTM layers	2
Batch size	32
Loss function	MSE + 0.5 × continuity loss
Optimizer	AdamW
Initial learning rate	1 × 10−4
Weight decay	1 × 10−4
Teacher forcing (init/min/decay)	0.8/0.01/0.95

summarizes the detailed parameter settings of the model. The training was conducted using the AdamW optimizer, and an L₂ regularization term was incorporated to mitigate overfitting. The loss function consists of two components: a primary loss, defined as the mean squared error between the imputed and InSAR deformation time series, and a continuity constraint term that penalizes the deviation between the first point of the filled segment and the last point of the observed sequence. This design effectively addresses the boundary shift issue introduced by the sliding window approach.

After training, the model performed missing data imputation on the missing segments using a sliding window approach. Each output was restored to the original scale through trend reconstruction and inverse normalization. Following the initial missing data imputation, the results were further refined through a posterior correction procedure, which leveraged short-term deformation trends extracted from GNSS monitoring data. By enforcing trend consistency and smoothing the transition across the gap period, this step ensured that the reconstructed time series maintained temporal continuity and remained aligned with the physical deformation patterns observed in the GNSS data.

To enable a more comprehensive and visual assessment of the reconstructed long-term deformation, nine cumulative deformation surface maps were produced at 200-day intervals, covering the period from 1 November 2018 to 20 March 2023 (Figure 6). Meanwhile, the time series of representative monitoring points were completed by filling in the missing segments, thus providing a continuous deformation record for further analysis (Figure 7). Details of the missing data imputation (quarterly sampling for representative monitoring points) are provided in Appendix A (

Table A1. Cumulative displacements of representative monitoring points after missing data imputation (quarterly sampling).

Date	P078 (mm)	P117 (mm)	P477 (mm)
30 April 2018	−9.08625	−8.8155	−4.357
31 July 2018	−19.15342	−20.557	−14.8835
31 October 2018	−16.90858	−35.10675	−24.71433
31 January 2019	7.65175	−25.08475	−29.94925
30 April 2019	0.933	−30.70267	−42.58533
31 July 2019	−0.568	−37.97467	−31.51033
31 October 2019	−5.8745	−38.1775	−40.5775
31 January 2020	−40.60367	−57.877	−39.899
30 April 2020	−81.99587	−96.74223	−46.54307
31 July 2020	−88.94933	−110.66167	−54.37
31 October 2020	−119.02725	−125.54475	−65.25675
31 January 2021	−133.01722	−144.48028	−61.17356
30 April 2021	−155.04006	−169.93448	−54.76952
31 July 2021	−151.6105	−162.56767	−57.44433
31 October 2021	−158.48758	−175.65467	−64.32953
31 January 2022	−167.56662	−189.83428	−69.2904
30 April 2022	−151.99594	−183.37887	−71.32601
31 July 2022	−154.26318	−190.10727	−79.95189
31 October 2022	−142.47695	−185.82915	−81.39671
31 January 2023	−155.81659	−194.569	−80.71175
30 April 2023	−156.42469	−241.52894	−94.27434
17 May 2023	−159.03469	−3280.81894	−37.02434

).

As shown in Figure 6, the reconstructed deformation field captures the full progression of the landslide process. During this period, the southern dump slope landslide experienced a cumulative subsidence of −234 mm and an uplift of up to 85.1 mm. Deformation initially emerged at the main scarp, gradually propagated through the main body, and eventually reached the toe. The most pronounced subsidence occurred near the boundary of the main scarp, while a small uplift zone was detected within the adjacent part of the main body. The majority of the toe experienced only slight deformation, while more noticeable uplift occurred along the toe boundary and at the junction between the toe and the main body. Considering the timing and intensity of deformation across different landslide zones, along with the observed surface morphology, the landslide can be classified as a slowly evolving translational landslide [45]. Initial movement occurred at the main scarp, exerting a downslope driving force on the main body and toe, which subsequently underwent progressive deformation. The uplift deformation observed at the junctions between different zones of the landslide may be attributed to compressive forces acting along the internal boundaries [46,47].

During the gap period in July and August 2022, the representative points entered an accelerated deformation phase several days after the heavy rainfall events. In April 2023, during the thaw period, deformation at the monitoring points accelerated rapidly, followed shortly by slope failure. Comparison between the imputed results and original InSAR monitoring indicates that the deformation behavior during the gap period closely mirrors the patterns recorded in the InSAR monitoring timeframe.

Representative monitoring points at different locations across the landslide body exhibited consistent deformation responses to external factors, highlighting the system’s sensitivity to such influences. Considering the deformation and failure mechanisms of landslides under intense rainfall and freeze–thaw conditions [48,49], we infer that (1) heavy rainfall increases pore water pressure through infiltration, which undermines the overall mechanical strength of the slope material and subsequently accelerates slope movement [50], and (2) freeze–thaw processes promote the development of tensile cracks within the slope, particularly in areas with poor surface drainage or heterogeneous distributions of ice-rich materials, further compromising slope stability [51].

Although the internal structure and material composition of the landslide fundamentally determine its deformation mechanisms, external factors often play a dominant role during critical stages, significantly influencing its development trajectory and deformation trends [52]. Coupling the imputed long-term deformation time series with rainfall and temperature data not only reveals the driving effects of external factors on landslide evolution but also confirms the effectiveness of the proposed missing data imputation approach in reconstructing missing deformation data.

5. Discussion

5.1. Model Evaluation for Missing Data Imputation

To evaluate the performance of different imputation methods for missing deformation data in the study area, we conducted a comparative analysis at three representative points—P078 (toe), P117 (main scarp), and P477 (main body) of the landslide. The methods assessed include linear regression, baseline LSTM, and the proposed Seq2Seq LSTM–Posterior Correction model. These three approaches, respectively, represent a conventional empirical method, a basic deep learning model, and the improved method proposed in this study—offering representative and meaningful comparisons.

Figure 8a–c clearly show that the linear regression method relies solely on extrapolating historical trends, making it inadequate for capturing the dynamic characteristics of deformation. It performs reasonably well only during periods of strong continuity in the displacement signal. The baseline LSTM model generally performs well in the early stages of the test period. However, as the time steps progress and deformation signals become increasingly variable, the single-layer architecture struggles to capture complex temporal patterns. In some cases, its performance in the later stages even falls behind that of the linear regression approach [53].

The Seq2Seq LSTM–Posterior Correction model consistently demonstrates superior performance across all three monitoring points, particularly during the later stages of the test period. It effectively captures the underlying deformation trends and exhibits significantly lower error accumulation over time compared to the other two methods.

To further quantify the performance of the three methods, we calculated the MSE, MAE, and PCC at each of the three representative monitoring points (Figure 9a–c). The results indicate that the Seq2Seq LSTM–Posterior Correction model exhibits a more concentrated error distribution with fewer outliers, demonstrating superior stability and generalization capability. In contrast, the linear regression and baseline LSTM models yield larger errors and more outliers at certain monitoring points. Although they show relatively good fits at specific locations, their overall accuracy and temporal consistency across the test period are inferior to those of the Seq2Seq LSTM–Posterior Correction model.

In summary, the Seq2Seq LSTM–Posterior Correction model demonstrates clear advantages in addressing missing data in landslide deformation monitoring. It effectively captures both local variability and overall trend patterns, making it well-suited for missing data imputation in nonlinear and complex time-series deformation scenarios.

5.2. Field Validation of Reconstruction Results

To further verify the accuracy of the imputed deformation data, we carried out a detailed field survey and UAV photogrammetry at the southern dump landslide of the Hesigewula South Open-Pit Coal Mine in May 2023. Based on integrated field and UAV data interpretation, the landslide was subdivided into five zones: Backscarp Source Zone, Compression Failure Zone, Transverse Sliding Zone, Central Slide Zone, and Frontal Rupture Zone.

In the Backscarp Source Zone (I), intense deformation has produced two stepped scarps at the backscarp, with lengths ranging from approximately 330 to 640 m and step heights between 0.3 and 15 m. A set of extensional cracks was observed up to approximately 70 m from the backscarp. Severe deformation is evident in this zone, where the downward displacement of two scarps imposed tensile stress on the upslope area. As a result, a series of arcuate transverse cracks developed behind the rear scarp and extended further upslope. In the Compressive Deformation Zone (II), pronounced compressional failure is observed. Due to the concave geometry of the sliding surface—gently inclined in the front and steep at the rear—the downslope movement of the Backscarp Source Zone exerts thrusting forces on the central slope, leading to extensive surface cracking and the development of two distinct uplifted zones (① and ②) within the mid-slope (Figure 10. II), with respective uplift heights of approximately 8 m and 10 m. The downslope movement in the Central Slide Zone exerted lateral tension on the adjacent Transverse Sliding Zone (III), inducing a horizontal sliding process across the entire area. A scarp has formed along the right boundary, accompanied by measurable displacements in both horizontal and vertical directions. In the Central Slide Zone (IV), the slope exhibits an overall translational movement driven by the displacement of the Backscarp Source Zone. Although the degree of deformation is relatively moderate, extensive surface cracking is observed throughout the area. A well-defined offset occurs along the left boundary, accompanied by echelon shear–tensile cracks. In the Frontal Rupture Zone (V), the ground surface is extensively fractured, indicating weak material properties. Uplift is evident at the interface with the Central Slide Zone due to compressional forces. Large-scale cracks are widely distributed, reflecting severe deformation and structural damage across the area.

The deformation features interpreted from field investigations—including the two-stepped scarps and localized uplift at zone boundaries—together with the spatiotemporal evolution they imply, closely correspond to the deformation trends reconstructed by the Seq2Seq LSTM–Posterior Correction model. Specifically, the landslide evolution interpreted from the reconstructed deformation time series shows strong spatial and kinematic agreement with the field-based interpretations in terms of both deformation intensity and spatial extent. The observed consistency underscores the accuracy of the Seq2Seq LSTM–Posterior Correction model in imputing missing deformation data across both time and space. The complete time series enables reliable identification of critical deformation areas and provides a faithful representation of the landslide developmental trajectory.

5.3. Limitations and Future Work

While the proposed Seq2Seq LSTM–Posterior Correction model shows strong performance in imputing missing data for dump-slope landslides in open-pit mining areas, its applicability to other geomorphic settings and deformation regimes remains to be systematically assessed. Different types of landslides exhibit significant variations in triggering mechanisms, failure processes, and internal structures [54,55], which may necessitate structural adaptations of the model or the use of more diverse training samples to effectively capture their respective deformation characteristics.

The model relies on long-term continuous monitoring data for training. Although trend decomposition and teacher forcing strategies have been incorporated to enhance temporal stability, their imputing performance may be compromised in cases of severe data loss or limited early-stage observations, thereby constraining their applicability under such conditions.

Comprehensive parameter uncertainty and sensitivity analyses for the posterior correction were not conducted due to data limitations and will be addressed in future work. The current model is entirely data-driven and does not incorporate the physical mechanisms underlying landslide initiation and evolution. Future work could integrate external influencing factors—such as rainfall, freeze–thaw cycles, and geotechnical structure—into the model as auxiliary variables via attention mechanisms [56], thereby enhancing its interpretability.

6. Conclusions

In this study, we integrated SBAS-InSAR and GNSS monitoring techniques to impute the data gaps (8 December 2021 to 20 March 2023) of the south dump landslide at the Hesigewula South Open-Pit Coal Mine, using the Seq2Seq LSTM–Posterior Correction model to enable long-term time-series analysis.

(1)

The Seq2Seq LSTM–Posterior Correction model first employs a residual-coupled Seq2Seq LSTM to extract nonlinear deformation features and impute the missing segments under continuity constraints. Subsequently, a posterior correction module based on deformation rate discrepancies was applied to align the imputed trend with GNSS-derived rates. This adjustment effectively reduced cumulative prediction errors over time and mitigated trend drift in the imputed sequences;

(2)

The SBAS–InSAR results and the imputed deformation data during the gap period exhibited strong consistency in their response to both heavy rainfall and freeze–thaw processes. The reconstructed long-term deformation series indicated a strong correlation between slope evolution and external climatic factors, particularly precipitation and freeze–thaw cycles. We infer that intense rainfall gradually increases pore water pressure through infiltration, thereby weakening the mechanical integrity of the dump slope landslide. Meanwhile, freeze–thaw processes induce the development of tensile cracks within the slope body, further accelerating deformation;

(3)

Compared with traditional imputation approaches, the proposed model achieved lower errors and higher trend consistency, further validated by field surveys and UAV-based optical modeling in May 2023, which confirmed high consistency between observed and imputed deformation;

(4)

To enhance the interpretability and applicability of the model, future research could incorporate explainable attention mechanisms to improve the model’s responsiveness to external factors and its ability to capture the stage-specific deformation characteristics of landslides, while parameter uncertainty and sensitivity analyses for the Posterior Correction module will also be explored when more data are available.