This study investigated the role of the number of differentialinterferograms and coherent threshold values on the accuracy of SBAS InSAR (small baseline subset interferometric synthetic aperture radar) results for specific applications in Jiyang Coal. Fifty-eight imageswere utilized to form fourdifferential interferogram timeseries with different numbers of interferograms and coherence thresholds. The four SBAS InSAR-monitored results, mining information of 15 working faces, and levelling-monitored results of 260 levelling points werecompared.The greater number of differential interferograms and lower coherent threshold values could better reflect the spatial distribution and variation trend of mining subsidence and demonstrate the advantages of SBAS InSAR. However, an excessive number of differential interferograms and excessively low coherent threshold values would increase the data processingdifficulty and the differences between SBAS InSAR- and levelling-monitoredresults. Location, spatial distributionandscopeofSBAS InSAR-monitored mining subsidence were consistent with the mining progress of the working faces.The accuracy ofSBASInSAR-monitored subsidence values followed a certain spatio-temporal variation law. The variation trend of absolute differences between SBAS InSAR-and levelling-monitored subsidence values was similar to the shape of the levelling-monitoredsubsidence basin, which was helpful to study the correction method of SBAS InSAR-monitored results.

In coal mining areas, surface subsidence poses significant risks to human life and property. Fortunately, surface subsidence caused by coal mining can be monitored and predicted by using various methods, e.g., probability integral method and deep learning (DL) methods. Although DL methods show promise in predicting subsidence, they often lack accuracy due to insufficient consideration of spatial correlation and temporal nonlinearity. Considering this issue, we propose a novel DL-based approach for predicting mining surface subsidence. Our method employs K-means clustering to partition spatial data, allowing the application of a gate recurrent unit (GRU) model to capture nonlinear relationships in subsidence time series within each partition. Optimization using snake optimization (SO) further enhances model accuracy globally. Validation shows our method outperforms traditional Long Short-Term Memory (LSTM) and GRU models, achieving 99.1% of sample pixels with less than 8 mm absolute error.

For the small baseline subset (SBAS) interferometric synthetic aperture radar (InSAR) technique, the construction and subsequent robust solution of a deformation model is a key factor in obtaining monitored surface deformation results with high precision and high reliability. Here, the performance of the least squares (LS) and singular value decomposition (SVD) methods for the robust solution of SBAS InSAR deformation models are compared via tests with simulation and real SAR data. The LS method is used to solve the SBAS InSAR deformation models of 62 and 48 multi-temporal differential interferogram series; the SVD method is used to solve the SBAS InSAR deformation models of 60, 41, 58 and 53 multi-temporal differential interferogram series; the solved deformation results of the six series by the LS and SVD methods are compared and verified with the simulated deformation values and global positioning system (GPS) measurements. The results indicate that there is a moderate ill-posed degree in solving the SBAS InSAR deformation model by the LS method. The LS method can correctly retrieve the deformation information without considering any errors; however, in the case of serious random error, the deformation information acquired through the LS method is different from that of the simulation and is affected by the error of the multi-temporal differential interferometric phase series. The LS-solved results of real SAR datasets of two series are consistent, but are not in good agreement with the results of five GPS measurements. When the number of subsets is two, all types of deformation information solved by the SVD method follow the same rules as the results solved by the LS method. However, when the number of subsets increases to three and four, the stability of the SVD method becomes very poor; the SVD method can then only correctly solve the distribution of deformation in the study area, and the other solved deformation information, such as deformation velocity, is no longer credible.

The optimal selection of multi-temporal differential interferogram series is an important step to monitor ground subsidence using the Stanford method for persistent scatterers (StaMPS)-based small baseline subset (SBAS) interferometric synthetic aperture radar (InSAR). Using a deformation model and its two solution methods, least squares and singular value decomposition, we present the composing mode and optimal selection of multi-temporal differential interferogram series and show that their quality and quantity affect the accuracy of monitored deformation information of SBAS InSAR. Using 29 ENVISAT ASAR images covering urban areas of Beijing, China, a different number of optimal multi-temporal differential interferogram series are formed to monitor urban ground subsidence by the StaMPS-based SBAS method. The comparison and verification of test results indicate that the quality and quantity of multi-temporal differential interferogram series substantially impact the singularity and degree of ill condition of the deformation model, locations of the selected slowly decorrelating filtered phase (SDFP) pixels, and monitored annual mean subsidence velocities. The suitable number of multi-temporal differential interferogram series under the optimal quality is 1–2 for a month in urban ground subsidence monitoring using StaMPS-based SBAS InSAR, a higher quantity of differential interferograms of the optimal quality is not always better.