# Mining Deformation Life Cycle in the Light of InSAR and Deformation Models
## 1 Introduction
### InSAR Deformations
A solution to deal with the overestimation of subsidence in the focus of the subsidence trough is the combination of two InSAR techniques--conventional for the fast motions and advanced for the residual subsidence. The DInSAR technique has one more priority in the study of mining subsidence. It may deliver valuable information about the subsidence dynamics. With the constellation of the satellites, Sentinel 1A and 1B, the map of the surface deformation can be obtained every six days. Thus, the operational dynamic of the mining subsidence is directly related to the coal extraction and the position, shape, and length of the mining front can be monitored in detail. In one of the first InSAR studies aimed at a precise understanding of mining subsidence [14], 10 ALOS PALSAR L-band images were used. This study investigated the accuracy of the predictions for subsidence using InSAR line-of-sight (LOS) deformation. The standard DInSAR processing was applied with the removal of Digital Elevation Model (DEM) errors and the application of careful atmosphere corrections. The model of deformation followed the Finite Element Method (FEM; FLAC3D by Itasca Consulting Group Inc., Shrewsbury, Shropshire, UK) based on the Mohr-Coulombfracture. The maximum predicted subsidence in the LOS direction revealed that it always shifted to the south-west and reduced by 10%-15% with respect to the vertical direction. A subsidence of 70 cm in the LOS was compared to the GNSS field and deformation modelling. The horizontal displacement was defined on the level of 30% to 50% of the vertical component. The verification with GNSS deformation showed that the InSAR underestimated LOS deformations, especially for the largest quantile, but the difference between InSAR and GNSS did not exceed 45 mm. The correlation between model deformation and InSAR deformation was very high and reaches 0.95. Discrepancies existed in the peak deformation and transition edges on the edge of deformation zone. Another mining subsidence study [21] provided a comparison between the SBAS and the consecutive and cumulative DInSAR for the estimation of mine subsidence using RADARSAT-2 data with a revisit period of 24 days. The SBAS showed a more detailed pattern and worked better for investigating the extent of the subsidence; however, differences between SBAS and DInSAR were on the level of 0.02 m in the LOS. Moreover, the results were not verified with levelling or other in-situ techniques. The area was extracted using the longwall technique, and the velocity of extraction varied between 3 and 13 m/d. The most reliable approach for verification of the DInSAR results is the comparison with in-situ measurements of the terrain deformation. The most precise observations of vertical displacements are obtained by conventional geodetic levelling, while the horizontal motions are usually determined by GNSS point positioning. Both techniques, in contrast to the vast coverage of DInSAR remote sensing, provide data for discrete sparsely located points and are also time and cost-consuming. Different approaches have been proposed for fusing these inhomogeneous results regarding datum, time, and space [22; 23; 24]. Nevertheless, these studies are limited to linear deformations or are in an early stage of development. In another studies [17; 25] it was proven that the SAR interferometry is applicable in the investigation of the mining subsidence dynamics and the spatial distribution with several examples from USCB, which opened new opportunities for urban planning and the protection of linear constructions such as roads, railways, and pipelines. The interferometric results showed a strong relation with the position, shape, and length of the mining fronts, the rate and techniques of mining activities, the geological structures in the investigated mines, and the presence of abandoned mine workings. The difference in the rate of subsidence in different areas depends on the thickness of the coal seams and on the presence of Quaternary sediment cover [17].