# Mining Deformation Life Cycle in the Light of InSAR and Deformation Models
## 1 Introduction
### Subsidence Modelling  
Over the past decades, subsidence models were developed [18] to simulate the effects of mining, including coal mining, on the land and infrastructure. According to [28], these methods are divided into two groups: Numerical and empirical methods for surface deformation prediction. The first group includes the FEM, finite-difference method, discrete element method, and cellular automata theory. Widely used in Chine is also the Probability Integration Method [29]. The second group comprises profile function, graphical method, the application of artificial neural networks, and the influence function. One of the most used methods that relate the subsidence and time is the influence function developed by [PERSON] [30]. The method assumes a normal distribution of influence. It was introduced for the first time in Poland in the 1950s, and, since then, it has become the main model used by the mining-related institutions in this country, The model is implemented in several pieces of software widely used in Poland like \"Damage\" designed in Central Mining Institute in Katowice, \"EDN\" designed in the Technical University in Gliwice, and \"Modez\" designed in the University of Science and Technology in Cracow. The main reason this model was adopted for common usage is that it has simplicity in assumptions and mathematic description. It also has a few parameters that can be modified which provide flexibility in the calculation. On the other hand, the Knothe model is in effective use in Poland since the subsidence prediction results are the basis for mining terrain classification. In addition, the mining exploitation plans and rules for structure protection are described by taking into account this result. Nowadays, the Knothe model is still developing according to different geological and mining conditions like deeper and multi-seam mining. The complexity of these types of extractions often results in non-full shape subsidence troughs. According to the classic approach to modelling mining-induced subsidence [18] there are three phases of deformation caused by longwall extraction: Phase I initial subsidence, starting with commencing excavation and finishing once the excavation face reaches the subsiding point; Phase II, the main subsidence that extends for a specified portion of time and is characterised by a steep increase of the subsidence; and Phase III, which follows the main subsidence and ends when the point reaches the asymptotic final subsidence. All phases are usually represented by simple model [30]. Initially, these parameters were estimated 60 years ago when mining exploitation was carried out with a low rate of advance (up to 2.5 m/day), most often in rock mass that had never been mined before and when geodetic surveys were performed in time intervals much longer than one day (usually every three or six months were available) [31]. Analysis of subsidence over the last 25 years, with one day or even a few hour intervals, enabled the generalisation of the model and accommodated a much quicker advance of the longwall [2; 32]. Further modifications to the same model are usually done to consider new extraction techniques, such as solid backfill mining [1]. Currently, subsidence modelling (fitting S-shape subsidence function) is performed using standard geodetic observations, such as levelling or tachymetry [1; 2]. Most recently, a few authors have also been testing the use of levelling and InSAR data to obtain subsidence function parameters [33] or only using InSAR [34; 35]. However, this is the initial stage of the research in this direction. Another approach to subsidence modelling is based on the Mohr-Coulomb model, which is a three-dimensional (3D) explicit finite-difference geological engineering tool [14; 36; 37]. These models are not in use for coal mines investigated in this study and are rarely in use for operational purposes. In another study [28], it is shown the range of influence of the used geodetic observations on the forecasting accuracy.