# An Overview of GIS-Based Assessment and Mapping of Mining-Induced Subsidence
## 3 Mine Subsidence Susceptibility/Hazard Assessment and Mapping
### Literature Review According to Analytic Methods and Approaches
#### 3.2.7 Vertical Displacement  
In this section, unlike previous studies that mainly showed the susceptibility or hazard of mining subsidence as zoning (horizontal subsided area), several studies have predicted the vertical displacement (z-axis) based on past actual settlement amounts using regression equations or collapse theories. These studies usually provided a difference distribution map between observed subsidence and predicted subsidence. Vertical displacements can have positive and negative increments. The prediction methods used in this section describe the vertical displacement as subsidences. The geographically weighted regression (GWR) method, which allows for spatial variability of subsidence factors, has been applied to map vertical displacement with subsidence zoning. In previous studies, most of the subsidence inventory data were binary type data, such as 0 (nonoccurrence) or 1 (occurrence). On the other hand, subsidence inventory data used in GWR techniques are mainly indicative of vertical displacement. [PERSON] [41] predicted and mapped vertical displacement with subsided zoning (in three axis directions) within complicated mining conditions in Poland. Seven subsidence contributory factor data types and subsidence inventory data between 1886 and 2009 within the study area were used as inputs for the GWR method. As a result, cavity factors (thickness, inclination, and depth) and surface slope factor were identified as significant parameters. Using the regression equation between past vertical displacement and factor values, a hybrid map of subsidence for the entire study area was produced. The maximum predicted subsidence in these areas was calculated to be \(-10.5\) m. Similarly, [PERSON] et al. [42] adopted the GWR model and five triggering factors to predict amount of settlement in the Sanshandao area, Laizhou, Shandon Province, China. The accuracy of determining subsidence in the area used for validation was \(\pm 8.5\) mm with a maximum calculated subsidence of \(-329.26\) mm. The maximum subsidence predicted with the model for the seabed was \(-63\) mm with a mean subsidence of \(-50\) mm. Conversely, a few studies predicted vertical displacement within mine areas using traditional theories or empirical equations. [PERSON] and [PERSON] [43] introduced the influence function methods called [PERSON]'s theory-based subsidence prediction approach. This theory allowed for the input of various parameters (e.g., distance from the center of elementary exploitation, volume extracted in the exploitation part, radius of the range of main influence of mining activities, exploitation depth, angle of the main influence range, extraction coefficient, and others) to calculate the vertical displacement for the entire study area. Figure 5 shows a \(5\) m \(\times\)\(5\) m raster grid-based map that demonstrates the surface subsidence that was measured and predicted, as well as the difference between the two values in 2005. [PERSON] et al. [44] simulated the phenomenon of progressive movement distribution and damage to structures from large sequential coal mining in China using a new 3D GIS coupling model. This model combines theoretical methods of predicting subsidence over time using a stochastic medium concept involving the Knothe time function for basic governing equations to calculate progressive movement. Through coupling with GIS, this model can effectively and spatially model the vertical