# Mining Deformation Life Cycle in the Light of InSAR and Deformation Models

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. InSAR Deformations

#### 1.2. Subsidence Modelling

#### 1.3. Gaps and Advantages of InSAR and Models

## 2. Materials and Methods

#### 2.1. Sentinel-1 Data and DInSAR Methodology

#### 2.1.1. DInSAR Processing and Post-Processing

- Step 1: Classical cumulative DInSAR processing,
- Step 2: Quality assessment of the radar signal,
- Step 3: Unification of the results in a common vertical datum by trend removal,
- Step 4: Decomposition from displacement in the direction to the satellite LOS into vertical and horizontal directions, and
- Step 5: Geospatial analysis for extraction of the area affected by the mine subsidence and the lower point of the subsidence trough.

#### 2.1.2. Signal Quality Evaluation

#### 2.1.3. Trend Removal

#### 2.1.4. Three-Dimensional Decomposition

#### 2.1.5. Geospatial and Statistical Analyses

#### 2.2. Deformation Modelling

#### 2.2.1. Generalised Dynamic Subsidence Modelling

#### 2.2.2. Model Application and Parameter Estimation

- –
- subsidence factor: $a=1.13$;
- –
- dispersion parameter of primary mining influences (rock mass parameter): $\mathrm{tan}\beta =3.6$ (the angle of draw is about 75°);
- –
- exploitation rim: $p=90m$;
- –
- time factors describing immediate mining influences: ${A}_{1}=0.8$ and ${c}_{1}=300$ per year;
- –
- time factors describing residual mining influences: ${A}_{2}=0.2$ and ${c}_{2}=6$ per year.

#### 2.3. Verification

#### 2.3.1. Time Aggregation

#### 2.3.2. Levelling

## 3. Case Study

^{2}, of which 5800 km

^{2}are in Poland (Figure 8). The Polish part along with the Lower Silesian Basin and Lublin Basin provides 92% of the needed electricity and 89% of the heat for Poland according to the World Energy Council [48]. The USCB has been intensively exploited since the nineteenth century, when coal and lignite extraction strengthened the industrialisation, followed by its peak in Eastern European countries during the post-Second World War period [49]. Nowadays, coal regions still have ongoing mining, which provides a number of workplaces for about 185,000 employees in the EU [50] and brings together a large population of people. Consequently, the USCB is one of the most densely populated zones in Poland (Figure 8). Since 1970, almost 40% of coal mining activities have been located under an urbanised area, where about 600 km

^{2}are affected by intensive underground coal extraction each month [17].

#### Geological and Mining Conditions in the Area of Interest

## 4. Results

#### 4.1. Cumulative Surface Deformations

#### 4.2. Monthly Deformation

#### 4.3. Verification with Levelling

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Ascending (blue) and descending (green) orbit footprints of Sentinel-1 data used in this study over the territory of the Polish part of Upper Silesian Coal Basin (USCB).

**Figure 4.**Quality assessment of the ascending (Asc) and descending (Desc) interferograms. The values in the bars show the perpendicular baselines of each interferogram.

**Figure 5.**An example of trend removal for the descending orbit, displacements between 2nd and 8th of January 2017: Original data (

**left**), trend function (

**middle**), and smoothed data (

**right**). The example is the local (image) coordinate system; deformation values in [m]. Please note different deformation scales in the original and smoothed images.

**Figure 6.**Distribution of steady ${w}_{k}\left(t\right)$ and dynamic $w\left(t\right)$ subsidence [2].

**Figure 7.**Levelling network in the Miechowice district (

**left**) and the chosen reference dates for each levelling cycle (

**right**).

**Figure 8.**Population density in Poland for 2011 (

**left**), according to the Central Statistical Office, and in the USCB (

**right**).

**Figure 9.**(

**a**) The range of the investigated longwalls No. 5 and 6 from seam 503 of the Bytom-III mining area located in the northern part of USCB (see Figure 8 right); (

**b**) depth of the longwalls with respect to the sea level. The numbers represent the starting date (YY.MM) for extractions from the corresponding panel; (

**c**) terrain elevation above the mined area from Shuttle Radar Topography Mission (SRTM) Digital Elevation Model (DEM).

**Figure 10.**Cumulative surface changes for the entire year of 2017: (

**a**) Displacements in the east-west direction from DInSAR, (

**b**) from the model, (

**c**) vertical subsidence derived from DInSAR, and (

**d**) from the model.

**Figure 11.**Areal resemblance between Differential satellite radar interferometric (DInSAR) measured and expected range of surface deformation;

**Left**: Example for March;

**Right**: Percentage in the overlay area.

**Figure 14.**Profile A′A′′ (longwall No. 6) through the DInSAR: The blue curves show the vertical subsidence by month in 2017. The grey vertical lines show the location of the panels of extractions according to the starting date (above each graph). The shaded area is the currently extracted panel for the presented month. On the bottom of the figure, profiles of the DEM surface and depth and thickness of coal seam are presented.

**Figure 15.**Profile A′A′′ (longwall No. 6) through the models. The red curves show the vertical subsidence by month in 2017. On the bottom of the figure, profiles of the DEM surface and depth and thickness of coal seam are presented.

**Figure 16.**Profile B′B′′ (longwall No. 5) through the DInSAR. The blue curves show the vertical subsidence by month in 2017. On the bottom of the figure, profiles of the DEM surface and depth and thickness of coal seam are presented.

**Figure 17.**Profile B′B′′ (longwall No. 5) through the models. The red curves show the vertical subsidence by month in 2017. On the bottom of the figure, profiles of the DEM surface and depth and thickness of coal seam are presented.

**Figure 18.**Amount of maximal subsidence by months detected by DInSAR (blue) and predicted from the model (red), compared with the estimated material extraction from coal seam 503. The black axis values on the right and bottom represent the subsidence and corresponding dates, respectively. The grey axis values on the left and above the graph relate to the amount of the extracted material and the time for these events.

**Figure 19.**Velocity (

**left**) and acceleration (

**right**) of the subsidence for the extremal points by months.

**Figure 20.**Comparison of the subsidence [in meter] along the levelling lines from Figure 7 between DInSAR results, levelling and predicted by the model data: (

**a**) profile along levelling line 1′1′′, (

**b**) profile along levelling line 2′2′′, (

**c**) profile along levelling line 3′3′′, (

**d**) profile along levelling line 4′4′′, (

**e**) profile along levelling line 5′5′′, (

**f**) profile along levelling line 6′6′′

**Figure 21.**(

**a**) Correlation between subsidence from the levelling (vertical axis) and DInSAR (blue) and model (red) along the horizontal axis; (

**b**) histogram of the distribution of errors between subsidence derived from levelling (L), DInSAR (D), and modelling (M); and fields of errors for (

**c**) L-D and (

**d**) L-M.

**Table 1.**Dataset of determined parameters of the Knothe–Budryk theory and standard deviation (Std) values of matching for exploitation of the 503 seam with longwalls No. 5 and 6.

Drawn Line (Profile Lines from Figure 7 in Brackets) | Determined Subsidence Parameters from the Knothe–Budryk Theory | Std of Subsidence Parameters Matching $\mathit{\sigma}$, mm | ||
---|---|---|---|---|

Subsidence Factor $\mathit{a}$ | Rock Mass Parameter $\mathbf{tan}\mathit{\beta}$ | Exploitation Rim $\mathit{p}$, m | ||

no 1 (2′-2′′) | 1.13 | 4.5 | 90 | 235 |

no 2 (1′-1′′) | 1.00 | 3.1 | 90 | 91 |

no 3 (4′-4′′, 2′-2′′, 6′-6′′) | 1.14 | 2.7 | 50 | 257 |

no 4 (6′-6′′) | 1.25 | 3.3 | 90 | 86 |

no 5 (5′-5′′, 6′-6′′, 4′-4′′) | 1.08 | 2.9 | 90 | 281 |

**Table 2.**Statistical assessment of the DInSAR (D) and model (M) data compared to the verification data from levelling (L).

$\mathit{R}$ | $\overline{\mathit{d}\mathit{w}},\text{}\mathbf{m}$ | ${\mathit{\sigma}}_{\overline{\mathit{d}\mathit{w}}},\text{}\mathbf{m}$ | |
---|---|---|---|

L-D | 0.89 | -0.04 | 0.183 |

L-M | 0.85 | 0.20 | 0.388 |

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## Share and Cite

**MDPI and ACS Style**

Ilieva, M.; Polanin, P.; Borkowski, A.; Gruchlik, P.; Smolak, K.; Kowalski, A.; Rohm, W.
Mining Deformation Life Cycle in the Light of InSAR and Deformation Models. *Remote Sens.* **2019**, *11*, 745.
https://doi.org/10.3390/rs11070745

**AMA Style**

Ilieva M, Polanin P, Borkowski A, Gruchlik P, Smolak K, Kowalski A, Rohm W.
Mining Deformation Life Cycle in the Light of InSAR and Deformation Models. *Remote Sensing*. 2019; 11(7):745.
https://doi.org/10.3390/rs11070745

**Chicago/Turabian Style**

Ilieva, Maya, Piotr Polanin, Andrzej Borkowski, Piotr Gruchlik, Kamil Smolak, Andrzej Kowalski, and Witold Rohm.
2019. "Mining Deformation Life Cycle in the Light of InSAR and Deformation Models" *Remote Sensing* 11, no. 7: 745.
https://doi.org/10.3390/rs11070745