# Estimation of Mining-Induced Horizontal Strain Tensor of Land Surface Applying InSAR

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area and Input Data

^{2}area that included sections of the mining sites of “Sieroszowice”, “Głogów Głęboki-Przemysłowy”, and “Gaworzyce” (Figure 1).

## 3. Research Methodology

## 4. Results and Discussion

#### 4.1. Experimental Data

#### 4.2. Real-World Case Study

^{2}. The maximum vertical displacements reached −167 mm with σ = ±${d}_{ALD}$ ranged from −110 mm to +62 mm with σ = ±8 mm. The detected land subsidence has a symmetrical distribution, with the highest values located in the centre of each subsidence trough (Figure 6A). The least visible trough is in the study area’s ${d}_{ALD}$ displacements (Figure 6B). The negative horizontal displacement values reflect westward movement while the positive values show movement into the east. Thus, the eastern parts of each trough have negative horizontal displacement values (displacements towards the centre of land subsidence trough), whereas the western parts have positive displacement values (displacements also towards the centre of land subsidence trough). This demonstrates that the land subsidence in the case study is a gravity-driven process.

^{2}of 0.805. In general, the region with the greatest absolute horizontal displacements corresponds to the highest values of the first derivative of vertical displacement (Figure 7).

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**A**) Location of the case study area in the map of Poland; (

**B**) mining areas belonging to the Kombinat Górniczo-Hutniczy Miedzi (KGHM) Company in the area of interest; (

**C**) main built-up areas and surface infrastructure in the case study.

**Figure 2.**(

**A**) 3-D overview of the model data used in the study during the theoretical computational experiment; (

**B**) vertical cross-section of the model.

**Figure 3.**The configuration of interferograms used in the investigation on a time plot, with the perpendicular baseline for Sentinel-1 satellite acquisitions in ascending (

**A**) and descending (

**B**) mode.

**Figure 5.**The vertical displacements (

**A**) and the horizontal strains (

**B**) obtained from model data. The calculated deformation values (

**C**) follow the same colour scheme as the model values. The disparity between theoretical and calculated values is displayed in (

**D**).

**Figure 6.**The results of the LOS decomposition into the vertical (

**A**) and ALD horizontal (

**B**) components of the land surface displacement field in the case study.

**Figure 7.**The relationship between ALD horizontal displacements and the directional derivative of the vertical displacement field in the case study.

**Figure 8.**The distribution of extreme horizontal strain values and isolines of vertical displacements in the case study. The ‘−10 mm’ isoline is represented by the dashed line, whereas isolines between ‘−20 mm’ and ’20 mm’ are denoted by continuous lines every ’20 mm’.

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## Share and Cite

**MDPI and ACS Style**

Witkowski, W.T.; Łukosz, M.; Guzy, A.; Hejmanowski, R. Estimation of Mining-Induced Horizontal Strain Tensor of Land Surface Applying InSAR. *Minerals* **2021**, *11*, 788.
https://doi.org/10.3390/min11070788

**AMA Style**

Witkowski WT, Łukosz M, Guzy A, Hejmanowski R. Estimation of Mining-Induced Horizontal Strain Tensor of Land Surface Applying InSAR. *Minerals*. 2021; 11(7):788.
https://doi.org/10.3390/min11070788

**Chicago/Turabian Style**

Witkowski, Wojciech T., Magdalena Łukosz, Artur Guzy, and Ryszard Hejmanowski. 2021. "Estimation of Mining-Induced Horizontal Strain Tensor of Land Surface Applying InSAR" *Minerals* 11, no. 7: 788.
https://doi.org/10.3390/min11070788