# Method Combining Probability Integration Model and a Small Baseline Subset for Time Series Monitoring of Mining Subsidence

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## Abstract

**:**

## 1. Introduction

## 2. Study Area and Datasets

## 3. Methodology

#### 3.1. Probability Integration Model

#### 3.2. SBAS

#### 3.3. PIM-SBAS

#### 3.4. Validation Methods of the Results

#### 3.4.1. TCPInSAR

_{i}is the total number of SLC images between the acquired time of master and slave images, t

_{k}is the acquired time of SLC images, λ is the wave length of the SAR,

**V**is the subsidence velocity vector, ${B}_{perp,l,m}^{i}$ is the perpendicular baseline of the TCP point (l, m), ${\theta}_{l,m}^{i}$ is the local incidence angle, and ${r}_{l,m}^{i}$ is the slant range between the land target and the satellite.

**P**is the priori weight matrix.

**P**in Equations (14)–(16), ${\mathit{Q}}_{\mathbf{\Delta}\widehat{\mathsf{\Phi}}\mathbf{\Delta}\widehat{\mathsf{\Phi}}}$ is the covariance matrix of the observation estimation value, which can be calculated by Equation (15) and $c$ is a constant (generally 3 or 4).

**L**and

**X**are the parameters of arcs and points respectively, $\mathit{X}=[\begin{array}{cc}{h}_{i}& {V}_{i}\end{array}]$ and

**U**is the coefficient matrix that links the arcs and points, which is shown in Equation (19). ${v}_{i}$ is the velocity of deformation of the $i\mathrm{th}$ interference pair.

#### 3.4.2. Leveling Measurements

## 4. Results

#### 4.1. Simulated Interferograms and Actual Interferograms

#### 4.2. PIM-SBAS Monitoring Results

#### 4.3. Monitoring Results of SBAS and TCPInSAR

## 5. Discussion

#### 5.1. Comparison of PIM-SBAS with SBAS and TCPInSAR

#### 5.2. Comparison of Results with Leveling Measurements

#### 5.3. Comparison of Monitoring Results above the Workface

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Location of the study area in Jining, Shandong Province, east China. The two black frames are the 9306 and 9308 workfaces, respectively. The purple frame represents the extent of mining from 25 December 2011 to 2 April 2012.

**Figure 4.**Simulated wrapped phase map using PIM (

**a**) and the wrapped phase map generated by SBAS (

**b**).

Master Image | Slave Image | Spatial Baseline/m | Temporal Baseline/day |
---|---|---|---|

25 Dec. 2011 | 5 Jan. 2012 | −25.1171 | 11 |

5 Jan. 2012 | 16 Jan. 2012 | 104.0496 | 11 |

16 Jan. 2012 | 27 Jan. 2012 | 7.2308 | 11 |

27 Jan. 2012 | 7 Feb. 2012 | 90.6461 | 11 |

7 Feb. 2012 | 18 Feb. 2012 | −140.2636 | 11 |

18 Feb. 2012 | 29 Feb. 2012 | 143.7575 | 11 |

29 Feb. 2012 | 11 Mar. 2012 | −162.4879 | 11 |

11 Mar. 2012 | 22 Mar. 2012 | 136.6069 | 11 |

22 Mar. 2012 | 2 Apr. 2012 | −90.9748 | 11 |

Surface Observation Points | SBAS | TCPInSAR | PIM-SBAS |
---|---|---|---|

B1 | 33 | 90 | 23 |

B2 | 47 | 85 | 16 |

B3 | 43 | 82 | 15 |

B4 | 79 | 86 | 14 |

B5 | 93 | 102 | 28 |

B6 | 59 | 89 | 11 |

B7 | 80 | 86 | 18 |

B8 | 76 | 73 | 13 |

B9 | 40 | 69 | 12 |

B10 | 41 | 63 | 20 |

B11 | 39 | 54 | 14 |

B12 | 20 | 46 | 18 |

B13 | 23 | 42 | 17 |

B14 | 15 | 33 | 15 |

B15 | 20 | 31 | 16 |

B16 | 7 | 17 | 5 |

B17 | 5 | 12 | 3 |

B18 | 10 | 11 | 7 |

B19 | 4 | 6 | 3 |

B20 | 5 | 6 | 4 |

B21 | 0 | 0 | 0 |

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**MDPI and ACS Style**

Fan, H.; Lu, L.; Yao, Y.
Method Combining Probability Integration Model and a Small Baseline Subset for Time Series Monitoring of Mining Subsidence. *Remote Sens.* **2018**, *10*, 1444.
https://doi.org/10.3390/rs10091444

**AMA Style**

Fan H, Lu L, Yao Y.
Method Combining Probability Integration Model and a Small Baseline Subset for Time Series Monitoring of Mining Subsidence. *Remote Sensing*. 2018; 10(9):1444.
https://doi.org/10.3390/rs10091444

**Chicago/Turabian Style**

Fan, Hongdong, Lu Lu, and Yahui Yao.
2018. "Method Combining Probability Integration Model and a Small Baseline Subset for Time Series Monitoring of Mining Subsidence" *Remote Sensing* 10, no. 9: 1444.
https://doi.org/10.3390/rs10091444