# A New Weighting Method by Considering the Physical Characteristics of Atmospheric Turbulence and Decorrelation Noise in SBAS-InSAR

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## Abstract

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## 1. Introduction

## 2. Methodology

#### 2.1. Review of SBAS-InSAR Technique

#### 2.2. The Variance-Covariance Matrix of Atmospheric Phase in SBAS-InSAR

#### 2.3. The Variance-Covariance Matrix of Decorrelation Noise in SBAS-InSAR

#### 2.4. The Weight of Each Pixel in SBAS-InSAR

## 3. Results

#### 3.1. Synthetic Test and Results

#### 3.2. Real Test Case Example: Big Island of Hawaii

## 4. Discussions

#### 4.1. The Necessity of Considering Decorrelation Noise

#### 4.2. Average Performance

#### 4.3. Validation of the Performances with GNSS Datasets

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Comparison between GPS daily observations in line of sight (LOS) direction (gray dots) and InSAR-derived time series displacement (red triangles) from four different weighting methods at 26 GPS stations in Figure 8. Each row represents a GPS site and the four columns represent the results from the unweighted, the GT, the NVCE and the new method, respectively.

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**Figure 1.**(

**a**) $N$ SAR images. (

**b**) $M$ interferograms. (

**c**) Spatial structure of SBAS-InSAR. Each grid in (

**a**) and (

**b**) represents a pixel. The red pixel denotes the reference point in SBAS-InSAR. Black dots (e.g., ${s}_{i}$) and black edges (e.g., ${I}_{i}$) in (

**c**) represent SAR images and interferograms formed by the corresponding SAR images. Bp and Bt are perpendicular and time baselines, respectively.

**Figure 2.**(

**a**) The simulated mean deformation velocity and (

**b**) the spatial-temporal baselines of the interferograms used in the simulation experiment; green dots represent the image time epochs and blue edges represent the interferograms.

**Figure 3.**(

**a**,

**d**,

**g**,

**j**) Estimated deformation velocities by using the unweighted method, the GT method, the NVCE method and the new method, respectively. (

**b**,

**e**,

**h**,

**k**) The differences between the simulated deformation velocity and the ones estimated from the four weighting methods respectively. (

**c**,

**f**,

**i**,

**l**) The corresponding histogram of the second column.

**Figure 4.**(

**a**) The black rectangle represents the study area, the red star is the reference point and the blue dot denotes the location of MOKP site. (

**b**) The spatial-temporal baselines of the interferograms used in the real data experiment; green dots represent the image time epochs and blue edges represent the interferograms.

**Figure 5.**(

**a**) The variance-covariance matrix (VCM) of the atmospheric turbulence. (

**b**) VCM of the decorrelation noise. (

**c**) The total VCM and (

**d**) the corresponding weight of the MOPK site.

**Figure 6.**Comparison between InSAR-derived time series displacement (red triangles with black error bars) and GPS daily observations in LOS direction (gray dots) at site MOKP. (

**a**–

**d**) The results from unweighted method, the GT method, the NVCE and the new method, respectively.

**Figure 7.**(

**a**–

**d**) Mean deformation velocity of the study area by using the unweighted method, the GT method, the NVCE method and the new weighting method, respectively. Blue triangles represent the 27 GPS stations which were used for validation and the corresponding name are AINP, ALAL, ALEP, ANIP, APNT, BLBP, KAON, KEAW, KHKU, KULE, MLCC, MLES, MLPR, MLRD, MLSP, MOKP, NIHO, NUPM, PG2R, PHAN, PIIK, PMAU, PUKA, SLPC, STEP, TOUO and YEEP, respectively.

**Figure 8.**Statistical quantitative comparison: the vertical movement estimations derived from the unweighted method (blue), the GT method (green), the NVCE method (yellow) and the new method (red) in mean, std, RMSE and corr, respectively.

**Figure 9.**RMSEs of time series displacement under the unweighted (purple triangles), the GT (green dots), the NVCE (blue rectangles) and the new method (red stars), respectively.

Method | std(mm/a) | Kurtosis | Skewness |
---|---|---|---|

The NVCE method | 2.01 | 3.53 | −0.28 |

The new method | 1.91 | 3.23 | −0.06 |

Number | Orbit Model | Orbit Number | Imaging Time | Time Baseline (Day) | Perpendicular Baseline (m) |
---|---|---|---|---|---|

1 | Descending | 09038 | 2018-01-05 | 0 | 0 |

2 | Descending | 09388 | 2018-01-29 | 24 | −66.35 |

3 | Descending | 09738 | 2018-02-22 | 48 | −142.10 |

4 | Descending | 10088 | 2018-03-18 | 72 | −60.95 |

5 | Descending | 10438 | 2018-04-11 | 96 | −38.77 |

6 | Descending | 10788 | 2018-05-05 | 120 | −84.43 |

7 | Descending | 10963 | 2018-05-17 | 132 | −104.36 |

8 | Descending | 11138 | 2018-05-29 | 144 | −115.50 |

9 | Descending | 11313 | 2018-06-10 | 156 | −58.11 |

10 | Descending | 11488 | 2018-06-22 | 168 | −112.54 |

11 | Descending | 11663 | 2018-07-04 | 180 | −39.20 |

12 | Descending | 11838 | 2018-07-16 | 192 | −151.86 |

13 | Descending | 12013 | 2018-07-28 | 204 | −74.30 |

14 | Descending | 12188 | 2018-08-09 | 216 | −127.93 |

15 | Descending | 12363 | 2018-08-21 | 228 | −59.77 |

16 | Descending | 12538 | 2018-09-02 | 240 | −88.92 |

17 | Descending | 12713 | 2018-09-14 | 252 | −70.85 |

18 | Descending | 12888 | 2018-09-26 | 264 | −120.01 |

19 | Descending | 13063 | 2018-10-08 | 276 | 11.81 |

20 | Descending | 13238 | 2018-10-20 | 288 | −22.91 |

21 | Descending | 13413 | 2018-11-01 | 300 | −15.14 |

22 | Descending | 13588 | 2018-11-13 | 312 | 27.40 |

23 | Descending | 24834 | 2018-12-01 | 330 | −77.53 |

24 | Descending | 25009 | 2018-12-13 | 342 | −130.78 |

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## Share and Cite

**MDPI and ACS Style**

Duan, M.; Xu, B.; Li, Z.; Wu, W.; Cao, Y.; Liu, J.; Wang, G.; Hou, J.
A New Weighting Method by Considering the Physical Characteristics of Atmospheric Turbulence and Decorrelation Noise in SBAS-InSAR. *Remote Sens.* **2020**, *12*, 2557.
https://doi.org/10.3390/rs12162557

**AMA Style**

Duan M, Xu B, Li Z, Wu W, Cao Y, Liu J, Wang G, Hou J.
A New Weighting Method by Considering the Physical Characteristics of Atmospheric Turbulence and Decorrelation Noise in SBAS-InSAR. *Remote Sensing*. 2020; 12(16):2557.
https://doi.org/10.3390/rs12162557

**Chicago/Turabian Style**

Duan, Meng, Bing Xu, Zhiwei Li, Wenhao Wu, Yunmeng Cao, Jihong Liu, Guanya Wang, and Jingxin Hou.
2020. "A New Weighting Method by Considering the Physical Characteristics of Atmospheric Turbulence and Decorrelation Noise in SBAS-InSAR" *Remote Sensing* 12, no. 16: 2557.
https://doi.org/10.3390/rs12162557