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

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 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.

## References

- Duan, M.; Xu, B.; Li, Z.W.; Cao, Y.M.; Hu, J.; Xu, W.B.; Wei, J.C.; Feng, G.C. Non-differential water vapor estimation from SBAS-InSAR. J. Atmos. Sol. Terr. Phys.
**2020**, 204, 105284. [Google Scholar] [CrossRef] - Mateus, P.; Miranda, P.M.A.; Nico, G.; Catalão, J.; Pinto, P.; Tomé, R. Assimilating InSAR maps of water vapor to improve heavy rainfall forecasts: A case study with two successive storms. J. Geophys. Res. Atmos.
**2018**, 123, 3341–3355. [Google Scholar] [CrossRef] - Miranda, P.M.; Mateus, P.; Nico, G.; Catalão, J.; Tomé, R.; Nogueira, M. InSAR meteorology: High-resolution geodetic data can increase atmospheric predictability. Geophys. Res. Lett.
**2019**, 46, 2949–2955. [Google Scholar] [CrossRef] [Green Version] - Tang, W.; Liao, M.; Zhang, L.; Li, W.; Yu, W. High-spatial-resolution mapping precipitable water vapor using SAR interferograms, GPS observations and ERA-Interim reanalysis. Atmos. Meas. Tech.
**2016**, 9, 4487–4501. [Google Scholar] [CrossRef] [Green Version] - Youhei, K.; Masanobu, S.; Masato, F. InSAR observation and numerical modeling of the water vapor signal during a heavy rain: A case study of the 2008 Seino event, central Japan. Geophys. Res. Lett.
**2013**, 40, 4740–4744. [Google Scholar] - Du, Y.N.; Zhang, L.; Feng, G.C.; Lu, Z.; Sun, Q. On the accuracy of topographic residuals retrieved by MTInSAR. IEEE Trans. Geosci. Remote Sens.
**2016**, 55, 1053–1065. [Google Scholar] [CrossRef] - Hu, J.; Li, Z.W.; Ding, X.L.; Zhu, J.J.; Zhang, L.; Sun, Q. Resolving three-dimensional surface displacements from InSAR measurements: A review. Earth Sci. Rev.
**2014**, 133, 1–17. [Google Scholar] [CrossRef] - Yang, Z.F.; Li, Z.W.; Zhu, J.J.; Preusse, A.; Hu, J.; Feng, G.C.; Yi, H.W.; Papst, M. Time-series 3D Mining-Induced Large Displacement Modeling and Roubst Estimation from a Single-Geometry SAR Amplitude Dataset. IEEE Trans. Geosci. Remote Sens.
**2018**, 56, 3600–3610. [Google Scholar] [CrossRef] - Liu, J.H.; Hu, J.; Li, Z.W.; Zhu, J.J.; Sun, Q.; Gan, J. A method for measuring 3-D surface deformations with InSAR based on strain model and variance component estimation. IEEE Trans. Geosci. Remote Sens.
**2018**, 56, 239–250. [Google Scholar] [CrossRef] - Liu, J.H.; Hu, J.; Xu, W.B.; Li, Z.W.; Zhu, J.J.; Ding, X.L.; Zhang, L. Complete three-dimensional coseismic deformation field of the 2016 central tottori earthquake by integrating left- and right-looking InSAR observations with the improved SM-VCE method. J. Geophys. Res. Solid Earth
**2019**, 124, 12099–12115. [Google Scholar] [CrossRef] [Green Version] - Wu, S.B.; Zhang, L.; Ding, X.L.; Perissin, D. Pixel-wise MTInSAR estimator for integration of coherent point selection and unwrapped phase vector recovery. IEEE Trans. Geosci. Remote Sens.
**2019**, 57, 2659–2668. [Google Scholar] [CrossRef] - Wu, S.B.; Yang, Z.F.; Ding, X.L.; Zhang, B.C.; Zhang, L.; Lu, Z. Two decades settlement of Hong Kong international airpory measured with multi-temporal InSAR. Remote Sens. Environ.
**2020**, 248, 111976. [Google Scholar] [CrossRef] - Zebker, H.A.; Rosen, P.A.; Hensley, S. Atmospheric effects in interferometric synthetic aperture radar surface deformation and topographic maps. J. Geophys. Res. Solid Earth
**1997**, 102, 7547–7563. [Google Scholar] [CrossRef] - Hanssen, R.F. Radar Interferometry: Data Interpretation and Error Analysis; Springer Science & Business Media: Berlin, Germany, 2001. [Google Scholar]
- Li, Z.W.; Cao, Y.M.; Wie, J.C.; Duan, M.; Wu, L.X.; Hou, J.X.; Zhu, J.J. Time-Series InSAR Ground Deformation Monitoring: Atmospheric Delay Modeling and Estimating. Earth Sci. Rev.
**2019**, 192, 258–284. [Google Scholar] [CrossRef] - Qu, C.Y.; Shan, X.J.; Zhang, G.H.; Song, X.G.; Guo, L.M. Influence of interferometric baseline on measurements of seismic deformation: A case study on the 1997 mani, tibet m 7.7 earthquake. Seismol. Geol.
**2012**, 34, 672–680. [Google Scholar] - Xu, B.; Li, Z.W.; Zhu, Y.; Shi, J.C.; Feng, G.C. SAR interferometric baseline refinement based on flat-earth phase without a ground control point. Remote Sens.
**2020**, 12, 233. [Google Scholar] [CrossRef] [Green Version] - Xu, B.; Li, Z.W.; Zhu, Y.; Shi, J.C.; Feng, G.C. Kinematic coregistration of Sentinel-1 TOPSAR images based on sequential least squares adjustment. IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens.
**2020**, 13, 3083–3093. [Google Scholar] [CrossRef] - Xu, W.B.; Li, Z.W.; Ding, X.L.; Zhu, J.J. Interpolating Atmospheric Water Vapor Delay by Incorporating Terrain Elevation Information. J. Geod.
**2012**, 85, 555–564. [Google Scholar] [CrossRef] - Li, Z.W.; Xu, W.B.; Feng, G.C.; Hu, J.; Wang, C.C.; Ding, X.L.; Zhu, J.J. Correcting atmospheric effects on InSAR with MERIS water vapor data and elevation-dependent interpolation model. Geophys. J. Int.
**2012**, 189, 898–910. [Google Scholar] [CrossRef] [Green Version] - Liang, H.Y.; Zhang, L.; Ding, X.L.; Lu, Z.; Li, X. Toward Mitigating Stratified Tropospheric Delays in Multitemporal InSAR: A Quadtree Aided Joint Model. IEEE Trans. Geosci. Remote Sens.
**2018**, 57, 291–303. [Google Scholar] [CrossRef] - Shirzaei, M.; Walter, T.R. Estimating the effect of satellite orbital error using wavelet-based robust regression applied to insar deformation data. IEEE Trans. Geosci. Remote Sens.
**2011**, 49, 4600–4605. [Google Scholar] [CrossRef] - Xu, B.; Li, Z.W.; Wang, Q.J.; Jiang, M.; Zhu, J.J.; Ding, X.L. A Refine Strategy for Removing Composite Errors of SAR Interferogram. IEEE Trans. Geosci. Remote Sens. Lett.
**2011**, 11, 143–147. [Google Scholar] [CrossRef] - Li, Z.H.; Fielding, E.J.; Cross, P.; Preusker, R. Advanced inSAR atmospheric correction: MERIS/MODIS combination and stacked water vapor models. Int. J. Remote Sens.
**2009**, 30, 3343–3363. [Google Scholar] [CrossRef] - Yu, C.; Li, Z.H.; Penna, N.T. Interferometric synthetic aperture radar atmospheric correction using a GPS-based iterative tropospheric decomposition model. Remote Sens. Environ.
**2018**, 204, 109–121. [Google Scholar] [CrossRef] - Doin, M.P.; Lasserre, C.; Peltzer, G.; Cavalié, O.; Doubre, C. Corrections of stratified tropospheric delays in SAR interferometry: Validation with global atmospheric models. J. Appl. Geophys.
**2009**, 69, 35–50. [Google Scholar] [CrossRef] - Jolivet, R.; Grandin, R.; Lasserre, C.; Doin, M.P.; Peltzer, G. Systematic InSAR tropospheric phase delay corrections from global meteorological reanalysis data. Geophys. Res. Lett.
**2011**, 38. [Google Scholar] [CrossRef] [Green Version] - Azeriansyah, R.; Harintaka. Integration PS-InSAR and MODIS PWV data to monitor land subsidence in Semarang city 2015–2018. In Proceedings of the 1st International Conference on Geodesy, Geomatics, and Land Administration, Semarang, Indonesia, 24–25 July 2019; pp. 66–76. [Google Scholar]
- Xu, C.J.; Wang, H.; Jiang, G.Y. Study on crustal deformation of Wenchuan Ms8.0 earthquake using wide-swath ScanSAR and MODIS. Geod. Geodyn.
**2011**, 2, 1–6. [Google Scholar] - Mateus, P.; Nico, G.; Catalão, J. Interpolating MERIS and GPS measurements of precipitable water vapor (PWV) to estimate atmospheric phase delay maps. Remote Sens. Clouds Atmos. XV
**2010**, 7827, 782713. [Google Scholar] - Puyssegur, B.; Michek, R.; Avouac, P. Tropospheric Phase Delay in Interferometric Synthetic Aperture Radar Estimated from Meteorological Model and Multispectral imagery. J. Geophys. Res. Solid Earth
**2007**, 112, B05419. [Google Scholar] [CrossRef] [Green Version] - Gong, W.; Meyer, F.; Webley, P.W.; Morton, D.; Liu, S. Performance analysis of atmospheric correction in InSAR data based on the Weather Research and Forecasting Model (WRF). In Proceedings of the IEEE International Geoscience and Remote Sensing Symposium, Honolulu, HI, USA, 25–30 July 2010; pp. 2900–2903. [Google Scholar]
- Mateus, P.; Nico, G.; Catalão, J. Uncertainty assessment of the estimated atmospheric delay obtained by a numerical weather model (NMW). IEEE Trans. Geosci. Remote Sens.
**2015**, 53, 6710–6717. [Google Scholar] [CrossRef] - Thomas, H.; Youhei, K.; Shingo, S.; Ryuichi, I.; Masato, F.; Tetsuro, K.; Yasuhiro, K. On the importance of accurately ray-traced troposphere corrections for Interferometric SAR data. J. Geod.
**2010**, 84, 537–546. [Google Scholar] - Kinoshita, Y.; Furuya, M.; Hobiger, T.; Ichikawa, R. Are numerical weather model outputs helpful to reduce tropospheric delay signals in InSAR data? J. Geod.
**2012**, 87, 267–277. [Google Scholar] [CrossRef] [Green Version] - Berardino, P.; Fornaro, G.; Lanari, R.; Sansosti, E. A new algorithm for surface deformation monitoring based on small baseline differential SAR interferograms. IEEE Trans. Geosci. Remote Sens.
**2002**, 40, 2375–2383. [Google Scholar] [CrossRef] [Green Version] - Ferretti, A.; Prati, C.; Rocca, F. Nonlinear subsidence rate estimation using permanent scatterers in differential SAR interferometry. IEEE Trans. Geosci. Remote Sens.
**2000**, 38, 2202–2212. [Google Scholar] [CrossRef] [Green Version] - Ferretti, A.; Prati, C.; Rocca, F. Permanent scatterers in SAR interferometry. IEEE Trans. Geosci. Remote Sens.
**2001**, 39, 8–20. [Google Scholar] [CrossRef] - Bovenga, F.; Giacovazzo, V.M.; Refice, A.; Veneziani, N. Multichromatic analysis of InSAR data. IEEE Trans. Geosci. Remote Sens.
**2013**, 51, 4790–4799. [Google Scholar] [CrossRef] - Biondi, F.; Clemente, C.; Orlando, D. An atmospheric phase screen estimation strategy based on multichromatic analysis for differential interferometric synthetic aperture radar. IEEE Trans. Geosci. Remote Sens.
**2019**, 57, 7269–7280. [Google Scholar] [CrossRef] - González, P.J.; Fernández, J. Error Estimation in Multitemporal InSAR Deformation Time Series, with Application to Lanzarote, Canary Islands. J. Geophys. Res. Solid Earth
**2011**, 116, B10404. [Google Scholar] [CrossRef] [Green Version] - Cao, Y.M.; Li, Z.W.; Wei, J.C.; Duan, M.; Feng, G.C. Stochastic Modeling for Time Series InSAR: With Emphasis on Atmospheric Effects. J. Geod.
**2018**, 92, 185–204. [Google Scholar] [CrossRef] - Reinisch, E.C.; Cardiff, M.; Feigl, K.L. Graph Theory for Analyzing Pair-Wise Data: Application to Geophysical Model Parameters Estimated from Interferometric Synthetic Aperture Radar Data at Okmok Volcano, Alaska. J. Geod.
**2018**, 91, 9–24. [Google Scholar] [CrossRef] [Green Version] - Cressie, N. Statistics for Spatial Data; John and Wiley and Sons: Hoboken, NJ, USA, 1993. [Google Scholar]
- Strozzi, T.; Wegmuller, U.; Werner, C.; Wiesmann, A. Measurement of slow uniform surface displacement with mm/year accuracy. In Proceedings of the IGARSS, Honolulu, HI, USA, 24–28 July 2000; Volume 5, pp. 24–28. [Google Scholar]
- Zebker, H.A.; Villasenor, J. Decorrelation in interferometric radar echos. IEEE Trans. Geosci. Remote Sens.
**1992**, 30, 950–959. [Google Scholar] [CrossRef] [Green Version] - Esfahany, S.S. Exploitation of Distributed Scatterers in Synthetic Aperture Radar Interferometry. Ph.D. Thesis, Delft University of Technology, Delft, The Netherland, 2017. [Google Scholar]
- Chen, K.J.; Smith, J.D.; Avouac, J.P.; Liu, Z.; Song, Y.T.; Gualandi, A. Triggering of The Mw 7.2 Hawaii Earthquake of 4 May 2018 by A Dike Intrusion. Geophys. Res. Lett.
**2019**, 46, 2503–2510. [Google Scholar] [CrossRef] - Casu, F.; Lanari, R.; Sansosti, E.; Poland, M.; Miklius, A.; Solaro, G.; Tzzani, P. SBAS-InSAR analysis of surface deformation at Mauna Loa and Kilauea volcanoes in Hawaii. In Proceedings of the 2009 IEEE International Geoscience and Remote Sensing Symposium, Cape Town, South Africa, 12–17 July 2009; Volume 4, pp. 41–44. [Google Scholar]
- Gui, Q.; Guo, J. Study on methods for solving ill-condition equations. J. Geod. Geodyn.
**2004**, 24, 15–18. [Google Scholar]

**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 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## 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