# Estimation of Tropospheric and Ionospheric Delay in DInSAR Calculations: Case Study of Areas Showing (Natural and Induced) Seismic Activity

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Background and Methods

- (I)
- delays due to turbulent mixing in the troposphere. These result from several factors, such as thermal convection, differences in wind speed and direction on different altitudes, friction, and complex weather patterns. Horizontal air currents are the carrier of atmospheric components, including water vapor, which is a significant factor influencing atmospheric signal in SAR images. As the troposphere has a heterogeneous character resulting from local changes, this delay is very difficult to model.
- (II)
- delays resulting from vertical temperature and air-pressure distribution in layers. Each layer has an individual refraction coefficient. The vertical range of atmospheric layers changes in time. For regions that have varied topography, the difference of the vertical distribution of refractions between two image acquisitions causes a phase difference between two image cells having different topographic height.

#### 2.1. Tropospheric Delay Correction

#### 2.2. Ionospheric Delay Correction

## 3. Application Examples

#### 3.1. Legnica-Glogow Copper Belt Area

#### 3.2. Induced Tremor on 29 November 2016

#### 3.3. Induced Tremor on 7 December 2017

#### 3.4. Induced Tremor on 29 January 2019

#### 3.5. Chile—Natural Earthquake on 11 March 2010

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Implementation of Iterative Tropospheric Decomposition model and split-spectrum method in SAR calculations using the differential InSAR (DInSAR) method (Sentinel 1).

**Figure 2.**Ground coverage of Sentinel 1A/B acquisitions for (

**left**) the Legnica-Glogow Copper Belt (LGCB) area and (

**right**) the ALOS-1 acquisitions for the Chile example site.

**Figure 3.**Sum of line-of-sight (LOS) displacements for LGCB mining areas, determined on the basis of data from Sentinel 1A/1B satellites, collected for the period of November 2014–May 2018 (

**top**). Calculation was based on 122 SAR images from Path 73 using the SBAS method (total number of pairs, 436). Black dashed line indicates mining-area borders. (

**Bottom**) increments of ground subsidences for two selected cross-sections.

**Figure 4.**(

**left**) Original Sentinel 1 interferogram from the LGCB area, containing the 2016 tremor (area marked with black polygon), (

**middle**) estimated ionospheric phase screen, and (

**right**) interferogram after ionospheric compensation.

**Figure 5.**(

**left**) Spatial range of original unwrap phase, (

**middle**) delay difference between slave and master images, and (

**right**) final result, unwrap phase including tropospheric delay.

**Figure 6.**Results for the 2016 tremor. (

**left**) LOS displacements calculated with the use of the DInSAR method (Sentinel 1, TOPS) for period of 28 November 2016–10 December 2016. Calculated values: (

**middle-top**) ionospheric component, (

**middle-bottom**) tropospheric component, and LOS displacements allowing for the above components.

**Graphs**: Calculated values: ionospheric component and tropospheric component for each of the cross-sections (

**top**). Comparison of results without allowance for corrections (red line) and with allowance (blue line) for ionospheric component and tropospheric component (

**bottom**).

**Figure 7.**Results obtained for the 2017 tremor, LOS displacements calculated with DInSAR (Sentinel 1, TOPS) for (

**left**) the period of 12 May 2017–11 December 2017; (

**right**) LOS displacements with allowance for the influence of the ionosphere and the troposphere. Red line indicates displacements without allowance for corrections, and blue line with allowance for corrections.

**Figure 8.**Obtained results for the 2019 tremor, LOS displacements calculated with DInSAR (Sentinel 1, TOPS) for (

**left**) the period of 26 January 2019–2 February 2019; (

**right**) LOS displacements with allowance for the influence of the ionosphere and the troposphere. Red line indicates displacements without allowance for corrections, and blue line with allowance for corrections.

**Figure 9.**Iterative Tropospheric Decomposition (ITD)-based calculations of tropospheric delay differences for successive calculation periods; dashed brown line indicates the Sudetic Marginal Fault.

**Figure 10.**(

**left**) Original ALOS-1 interferogram from the Cardenal Caro area containing the 2010 earthquake, (

**middle**) estimated ionospheric phase screen, and (

**right**) interferogram after ionospheric compensation.

**Figure 11.**Spatial range of tropospheric delay for the following images: (

**left**) slave (

**middle**) master and (

**right**) delay difference.

**Figure 12.**Displacements calculated with the use of DInSAR method for two frames from Path 114 (

**left**) without corrections and (

**right**) with corrections; comparison of displacements before and after corrections in a selected profile (

**bottom**).

**Figure 13.**Total Electron Content (TEC) International GNSS Service (IGS) maps for successive SAR images; white polygons represent analyzed areas.

**Figure 14.**Comparison of observed displacement fluctuations in the profiles. Black line denotes the original data; green line, results including ionospheric correction; blue line, results including both ionospheric and tropospheric corrections.

**Table 1.**Review of methods for determining atmospheric corrections for measurements based on synthetic aperture radar interferometry (InSAR) techniques.

Techniques | Delay | Equation | Selected References | |
---|---|---|---|---|

Linear | Both-combined | $\Delta {\varphi}_{tropo}={K}_{\Delta \varphi}h+\Delta {\varphi}_{0}$ | [28,29,30] | |

(without turbulence) | ||||

Power-law | $\Delta {\varphi}_{tropo}={K}_{\Delta \varphi}{(h-{h}_{0})}^{\alpha}+\Delta {\varphi}_{0}$ | [31] | ||

Empirical | ANC | Tropospheric, ionospheric | $AN{C}_{i}=(10.0){({R}_{max})}^{-1}\sqrt{{\displaystyle \frac{1}{M}\sum _{m=1}^{M}{({\alpha}_{i}({X}_{m})-\overline{{\alpha}_{i}})}^{2}}}$ | [7,32] |

and orbital artifacts | ||||

Split-spectrum | Ionospheric | $\Delta {\varphi}_{iono}=\frac{{f}_{L}{f}_{H}}{{f}_{0}({f}_{H}^{2}{f}_{L}^{2})}(\Delta {\varphi}_{L}{f}_{H}-\Delta {\varphi}_{H}{f}_{L})$ | [14,15,16] | |

Era-Interim ECMWF | [30,33,34,35] | |||

HRES ECMWF | Dry | $ZHD=0.0022768\frac{P}{1-0.00266cos2\phi -0.00028h}$ | ||

Weather | ||||

models | WRF | Wet | $ZWD=\mathsf{\Pi}\xb7PWV$ | [30,36] |

MERRA | $\mathsf{\Pi}={R}_{v}{\rho}_{w}{10}^{-6}\left({k}_{2}^{\prime}\frac{{k}_{3}}{{T}_{m}}\right)$ | [35] | ||

MERIS | [30,37,38,39] | |||

Spectrometer | Wet only | Same as for weather models | ||

MODIS | [30,37,39] | |||

Wet and dry | Same as for weather models | [38,40] | ||

GNSS | ||||

Ionospheric | ${\varphi}_{iono}=-2\pi \frac{K}{c{f}_{0}^{2}}TEC$ | [41] |

Date and Time of Event (UTC) (Day/Month/Year) | Type | Strength [${\mathit{M}}_{\mathit{w}}$] | Event Location | Satellite | Master Date and Time (UTC) (Day/Month/Year) | Slave Date and Time (UTC) (Day/Month/Year) | Path |
---|---|---|---|---|---|---|---|

29/11/2016 8:09:39 P.M. | Induced tremor | 4.2 | Sentinel 1A | 28/11/2016 4:43:20 P.M. | 10/12/2016 4:43:20 P.M. | 73 | |

7/12/2017 5:42:50 P.M. | Induced tremor | 4.5 | Poland, the LGCB region | Sentinel 1A/1B | 5/12/2017 4:43:33 P.M. | 11/12/2017 4:42:51 P.M. | |

29/1/2019 12:53:45 P.M. | Induced tremor | 4.1 | Sentinel 1A/1B | 26/1/2019 5:09:03 A.M. | 1/2/2019 5:08:27 A.M. | 22 | |

11/3/2010 2:55:27 P.M. | Natural earthquake | 7.0 | Chile, Cardenal Caro province | ALOS 1 | 9/3/2010 4:03:29 A.M. | 24/4/2010 4:03:06 A.M. | 114 |

9/3/2010 4:03:03 A.M. | 24/4/2010 4:03:15 A.M. |

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**MDPI and ACS Style**

Milczarek, W.; Kopeć, A.; Głąbicki, D.
Estimation of Tropospheric and Ionospheric Delay in DInSAR Calculations: Case Study of Areas Showing (Natural and Induced) Seismic Activity. *Remote Sens.* **2019**, *11*, 621.
https://doi.org/10.3390/rs11060621

**AMA Style**

Milczarek W, Kopeć A, Głąbicki D.
Estimation of Tropospheric and Ionospheric Delay in DInSAR Calculations: Case Study of Areas Showing (Natural and Induced) Seismic Activity. *Remote Sensing*. 2019; 11(6):621.
https://doi.org/10.3390/rs11060621

**Chicago/Turabian Style**

Milczarek, Wojciech, Anna Kopeć, and Dariusz Głąbicki.
2019. "Estimation of Tropospheric and Ionospheric Delay in DInSAR Calculations: Case Study of Areas Showing (Natural and Induced) Seismic Activity" *Remote Sensing* 11, no. 6: 621.
https://doi.org/10.3390/rs11060621