# Analysis of Seismic Deformation from Global Three-Decade GNSS Displacements: Implications for a Three-Dimensional Earth GNSS Velocity Field

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## Abstract

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## 1. Introduction

## 2. Data and Methods

#### 2.1. GNSS Observations and Seismic Records

#### 2.2. Processing Strategies for GNSS and Seismic Data

^{−9}[38]. Figure 3 shows the flow of high-precision GNSS data processing using GAMIT/GLOBK in our works.

- GNSS data preparation and preprocessing: We need to download navigation ephemeris (BRDC) and precise ephemeris (SP3) corresponding to observation files (RINEX) in advance, and the tables file used for GAMIT/GLOBK, and preprocess RINEX (Receiver Independent Exchange Format) files by TEQC [41] or GFZRNX tools [42];
- Stations subnet division: To improve data processing efficiency, we divide the global sites into multiple subnets. Any subnet should have 3–6 common sites with its immediate neighboring subnet;
- Baseline processing: Daily GNSS baseline solutions for all subnets are carried out by GAMIT/GLOBK software with a distributed processing approach [38];
- Subnet fusion: The common sites between subnets are used to merge all subnets into a global network by GLRED [38] software;
- Comprehensive adjustment: We will finally obtain the high-precision GNSS coordinate time series of global sites using GLRED software.

- Input the seismic records, including the location of the epicenter, magnitude, epoch, etc.;
- Search for all GNSS sites within a specific range of the epicenter (difference in longitude ≤ 3 × Mv, the difference in latitude ≤ 2 × Mv);
- Extract the two subsequences called sub1 and sub2 at the epoch of a seismic event. Then, find the median difference between sub1 and sub2. If the difference is greater than the default threshold, mark the earthquake and site;
- Repeat step 3 until the sites of step 2 are traversed;
- Repeat steps 1–4 until all earthquakes are traversed. We finally obtain all earthquakes and sites impacted by seismic deformation.

#### 2.3. An Integrated Time Series Method for GNSS Displacements

#### 2.3.1. The Estimation of Seismic Relaxation Time Factor

#### 2.3.2. The Estimation of Other Time Series Parameters

- Set the initial value of seismic relaxation time (tau), with the default value of tau being one year;
- Perform the first IRLS solver and obtain the initial values of other parameters;
- The estimated parameters in step 2 are used as the initial values of the parameters of the CNO model. Set appropriate parameter constraints;
- Perform the CNO solver and obtain the tau’s optimal solution;
- Perform the second IRLS solver and obtain the time series parameter’s optimal solution;
- Perform the BTSM solver for accuracy evaluation and parameter analysis.

## 3. Results and Analysis

#### 3.1. Analysis of GNSS Time Series Preprocessing

- Weak observation criteria based on the formal errors. If the formal sigma of one site is more significant than the criteria at one epoch, the solution of this site at this epoch will be ignored;
- Outliers criteria based on the post-fit residuals. If the residuals of one site are bigger than the criteria at one epoch, the solution of this site at this epoch will be ignored;
- Bad observation criteria based on the outlier threshold. If the values have outliers, the initial adjustment will be biased. They will be removed before the adjustment.

#### 3.2. Feasibility Analysis of Relaxation Time Selection

#### 3.3. Analysis of Case Result on Different Model

- The accuracy of the velocity solution was hardly affected by the periodic term because the length of the time series we used was more than two years. However, if the duration is less than one year, the accuracy of velocity (especially vertical velocity solution) may decrease;
- The periodic variation in the horizontal direction was not obvious, while the periodic variation in the vertical direction was noticeable. This is because the periodic change caused by the change of surface load which is mainly reflected in the vertical direction.

#### 3.4. Comparison and Analysis of the New Global GNSS Velocity Field

- The observation’s duration of the GNSS site is different. ITRF14 uses GNSS observation data util 2014, while GGV2020 uses all data from 1990 to 2020, so the latter has a larger amount of data, and the dataset is updated;
- The solution models of time series analysis are different. Compared with ITRF2014, GGV2020 is obtained by using the ITSM model, which considers as many factors as possible in GNSS coordinate time series, especially considering the nearby major seismic activities;
- The geodetic techniques are different. In addition to GNSS technology, ITRF2014 also integrates VLBI, SLR, and DORIS technologies. Therefore, the results of the two will inevitably have a minor difference.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 9.**Influence of tau selection (a. true × 0.1, b. true × 10, c. true × 1.0) on the post-seismic deformation model with different combinations (a. Offset + Velocity, b. Offset + Velocity + PSD, c. Offset + Velocity + PSD + Period).

**Figure 10.**Analysis results of time series fitting models with different combinations (a. Offset + Velocity, b. Offset + Velocity + PSD, c. Offset + Velocity + PSD + Period).

**Figure 17.**Comparison of the ITRF2014 and GGV2020 global GNSS velocity fields. (

**a**) ITRF2014 horizontal velocity field; (

**b**) ITRF2014 vertical velocity field; (

**c**) GGV2020 horizontal velocity field; (

**d**) GGV2020 vertical velocity field; (

**e**) ITRF14 and GGV2020 horizontal merging velocity field; (

**f**) ITRF14 and GGV2020 vertical merging velocity field.

Time Span (a) | Number | Percentage (%) | Mean (a) |
---|---|---|---|

0–2 | 215 | 19.03 | 10.48 |

2–10 | 467 | 41.33 | |

10–30 | 448 | 39.65 |

Criteria | North (mm) | East (mm) | Up (mm) |
---|---|---|---|

weak data | 20 | 20 | 40 |

outlier | 20 | 20 | 40 |

very bad data | 1000 | 1000 | 3000 |

**Table 3.**The fitting RMSE (Root Mean Square Error) of the GNSS sites impacted by seismic deformation.

RMSE | North (mm) | East (mm) | Up (mm) |
---|---|---|---|

min | 1.19 | 1.62 | 4.21 |

max | 7.27 | 7.03 | 13.64 |

mean | 2.83 | 2.90 | 6.72 |

Velocity | Earthquake | CSD | PSD | Annual | Semi-Annual | |
---|---|---|---|---|---|---|

Slope (mm/a) Sigma (mm/a) | Time (a) Tau (a) | Offset (mm) Sigma (mm) | Exp and Log Coefficient (mm) Sigma (mm) | Amplitude (mm) Sigma (mm) Phase (rad) | Amplitude (mm) Sigma (mm) Phase (rad) | |

N | 9.98 | 2010.1575 | 196.02 | −6.94, 32.72 | 0.41 | 0.34 |

0.70 | 0.2601 | 0.64 | 1.12, 0.39 | 0.14 | 0.14 | |

−0.0489 | 0.3514 | |||||

E | 13.07 | 2010.1575 | −880.54 | 65.75, −165.70 | 1.13 | 0.50 |

0.09 | 0.2601 | 1.01 | 1.65, 0.50 | 0.10 | 0.10 | |

0.2633 | 0.1044 | |||||

U | 3.53 | 2010.1575 | −28.1 | −17.67, 49.19 | 5.81 | 0.98 |

0.13 | 0.2601 | 1.22 | 2.13, 0.75 | 0.15 | 0.15 | |

0.0042 | 0.6022 |

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**MDPI and ACS Style**

Ren, Y.; Lian, L.; Wang, J.
Analysis of Seismic Deformation from Global Three-Decade GNSS Displacements: Implications for a Three-Dimensional Earth GNSS Velocity Field. *Remote Sens.* **2021**, *13*, 3369.
https://doi.org/10.3390/rs13173369

**AMA Style**

Ren Y, Lian L, Wang J.
Analysis of Seismic Deformation from Global Three-Decade GNSS Displacements: Implications for a Three-Dimensional Earth GNSS Velocity Field. *Remote Sensing*. 2021; 13(17):3369.
https://doi.org/10.3390/rs13173369

**Chicago/Turabian Style**

Ren, Yingying, Lizhen Lian, and Jiexian Wang.
2021. "Analysis of Seismic Deformation from Global Three-Decade GNSS Displacements: Implications for a Three-Dimensional Earth GNSS Velocity Field" *Remote Sensing* 13, no. 17: 3369.
https://doi.org/10.3390/rs13173369