# Implication between Geophysical Events and the Variation of Seasonal Signal Determined in GNSS Position Time Series

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## Abstract

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## 1. Introduction

_{w}Amatrice earthquake (central Italy) obtained from high-rate GPS data [43] and the 2009 L’Aquila earthquake [44]. Moreover, monitoring of earthquakes; active landslides in Italy [45], Croatia and Portugal; coal mine subduction areas in Hungary and Romania [46] and active volcanos in Italy, Iceland [47] and the Azores facilitates a greater perspective of the predominant geophysical phenomena in Europe. All the significant geophysical phenomena that have occurred in Europe during the past two decades have had a strong local impact, except for the 2010 volcanic eruptions of Eyjafjallajökull (Iceland) when a cloud of ash covered a large section of the Northern Hemisphere.

## 2. Data and Analysis Methods

- $det$ denotes the determinant of the matrix;
- $\mathit{C}$ represents the covariance matrix of the assumed noise in the data;
**N**is the number of epochs;

- $a$ represents the scale;
- $b$ denotes the translation;
- $\psi $ represents the mother wavelet;
- * denotes the complex conjugate.

- f denotes the centre frequency;
- f
_{b}represents the bandwidth.

_{b}= 2.0 for all the coordinate time series analysed. The parameter values were selected empirically to ensure a balance between the time and frequency resolution satisfactory for analysed data.

## 3. Results

#### 3.1. Seasonal Amplitudes

#### 3.2. Analysis of the Impact of Geophysical Events on Seasonal Signals

**.**were further analysed by grouping the CORS stations determined by GNSS as a function of the radius from the geophysical event—from 0 km to 100 km and considering the stations identified within those radiuses, which are presented in Table 1.

- (a)
- Seasonal signal values were computed by taking into account the entire length of the time series; this strategy was called ‘all the data’;
- (b)
- The seasonal signal values were computed based on the four years of data prior to the geophysical event, up to the beginning of the year when the geophysical event occurred; this strategy was called ‘before the event’;
- (c)
- The seasonal signal values were computed based on three years of data, in which the year when the geophysical event occurred was in the middle of the timespan; this strategy was named ‘during the event’;
- (d)
- The seasonal signal values were computed based on the four years of data after the geophysical event, beginning from the year after the geophysical event occurred; this strategy was named ‘after the event’.

#### 3.2.1. The East Component

#### 3.2.2. The North Component

#### 3.2.3. The UP Component

#### 3.3. Overlapping Hadamard Variation

#### 3.4. Time–Frequency Analysis

^{−1}years was observed for the East coordinate (Figure 9e). In contrast to the two previously presented examples, the time-frequency spectra for the East and North coordinates of the ESCO station were similar. A comparison of the coordinate East time–frequency spectra of two different stations, BAIA and BACA (Figure 9g,h), showed that despite a considerable distance between the two stations (approximately 300 km), the changes in the periodic components were similar. In the time series of the East coordinate for the BAIA and BACA stations, a dominant component with a period of half a year was observed for 2012–2020, and a component with a period of a third of a year was observed at the beginning of the period analysed (2007–2010). The reason for the similarity of changes in the East coordinate for these two stations requires further research. Variability in the amplitude and frequency of station coordinates can be related to geophysical phenomena but also to changes in station equipment (antenna, receiver) or environmental changes in the station immediate vicinity.

## 4. Discussion of Results

## 5. Summary and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Seasonal signals for the East component in the presence of geophysical events using the four above-mentioned computational strategies.

**Figure 5.**Seasonal signal values for the North component in the presence of a geophysical event using the four above-mentioned computational strategies.

**Figure 6.**Seasonal signal values for the Up component in the presence of a geophysical event using the four above-mentioned computational strategies.

**Figure 7.**(

**a**–

**i**) OHVAR of each coordinate component for the three periods analysed: 1995–1999 (left column), 2000–2004 (centre) and 2005–2009 (right column).

**Figure 8.**(

**a**–

**c**) Mean values of the OHVAR (Y-axis) as a function of τ (averaging time, X-axis) for each of the components and periods in the time series analysed.

**Figure 9.**(

**a**–

**h**) Time–frequency spectra using CWT of the North and East components of the ZARA, ONSA and ESCO stations and the East component of the BAIA and BACA stations. The white dash-dot lines correspond to the tropical year and its 2nd, 3rd and 4th harmonics (bottom to top).

Date | Hour (UTC) | Event Type | Magnitude (M _{w}) | Depth (km) | Location | Coordinates | Sites <30 km | Sites <60 km | Sites <100 km |
---|---|---|---|---|---|---|---|---|---|

11/26/2019 | 02:54:12 | Earthquake | 6.4 | 22 | Albania | 41.514°N 19.526°E | TIRA | SHK0 | |

6/12/2017 | 12:28:39 | Earthquake | 6.3 | 12 | Greece | 38.930°N 26.365°E | IZMI | ||

10/30/2016 | 06:40:18 | Earthquake | 6.6 | 8 | Central Italy | 42.862°N 13.096°E | AQUI, UNTR, UNPG | ||

10/26/2016 | 19:18:08 | Earthquake | 6.1 | 10 | Central Italy | 42.956°N 13.066°E | AQUI, UNTR, UNPG | ||

8/24/2016 | 01:36:32 | Earthquake | 6.2 | 4 | Central Italy | 42.723°N 13.188°E | AQUI, UNTR, UNPG | ||

10/12/2013 | 13:11:53 | Earthquake | 6.6 | 40 | Greece | 35.514°N 23.252°E | TUC2 | ||

5/20/2012 | 02:03:52 | Earthquake | 6 | 6 | North Italy | 44.890°N 11.230°E | MOPS, BOLG, MSEL | GARI | |

4/6/2009 | 01:32:39 | Earthquake | 6.3 | 9 | Central Italy | 42.334°N 13.334°E | AQUI | UNTR, UNPG | |

5/29/2008 | 15:46:00 | Earthquake | 6.3 | 9 | Iceland | 64.005°N −21.013°E | REYK | ||

1/8/2006 | 11:34:55 | Earthquake | 6.7 | 66 | Greece | 36.311°N 23.212°E | KITH | TUC2 | |

10/14/2010 | 09:00:00 | Landslide | - | - | Gondo, Switzerland | 46.167°N 8.117°E | COMO, ZIMM | ||

4/12/2010 | - | Landslide | - | - | Laces, Italy | 46.617°N 10.867°E | ROVE | ||

10/1/2009 | - | Landslide | - | - | Messina, Italy | 38.067°N 15.467°E | MSRU, VLSG | ||

3/20/2010 | - | Volcanic | - | - | Eyjafjallajökull, Iceland | 63.633°N −19.60°E | REYK | ||

2004–2016 | - | Volcanic | - | - | Campi Flegrei Caldera, Italy | 40.827°N 14.139°E | ISCH, IPRO, LICO, FRUL, ENAV |

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**MDPI and ACS Style**

Nistor, S.; Suba, N.-S.; El-Mowafy, A.; Apollo, M.; Malkin, Z.; Nastase, E.I.; Kudrys, J.; Maciuk, K.
Implication between Geophysical Events and the Variation of Seasonal Signal Determined in GNSS Position Time Series. *Remote Sens.* **2021**, *13*, 3478.
https://doi.org/10.3390/rs13173478

**AMA Style**

Nistor S, Suba N-S, El-Mowafy A, Apollo M, Malkin Z, Nastase EI, Kudrys J, Maciuk K.
Implication between Geophysical Events and the Variation of Seasonal Signal Determined in GNSS Position Time Series. *Remote Sensing*. 2021; 13(17):3478.
https://doi.org/10.3390/rs13173478

**Chicago/Turabian Style**

Nistor, Sorin, Norbert-Szabolcs Suba, Ahmed El-Mowafy, Michal Apollo, Zinovy Malkin, Eduard Ilie Nastase, Jacek Kudrys, and Kamil Maciuk.
2021. "Implication between Geophysical Events and the Variation of Seasonal Signal Determined in GNSS Position Time Series" *Remote Sensing* 13, no. 17: 3478.
https://doi.org/10.3390/rs13173478