# On the Patterns and Scaling Properties of the 2021–2022 Arkalochori Earthquake Sequence (Central Crete, Greece) Based on Seismological, Geophysical and Satellite Observations

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{L}5.3. Following the recent report by ITSAK [20], the recorded PGA at the epicentral area (Arkalochori) was 0.62 g in the horizontal component (N-S) and 0.82 g in the vertical one, with a duration of strong ground motion (>0.1 g) almost 6 s. Its focal mechanism is characterized by an SSW-NNE to SW-NE-trending, nearly dip-slip normal faulting. Its strike generally ranges from N200° E–N230° E and its dip angle varies between 40° and 60°. The active fault associated with the main event is the Kastelli Fault, which has a progressive change in the strike from 225° to 265° northeastwards and dips between 60°–80° northwestwards [9,21,22,23].

## 2. Seismological Data and Earthquake Sequence Analysis

#### 2.1. Data Analysis

- 13 January–27 September 2021 (period A), consisting of 620 events;
- 27 September–28 September 2021 (period B), the first day of the aftershock sequence and just a few hours before the greatest aftershock (M5.3), composed of 90 events;
- 28 September–12 October 2021 (period C), just after the occurrence of the M = 5.3 aftershock at 04:48 UTC, consisting of 803 events;
- 12 October–31 October 2021 (period D), where the M = 4.0 event took place after a significant decay in the aftershocks number in Arkalochori;
- 1 November–31 January 2022 (period E), which comprises small to moderate magnitude events in a deeper part of the crust (H > 20 km) located near Herakleion.

#### 2.2. Hypocentral Relocation of the Earthquake Sequence

_{L}≥ 0.6, comprising 58,777 phases, were relocated with hypoDD. Among the main factors that had been taken into consideration during the relocation procedure were the following: (a) network coverage of the area, (b) the size of the dominant clusters, and (c) their maximum separation distance. This led to the formation of 98,070 P- and 43,812 S-phase pairs, respectively, for the whole volume, while in the central cluster (cluster #1), where the mainshock (M = 6.0) largest aftershock (Mw = 5.3) is situated, 98,070 P- and 18,673 S-phase pairs were formed.

_{L}= 3.3 and continued throughout the first two months of 2022 as the latest contribution to the seismic sequence. The hypocenters appear to be located in deeper parts of the crust and they have an apparent dip towards the WNW.

## 3. Travel Time Tomography

_{P}and Vs (V

_{P}–V

_{S}scheme) using P and S travel-time residuals (dt

_{P}and dt

_{S}) and inversion for V

_{P}and V

_{P}/V

_{S}ratio (V

_{P}–V

_{P}/V

_{S}scheme) using dt

_{P}and differential residuals, dt

_{S}–dt

_{P}. In this work, inversion was performed for V

_{P}–V

_{S}and V

_{P}–V

_{P}/V

_{S}schemes, in order to obtain additional constraints concerning the V

_{P}and Vs anomalies [33,34].

_{P}anomalies (Figure 6) are identified along the west-dipping Agnos normal fault. Furthermore, cross-sections B-B’ and C-C’ in both primary (P) and secondary (S) wave velocity anomalies (Figure 8 and Figure 9), reveal this west-dipping structure that may be related to Agnos high-angle (~60°) normal fault [13,21,22,23,36,37].

## 4. Co-Seismic Ground Deformation

#### 4.1. Interferometric Data and Results

#### 4.2. GNSS Data and Results

## 5. Spatial Footprint of Coulomb Stress Changes

_{f}Δσ

_{f}is the effective friction coefficient [51,52,53]. For the shear modulus and Poisson’s ratio, we used the values of 3.3 MPa and 0.25, respectively, and a mean value for the coefficient of friction equal to μ

_{f}= 0.4 [54].

## 6. Frequency-Magnitude Scaling Properties of the Foreshock and Aftershock Sequences in Terms of Non-Extensive Statistical Physics

_{m}is the entropic index and α

_{m}a model parameter that expresses the proportionality between the seismic energy and the size of the fragments. In [74] updated the derived equation to include the minimum earthquake magnitude M

_{0}in a seismic catalog, which now reads as:

_{m}value for the SW cluster indicates greater tectonic instability in this region where the mainshock and the major aftershocks occurred.

## 7. Temporal Properties of the Aftershock Sequence

#### 7.1. Aftershock Production Rate and Modelling

_{c}) with time is shown for the two spatial clusters along with the modified Omori’s law (Equation (8)), which generally provides a fair fit for the parameter values given in Table 7. However, large aftershocks may trigger secondary aftershock sequences embedded in the aftershock sequence of the mainshock. In this case, several Omori regimes may be used to model the aftershocks production rate n(t) [89,90,91]:

_{2}, t

_{3}indicates the occurrence times of secondary aftershock sequences. In Figure 16, breaks are observed in the cumulative number of aftershocks for both spatial clusters that are associated with strong aftershocks and the generation of secondary aftershock sequences. Hence, we investigate if the composite model of Equation (9) fits better the observed distribution. By setting t

_{2}= 22.8 days and t

_{3}= 67.4 days that designate the occurrence times of strong aftershocks following the mainshock for the NE cluster (Table 7), we find that the composite model provides a better fit to the observed distribution (Figure 16), which is further confirmed by the smaller Akaike Information Criterion (AIC) value in comparison to the single Omori regime (Table 7).

_{2}= 24.1 days and t

_{3}= 32.8 days which mark the occurrence times of strong aftershocks in the SW cluster (Table 7). The composite model provides a better fit to the observed distribution, in comparison to the single Omori regime, for the parameter values given in Table 7.

#### 7.2. The Interevent Times Distributions for the Foreshock and Aftershock Sequences

_{i}= t

_{i}

_{+1}− t

_{i}, where t

_{i}is the time of occurrence of the ith event {i = 1, 2, …, N − 1} and N the total number of events. First, we construct the cumulative distribution of the interevent times (M ≥ M

_{c}) for the foreshock and aftershock sequences, as well as for the NE and SW spatial clusters. We then model the observed distributions with the q-exponential function, derived in the framework of NESP [72,82,84,86,92,93,94,95,96]. It has been shown in various studies that the q-exponential function appropriately describes the distribution of interevent times in global, regional, and volcanic earthquake activity, as well as in aftershock sequences [73,74,75,76,77,78,79,80,81,82,83,84,85,86,91,92,93,94,95,96].

_{0}is the cumulative distribution function (CDF) of the interevent times, with N(>τ) the number of interevent times with a value greater than τ and Ν

_{0}their total number, then the q-exponential cumulative distribution is given by [92]:

_{0}is a constant in time units and exp

_{q}(x) is the q-exponential function defined as:

_{q}(x) = 0 in all the other cases. Its inverse is the q-logarithmic function: ${\mathrm{ln}}_{q}\left(x\right)=\frac{1}{1-q}\left({x}^{1-q}-1\right)$. In the limit of q → 1, the q-exponential and q-logarithmic functions lead to the ordinary exponential and logarithmic functions, respectively.

_{q}P(>τ) with τ [77], which are shown in the right panels of Figure 17. In all cases, the q-logarithmic function describes the observed distributions with high correlation coefficients, shown in the corresponding panels. The high values of q

_{τ}(Table 6) indicate long-range temporal correlations in the evolution of the earthquake activity and further confirm the high q

_{τ}values observed in aftershock sequences [84,96,97,98].

#### 7.3. Scaling of the Aftershocks Focal Zone with Time

_{+}and V

_{L}are the sliding velocity just after the end of co-seismic rupture and the long-term loading velocity after the mainshock and t

_{r}the duration of the post-seismic phase. Considering the previous equation, the seismicity rate R(t) can then be given by:

_{+}and R

_{L}are the seismicity rates just after the end of co-seismic rupture and the long-term one after the mainshock, respectively. If $\dot{\tau}$ is the stressing rate and ΔCFS the co-seismic Coulomb stress changes induced by the mainshock, then the parameters t

_{r}and R

_{+}are given by ${t}_{r}=A\prime /\dot{\tau}$ and ${R}_{+}={R}_{L}exp\left(\Delta CFS/A\prime \right)$, where ${A}^{\prime}=\left(a-b\right)\sigma $, with a and b the rate and state frictional parameters and σ the effective normal stress. For $t/{t}_{r}\ll 1$, Equation (13) yields a decay rate for R(t) proportional to $1/t$, which is consistent with a modified Omori decay rate with p = 1 [87].

_{p}of the aftershocks focal zone, in the early stage of the post-seismic phase, which typically lasts several weeks or months after the mainshock, is given by [103]:

_{a}between time t

_{i}and t (t > t

_{i}) is now given by:

_{c}is the radius of the co-seismic rupture, Δσ the mean value of the mean co-seismic stress drops and ζ a constant. For an idealized Coulomb stress field, ζ takes the value of 2.77 [103].

_{c}= 2.5 to estimate the mean distance of aftershocks from the mainshock $\langle \Delta {L}_{a}\left(t\right)\rangle $ with time t, along the horizontal dimensions. The result is shown in Figure 18, as a function of the logarithm with time. The expansion of the aftershocks zone becomes apparent, as $\langle \Delta {L}_{a}\left(t\right)\rangle $ grows systematically with time after the surpass of one day from the mainshock. This growth can well be described by the afterslip front (Equation (16)) for over a period of one hundred days (R

^{2}= 0.97). We note that the logarithmic time dependence starts almost after the first day from the main event, possibly suggesting that after that time the system starts to be driven by an afterslip process.

_{a}of the afterslip front is known. From Figure 18, we obtain s

_{a}= 0.320 ± 0.003. Then, from Equation (16), ${s}_{a}=\frac{d\langle {L}_{a}\left(t\right)\rangle}{dlnt}=\zeta {A}^{\prime}\frac{{l}_{c}}{\Delta \sigma}$, where l

_{c}is the radius of the co-seismic rupture and Δσ the co-seismic stress drop. For a simple model of circular rupture, l

_{c}can approximately be determined as ${l}_{c}={\left(\frac{7}{2}\frac{{M}_{o}}{\Delta \sigma}\right)}^{1/3}$ [51]. Τhe average stress drop for normal fault earthquakes in Greece is Δσ = 5.5 ± 1.5 MPa [108,109], while the mainshock’s seismic moment is M

_{o}= 1.1 × 10

^{18}Nm (Table 4) [21,22,23]. Then, we estimate the value of l

_{c}≈ 8.9 km for the co-seismic rupture. For ζ = 2.77, the rheological parameter A′ takes the value of A′ ≈ 0.71 MPa, which is within the range 0.1–1 MPa of A′ values that are usually found [97,98,103]. This value is considerably higher than other A′ values that were estimated for recent normal fault mainshocks in Greece, as [97] estimated A′ ≈ 0.041 MPa for the 2020 Mw7.0 Samos earthquake, while [98] estimated the value of A′ ≈ 0.29 MPa for the 2021 Mw6.3 Northern Thessaly earthquake.

## 8. Concluding Remarks

_{P}anomalies is identified along the west-dipping Agnos normal fault. Furthermore, cross-sections created in both primary (P) and secondary (S) wave velocity anomalies, reveal this west-dipping structure that may be related to Agnos high-angle (~60°) normal fault.

_{m}-value was estimated for the SW aftershocks cluster, consistent with a lower b-value, indicating greater tectonic instability in this region where the mainshock and the greatest aftershock occurred. Scaling was also found in the temporal properties of the sequence. The aftershocks production rate, in both the SW and NE clusters, decays according to a composite model of three modified Omori regimes, signifying the generation of secondary aftershock sequences embedded in the aftershock sequence of the Mw6.0 mainshock. Furthermore, the cumulative distributions of the inter-event times between the successive events for the foreshock and aftershock sequences, as well as for the NE and SW aftershock clusters, scale according to the q-exponential distribution derived in the framework of NESP, indicating clustering and long-range correlations in the temporal evolution of seismicity.

## Supplementary Materials

^{2}. The confidence area is included within the dashed-outline polygon; Figure S4: Reconstruction of S-wave anomalies for the depth slices of 5, 15, 20, and 25 km with anomaly cell size of 10 × 10 km

^{2}. The confidence area is included within the dashed-outline polygon; Figure S5: Time Series for GNSS sites ARKL and HERA. Red line indicates the strong Mw5.8 seismic event in Arkalochori village; Figure S6: Time Series for GNSS sites MOI1 and IERA, located WSW and ESE from epicentral area, respectively. Red line indicates the 27 September 2021 earthquake. Table S1: Velocity components for the four continuous GNSS stations on the central-eastern part of Crete.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Delibasis, N.; Drakopoulos, J.K.; Fytrolakis, N.; Katsikatsos, G.; Makropoulos, K.C.; Zamani, A. Seismotectonic Investigation of the area of Crete Island. Proc. Intern. Symp. Hellenic Arc. Trench.
**1981**, 1, 121–138. [Google Scholar] - Drakopoulos, J.; Delibasis, N. The focal mechanism of earthquakes in the major area of Greece for the period 1947–1981. Seismol. Lab. Univ. Athens Publ.
**1982**, 2, 1–72. [Google Scholar] - Ganas, A.; Parsons, T. Three-dimensional model of Hellenic Arc deformation and origin of the Cretan uplift. J. Geophys. Res.
**2009**, 114, B06404. [Google Scholar] [CrossRef] [Green Version] - Kiratzi, A.; Benetatos, C.; Vallianatos, F. Seismic Deformation Derived from Moment Tensor Summation: Application Along the Hellenic Trench (Book Chapter). In Moment Tensor Solutions; D’Amico, S., Ed.; Springer Natural Hazards; Springer International Publishing: Berlin/Heidelberg, Germany, 2018. [Google Scholar] [CrossRef]
- Papadimitriou, E.; Karakostas, V.; Mesimeri, M.; Vallianatos, F. The Mw 6.7 12 October 2013 western Hellenic Arc main shock and its aftershock sequence: Implications for the slab properties. Int. J. Earth Sci.
**2016**, 105, 2149–2160. [Google Scholar] [CrossRef] - Ten Veen, J.H.; Meijer, P.T. Late Miocene to recent tectonic evolution of Crete (Greece): Geological observations and model analysis. Tectonophysics
**1998**, 298, 191–208. [Google Scholar] [CrossRef] - Papanikolaou, D.; Vassilakis, E. Thrust faults and extensional detachment faults in Cretan tectono-stratigraphy: Implications for Middle Miocene extension. Tectonophysics
**2010**, 488, 233–247. [Google Scholar] [CrossRef] - Fassoulas, C. The tectonic development of a Neogene basin at the leading edge of the active European margin: The Heraklion basin, Crete, Greece. J. Geodyn.
**2001**, 31, 49–70. [Google Scholar] [CrossRef] - Caputo, R.; Catalano, S.; Monaco, C.; Romagnoli, R.; Tortorici, G.; Tortorici, L. Active faulting on the island of Crete (Greece). Geophys. J. Int.
**2010**, 183, 111–126. [Google Scholar] [CrossRef] - Caputo, R.; Catalano, S.; Monaco, C.; Romagnoli, G. Middle-late quaternary geodynamics of Crete, southern Aegean, and seismotectonic implications. Bull. Geol. Soc. Greece
**2010**, 43, 400–408. [Google Scholar] [CrossRef] [Green Version] - Ganas, A.; Kourkouli, P.; Briole, P.; Moshou, A.; Elias, P.; Parcharidis, I. Coseismic Displacements from Moderate-Size Earthquakes Mapped by Sentinel-1 Differential Interferometry: The Case of February 2017 Gulpinar Earthquake Sequence (Biga Peninsula, Turkey). Remote Sens.
**2018**, 10, 1089. [Google Scholar] [CrossRef] [Green Version] - Mason, J.; Reicherter, K. The palaeoseismological study of capable faults on Crete. In Minoan Earthquakes-Breaking the Myth through Interdisciplinarity, 1st ed.; Jusseret, S., Sintubin, M., Eds.; Leuven University Press: Leuven, Belgium, 2017; pp. 191–216. [Google Scholar]
- Vassilakis, E. Study of the Tectonic Structure of the Messara Basin, Central Crete, With the AID of Remote Sensing Techniques and G.I.S. Ph.D. Thesis, National and Kapodistrian University of Athens, Athens, Greece, 2006; p. 564. [Google Scholar]
- Ganas, A.; Elias, P.; Kapetanidis, V.; Valkaniotis, S.; Briole, P.; Kassaras, I.; Argyrakis, P.; Barberopoulou, A.; Moshou, A. The 20 July 2017 M6.6 Kos Earthquake: Seismic and Geodetic Evidence for an Active North-Dipping Normal Fault at the Western End of the Gulf of Gökova (SE Aegean Sea). Pure Appl. Geophys.
**2019**, 176, 4177–4211. [Google Scholar] [CrossRef] - Zygouri, V.; Koukouvelas, I.; Ganas, A. Palaeoseismological analysis of the East Giouchtas fault, Heraklion basin, Crete (preliminary results). Bull. Geol. Soc. Greece
**2016**, 50, 563–571. [Google Scholar] [CrossRef] [Green Version] - Stucchi, M.; Rovida, A.; Gomez Capera, A.A.; Alexandre, P.; Camelbeeck, T.; Demircioglu, M.B.; Gasperini, P.; Kouskouna, V.; Musson, R.M.W.; Radulian, M.; et al. The SHARE European Earthquake Catalogue (SHEEC) 1000–1899. J. Seismol.
**2013**, 17, 523–544. [Google Scholar] [CrossRef] [Green Version] - Papazachos, B.C.; Papazachou, C.B. The Earthquakes of Greece; Ziti: Thessaloniki, Greece, 2003; p. 304. [Google Scholar]
- Guidoboni, E.; Comastri, A. Catalogue of Earthquakes and Tsunamis in the Mediterranean Area from the 11th to the 15th Century; INGV-SGA: Rome, Italy, 2005; p. 1037. [Google Scholar]
- Vallianatos, F.; Michas, G.; Hloupis, G.; Chatzopoulos, G. The Evolution of Preseismic Patterns Related to the Central Crete (Mw6.0) Strong Earthquake on 27 September 2021 Revealed by Multiresolution Wavelets and Natural Time Analysis. Geosciences
**2022**, 12, 33. [Google Scholar] [CrossRef] - ITSAK. Arkalochori Earthquakes, Μ 6.0 on 27/09/2021 & Μ 5.3 on 28/09/2021: Preliminary Report—Recordings of the ITSAK Accelerometric Network and Damage on the Natural and Built Environment; ITSAK Research Unit: Thessaloniki, Greece, 2021; p. 44. [Google Scholar]
- Triantafyllou, I.; Karavias, A.; Koukouvelas, I.; Papadopoulos, G.A.; Parcharidis, I. The Crete Isl. (Greece) M
_{w}6.0 Earthquake of 27 September 2021: Expecting the Unexpected. GeoHazards**2022**, 3, 106–124. [Google Scholar] [CrossRef] - Vassilakis, E.; Kaviris, G.; Kapetanidis, V.; Papageorgiou, E.; Foumelis, M.; Konsolaki, A.; Petrakis, S.; Evangelidis, C.P.; Alexopoulos, J.; Karastathis, V.; et al. The 27 September 2021 Earthquake in Central Crete (Greece)—Detailed Analysis of the Earthquake Sequence and Indications for Contemporary Arc-Parallel Extension to the Hellenic Arc. Appl. Sci.
**2022**, 12, 2815. [Google Scholar] [CrossRef] - Ganas, A.; Hamiel, Y.; Serpetsidaki, A.; Briole, P.; Valkaniotis, S.; Fassoulas, C.; Piatibratova, O.; Kranis, H.; Tsironi, V.; Karamitros, I.; et al. The Arkalochori Mw = 5.9 Earthquake of 27 September 2021 Inside the Heraklion Basin: A Shallow, Blind Rupture Event Highlighting the Orthogonal Extension of Central Crete. Geosciences
**2022**, 12, 220. [Google Scholar] [CrossRef] - Hellenic Mediterranean University Research Center (former Technological Educational Institute of Crete). Seismological Network of Crete; 10.7914/SN/HC; International Federation of Digital Seismograph Networks: Crete, Greece, 2006. [Google Scholar]
- Behr, Y.; Clinton, J.F.; Cauzzi, C.; Hauksson, E.; Jónsdóttir, K.; Marius, C.G.; Pinar, A.; Salichon, J.; Sokos, E. The Virtual Seismologist in SeisComP3: A New Implementation Strategy for Earthquake Early Warning Algorithms. Seism. Res. Let.
**2016**, 87, 363–373. [Google Scholar] [CrossRef] [Green Version] - Lee, W.H.K.; Lahr, J.C. HYP071 (Revised): A Computer Program for Determining Hypocenter, Magnitude, and First Motion Pattern of Local Earthquakes; U.S. Geological Survey Open File Report 75-311; U.S. Geological Survey: Reston, VA, USA, 1975. [Google Scholar]
- Karakonstantis, A. 3-D Simulation of Crust and Upper Mantle Structure in the Broader Hellenic Area through Seismic Tomography. Ph.D. Thesis, Department of Geophysics-Geothermics, Faculty of Geology, University of Athens, Athens, Greece, 2017. (In Greek). [Google Scholar]
- Delibasis, N.D.; Ziazia, M.; Voulgaris, N.; Papadopoulos, T.; Stavrakakis, G.N.; Papanastassiou, D.; Drakatos, G. Microseismic activity and seismotectonics of Heraklion Area (central Crete Island, Greece). Tectonophysics
**1999**, 308, 237–248. [Google Scholar] [CrossRef] [Green Version] - Becker, D.; Meier, T.; Bohnhoff, M.; Harjes, H.P. Seismicity at the convergent plate boundary offshore Crete, Greece, observed by an amphibian network. J. Seismol.
**2010**, 14, 369–392. [Google Scholar] [CrossRef] [Green Version] - Klein, F.W. User’s Guide to HYPOINVERSE-2000, a Fortran Program to Solve for Earthquake Locations and Magnitudes, 2002-171; United States Department of the Interior Geological Survey: Menlo Park, CA, USA, 2002; p. 123. [Google Scholar]
- Ganas, A.; Oikonomou, I.A.; Tsimi, C. NOAfaults: A digital database for active faults in Greece. Bull. Geol. Soc. Greece
**2017**, 47, 518–530. [Google Scholar] [CrossRef] [Green Version] - Waldhauser, F. hypoDD-A Program to Compute Double-Difference Hypocenter Locations, Open-File Report, 01-113; U.S. Geological Survey: Menlo Park, CA, USA, 2001. [Google Scholar]
- Koulakov, I. LOTOS code for local earthquake tomographic inversion: Benchmarks for testing tomographic algorithms. Bull. Seismol. Soc. Am.
**2009**, 99, 194–214. [Google Scholar] [CrossRef] - Jaxybulatov, K.; Koulakov, I.; Ibs-von Seht, M.; Klinge, K.; Reichert, C.; Dahren, B.; Troll, V.R. Evidence for high fluid/melt content beneath Krakatau volcano (Indonesia) from local earthquake tomography. J. Volcanol. Geotherm. Res.
**2011**, 206, 96–105. [Google Scholar] [CrossRef] - Toomey, D.R.; Foulger, G.R. Tomographic inversion of local earthquake data from the Hengill–Grensdalur central volcano complex, Iceland. J. Geophys. Res.
**1989**, 94, 17497–17510. [Google Scholar] [CrossRef] - Ganas, A.; Fassoulas, C.; Moschou, A.; Bozionelos, G.; Papathanassiou, G.; Tsimi, C.; Valkaniotis, S. Geological and seismological evidence for NW-SE crustal extension at the southern margin of Heraklion Basin, Crete. Bull. Geol. Soc. Greece
**2017**, 51, 52–75. [Google Scholar] [CrossRef] [Green Version] - Kassaras, I.; Kapetanidis, V.; Ganas, A.; Tzanis, A.; Kosma, C.; Karakonstantis, A.; Valkaniotis, S.; Chailas, S.; Kouskouna, V.; Papadimitriou, P. The New Seismotectonic Atlas of Greece (v1.0) and Its Implementation. Geosciences
**2020**, 10, 447. [Google Scholar] [CrossRef] - Curlander, J.; McDonough, R. Synthetic Aperture Radar: Systems and Signal Processing; John Wiley & Sons.: Hoboken, NJ, USA, 1991; ISBN 978-0-471-85770-9. [Google Scholar]
- Hooper, A.; Bekaert, D.; Spaans, K.; Arıkan, M. Recent advances in SAR interferometry time series analysis for measuring crustal deformation. Tectonophysics
**2012**, 514–517, 1–13. [Google Scholar] [CrossRef] - Massonnet, D.; Rabaute, T. Radar interferometry: Limits and potential. IEEE Geosci. Remote Sens.
**1993**, 8, 455–464. [Google Scholar] [CrossRef] - Bamler, R.; Hartl, P. Synthetic Aperture Radar Interferometry. Inverse Probl.
**1998**, 14, 1–54. [Google Scholar] [CrossRef] - Elliott, J.; Walters, R.; Wright, T. The role of space-based observation in understanding and responding to active tectonics and earthquakes. Nat. Commun.
**2016**, 7, 13844. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Markogiannaki, O.; Karavias, A.; Bafi, D.; Angelou, D.; Parcharidis, I. A geospatial intelligence application to support post-disaster inspections based on local exposure information and on co-seismic DInSAR results: The case of the Durres (Albania) earthquake on November 26, 2019. Nat. Hazards
**2020**, 103, 3085–3100. [Google Scholar] [CrossRef] - Sakkas, V. Ground Deformation Modelling of the 2020 Mw6.9 Samos Earthquake (Greece) Based on InSAR and GNSS Data. Remote Sens.
**2021**, 13, 1665. [Google Scholar] [CrossRef] - Goldstein, R.M.; Werner, C.L. Radar interferogram filtering for geophysical applications. Geophys. Res. Lett.
**1998**, 25, 4035–4038, Erratum in Remote Sens.**2021**, 13, 1665. [Google Scholar] [CrossRef] [Green Version] - Dach, R.; Lutz, S.; Walser, P.; Fridez, P. Bernese GNSS Software Version 5.2; User Manual; Astronomical Institute, University of Bern, Bern Open Publishing: Bern, Switzerland, 2015. [Google Scholar]
- Briole, P.; Ganas, A.; Elias, P.; Dimitrov, D. The GPS velocity field of the Aegean. New observations, contribution of the earthquakes, crustal blocks model. Geophys. J. Int.
**2021**, 226, 468–492. [Google Scholar] [CrossRef] - King, G.C.; Stein, R.S.; Lin, J. Static stress changes and the triggering of earthquakes. Bull. Seismol. Soc. Am.
**1994**, 84, 935–953. [Google Scholar] - Alkan, H.; Büyüksaraç, A.; Bektaş, Ö.; Isik, E. Coulomb stress change before and after 24.01.2020 Sivrice (Elazığ) Earthquake (Mw = 6.8) on the East Anatolian Fault Zone. Arab. J. Geosci.
**2021**, 14, 2648. [Google Scholar] [CrossRef] - Toda, S.; Stein, R.S.; Sevilgen, V.; Lin, J. Coulomb 3.3 Graphic-rich deformation and stress-change software for earthquake, tectonic, and volcano research and teaching—User guide. US Geol. Surv. Open-File Rep.
**2011**, 1060, 63. [Google Scholar] - Scholz, C. The Mechanics of Earthquakes and Faulting, 3rd ed.; Cambridge University Press: Cambridge, UK, 2019. [Google Scholar]
- Cocco, M.; Rice, J.R. Pore pressure and poroelasticity effects in Coulomb stress analysis of earthquake interactions. J. Geophys. Res. Solid Earth
**2002**, 107, ESE-2. [Google Scholar] [CrossRef] - Lin, J.; Stein, R.S. Stress triggering in thrust and subduction earthquakes and stress interaction between the southern San Andreas and nearby thrust and strike-slip faults. J. Geophys. Res. Solid Earth
**2004**, 109. [Google Scholar] [CrossRef] [Green Version] - Harris, R.A.; Simpson, R.W. Suppression of large earthquakes by stress shadows: A comparison of Coulomb and rate-and-state failure. J. Geophys. Res. Solid Earth
**1998**, 103, 24439–24451. [Google Scholar] [CrossRef] - Wells, D.L.; Coppersmith, K.J. New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement. Bull. Seismol. Soc. Am.
**1994**, 84, 974–1002. [Google Scholar] - Gutenberg, B.; Richter, C. Frequency of earthquakes in California. Bull. Seismol. Soc. Am.
**1944**, 34, 185–188. [Google Scholar] [CrossRef] - Frohlich, C.; Davis, S.D. Teleseismic b values; or, much ado about 1.0. J. Geophys. Res.
**1993**, 98, 631–644. [Google Scholar] [CrossRef] - Schorlemmer, D.; Wiemer, S.; Wyss, M. Variations in earthquake-size distribution across different stress regimes. Nature
**2005**, 437, 539–542. [Google Scholar] [CrossRef] [PubMed] - Mogi, K. Some discussion on aftershocks, foreshocks and earthquake swarms–the fracture of a semi-infinite body caused by an inner stress origand its relation to the earthquake phenomena (3rd paper). Bull. Earthq. Res. Inst. Univ. Tokyo
**1963**, 41, 615–658. [Google Scholar] - Suyehiro, S.; Sekiya, H. Foreshocks and earthquake prediction. Tectonophysics
**1972**, 14, 219–225. [Google Scholar] [CrossRef] - Papazachos, B.C. Foreshocks and earthquake prediction. Tectonophysics
**1975**, 28, 213–226. [Google Scholar] [CrossRef] - Jones, L.M.; Molnar, P. Some characteristics of foreshocks and their possible relationship to earthquake prediction and premonitory slip on faults. J. Geophys. Res.
**1979**, 84, 3596–3608. [Google Scholar] [CrossRef] - Main, I.; Meredith, P.G.; Jones, C. A reinterpretation of the precursory seismic b-value anomaly from fracture mechanics. Geophys. J. Internat.
**1989**, 96, 131–138. [Google Scholar] [CrossRef] - Chan, C.-H.; Wu, Y.-M.; Tseng, T.-L.; Lin, T.-L.; Chen, C.-C. Spatial and temporal evolution of b-values before large earthquakes in Taiwan. Tectonophysics
**2012**, 532–535, 215–222. [Google Scholar] [CrossRef] [Green Version] - Kato, A.; Obara, K.; Igarashi, T.; Tsuruoka, H.; Nakagawa, S.; Hirata, N. Propagation of slow slip leading up to the 2011 Mw 9.0 Tohoku-Oki earthquake. Science
**2012**, 335, 705–708. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Nanjo, K.Z.; Hirata, N.; Obara, K.; Kasahara, K. Decade-scale decrease b value prior to the M9-class 2011 Tohoku and 2004 Sumatra quakes. Geophys. Res. Lett.
**2012**, 39, 1–4. [Google Scholar] [CrossRef] - Papadopoulos, G.A.; Minadakis, G. Foreshock Patterns Preceding Great Earthquakes in the Subduction Zone of Chile. Pure Appl. Geophys.
**2016**, 173, 3247–3271. [Google Scholar] [CrossRef] - Papadopoulos, G.A.; Minadakis, G.; Orfanogiannaki, K. Short-Term Foreshocks and Earthquake Prediction. In AGU Geophysical Monograph Series Book, 1st ed.; Ouzounov, D., Pulinets, S., Hattori, K., Taylor, P., Eds.; John Wiley and Sons Inc.: Hoboken, NJ, USA, 2018; pp. 127–147. [Google Scholar]
- Wiemer, S.; Wyss, M. Minimum magnitude of complete reporting in earthquake catalogs: Examples from Alaska, the Western United States, and Japan. Bull. Seismol. Soc. Am.
**2000**, 90, 859–869. [Google Scholar] [CrossRef] - Sotolongo-Costa, O.; Posadas, A. Fragment-asperity interaction model for earthquakes. Phys. Rev. Lett.
**2004**, 92, 048501. [Google Scholar] [CrossRef] - Tsallis, C. Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys.
**1988**, 52, 479–487. [Google Scholar] [CrossRef] - Tsallis, C. Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World; Springer: Berlin, Germany, 2009. [Google Scholar]
- Silva, R.; França, G.S.; Vilar, C.S.; Alcaniz, J.S. Nonextensive models for earthquakes. Phys. Rev. E
**2006**, 73, 026102. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Telesca, L. Tsallis-Based Nonextensive Analysis of the Southern California Seismicity. Entropy
**2011**, 13, 1267–1280. [Google Scholar] [CrossRef] [Green Version] - Vallianatos, F.; Papadakis, G.; Michas, G. Generalized statistical mechanics approaches to earthquakes and tectonics. Proc. R. Soc. A
**2016**, 472, 2196. [Google Scholar] [CrossRef] [Green Version] - Vallianatos, F.; Michas, G.; Hloupis, G. Seismicity Patterns Prior to the Thessaly (Mw6. 3) Strong Earthquake on 3 March 2021 in Terms of Multiresolution Wavelets and Natural Time Analysis. Geosciences
**2021**, 11, 379. [Google Scholar] [CrossRef] - Vallianatos, F. A non extensive statistical physics approach to the polarity reversals of the geomagnetic field. Phys. A Stat. Mech. Appl.
**2011**, 390, 1773–1778. [Google Scholar] [CrossRef] - Vallianatos, F.; Sammonds, P. Is plate tectonics a case of non-extensive thermodynamics? Phys. A Stat. Mech. Appl.
**2010**, 389, 4989–4993. [Google Scholar] [CrossRef] - Vallianatos, F.; Telesca, L. Statistical mechanics in earth physics and natural hazards. Acta Geophys.
**2012**, 60, 499–501. [Google Scholar] [CrossRef] - Vallianatos, F.; Michas, G.; Papadakis, G.; Tzanis, A. Evidence of non-extensivity in the seismicity observed during the 2011–2012 unrest at the Santorini volcanic complex, Greece. Nat. Hazards Earth Syst. Sci.
**2013**, 13, 177–185. [Google Scholar] [CrossRef] [Green Version] - Vallianatos, F.; Sammonds, P. Evidence of non-extensive statistical physics of the lithospheric instability approaching the 2004 Sumatran-Andaman and 2011 Honshu mega-earthquakes. Tectonophysics
**2013**, 590, 52–58. [Google Scholar] [CrossRef] - Papadakis, G.; Vallianatos, F.; Sammonds, P. Evidence of Nonextensive Statistical Physics behavior of the Hellenic Subduction Zone seismicity. Tectonophysics
**2013**, 608, 1037–1048. [Google Scholar] [CrossRef] - Papadakis, G.; Vallianatos, F.; Michas, G. The earthquake intervent time distribution along the Hellenic subduction Zone. Bull. Geol. Soc. Greece
**2013**, XLVII, 1194–1200. [Google Scholar] [CrossRef] - Vallianatos, F.; Karakostas, V.; Papadimitriou, E. A Non-Extensive Statistical Physics View in the Spatiotemporal Properties of the 2003 (Mw6.2) Lefkada, Ionian Island Greece, Aftershock Sequence. Pure Appl. Geophys.
**2014**, 171, 1343–1534. [Google Scholar] [CrossRef] - Chochlaki, K.; Vallianatos, F.; Michas, G. Global regionalized seismicity in view of Non-Extensive Statistical Physics. Phys. A Stat. Mech. Appl.
**2018**, 493, 276–285. [Google Scholar] [CrossRef] - Vallianatos, F.; Michas, G.; Papadakis, G. Non Extensive statistical Seismology: An overview. In Complexity of Seismic Time Series; Measurement and Application; Chelidze, T., Telesca, L., Elsevier, F., Eds.; Elsevier: Amsterdam, The Netherlands, 2018. [Google Scholar]
- Omori, F. On after-shocks of earthquakes. J. Coll. Sci. Imp. Univ. Tokyo
**1894**, 7, 111–200. [Google Scholar] - Utsu, T. A statistical study on the occurrence of aftershocks. Geo-Phys.
**1961**, 30, 521–605. [Google Scholar] - Utsu, T.; Ogata, Y.; Matsu’ura, R.S. The Centenary of the Omori Formula for a Decay Law of Aftershock Activity. J. Phys. Earth
**1995**, 43, 1–33. [Google Scholar] [CrossRef] - Ogata, Y. Estimation of the parameters in the modified Omori formula for aftershock frequencies by the maximum likelihood procedure. J. Phys. Earth
**1983**, 31, 115–124. [Google Scholar] [CrossRef] - Michas, G.; Vallianatos, F. Scaling properties, multifractality and range of correlations in earthquake timeseries: Are earthquakes random? In Statistical Methods and Modeling of Seismogenesis; Limnios, N., Papadimitriou, E., Tsaklidis, G., Eds.; ISTE John Wiley: London, UK, 2021. [Google Scholar]
- Abe, S.; Suzuki, N. Scale-free statistics of time interval between successive earthquakes. Phys. A Stat. Mech. Appl.
**2005**, 350, 588–596. [Google Scholar] [CrossRef] [Green Version] - Michas, G.; Vallianatos, F.; Sammonds, P. Non-extensivity and long-range correlations in the earthquake activity at the West Corinth rift (Greece). Nonlinear Processes Geophys.
**2013**, 20, 713–724. [Google Scholar] [CrossRef] [Green Version] - Vallianatos, F.; Michas, G.; Benson, P.; Sammonds, P. Natural time analysis of critical phenomena: The case of acoustic emis-sions in triaxially deformed Etna basalt. Phys. A Stat. Mech. Appl.
**2013**, 392, 5172–5178. [Google Scholar] [CrossRef] - Chochlaki, K.; Michas, G.; Vallianatos, F. Complexity of the Yellowstone Park Volcanic Field Seismicity in Terms of Tsallis Entropy. Entropy
**2018**, 20, 721. [Google Scholar] [CrossRef] [Green Version] - Vallianatos, F.; Michas, G.; Papadakis, G.; Sammonds, P. A non-extensive statistical physics view to the spatiotemporal properties of the June 1995, Aigion earthquake (M6.2) aftershock sequence (West Corinth rift, Greece). Acta Geophys.
**2012**, 60, 758–768. [Google Scholar] [CrossRef] - Vallianatos, F.; Pavlou, K. Scaling properties of the Mw7.0 Samos (Greece), 2020 aftershock sequence. Acta Geophys.
**2021**, 69, 1–18. [Google Scholar] [CrossRef] - Michas, G.; Pavlou, K.; Avgerinou, S.E.; Anyfadi, E.A.; Vallianatos, F. Aftershock patterns of the 2021 Mw 6.3 Northern Thessaly (Greece) earthquake. J. Seismol.
**2022**, 26, 1–25. [Google Scholar] [CrossRef] - Peng, Z.; Zhao, P. Migration of early aftershocks following the 2004 Parkfield earthquake. Nat. Geosci.
**2009**, 2, 877–881. [Google Scholar] [CrossRef] - Obana, K.; Kodaira, S.; Nakamura, Y.; Sato, T.; Fujie, G.; Takahashi, T.; Yamamoto, Y. Aftershocks of the December 7, 2012 intraplate doublet neat the Japan Trench axis. Earth Planets Space
**2014**, 66, 24. [Google Scholar] [CrossRef] [Green Version] - Tang, C.C.; Lin, C.H.; Peng, Z. Spatial-temporal evolution of early aftershocks following the 2010 ML6.4 Jiashian earthquake in southern Taiwan. Geophys. J. Int.
**2014**, 199, 1772–1783. [Google Scholar] [CrossRef] - Frank, W.B.; Poli, P.; Perfettini, H. Mapping the rheology of the Central Chile subduction zone with aftershocks. Geophys. Res. Lett.
**2017**, 44, 5374–5382. [Google Scholar] [CrossRef] - Perfettini, H.; Frank, W.B.; Marsan, D.; Bouchon, M. A model of aftershock migration driven by afterslip. Geophys. Res. Lett.
**2018**, 45, 2283–2293. [Google Scholar] [CrossRef] - Ariyoshi, K.; Matsuzawa, T.; Hasegawa, A. The key frictional parameters controlling spatial variations in the speed of postseismic-slip propagation on a subduction plate boundary. Earth Planet Sci. Lett.
**2007**, 256, 136–146. [Google Scholar] [CrossRef] - Kato, A.; Iidaka, T.; Kurashimo, E.; Nakagawa, S.; Hirata, N.; Iwasaki, T. Delineation of probable asperities on the Atotsugawa fault, central Japan, using a dense temporary seismic network. Geophys. Res. Lett.
**2007**, 34, L09318. [Google Scholar] [CrossRef] - Perfettini, H.; Avouac, J.P. Postseismic relaxation driven by brittle creep: A possible mechanism to reconcile geodetic measurements and the decay rate of aftershocks, application to the Chi-Chi earthquake, Taiwan. J. Geophys. Res.
**2004**, 109, B02304. [Google Scholar] [CrossRef] - Dieterich, J.H. A constitutive law for earthquake production and its application to earthquake clustering. J. Geophys. Res.
**1994**, 99, 2601–2618. [Google Scholar] [CrossRef] - Margaris, B.N.; Hatzidimitriou, P.M. Source spectral scaling and stress release estimates using strong-motion records in Greece. Bull. Seismol. Soc. Am.
**2002**, 92, 1040–1059. [Google Scholar] [CrossRef] - Allmann, B.P.; Shearer, P.M. Global variations of stress drop for moderate to large earthquakes. J. Geophys. Res.
**2009**, 114, B01310. [Google Scholar] [CrossRef] [Green Version] - Papadimitriou, P.; Voulgaris, N.; Kassaras, I.; Kaviris, G.; Delibasis, N.; Makropoulos, K. The Mw = 6.0, 7 September 1999 Athens Earthquake. Nat. Hazards
**2002**, 27, 15–33. [Google Scholar] [CrossRef] - Kapetanidis, V.; Karakonstantis, A.; Papadimitriou, P.; Pavlou, K.; Spingos, I.; Kaviris, G.; Voulgaris, N. The 19 July 2019 earthquake in Athens, Greece: A delayed major aftershock of the 1999 Mw = 6.0 event, or the activation of a different structure? J. Geodyn.
**2020**, 139, 101766. [Google Scholar] [CrossRef] - Triantafyllou, I.; Papadopoulos, G.A.; Lekkas, E. Impact on built and natural environment of the strong earthquakes of April 23, 1933, and July 20, 2017, in the southeast Aegean Sea, eastern Mediterranean. Nat. Hazards
**2020**, 100, 671–695. [Google Scholar] [CrossRef] - Papadimitriou, P.; Kapetanidis, V.; Karakonstantis, A.; Spingos, I.; Kassaras, I.; Sakkas, V.; Kouskouna, V.; Karatzetzou, A.; Pavlou, K.; Kaviris, G.; et al. First Results on the Mw=6.9 Samos Earthquake of 30 October 2020. Bull. Geol. Soc. Greece
**2020**, 56, 251–279. [Google Scholar] [CrossRef] - Karakostas, V.; Tan, O.; Kostoglou, A.; Papadimitriou, E.; Bonatis, P. Seismotectonic implications of the 2020 Samos, Greece, Mw 7.0 mainshock based on high-resolution aftershock relocation and source slip model. Acta Geophys.
**2021**, 69, 979–996. [Google Scholar] [CrossRef]

**Figure 1.**Seismicity rate in terms of events per day (blue vertical bars) and cumulative number of events (solid black line) during June 2021–January 2022 in the area of Arkalohori. The occurrence of events with M

_{L}≥ 4 is marked by red stars (M

_{L}magnitude in the red axis to the right).

**Figure 2.**Spatial distribution of the 2021–2022 Arkalochori sequence, for 4750 events that occurred during the period between 13 January 2021 to 31 January 2022. The locations of the permanent (red triangles) and the temporary (blue triangles) stations are presented. The M ≥ 4.0 earthquakes are depicted by yellow stars. Faults are marked as red lines (see text for details). On the top left corner, the location of Greece is indicated in the red triangle while on the bottom left one the study area is included in the red rectangle.

**Figure 3.**Temporal distribution of the 2021–2022 Arkalochori sequence for 4750 events. Periods A, B, C, D, and E are marked with orange, yellow, green, purple, and violet circles, respectively. The M ≥ 4.0 earthquakes are depicted by yellow stars. Faults are marked as red lines (see text for details).

**Figure 4.**(

**a**) Location of the 2021–2022 Arkalochori sequence for 4750 events (

**b**) relocated events of the aftershock sequence using hypoDD. The locations of the permanent (red triangles) and the temporary (blue triangles) are presented (see text for details). The M ≥ 4.0 earthquakes are depicted by yellow stars. Faults are marked as red lines (see text and [30] for details).

**Figure 5.**Presentation of the map of the 5 cross-sections, 5 km wide (

**A**–

**A’**,

**B**–

**B’**,

**C**–

**C’**,

**D**–

**D’**, and

**E**–

**E’**) on the left side of the figure and the results of the SSW-NNE oriented cross-sections (upper panel) and the results of WNW-ESE oriented cross-sections (lower panel) on the right side. The projection of the 27 September mainshock is depicted by yellow star on sections (

**B**–

**B**’) and (

**C**–

**C’**).

**Figure 6.**Lateral V

_{P}(%) perturbations at 5, 10, 15, and 20 km depths. Areas with lower resolution are masked (darkened). Fault traces derived by [31].

**Figure 7.**Lateral vs. (%) perturbations at 5, 10, 15 and 20 km depths. Areas with lower resolution are masked (darkened). Fault traces derived by [31].

**Figure 8.**Cross-sections of V

_{P}(%) perturbations. The cross-section traces are the same with the first four ones of Figure 5.

**Figure 9.**Cross-sections of vs. (%) perturbations. The cross-section traces are the same with the first four ones of Figure 5.

**Figure 10.**Upper maps: wrapped ascending (

**left**) and descending (

**right**) co-seismic interferograms over the Arkalochori area. The interferograms are draped over shaded relief. Lower maps: co-seismic displacement maps generated using the ascending and the descending image pairs and draped over shaded relief.

**Figure 11.**Displacement maps for (

**a**) the vertical (up–down) and (

**b**) the E–W displacement components for the Arkalochori earthquake overlain by the earthquakes with magnitude greater than 3 and the active faults of the broader area. Positive values on the E–W component indicate eastward motion, while the negative ones describe westward motion.

**Figure 12.**(

**Up**) Coulomb stress changes distribution due to Mw = 4.9 event (yellow star) at centroid depth of 8.0 km. The red rectangle indicates the fault model for the kinematics of Mw = 4.9, while the blue one is the projection of the fault model of Mw = 6.0 main shock (listed in Table 3). (

**Down**) Coulomb stress changes along the vertical cross-section AB. The green circles are the relocated hypocenters of the aftershocks which occurred after the Mw = 4.9 and before the major earthquake Mw = 6.0. The green lines show the surface projections of the two fault models.

**Figure 13.**(

**Left**) Coulomb stress changes distribution due to Mw = 6.0 event (yellow star) at centroid depth of 10.0 km. The red rectangle indicates the fault model for the kinematics of Mw = 6.0, while the blue one is the projection of the fault model of Mw = 4.9 events (listed in Table 3). (

**Right**) Coulomb stress changes along the vertical cross-sections A-B, C-D, E-F, and the parallel cross-section G-H (from up to down). The green circles are the relocated hypocenters of the aftershocks which occurred after the Mw = 6.0 main shock. The green lines show the surface projections of the two fault models.

**Figure 14.**(

**Left**) Coulomb stress changes distribution due to Mw = 5.4 major aftershock (yellow star) at centroid depth of 9.0 km. The red rectangle indicates the fault model for the kinematics of Mw = 5.4, while the blue ones are the projections of the fault models of Mw = 4.9 and Mw = 6.0 events (listed in Table 3). (

**Right**) Coulomb stress changes along the cross-sections AB, CD. The green circles are the relocated hypocenters of the aftershocks which occurred after the Mw = 6.0 main shock. The green lines show the surface projections of the two fault models.

**Figure 15.**The frequency-magnitude distribution of earthquakes (squares) for the (

**a**) foreshock sequence, (

**b**) aftershock sequence, (

**c**) NE aftershocks cluster, (

**d**) SW aftershocks cluster. The corresponding fit according to Equation (6) is shown with the solid line, for the parameter values shown in the down left corner and Table 6. The dotted lines represent the 95% confidence intervals.

**Figure 16.**The cumulative number of events for M ≥ M

_{c}(symbols) with time that followed the Mw6.0 mainshock in the (

**a**) NE cluster and (

**b**) the SW cluster. The solid lines represent the composite model of three modified Omori regimes, while the dashed line the model for a single modified Omori regime, for the parameter values shown in Table 7.

**Figure 17.**The cumulative distribution function P(>τ) of the inter-event times τ (in minutes) (left panels) and the corresponding q-logarithmic function (right panels), represented by circles, for the (

**a**,

**b**) foreshock sequence, (

**c**,

**d**) aftershock sequence, (

**e**,

**f**) NE aftershocks cluster, (

**g**,

**h**) SW aftershocks cluster. Fitting with the q-exponential function (Equation (10)) is shown with the solid lines, for the parameter values and the corresponding correlation coefficients shown in the down left corners.

**Figure 18.**The average expansion (in km) of the aftershock zone as function of the logarithm of time (symbols) for Central Crete 2022, Mw6.0 aftershock sequence. The solid line represents the logarithmic growth of the aftershocks zone.

Model | Model 1 | Model 2 |
---|---|---|

Mean RMS (s) | 0.26 | 0.26 |

Mean ERH (km) | 1.30 | 1.31 |

Mean ERZ (km) | 4.41 | 4.52 |

Mean Depth (km) | 9.43 | 13.94 |

**Table 2.**Average absolute values of P- and S-wave residuals and their cumulative reduction percentage during the inversion of experimental data.

Iteration | P-Residual (s) | P-residual Reduction (%) | S-Residual (s) | S-Residual Reduction (%) |
---|---|---|---|---|

1 | 0.269 | 0.00 | 0.437 | 0.00 |

2 | 0.211 | 21.50 | 0.248 | 43.14 |

3 | 0.194 | 27.63 | 0.222 | 49.12 |

4 | 0.188 | 30.08 | 0.218 | 50.10 |

5 | 0.186 | 30.85 | 0.211 | 51.69 |

Ascending Image Pair | ||||||
---|---|---|---|---|---|---|

Satellite | Ref./Repeat | Acquisition | Track | Orbit | Bperp (m) | Btemp (days) |

S1B | Reference | 23 September 2021 | 102 | 28,828 | −111.36 | 6 |

S1A | Repeat | 29 September 2021 | 102 | 39,899 | ||

Descending Image Pair | ||||||

Satellite | Ref./Repeat | Acquisition | Track | Orbit | Bperp (m) | Btemp (Days) |

S1A | Reference | 25 September 2021 | 36 | 39,833 | −28.08 | 6 |

S1B | Repeat | 1 October 2021 | 36 | 28,937 |

Site | Latitude (°) | Longitude (°) | D_{East}(cm) | D_{North}(cm) | D_{Up}(cm) |
---|---|---|---|---|---|

ARKL | 35.1339 | 25.2689 | 4.51 ± 0.11 | 7.85 ± 0.14 | −15.45 ± 0.60 |

HERA | 35.4241 | 25.1415 | −0.54 ± 0.09 | 0.62 ± 0.19 | 0.57 ± 0.39 |

Date | Hour | Minute | Lat. | Long. | Depth (km) | Mw | Strike | Dip | Rake | Agency | Length | Width | Mo (Nm) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

24 July 2021 | 2 | 7 | 35.1676 | 25.2286 | 8 | 4.9 | 214 | 52 | −95 | NOA | 2.3 | 2.56 | 9.116 × 10^{15} |

27 September 2021 | 6 | 17 | 35.1421 | 25.2734 | 10 | 6.0 | 218 | 57 | −85 | GFZ | 7.61 | 10.3 | 1.1 × 10^{18} |

28 September 2021 | 4 | 48 | 35.1356 | 25.2312 | 9 | 5.3 | 182 | 22 | −95 | UOA | 4.41 | 4.88 | 1.30 × 10^{17} |

**Table 6.**Parameter values for the foreshock and aftershock sequences in Arkalochori, as well as for the NE and SW aftershock clusters. N is the number of events (with M ≥ M

_{c}), Mc the magnitude of completeness, a

_{m}, q

_{m}the parameters of the NESP model (Equation (6)) and τ

_{0}, q

_{τ}the parameters of the q-exponential function for the inter-event time distribution (Equation (10)).

N | M_{c} | α_{m} | q_{m} | τ_{0} | q_{τ} | |
---|---|---|---|---|---|---|

Foreshocks | 410 | 2.8 | 3005 ± 734 | 1.46 ± 0.02 | 732.2 ± 47.9 | 1.72 ± 0.11 |

Aftershocks (both NE and SW clusters) | 4465 | 2.5 | 384 ± 99 | 1.50 ± 0.01 | 69.2 ± 12.3 | 1.78 ± 0.09 |

NE cluster | 1815 | 2.5 | 518 ± 84 | 1.43 ± 0.01 | 204.9 ± 12.4 | 1.81 ± 0.12 |

SW cluster | 2431 | 2.5 | 409 ± 101 | 1.53 ± 0.01 | 61.8 ± 4.3 | 2.16 ± 0.17 |

**Table 7.**The considered mainshock, the duration (in days), the number of events (N), and the MLE of the modified Omori formula parameters for the NE and SW aftershock clusters, along with their associated uncertainties. AIC is the estimated Akaike Information Criterion for each model.

Cluster | Model | Mainshock | Duration (Days) | N | K | c (Days) | p | AIC |
---|---|---|---|---|---|---|---|---|

NE cluster | Single model | M5.8 27/09/21 | 119.3 | 256 | 71.02 ± 14.45 | 28.35 ± 0.57 | 1.85 ± 0.08 | –72.4 |

Composite model | M5.8 27/09/21 | 22.8 | 120 | 10.57 ± 7.18 | 0.01 ± 1.63 | 0.35 ± 0.12 | –125.7 | |

M4.3 20/10/21 | 44.6 | 92 | 10.95 ± 3.98 | 0.24 ± 0.65 | 0.66 ± 0.06 | |||

M3.7 03/12/21 | 51.9 | 44 | 11.57 ± 8.56 | 1.50 ± 1.63 | 1.10 ± 0.28 | |||

SW cluster | Single model | M5.8 27/09/21 | 114.8 | 446 | 165.65 ± 126.80 | 1.76 ± 1.33 | 1.18 ± 0.16 | –1130 |

Composite model | M5.8 27/09/21 | 24.1 | 290 | 81.09 ± 35.98 | 0.67 ± 1.15 | 1.01 ± 0.36 | –1304 | |

M4.5 21/10/21 | 8.7 | 68 | 12.00 ± 4.66 | 0.01 ± 0.11 | 0.86 ± 0.19 | |||

M3.7 03/12/21 | 82.0 | 88 | 10.00 ± 4.55 | 0.26 ± 0.32 | 0.77 ± 0.08 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Vallianatos, F.; Karakonstantis, A.; Michas, G.; Pavlou, K.; Kouli, M.; Sakkas, V.
On the Patterns and Scaling Properties of the 2021–2022 Arkalochori Earthquake Sequence (Central Crete, Greece) Based on Seismological, Geophysical and Satellite Observations. *Appl. Sci.* **2022**, *12*, 7716.
https://doi.org/10.3390/app12157716

**AMA Style**

Vallianatos F, Karakonstantis A, Michas G, Pavlou K, Kouli M, Sakkas V.
On the Patterns and Scaling Properties of the 2021–2022 Arkalochori Earthquake Sequence (Central Crete, Greece) Based on Seismological, Geophysical and Satellite Observations. *Applied Sciences*. 2022; 12(15):7716.
https://doi.org/10.3390/app12157716

**Chicago/Turabian Style**

Vallianatos, Filippos, Andreas Karakonstantis, Georgios Michas, Kyriaki Pavlou, Maria Kouli, and Vassilis Sakkas.
2022. "On the Patterns and Scaling Properties of the 2021–2022 Arkalochori Earthquake Sequence (Central Crete, Greece) Based on Seismological, Geophysical and Satellite Observations" *Applied Sciences* 12, no. 15: 7716.
https://doi.org/10.3390/app12157716