#
Seismicity Patterns Prior to the Thessaly (M_{w}6.3) Strong Earthquake on 3 March 2021 in Terms of Multiresolution Wavelets and Natural Time Analysis

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## Abstract

**:**

_{w}6.3, occurred in northern Thessaly (Central Greece). To investigate possible complex correlations in the evolution of seismicity in the broader area of Central Greece before the M

_{w}6.3 event, we apply the methods of multiresolution wavelet analysis (MRWA) and natural time (NT) analysis. The description of seismicity evolution by critical parameters defined by NT analysis, integrated with the results of MRWA as the initiation point for the NT analysis, forms a new framework that may possibly lead to new universal principles that describe the generation processes of strong earthquakes. In the present work, we investigate this new framework in the seismicity prior to the M

_{w}6.3 Thessaly earthquake. Initially, we apply MRWA to the interevent time series of the successive regional earthquakes in order to investigate the approach of the regional seismicity at critical stages and to define the starting point of the natural time domain. Then, we apply the NT analysis, showing that the regional seismicity approached criticality a few days before the occurrence of the M

_{w}6.3 earthquake, when the κ

_{1}natural time parameter reached the critical value of κ

_{1}= 0.070.

## 1. Introduction

_{W}6.3 earthquake occurred in northern Thessaly (Central Greece), close to the cities of Tyrnavos, Elassona and Larisa (Figure 1). The earthquake occurred in a region that is one of the most seismically active in Greece, mainly characterized by normal faulting along NW–SE striking faults, which belong to the Thessaly fault zone [1,2,3,4,5,6,7,8,9,10]. Based on the provided focal plane solutions [11], the mainshock was generated by the activation of an NW–SE striking normal fault (Figure 1) [12]. The mainshock was widely felt in the Thessaly basin and in the surrounding areas, from Athens in the south to the northern borders of Greece.

_{w}6.3 Thessaly strong event. The recent upgrading of the regional seismological networks [48] provides an accurate catalogue of microseismicity in the area and enables the application of such methodologies. The earthquake catalogs used herein are taken from the Hellenic Unified Seismological Network (HUSN) (http://eida.gein.noa.gr/, last accessed on 27 May 2021), where instruments belonging to the HL (National Observatory of Athens, Institute of Geodynamics, 1997) [49] and HT (Aristotle University of Thessaloniki Seismological Network, 1981) [50] networks provide a complete spatial coverage in the broader area of Greece, with a magnitude of completeness (Mc) down to 2.0. Figure 2 presents the seismic activity observed in the region of Thessaly for a period starting in January 2016, approximately 1900 days before the 3 March 2021 mainshock and within an area of radius, R = 80 km, around its epicenter. The main objective of this study is to investigate the applicability of NT analysis, as presented in the regional seismic activity prior to the M

_{w}6.3 Thessaly earthquake, integrated with the results of MRWA applied to the interevent time series of the successive events, in order to define, with an objective technique, the starting point for the analysis in the NT domain. The description of seismicity evolution with the NT parameters, integrated with the results of MRWA, represents a novel framework that may lead to a better understanding of the evolution of earthquake generation processes.

## 2. Multiresolution Wavelets Analysis in the Seismicity of Thessaly Region

_{i}analysed and ψ is the wavelet function. The DWT is evaluated at the points (m, n) in the scale-interval-number plane. Smaller scales correspond to more rapid variations and, therefore, to higher frequencies.

_{th}= 2.0. The time period that was covered for MRWA of interevent times spanned from January 2016 until 3 March 2021, when the main event of M

_{w}6.3 occurred. In Figure 4 the time– earthquake magnitude plot for a radius R = 80 km around the epicenter and a magnitude threshold, M

_{th}= 2.0 is presented.

_{wav}(m), using fixed event number windows of 16 events shifting through the entire series. The shift between successive windows was set in two events. Consistently with the length of the time window, we analysed the time variation of the σ

_{wav}(m) for lower scales (m = 1 to 4) since the number of available events is limited. Each calculated value is associated with the time of the last event in the window. Figure 5 shows a representative set of results for the time evolution of the σ

_{wav}(m) using the db4 wavelet with four scales for MRWA, for the seismicity observed in three circles around the epicenter of the mainshock and within a radius of 30 km, 50 km and 80 km, respectively.

_{wav}

_{,}m(t) appeared, especially at lower scales. Plots at Figure 5 dictate the search for a time marker beginning several months before the major event for all the scales analyzed. The sharp decrease at lower scales (m = 1 and m = 2), which is observed before the major event, can be qualified as such a time marker since the decrease is evident for several days and is clearly identifiable.

## 3. Natural Time Analysis of Seismicity before the Thessaly Mw6.3, March 2021 Earthquake

^{th}event out of N total events. The seismic moment released during the k

^{th}event is then considered, forming the pair (χ

_{k}, M

_{k}) for further analysis (see [28]). The evolution of (χ

_{k}, M

_{k}) is further described by the continuous function F(ω), defined as: $F\left(\omega \right)={\displaystyle \sum}_{k=1}^{N}{M}_{k}exp\left(i\omega \frac{k}{N}\right)$ (3) where $\omega =2\pi \varphi $ and $\varphi $ stands for the natural frequency.

_{k}describes the probability to observe an earthquake event at natural time χ

_{k}. The normalized power spectrum can then be obtained from (4), as $\mathsf{\Pi}\left(\omega \right)=|\mathsf{\Phi}\left(\omega \right){|}^{2}$. In the context of probability theory, and for natural frequencies of $\varphi $ less than 0.5, Π(ω) reduces to a characteristic function for the probability distribution p

_{k}. It has been shown that the following relation holds [29,56]

_{1}is the variance in natural time, given as

_{1}= 0.07, can signify the approach of a complex system towards some critical point [35], such as that of an impending large earthquake (see [24,31,37] and references therein). Figure 6 shows an earthquake timeseries in conventional (Figure 6a) and natural time (Figure 6b) domains. Figure 6c shows the corresponding power spectrum Π(ω) for the critical stage with κ

_{1}= 0.070, based on Equation (6), while the two other curves are for non-critical stages. Theoretically, it has been shown that κ

_{1}approaches 0.083 as N → ∞, when there are no long-ranged correlations in the system [35].

_{k}, p

_{k}) is rescaled and κ

_{1}varies. It has been verified that when the parameter κ

_{1}converges to the value 0.070, the system enters a critical state [33,35,56].

_{nt}, is defined as [35]

_{nt}, is a dynamic quantity that depends on the sequential order of events. Moreover, upon the time reversal T, i.e., Tp

_{m}= p

_{N}

_{− m + 1}, the entropy, S

_{nt}

_{−}, is further defined. When the analysed seismicity approaches a “true” critical state, the following conditions should be fulfilled [35,56]:

- (i).
- The “average” distance D, defined by the normalized power spectra Π(ω) of the evolving seismicity and by the theoretical estimation of Π(ω) for κ
_{1}= 0.070, should be less than 10^{−2}. - (ii).
- The parameter κ
_{1}should approach the critical value of κ_{1}= 0.070 by “descending from above”. - (iii).
- Both natural time entropies, S
_{nt}and S_{nt}_{−}, should be lower than the entropy of uniform noise S_{u}= (ln2/2) − 1/4 when κ_{1}approaches 0.070. - (iv).
- Since the dynamic evolution of the system is expected to be self-similar in the critical state, the time of the true coincidence should not vary upon changing (within reasonable limits) either the magnitude threshold, M
_{th}, or the area used in the calculation.

_{th}= 2.0 and for areas of radius R = 30 km, R = 50 km and R = 80 km, respectively, around the epicenter of the main event. This analysis clearly demonstrates that, from 28 February to 2 March 2021, one to three days before the M

_{w}6.3 earthquake of 3 March 2021, the critical Π(ϕ) was approached. In all cases, for R = 30 km, R = 50 km and R = 80 km, the NT analysis starts at approximately one to two months around the corresponding time markers indicated by MRWA (see Figure 5). It may, thus, be considered that the critical point for the regional seismicity was approached around that time. What happened during the last time period before the main event can be seen in Figure 7, which depicts the time evolution of Π(ϕ), for 0 ≤ ϕ ≤ 0.5, for M

_{th}≥ 2.0 and R = 30 km, 50 km and 80 km, when calculations started on 6 August 2019 for R = 30 km and R = 50 km and on 7 November 2019 for R = 80 km. It also becomes interesting that around that time, when the critical point was reached, seismicity started to occur in the epicentral region registering a few shallow, weak earthquakes prior to the mainshock. These events, which may be considered as foreshocks, do not affect the analysis, as their occurrence coincides with the approach to the critical point.

_{w}6.3 event in the Thessaly region, starting the analysis from approximately the time markers in the lower scales indicated by MRWA and up to the time of the mainshock occurrence, we observe that all criticality requirements are fulfilled. The latter is more clearly demonstrated by the parameters D, κ

_{1}, S

_{nt}and S

_{nt}

_{−}, as they evolved event by event, and are computed and plotted in the natural time domain and in the conventional time, approximately 100 days before the mainshock (Figure 8). In Figure 8, we observe that all the requirements are fulfilled a few days before the mainshock for all three cases that we study, i.e., for R = 30 km, R = 50 km and R = 80 km around the epicenter of the mainshock. The results, thus, indicate that the regional seismicity presented criticality characteristics a few days before the main event.

## 4. Concluding Remarks

_{w}6.3) strong earthquake on 3 March 2021, by applying MRWA and NT analysis, two methods that have been used for the identification of critical stages in the preparation process of major earthquakes. The analysis was performed in the natural time domain, with an approximate starting point indicated by MRWA. The latter showed a decrease in the standard deviation of the wavelet coefficients σ

_{wav}(m) at much lower scales, similar to the observations in [26,27,54] prior to the occurrence of major events. Within this joint approach, the initial application of MRWA in regional seismicity around the epicenter, and for a wide time period before the mainshock, indicated a time segment where the NT analysis was applied in order to explore possible indicators that suggested the entrance to a critical stage.

_{w}6.3 earthquake that occurred on 3 March 2021 in the Thessaly region, in agreement with the results in [57]. In other words, the curve of the power spectrum, Π(ϕ), in the natural time domain that characterizes the evolution of the regional seismicity, coincided with the theoretical curve of critical point phenomena a few days before the M

_{w}6.3 mainshock, in a similar way to that of non-equilibrium critical systems. Hence, the analysis of the regional seismicity in the natural time domain, initiated at approximately the time marks indicated by the results of MRWA, pointed to an approximate date of the impending large M

_{w}6.3 earthquake of 3 March 2021, within a narrow time window in the order of a few days. These results lay further support to the methodology introduced in [28] regarding the combination of MRWA and NT analyses for the identification of critical stages of regional seismicity prior to strong earthquakes, providing a novel and promising framework for better understanding the evolution of earthquake generation processes.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Earthquake epicenters of the aftershock sequence of the 3 March 2021, Thessaly earthquake (yellow star), from 3 March 2021 to 18 April 2021 (M ≥ 2.0). The focal mechanisms of the mainshock and the largest aftershock are also indicated, along with the regional faults shown with black solid lines (for details see the text).

**Figure 2.**The observed seismicity in the Thessaly region between January 2016 and 3 March 2021, in an area of radius R = 80 km around the mainshock (star).

**Figure 3.**Interevent times between two successive events versus occurrence time of each event for a radius R = 80 km around the epicenter and a magnitude threshold, M

_{th}= 2.0.

**Figure 4.**Time–Magnitude plot for a radius R = 80 km around the epicenter and a magnitude threshold, M

_{th}= 2.0.

**Figure 5.**Time variation of σ

_{wav}(m) with scale m ranging from 1 up to 4, for moving windows with length of 16 events and a shift of 2 events. Interevent times were estimated using the HUSN catalogue (from January 2016 until 3 March 2021), for events within a radius R = 30 km (

**top 4 plots**), 50 km (

**middle 4 plots**) and 80 km (

**bottom 4 plots**) around the M

_{w}= 6.3 epicenter and a magnitude threshold, M

_{th}= 2.0. Red vertical line indicates the day of minimum in variance, observed at each scale.

**Figure 6.**Time series of seismic events (

**a**) in conventional time t and (

**b**) in the natural time χ. (

**c**) Schematic diagram showing the power spectrum Π(ϕ) in natural time. Solid line is Π(ϕ) obtained from Equation (4) for the critical stage (κ

_{1}= 0.070), whereas two other lines are for κ

_{1}> 0.07 and κ

_{1}< 0.07.

**Figure 7.**Time evolution of Π(ϕ), for 0 ≤ ϕ ≤ 0.5, of the seismic activity, for M

_{th}≥ 2.0 and R = 30 km (

**top**), R = 50 km (

**middle**), and R = 80 km (

**bottom**), when calculations start on 6 August 2019 for R = 30 km and R = 50 km and on 7 November 2019 for R = 80 km. Π(ϕ) curves (dashed lines) fall on the theoretical Π(ϕ) curve (red solid lines), calculated from Equation (6), as the critical stage is approached.

**Figure 8.**Time evolution of the NT analysis parameters κ

_{1}, D, S

_{nt}and S

_{nt−}, in natural time (

**left**) and conventional time (

**right**), as they evolve event by event prior to the Thessaly M

_{w}6.3 mainshock, considering an area with radius of R = 30 km (

**top**), R = 50 km (

**middle**), and R = 80 km (

**bottom**) around the epicenter and for a magnitude threshold M

_{th}= 2.0. The analysis was started on 6 August 2019 for R = 30 km and R = 50 km and on 7 November 2019 for R = 80 km. The dashed horizontal lines indicate the entropy limit of S

_{u}= 0.0966 and the value κ

_{1}= 0.070. The shaded rectangle marks the time when the critical stage is approached.

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Vallianatos, F.; Michas, G.; Hloupis, G.
Seismicity Patterns Prior to the Thessaly (M_{w}6.3) Strong Earthquake on 3 March 2021 in Terms of Multiresolution Wavelets and Natural Time Analysis. *Geosciences* **2021**, *11*, 379.
https://doi.org/10.3390/geosciences11090379

**AMA Style**

Vallianatos F, Michas G, Hloupis G.
Seismicity Patterns Prior to the Thessaly (M_{w}6.3) Strong Earthquake on 3 March 2021 in Terms of Multiresolution Wavelets and Natural Time Analysis. *Geosciences*. 2021; 11(9):379.
https://doi.org/10.3390/geosciences11090379

**Chicago/Turabian Style**

Vallianatos, Filippos, Georgios Michas, and George Hloupis.
2021. "Seismicity Patterns Prior to the Thessaly (M_{w}6.3) Strong Earthquake on 3 March 2021 in Terms of Multiresolution Wavelets and Natural Time Analysis" *Geosciences* 11, no. 9: 379.
https://doi.org/10.3390/geosciences11090379