Strong Earthquake Sequences in Greece during 2008-2014: Moment Tensor Inversions and Fault Plane Discrimination

As is well known, Greece has a significant number of earthquakes each year. Ιn recent years, several earthquakes have occurred in Greece. For this scope, a methodology was used to determine the source parameters. This methodology is based on minimizing the difference between the observed and the synthetic waveforms, using the method Source Parameters Calculation—SPCa [1]. The source parameters, using the proposed methodology, are calculated by comparing observed seismograms and synthetic by inverting data. The synthetics are calculated using the reflectivity method (Kennett, 1983) as implemented by Randall et al. (1994) for a given earth structure. This study includes inversion results for the strongest events that occurred in Greece from 2008 to 2014. For the same events calculated the main fault plane, using the method of Hypocenter Centroid-plot (HC-plot) [2] [3]. This methodology is a simple geometrical method based on the combination between the hypo-central position and the two possible fault planes.


Introduction
The seismic moment tensor constitutes the most important source parameter since it describes in a first-order approximation the equivalent forces applied on a fault plane and can be calculated by body wave modeling. The moment tensor as a mathematical description of equivalent forces and moments is used to study the source processes. The propagation and the source effects characterize varia-tions of the observed seismograms. Mathematically, each one of these effects can be calculated to generate synthetic seismograms that can be compared directly to the corresponding observed ones. The best solution is obtained by the minimization of the difference between the observed and the synthetic seismograms (Aki and Richards, 1980). General a seismic source can be representing by a symmetric square matrix (3 × 3) with 6 independent elements. Eigenvalue and eigenvector analysis of the moment tensor can be used to determine the components of the moment tensor. All the mathematical expressions described analytically in the studies [4] [5].
The linear dipole is compensated by two other linear dipoles along with the other two perpendicular directions. The eigenvalues describe the isotropic component of the moment tensor. In the case that the sum of the eigenvalues is vanished the applied forces constitute a pure double couple source. In this case, the seismic moment tensor has only deviatoric components [5] [6]. In general, a complete moment tensor is the superposition of the two vector dipoles (DC and CLVD) and isotropic component [5] [6]. In the case of an earthquake, the isotropic part is zero.

Applied Methodology and Preparation of Data
Seismological digital broadband data from the Hellenic Unified Seismological Network (HUSN) were collected and analyzed to calculate the source parameters of the strongest earthquakes that occurred in the Greece area, for the last six years. For this purpose, a methodology based on a moment tensor inversion was used, using the software of Ammon [7]. This method calculates synthetic seismograms directly compared with the observed ones for a given velocity structure. The reflectivity method of Kennett [8] as implemented by Randall [9] was applied to determine the Green Functions, initially calculated for different depths by the analyst. Iterative inversions were performed at depth intervals of 5 km followed by a finer one of 1 -2 km steps around the depth exhibiting the lowest misfit.
Regional data at least five broadband stations, at different azimuthal coverage and epicentral distances less than 3˚, equipped with three components seismometers, were selected and analyzed. The preparation of the data, includes the deconvolution of instrument response, following the velocity was integrated to displacement and finally, the horizontal components rotated to radial and transverse ones. Then the method uses the long period part of the signal to invert.
A bandpass filter is applied both on the observed waveforms and synthetics, having a fixed length of 70 sec. The inversion results indicate that inverting waveforms longer than 70 sec resulted in higher misfits. The quality of the results of moment tensor solutions can be evaluated by considering the average misfit and the compensated linear vector dipole (CLVD). For each solution, there is a quality code that consists of the letters A -D, for the minimum misfit and between the numbers 1 -4 for the percent of CLVD [9].
Finally, for all the previous events we determined the main fault plane that activated, using the Hypocenter Centroid-plot (HC-plot). In this methodology is putting hypocenter and centroid of the 3 components local waveform inversion is located in three-dimensional space, and later calculate its distance to both faulting planes. If the hypocenter is located on one of the two plane faults, so the fault plane is the real fault plane. If the hypocenter is not located in one of the two-fault planes the real fault plane is the closest one to the hypo-center [2] [3].

Applications
The proposed methodology was applied to the largest earthquakes that occurred recently in Greece. The first two applications concern the 2006 Kythira and the 2008 Leonidio earthquakes (deep events), while the last five concern the seismic sequences that occurred in Greece last year.
On February 2008, three strong events (Mw = 6.7, 6.1 and 6.0) occurred South of Methoni, at a segment of the Hellenic arc which was not activated during the instrumental period. This sequence was followed by a large number of aftershocks, the strongest of which were processed to calculate their source parameters. On the other hand, the aftershock distribution of the 2008 Andravida (Mw = 6.4) earthquake extended to an area significantly larger than the one expected according to the magnitude of the main event. Also, the source parameters for the three seismic sequences in Limnos Island (08/01/2013), in Kallidromon Mountain (Central Greece, 07/08/2013) and finally the most recent in Kefallinia Island (26/01/2014) were calculated. The obtained source parameters were compared to the seismotectonic characteristics of each seismogenic area. These events occurred in different seismotectonic settings, the fact that permits us to evaluate the reliability of the method.  23.406˚E, and the focal depth at 69 Km. This event is located in the Hellenic subduction zone which characterizes the Southern part of Greece. The shock was felt in a spatially extended area that covered Greece, Italy, Turkey, Egypt, Cyprus, Israel, Syria, Jordan, and Lebanon. This event is one of the largest earthquakes, after the event of 1903 (M = 7.3), which occurred in the same area. Previous works indicate the existence of a seismic gap in this region [10]. The major part of the seismic activity in this region is related to the active subduction zone along the Hellenic Arc, as well as the backarc area. Consequently, the area presents complex deformation, where the southern part of the Aegean region is moving towards the southwest at approximately 40 mm/yr [11] [12]. The area is characterized by active normal faults (Danamos, 1992) with an almost vertical orientation concerning the subduction zone. The main event was followed by a small number of aftershocks, as it appeared in Figure 1.

The
Thrust type faulting was revealed after applying moment tensor inversion. The obtained focal mechanism is strike = 205˚, dip = 48˚ and rake = 59˚ with a seismic moment equal to 8.4 × 10 25 dyn·cm, and a focal depth equal to 65 km ( Figure 2).
The obtained focal mechanism calculated using data in regional distances is in agreement with the one proposed by the Harvard CMT solution, using teleseismic data.
Using manually locations of HRV, NOA and UOA and their respectively Moment Tensors (Table 1) with the varied depth we obtain H-C consistent solution.
The fault plane is the nodal plane with strike = 205˚, dip = 48˚ and strike = 59˚. The distance of the hypocenter from this plane is 7.5 km, while the distance from the other plane is 22.30 km. The distance between Hypocenter and Centroid is 33 km (Figure 3).

The Mw = 6.0, 2008 Leonidio Earthquake
On January 6, 2008 (05:14, UTC) a strong earthquake happened near the Leonidio    Figure 4).  Three-component seismological data from stations belonging to the ORFEUS Institute were used. The inversion procedure provided a thrust type faulting with source parameters: strike = 114˚, dip = 75˚ and rake = 120˚. The depth is calculated at 85 km and the seismic moment M 0 = 1.6 × 10 25 dyn•cm. The obtained result showed a good fit between the observed and the synthetic waveforms ( Figure 5).
To apply the HC-plot method, the following 6 hypocenters manually locations ( Table 2) were considered.
The fault plane is the nodal plane with strike = 225˚, dip = 36˚ and strike = 19˚. The distance of the hypocenter from this plane is 11.62 km, while the distance from the other plane is 26.30 km. The distance between Hypocenter and Centroid is 33.26 km ( Figure 6). These results are in good agreement with this   one obtained by Zahradnik [2] [3].

The Mw = 6.7, and 6.1, 2008 Methoni Earthquakes
On February 2008 an earthquake sequence including three strong events (Mw = 6.7, 6.1 and 6.0) occurred South of Methoni town, at a segment of the Hellenic arc which was not activated during the instrumental period. This sequence was followed by a large number of aftershocks, the strongest of which were processed to calculate their source parameters. The first one occurred on 14 February 2008 (10:09, UTC) and the epicenter was located (36.50˚N, 21.78˚E) 230 km southwest of Athens. Two hours later (12:08, UTC) the second one occurred close to the first with epicenter (36.22˚N, 21.75˚E) and magnitude Mw = 6.1, according to the National Observatory of Athens. These two strong events were followed by another earthquake six days later on 20 February 2014 with a similar magnitude (Mw = 6.0). The moment tensor inversion indicates for the two first earthquakes the activation of a thrust-faulting type, while for the third event the inversion indicates a strike-slip type faulting.
Following we present the result of the inversion for the first event. For this purpose, the data of 6 stations from Hellenic Unified Seismological Network (HUSN) at epicentral distances less than 360 km, were used. Reverse type faulting was revealed after applying inversion. The obtained focal mechanism is strike = 290˚, dip = 16˚ and rake = 69˚. The seismic moment is equal to M0 = 1.56 × 10 26 dyn•cm, for a focal depth equal to 29 km ( Figure 7). The inversion   Table 3 and are plotted later in Figure 8.  The constrained focal mechanism solution indicates strike-slip faulting with source parameters strike = 290˚, dip = 70˚ and rake = 1˚, the seismic moment is equal to M 0 = 4.49 × 10 25 dyn·cm, while the focal depth was equal to 22 km ( Figure 9). Taking to account the aftershock activity the fault plane is the one with the NE-SW direction.
To apply the HC-plot method, the following 6 hypocenters manually locations (Table 4) were considered.
The following CMT solutions were considered: HRV, USGS, ETHZ, INGV, AUTH and NOA ( Figure 10). All these solutions are characterized by similar strike-dip-rake angles, with one nodal plane, strike~265˚, dip~85˚ and rake~4˚ plotted in green and hereafter referred to as the green plane and the other one, strike~300˚, dip~75˚ and rake~160˚ as the red plane ( Figure 10).
The fault plane is the nodal plane with strike = 290˚, dip = 70˚ and strike = 1˚.   The distance of the hypocenter from this plane is 2.86 km, while the distance from the other plane is 9.52 km. The distance between Hypocenter and Centroid is 11.72 km ( Figure 11). This result is in good agreement with those from other studies [2] [3] [13]. Following we present the inversions results for 28 events with magnitudes M w > 3.5 that occurred in the same region (Table 5).

The M w = 5.7, 2013 Limnos Earthquake
On 8 January 2013 at 14:16:08.3 UTC, a moderate earthquake of magnitude Mw = 5.7 occurred off the southern coast of Limnos island. The event was strongly felt in nearby north Aegean islands, the neighboring Turkish coasts and the northeastern Greek mainland but caused no damage [14]. The epicenter was manually located at 39.6663˚N, 25.5620˚E, depth = 31 km with a local magnitude M L = 5.8 according to National Observatory of Athens, http://bbnet.gein.noa.gr/alerts_manual/2013/01/evman130108141608_info.html.
The location of the earthquake indicates that it ruptured a fault segment running south of the North Aegean Trough near the island of Limnos [15] [16] [17], where the main, northern branch of the North Anatolian Fault (NAF) enters  [20]. The main event of January 8, 2013, was followed by a large number of aftershocks. For the next two months, a total number of 495 events (1 ≤ M L ≤ 4.5) were recorded and analyzed. The main shock, as well as the aftershocks were relocated [21]. The aftershock distribution of the mainshock reveals a NE-SW stricking fault about 40 km offshore Limnos Island that extends from 2 km up to a depth of 14 km [21]. The next two months 7 events with magnitude M w ≥ 3.7 occurred and the source parameters of them calculated and presented in Table 6.
We applied moment tensor inversion to calculate the source parameters of the main event (January 8, 2013 14:16, UTC). Seismological data from HUSN, of 8 stations at epicentral distances less than 350 km were used. A band-passed filtering at frequencies 0.05 -0.08 Hz was used both of recorded waveforms of three components and calculated synthetics seismograms. The inversion indicated a strike slip faulting, and the source parameters were calculated: strike = 315˚, dip = 86˚, rake = 5˚ with a depth 8 km while the moment magnitude determined M 0 = 3.90 × 10 24 dyn•cm. The calculated double couple found 95% ( Figure 11).
To apply the HC-plot method, the followed 7 hypocenters manually locations (Table 7) were considered.
The following CMT solutions were considered: HRV, USGS, GFZ, INGV, AUTH and UOA ( Figure 13). All these solutions are characterized by similar strike-dip-rake angles, with one nodal plane, strike~300˚, dip~80˚ plotted in green and hereafter referred to as the "green" plane and the other one dipping, strike~65˚ deg, dip~80˚ as the "red" plane. The distance of hypocenter from this plane is 6.11 km, while the distance from the other plane is 1.61 km. The distance between Hypocenter and Centroid is 6.89 km ( Figure 12). The main fault is this with source parameters: strike = 45˚, dip = 85˚ and rake = −175˚ and it is in agreement with these from the study [13].     2) were recorded and relocated [22]. The moment tensor solutions for events with magnitudes, M w ≥ 3.7, were calculated and presented in the following table (Table 8). Regional waveforms at epicentral distances less than 3˚ were used to determine the source parameters of the main event as well as all the aftershocks.
The inversion indicated the activation of a normal fault for all the studied events with a variation of the dip value between 30˚ and 40˚ and a focal depth varied between 8 -13 km. For the first event (August, 7 2013 -09:06 UTC) the regional data from 8 stations with good azimuthally coverage was used. The source parameters as they calculated applying the moment tensor inversion method found: strike = 270˚, dip = 45˚, rake = -80˚ the seismic moment M 0 = 1.2 × 10 24 dyn·cm for a depth of 12 km. The calculated double couple was found equal to 96%, while the compensated linear vector dipole (CLVD) to 4%. The results of the applied procedure are presented in Figure 13.
To apply the HC-plot method, the followed 5 hypocenter manually locations (Table 9) were considered ( Figure 14).
The previous solutions were considered: HRV, INGV, GFZ, AUTH and NOA. All these solutions are characterized by similar strike-dip-rake angles, with one nodal plane, strike~265˚, dip~50˚, plotted in green and hereafter referred to as the "green" plane and the other one dipping, strike~75˚, dip~50˚, as the "red" plane.

The M w = 6.1, 2014 Kefallinia Earthquake
On January 26, 2014 (13:55, UTC) two strong earthquakes of magnitude M w = 6.1 and M w = 5.2 (18:45, UTC) occurred on the island of Kefallinia, Ionia Sea. These events inducing extensive structural damages, mainly in the western and central parts. Eight days later on February 3, 2014 (03:08, UTC) a second strong event with a magnitude similar to the first (M w = 6.0) happened at the north section of Lixouri town. These two earthquakes (M w = 6.1 and M w = 6.0) occurred in the same island as the destructive events of 1953. Between August 9 th and 12th of 1953, three earthquakes of magnitude 6.4, 6.8 and 7.2 took place in Cephalonia leading to hundreds of casualties and strong damages all over the island, but also in Zante and Ithaca. These events were followed by a serious number of aftershocks. We noted that  two months after the main event was recorded and analyzed more than 4000 events. The three large earthquakes, as well as all the aftershocks were relocated [1] [22] [23]. The source parameters for the strongest of these earthquakes (M w ≥ 4.0) were calculated, using the moment tensor inversion and presented in Table 10. Follow, we will present the focal mechanism for January 26, 2013 (13:55, UTC) earthquake, M w = 6.1 ( Figure 15). The data of 6 stations at regional data in epicentral distances less than 370 km were used and inverted, as it appeared in Figure 10. The inversion indicated the activation of a strike-slip faulting with source parameters strike = 23˚, dip = 68˚, rake = 175˚ the depth calculated at 13 km and the moment magnitude M 0 = 1.51 × 10 25 dyn•cm. The fit between observed and synthetic waveforms and the misfit/CLVD versus depth diagram presented in Figure 15.
The following CMT solutions were considered: HRV, GFZ, INGV, AUTH, UOA and NOA ( Figure 16). All these solutions are characterized by similar strike-dip-rake angles, with one nodal plane, strike~20˚, dip~70˚, plotted in green and hereafter referred to as the "green" plane and the other one, with strike~130˚, dip~80˚, as the "red" plane.
The distance of the hypocenter from this plane is 3.46 km, while the distance from the other plane is 3.87 km. The distance between Hypocenter and Centroid is 8.05 km (Figure 17). A preliminary result, about the activation of the main fault, is this with source parameters: strike = 23˚, dip = 68˚ and rake = 175˚. As it appears in Figure 16 the distance between the plane and the Hypocenter-Centroid is similar.  Figure 15. Moment tensor solution of the event that occurred on 26 January 2014 (13:55, UTC). Observed and synthetic displacement waveforms (continuous and dotted lines respectively) at the inverted stations for the radial, tangential and vertical components. Down of these, are presented (from left to right) the selected, solution is highlighted with the green arrow, in the misfit/CLVD-versus-depth diagrams and the summary of the solution and the corresponding beach ball.

Conclusions
The knowledge of the source parameters for moderate earthquakes is very important for seismically active regions, especially in the case where no large events occur. In general, it allows analytical studies; reveals the tectonics and the seismogenic characteristics of a specific region. The methodology that was used in this study is applied to the seven largest events that occurred recently in Greece. Mountain (Central Greece) [26] and finally the most recent event the 2014 Kefallinia Island were determined using the proposed methodology. For this purpose, regional data from Hellenic Unified Seismological Network, with epicentral distances less than 350 km, were selected and analyzed. The methodology is based on the generation of synthetics seismograms using the method of Kennett [8] for given earth-structure and then they compared with the corresponding observed. The next step was the deconvolution of the instrument response from the waveforms and then their integration to produce displacement. A band-pass filter was applied both to synthetics and observed seismograms and finally horizontal components rotated to radial and transverse. For all the events with magnitude, M w > 5.5 that occurred in Greece at the last years the source parameters as well as the fault that re-activated was calculated and present in Table 12. With bold represent the main fault, after the text edit has been completed, the paper is ready for the template. Duplicate the template file by using the Save as command, and use the naming convention prescribed by your journal for the name Figure 17. Focal mechanisms solutions, determined using regional data, in this study between 2006-2014.
of your paper. In this newly created file, highlight all of the contents and import your prepared text file. You are now ready to style your paper. The method was applied for a large variety of magnitudes and could determine the fault plane orientation and the seismic moment even under conditions of poor azimuthal coverage, as the fit of data and synthetics was well predicted for most events. All the solutions were compared with those from other institutes and they were in very good agreement. The focal mechanisms solutions for the events determined in this study appear in Figure 17.

Acknowledgements
I acknowledge the use of Hellenic Unified Seismograph Network (HUSN) data and I would like to thank the NOA scientific personnel for phase picking. The open-source software GMT http://www.soest.hawaii.edu/gmt/ was used to make several figures.
I gratefully thank the operators of the European permanent seismic networks who make their data available through EIDA, http://www.orfeus-eu.org/eida. In this study data from the following Institutes were used.

Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this paper.