Synthetic earthquake catalogs simulating ... - Wiley Online Library

PUBLICATIONS Journal of Geophysical Research: Solid Earth RESEARCH ARTICLE 10.1002/2014JB011765 Key Points: • Application of an originally developed earthquake simulator algorithm • The synthetic catalog contains 500,000 earthquakes in a period of 100,000 years • The simulator can replicate real features of the observed seismicity

Supporting Information: • Readme • Figure S1 • Figure S2 • Table S1 Correspondence to: R. Console, [email protected]

Citation: Console, R., R. Carluccio, E. Papadimitriou, and V. Karakostas (2015), Synthetic earthquake catalogs simulating seismic activity in the Corinth Gulf, Greece, fault system, J. Geophys. Res. Solid Earth, 120, 326–343, doi:10.1002/2014JB011765. Received 14 NOV 2014 Accepted 2 DEC 2014 Accepted article online 9 DEC 2014 Published online 25 JAN 2015

Synthetic earthquake catalogs simulating seismic activity in the Corinth Gulf, Greece, fault system Rodolfo Console1, Roberto Carluccio2, Eleftheria Papadimitriou3, and Vassilis Karakostas3 1

Center of Integrated Geomorphology for the Mediterranean Area, Potenza, Italy, 2Istituto Nazionale di Geofisica e Vulcanologia, Rome, Italy, 3Geophysics Department, Aristotle University of Thessaloniki, Thessaloniki, Greece

Abstract The characteristic earthquake hypothesis is the basis of time-dependent modeling of earthquake recurrence on major faults. However, the characteristic earthquake hypothesis is not strongly supported by observational data. Few fault segments have long historical or paleoseismic records of individually dated ruptures, and when data and parameter uncertainties are allowed for, the form of the recurrence distribution is difficult to establish. This is the case, for instance, of the Corinth Gulf Fault System (CGFS), for which documents about strong earthquakes exist for at least 2000 years, although they can be considered complete for M ≥ 6.0 only for the latest 300 years, during which only few characteristic earthquakes are reported for individual fault segments. The use of a physics-based earthquake simulator has allowed the production of catalogs lasting 100,000 years and containing more than 500,000 events of magnitudes ≥ 4.0. The main features of our simulation algorithm are (1) an average slip rate released by earthquakes for every single segment in the investigated fault system, (2) heuristic procedures for rupture growth and stop, leading to a self-organized earthquake magnitude distribution, (3) the interaction between earthquake sources, and (4) the effect of minor earthquakes in redistributing stress. The application of our simulation algorithm to the CGFS has shown realistic features in time, space, and magnitude behavior of the seismicity. These features include long-term periodicity of strong earthquakes, short-term clustering of both strong and smaller events, and a realistic earthquake magnitude distribution departing from the Gutenberg-Richter distribution in the higher-magnitude range. 1. Introduction The characteristic earthquake hypothesis was introduced more than 30 years ago [Shimazaki and Nakata, 1980; Schwartz and Coppersmith, 1984] and has been widely applied since then. The basic idea of this hypothesis, following the elastic rebound theory of Reid [1910], is that relevant earthquakes have a general trend to repeat themselves along the same fault segment. A characteristic earthquake ruptures the entire segment and relieves tectonic stress within the segment. Assuming a constant stressing rate and a constant strength on the fault, a consequence of this model is that the time interval between consecutive characteristic earthquakes is described by a renewal model with a relatively small coefficient of variation. Typically, a renewal model predicts that hazard is small immediately following the previous large earthquake and increases with time since the latest event on a certain fault segment. Fault segmentation and characteristic earthquake hypothesis are basic ingredients, for instance, of the studies published by the Working Group on California Earthquake Probabilities (WGCEP) in 1988 and 1990 [Field, 2007]. In his review of the previous WGCEP reports, Field [2007] noted that from his own perspective, the segmentation assumption was made a priori and that the data were then interpreted within this paradigm. The characteristic earthquake hypothesis ignores the contribution of the smaller-magnitude seismicity to the stress released by a fault. In this respect, it does not match the Gutenberg-Richter magnitude distribution [Gutenberg and Richter, 1944] at least as far as the magnitude of earthquakes of a single fault segment is concerned. A variant of the plain characteristic earthquake hypothesis includes the possibility that two or more segments rupture simultaneously, giving rise to larger-magnitude events (called cascade events in the reports of the WGCEP published in 1995 and 2002 [Field, 2007]). In spite of their popularity, the characteristic earthquake hypothesis and fault segmentation model are not fully supported by observational evidence. For instance, Mosca et al. [2012] analyzing 19 well-documented paleoseismological and historical sequences with 5 up to 14 dated events on a single fault segment found that a renewal model, associated with time-dependent hazard assessment, and some kind of predictability of the

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next large earthquake on a fault segment, is significantly better than a plain time-independent Poisson model only for four out of the 19 sites examined in their study. Similarly, focusing on eight fault segments consisting in an almost continuous fault zone bounding the southern coastline of the Corinth Gulf (Greece), Console et al. [2013] found poor evidence for a better performance of the renewal model based on the characteristic earthquake hypothesis with respect to the time-independent Poisson model. Recently, the concept of unsegmented faults, comprising more than one known fault segment where earthquakes of any magnitude may occur regardless of an a priori segmentation scheme, was considered by several authors [Weldon et al., 2005; Field and Page, 2011; Parsons, 2012, among others]. Recognizing the possibility that earthquakes may occur across segment boundaries, a recent report of the Working Group on California Earthquake Probabilities [2008] followed also the option of considering unsegmented faults for the best known (Type A) faults (adopting a Gutenberg-Richter distribution characterized by a b value equal to 0.0), as an alternative to the aforementioned models considering segmentation. However, this hypothesis was assigned a weight of only 10% compared to the model of segmented fault adopted in the previous reports. Testing and validating different hypotheses of long-term earthquake occurrence remains a challenging problem. In fact, in the study of the largest earthquakes, our observation record is too short and incomplete for statistical assessment of such models. To overcome these difficulties, the application of earthquake simulators, which can span periods of time much longer than our temporally constrained observations, has been considered useful by several seismologists. In order to test the preference between a characteristic earthquake hypothesis and a simpler time-independent hypothesis, Parsons and Geist [2009] applied a simple simulator-based model to paleoseismological records collected at Wrightwood on the San Andreas Fault and Wasatch Fault segments. Their simulations were constrained by the slip rate values and were based on the Gutenberg-Richter magnitude distribution. They showed that the Gutenberg-Richter distribution can be confidently used as an earthquake occurrence model on subsegments of different size on individual faults in probabilistic earthquake forecasting. Another application of the same simulator was tried by Parsons et al. [2013] on the Nankai-Tonankai-Tokai subduction zones in Japan. They found that using convergence rate as a primary constraint allows the simulator to replicate much of the spatial distribution of observed segmented rupture rates along the Nankai, Tonankai, and Tokai subduction zones, although rate differences between the two forecast methods were noted. Rather powerful algorithms have been recently developed to model long histories of earthquake occurrence and slip using various approximations of what is known about the physics of stress transfer due to the fault slip and the rheological properties of faults. In particular, these algorithms have been successfully applied to a fault model that encompasses a comprehensive set of faults in California [Tullis, 2012]. These physics-based earthquake simulators can reproduce dynamic rupture on geographically correct and complex systems of interacting faults [e.g., Ward, 2012; Richards-Dinger and Dieterich, 2012]. In the present study we aim to follow the work done by the above mentioned authors for simulating the seismic activity in the Corinth Gulf, Greece Fault System (CGFS). Although based on some of the principles adopted in those papers, our simulation algorithm has been independently developed, aiming at demonstrating that a model characterized by few, simple, and reasonable assumptions allows the replication not only of the spatial features but also of the temporal behavior and the scaling laws of the observed seismicity. The relations among source parameters used in our study have a physical justification and are consistent with the empirical relations known from the literature (Appendix A).

2. Algorithm of the Simulator Code The algorithm applied in this study was developed upon the conceptions introduced for earthquake simulators in California [Tullis, 2012] such as the constraint from the long-term slip rate on fault segments and the adherence to a physically based model of rupture growth, without making use of time-dependent rheological parameters on the fault. Because of its limited sophistication, our algorithm is suitable for the production of synthetic catalogs resembling the long-term seismic activity of relatively simple fault systems, including hundreds of thousands earthquakes of moderate magnitude, even using quite modest computing resources.

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Figure 1. Flow chart of the computer code for earthquake simulation adopted in this study.

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Figure 2. Seismotectonic setting of the Corinth Gulf area with all known active faults. The fault segments bounding the southern coastline are traced in blue color. Fault plane solutions of M ≥ 5.0 that occurred in the last few decades are plotted as equal area lower hemisphere projections.

The basic concepts, upon which our algorithm is built, are shown in the flow chart of Figure 1. A detailed outline of the computer code is provided in Appendix B. Here we recall only the main features of this algorithm. In the present version of the code, the seismogenic source is approximated as a rectangle, composed of a number of cells with assigned dimensions in along-strike and downdip directions. The rectangular fault is then divided into an arbitrary number of segments, without constituting any barrier to rupture growth. They have the only role of making it possible to assign different slip rates associated to tectonic loading onto each of them. There is no any limitation to consider, in the future development of the code, a nonrectangular shape of the fault, and a smooth distribution of the slip rate, with tapering at any of the edges. Each cell is randomly assigned an initial stress budget within a given interval around an arbitrary average value. This is to accommodate our lack of knowledge about the initial status of stress and strength on each point of the fault. The stress budget on a cell is progressively changed in three ways. 1. It is increased at every time step (e.g., 1 day) through equation (A14), according to the long-term slip rate (tectonic loading) mainly constrained by geodetic measurements. 2. It is decreased at the occurrence time of every rupture, by a given amount (e.g., 3.3 MPa); the same cell can rupture more than once in the same earthquake. 3. It is increased by a Coulomb stress change associated to a point source at the center of any other cell that ruptures during an earthquake; as all cells are assumed to rupture approximately with the same mechanism and the same fault plane, this stress change is always positive (see Appendix B for details); a further development of the algorithm might include nonplanar faults and a more general Coulomb stress change computation. The events are initiated one by one on the cell with the largest stress budget, but only if it exceeds a given stress threshold. This is assumed spatially constant through the entire source area for the sake of simplicity, but it could be easily let change, if the necessary information on the spatial strength distribution were known. The second ruptured cell of the specific event is chosen as that of largest stress budget among the eight cells surrounding the nucleation cell, and so on for the next ruptured cells, until the stopping condition is met, when none of the cells, including and surrounding the cells previously ruptured in the same event, has a stress budget exceeding the threshold. Particular attention has been given to the part of the simulator code that tunes the conditions of stopping an already initiated rupture. We obtained reasonable results by introducing a pair of “heuristic” rules to modulate the stress threshold to be exceeded for expanding an ongoing event into new cells or repeating

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Figure 3. Epicentral distribution in the study area along with fault traces. Different symbols were used to denote different magnitudes or times of occurrence. Stars represent earthquakes with magnitudes M ≥ 6.2, since 1700 (open stars) or 1900 (yellow stars). Dark red big circles denote earthquakes with 6.2 > M ≥ 5.6 since 1900 and small red circles earthquakes with 5.6 > M ≥ 5.0 since 1900. Open circles depict earthquakes with 5.0 > M ≥ 4.5 since 1964. Almost all the earthquakes with M ≥ 5.6 are connected with the major faults.

the slip on an already ruptured cell. These rules, which have relevant impact on the magnitude distribution of the synthetic catalogs, are as follows. 1. The stress threshold adopted for the nucleation of an event is decreased, after the initial rupture of the nucleation cell, by a quantity which is proportional to the square root of the number of the already ruptured cells, multiplied by a free parameter called “strength reduction coefficient”; this feature mimics the sharp decrease of strength at the edges of an expanding rupture. 2. The square root of the already ruptured cells is limited to a number equal to the width of the fault system, divided by the size of a cell and multiplied by a free parameter called “fault aspect ratio.” Although the first of these two empirical rules enhances the capability of an already nucleated event to expand into a larger rupture, the second one limits this enhancement to a size that does not exceed by many times the width of the fault system. As is has been proved by numerous tests and it will be shown in the following section, the strength reduction coefficient (of the order of few percent) influences the proportion of seismic moment released by small and that released by large earthquakes: the smaller this parameter is, the larger is the number of small events. On the contrary, for the fault aspect ratio, it has no influence on the magnitude distribution of the background activity but affects the shape of the magnitude distribution in the large-magnitude range. This simple algorithm ensures a stable process, during which the stress budget is maintained below the nucleation threshold and never vanishes, if a suitable initial value is chosen. The earthquake rate is modulated by the slip rate assigned to each fault segment. Only one earthquake may be produced at a single time step. This is a reasonable assumption, taking into account the different orders of magnitude of the interevent times and the time step, if the latter is assigned a sufficiently small value. The smallest magnitude produced by the simulator is that corresponding to the rupture of a single cell; however, the computer code allows the user to arbitrarily choose the smallest magnitude reported in the synthetic catalog (which cannot be smaller than the magnitude associated to an event rupturing an area equal to only one cell). Moreover, the computer code includes an option for running in warm-up fashion for the desired number of years in order to reach a stable situation before the real start of the synthetic catalog. It was proved by many tests that the values arbitrarily assigned to the initial stress budget of any cell do not affect the statistical properties of the synthetic catalogs if the selected warm-up time is long enough (e.g., 1000 years). The simulation algorithm, in its simplicity, provides preference for new ruptures to nucleate at the points of the fault where the stress budget is higher, i.e., where the time elapsed since the latest event is longer. Once it

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Table 1. Characteristic Earthquakes of the Southern CGFS Since 1714 A.D Event Number

Year

Month

Day

M

Segment Name

Segment Number

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

1714 1742 1748 1753 1775 1806 1817 1861 1887 1888 1928 1965 1970 1981 1981 1992 1995

7 2 5 3 4 1 8 12 10 9 4 7 4 2 2 11 6

29 21 25 6 16 24 23 26 3 9 22 6 8 24 25 18 15

6.2 6.7 6.6 6.1 6.0 6.2 6.6 6.7 6.5 6.3 6.3 6.3 6.2 6.7 6.4 5.7 6.5

Psathopyrgos Xylokastro Aigion Xylokastro Offshore Perachora Psathopyrgos Aigion Eliki Offshore Perachora Aigion Offshore Perachora East part of Eliki East part of Xylokastro Skinos Alepochori Offshore Akrata Aigion

1 5 2 5 6 1 2 3 6 2 6 3 5 7 8 4 2

is nucleated, the rupture expands in the directions where the stress budget is still higher, thus simulating a preference for filling preexisting gaps and epicenter migration. Moreover, because of the stress transfer included in the model, earthquakes are more likely to occur close to the borders of the rupture of a preceding large earthquake, simulating a feature similar to aftershock production.

3. The Seismicity of the Corinth Gulf Fault System 3.1. Seismotectonic Features The Gulf of Corinth has long been recognized as one of the most prominent active structures in the Aegean, which separates continental Greece from Peloponnese [McKenzie, 1978]. It forms, in general, an asymmetric half graben in an almost east-west direction, with an uplifted southern footwall and downward flexed hanging wall with minor antithetic faulting. The faults that seem to be seismically active are mainly the north dipping faults that bound the Gulf to the south (Figure 2). Seismicity is associated with the Psathopyrgos, Aigion, Eliki, Offshore Akrata, and Xylokastro fault segments in the western and central parts of the Gulf and to the Offshore Perachora, Skinos, and Alepohori fault segments in the eastern part of the Gulf. Most of the well-determined mechanisms indicate that the western fault segments have an average strike of N90–105°E under a N-S extension, a nodal plane with a northward dip of about 50° near the surface, and 10–25° at the bottom of the seismogenic layer and a steep south dipping plane [Jackson, 1987; Taymaz et al., 1991; Hatzfeld et al., 1996; Bernard et al., 1997; Baker et al., 1997]. This is also the case for microearthquake mechanisms [Hatzfeld et al., 1990, 2000; Rigo et al., 1996]. At the eastern extremity of the gulf, the main active normal fault segments strike more northeastwards (N70–90°E) and cut obliquely across both structures and the relief. Geological and morphological observations were modeled and gave a slip rate of 11 + 3 mm yr1 on the main rift-bounding fault over the last 350 kyr, which is more than 10 times higher than in the rest of Table 2. Parameters of the Corinth Gulf Fault System the Aegean and elsewhere in the Segment Segment Length Width Slip Rate world [Armijo et al., 1996]. Geodetic Number Name (km) (km) (mm/yr) information, and in particular 1 Psathopyrgos 15 12 6 comparison of GPS measurements 2 Aigion 16 12 6 with old triangulations, give an N-S 3 Eliki 22 12 6 extension of about 15 mm yr1 in the 4 Offshore Akrata 8 8 5 western part of the gulf and about 5 Xylokastro 20 12 5 6 Offshore Perachora 18 12 4 10 mm yr1 in the eastern part 7 Skinos 19 12 3 [Billiris et al., 1991; Clarke et al., 1997; 8 Alepochori 13 12 3 Davies et al., 1997; Briole et al., 2000].

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A comparison between several GPS surveys measured over a shorter duration gives slightly higher extension values, but with the same difference between the western and eastern ends of the Gulf [Hatzfeld et al., 2000]. The eight segments located along the southern coast comprise a fault zone, which is our target area. The consideration of a unique fault zone is supported by the statement of Jackson and McKenzie [1988] stating that the deformation of a zone at length scales much larger than a single fault is best described as a continuum. Usually, the dimensions along the strike of normal faults do not exceed 20–25 km [Jackson and White, 1989], which implies an upper limit for the magnitude of the earthquakes that Figure 4. Cumulative frequency of the earthquakes observed in the can occur on individual fault segment. Corinth Gulf area in relation with their magnitudes for four different However, it is not clear whether the complete data sets. discontinuities separating the different segments are stable and will never break, or occasionally, the rupture can jump from one segment to another, thereby leading to an earthquake of greater magnitude [Jackson and White, 1989; Hatzfeld et al., 2000]. Several strong (M ≥ 6.0) earthquakes have repeatedly occurred in our study area, causing severe damage in the cities as it became known from historical information for more than 25 centuries before our era [Papazachos and Papazachou, 2003; Ambraseys, 2009]. The most outstanding is the 373 B.C. Heliki earthquake, which caused the sinking of this important city. Testimonies also exist about catastrophic earthquakes in Delphi Oracle and ancient Corinth. Recurrence intervals range between one to three centuries [Console et al., 2013, and references therein]. The maximum known earthquake magnitude in the area is almost 7.0, which probably reflects the lack of continuity of faults, as already mentioned. Instrumental seismicity manifests the intense active deformation with several shocks of 6.0 ≤ M ≤ 6.7, most of them seriously damaging the urban areas and significant cities of the area (Aigion city, for example, struck by the 1995 M 6.4 main shock). For a comprehensive discussion on the seismicity characteristics three complete data samples were used and are shown in Figure 3. Earthquakes with M ≥ 6.0 (Table 1, depicted by stars in Figure 3) constitute a complete data sample since 1700 [Console et al., 2013] and are obviously more concentrated in the western than in the eastern part, an asymmetry also seen in the overall geological structure of the Corinth rift. Moderate (5.9 ≥ M ≥ 5.0, since 1900, red circles in Figure 3) and small (M ≥ 4.5, since 1964, small open circles in Figure 3) earthquakes follow the same pattern, with the majority being concentrated near Psathopyrgos and Aigion faults. The maximum of activity is found at 6–10 km depth, with 98% of them having focal depths less than 13–14 km [Rigo et al., 1996]. Table 3. Estimated b Values for Different Data Sets and Corresponding Completeness Periods Time Interval and Magnitude Threshold Magnitude Interval 4.5 ≤ M ≤ 5.5 5.0 ≤ M < 5.5 5.6 ≤ M < 6.2 6.2 ≤ M

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1964–2013

1900–2013

1800–2013

1700–2013

Mc ≥ 4.5

Mc ≥ 5.0

Mc ≥ 6.2

Mc ≥ 6.2

1.00 0.22 1.90

1.91

1.30

1.15 0.28 1.64


Based on the consideration made above, we assumed the parameters given in Table 2 for the segmentation of the fault system bordering the southern coast of the Corinth Gulf. According to equation (A1), the total moment rate released by this fault system is equal to 23.6 · 1016 N m/yr.

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3.2. The Question of Multisegmented Ruptures As already mentioned, several segments comprise a complex fault system, recognized and defined upon geologic evidence, whereas historical information was added for some important events in particular. There is, however, evidence that individual segments were joined together and engendered larger earthquakes. For seismic hazard purposes in multisegmented fault systems like the study area, and in particular their proximity to urban areas (the evanescence of the ancient blooming city of Eliki in 373 B.C. being the most impressive), such evaluation constitutes indispensable component. Therefore, relevant information is seeking from detailed studies and historical descriptions for the larger-magnitude (M ~ 6.7–6.8) earthquakes that involve more than one individual segment. The historical record of the last three centuries provides no evidence for a truly large shallow earthquake (Ms > 7.0) in the region, and no event in this region has been found which was responsible for a great loss of life or for bringing about even a minor social crisis [Ambraseys and Jackson, 1997]. There are testimonies in a handful of cases for temporarily very close events (the last case the 24 and 25 February 1981 earthquakes with M 6.7 and M 6.4, respectively, with a time difference of 6 h) that also consist a remarkable feature to be included in seismic hazard studies. In particular, Mouyaris et al. [1992] refer to a Venetian account of the 1402 earthquake, which points to unusual features, as that the Figure 5. Frequency-magnitude distribution of the earthquakes in the earthquake destroyed a series of synthetic catalogs obtained from the simulation algorithm with different castles from Aigion to Xylokastron and combinations of two free parameters described in the text. (a–c) Labels (1) the provoked sea wave affected both and (2) refer to the values of parameters strength reduction coefficient and the northern and southern shores of fault aspect ratio, respectively. The total seismic moment released by the events in all the synthetic catalogs is the same. The bottom data refer to the the Gulf, whereas they account also hints at faulting along the coast. The earthquakes observed in the area starting in 1911. same authors refer similar effects that are attributed to the 373 B.C. earthquake [Bousquet and Pechoux, 1978]. Although the earthquake is mentioned by Aristotle, the first informative account comes three centuries later in Strabo, who concludes CONSOLE ET AL.


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that Eliki was washed out to sea by a wave and that Boura disappeared into a chasm. Like the A.D. 1402 event, the 373 B.C. earthquake appears to have reactivated more than one fault segment. Bernard et al. [2006] Figure 6. Map of the total slip released during a simulation of 100,000 years of investigating the en echelon seismic activity across the CGFS. The color scale gives the slip in meters. Kamarai normal fault connecting the Aigion fault to the Psathopyrgos fault consider that it can significantly participate to the rupture of the nearby, larger segments, increasing their potential magnitude. Thus, the simultaneous slip of this fault, to the east with that of the Aigion or offshore fault, or to the west with the Psathopyrgos fault, makes the potential for a magnitude 6.2 to 6.7 earthquake, possibly ruptured in such a way, with the Aigion fault, in 1748 or 1817. Adjacent ruptures close in time or involving more than one fault segment have to be considered in our modeling. 3.3. Magnitude Distribution We carried out a simple analysis on the frequency-magnitude distribution of the Corinth Gulf earthquakes, aiming at recognizing features that could suggest a characteristic earthquake behavior. Table S1 in the supporting information contains the seismic data reported for the study area, starting from the oldest known historical earthquake occurred in 480 B.C. Figure 4 shows the cumulative frequency-magnitude distribution of the earthquakes for four different complete data sets. Data of the twentieth century clearly show a different trend in three different magnitude ranges, with a deficit of earthquakes in the range 5.6 ≤ M ≤ 6.2. As shown in Table 3, the b values range between 1.0 and 1.1 for the earthquakes with M ≤ 5.5. For the earthquakes with M ≥ 6.2, all the curves appear to have higher slopes, with two of them (since 1800 and 1900, respectively) having a value equal to 1.9. From the data shown in Figure 4 and reported in Table 3, we noticed that there is no continuity in “scale invariance” but a lack of faults capable to fail in moderate-magnitude earthquakes (5.6 ≤ M ≤ 6.2). From this, we might infer that the M ≥ 6.2 events do not belong to the same “family” of the “background” seismicity of M ≤ 5.5, in support of the characteristic earthquake hypothesis for the CGFS. Further analysis, based on the catalog of the only events occurring on the fault system (see Figure S2b in the supporting information), confirms the same features.

4. Application of the Simulator In the application of the simulator, the rectangular source area representing the CGFS was discretized in cells of 0.5 km × 0.5 km. We chose for the synthetic catalogs a minimum magnitude of 4.0, which is produced approximately by the rupture of six cells. The duration of all the synthetic catalogs was 100,000 years. In order to explore the effect of the two free parameters, strength reduction coefficient and fault aspect ratio separately, we carried out a series of eight simulations, each time using different combinations of these parameters. This effect is illustrated in Figure 5 by the magnitude-frequency density distribution of the earthquakes contained in the respective synthetic catalogs. Figures 5a and 5b show that the first free parameter, strength reduction coefficient, does have influence on the total number of earthquakes contained in the catalogs. The difference clearly comes from the substantial contribution given to the moment released by the high-magnitude range, maintaining the same constraint for the moment rate released by the entire fault system. Figure 5c, where the three plots refer to three different values of Figure 7. Map of the stress budget available after a simulation of the second free parameter fault 100,000 years of seismic activity across the CGFS. The color scale gives the aspect ratio, does not show visible differences in the distribution below stress in MPa.

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magnitude 6.0 but a clear difference of the shape above this threshold. All the plots shown in Figure 5 show a clear deviation of the magnitude distribution obtained by the simulation algorithm from a plain linear Gutenberg-Richter distribution, a feature that is consistent with the cumulative distributions obtained from the real observations described in section 3.3. In some cases, the magnitude distributions show a sharp “bump” around a value of magnitude that could be defined as “characteristic.” All the three panels of Figure 5 show also the magnitude density distribution of the real earthquakes observed in the Corinth fault system and reported in the seismic catalog since 1911. On the basis of a visual comparison, it seems possible to recognize the set of free parameters (0.10, 1.0) as the one that exhibits the best match between the real and simulated catalogs (Figure 5b), taking into account the large difference in the different scale of the total number of events. This combination of parameters produces a nearly flat magnitude distribution (i.e., a b value equal to 0) in the magnitude range 5.5 < M < 6.5 that reminds us the unsegmented option of the WGCEP [2008] report already mentioned in section 1.

Figure 8. Space-time features of synthetic catalogs concerning earthquakes with M ≥ 6.0 for the first 2500 years (blue bars). Red squares show the occurrence time and location of the observed earthquakes reported in Table 1.

In the following we shall show results of a simulation lasting 100,000 years obtained running our algorithm with the selected free parameters strength reduction coefficient and fault aspect ratio respectively equal to 0.1 and 1.0. Figure 6 shows a map representing in color scale the total slip released by the cells of the Corinth fault system during the 100,000 years simulation. The colors clearly delineate the different slip rate assigned to fault segments in four different areas. Figure 7, showing the map of the stress budget remaining available at the end of the simulation process, exhibits values in a range of the order of 3 MPa, as expected. The large bluish areas are the sources of the latest large earthquakes. The reddish areas are “gaps” prone to imminent large earthquakes. The small reddish spots are “asperities” ready to nucleate new events.

5. Temporal Features of the Synthetic Catalogs

Figure 9. Interevent time distribution from a simulation of 100,000 years of seismic activity across the CGFS.

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In order to test the potential use of the simulation algorithm for drawing conclusions about the predictability of large earthquakes, it would be desirable to make a comparison between the synthetic and the real catalog. However, this is not a trivial task, because the two kinds of catalogs are conceptually different. The list of 17 earthquakes of magnitude equal to or larger than 6.0 (except that for event 16, having magnitude 5.7) reported in Table 1 for the latest three centuries assumes that each event occurred onto a single segment. Nevertheless, the

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Journal of Geophysical Research: Solid Earth Table 4. Statistical Parameters of the Synthetic Catalog Segment Number/Name

Tr(yr)

σ (yr)

Cv

dlogL

1. Psathopyrgos 2. Aigion 3. Eliki 4. Offshore Akrata 5. Xylokastro 6. Offshore Perachora 7. Skinos 8. Alepochori

82.7 78.7 66.1 276.4 82.3 146.9 155.4 209.4

47.1 45.2 23.1 298.0 34.0 89.2 90.5 141.4

0.57 0.57 0.35 1.08 0.41 0.61 0.58 0.67

596.9 640.4 1025.9 58.9 675.3 259.0 269.6 165.2

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magnitude of earthquakes referring to the same segment is not uniform. This implies that a single earthquake could have ruptured a single segment just partly for the smaller magnitudes or more than one segment together for the larger magnitudes, in agreement with the assumption made in our simulation algorithm.

Aiming at reproducing an earthquake catalog resembling the features of the real one, the analysis was based upon some arbitrary criteria to attribute a specific earthquake to one or more segments. The rules adopted for this purpose are the following: (1) the earthquake must have a minimum magnitude of 6.0; (2) the earthquake is first assigned to the segment which contains the largest number of fractured cells; and (3) the same earthquake can be also assigned to other segments if the number of cells ruptured by the event exceeds the number of 600 or at least 80% of the total number of cells for the specific segment. It should be noted that the number of cells of the smallest segment in the fault system (number 4, offshore Akrata) is 384 (equivalent to a magnitude 5.9 earthquake) and that of the largest one (number 3, Eliki) is 1056 (equivalent to a magnitude 6.4 earthquake). Examples of time-space plots of the synthetic catalogs obtained after applying the above mentioned criteria to the first 2500 years are shown by blue bars in Figure 8. For the sake of comparison, this figure shows also the 17 earthquakes that occurred since A.D. 1700 and are reported in Table 1 (red squares). A visual inspection of Figure 8 does not reveal any systematic behavior that can be recognized as substantial discrepancy between the synthetic and the real catalogs. Note that Figure 8 displays all the ruptures that constitute a single earthquake as individual events. This justifies the apparent larger number of synthetic events with respect to those reported in the real catalog (which assigns each earthquake to a single segment, independently of its size). We observe a nonperiodical time distribution, with interevent times ranging from few years to hundreds of years on the same segment. We can also see earthquakes that rupture different segments as a unique event or more events that occur with very short time separation. This feature is not inconsistent with the historical observations. In fact, Table 1 reports doublets of events as numbers 9–10 (1887–1888) and numbers 14–15 (1981). Moreover, the two #2 and #4 (1742 and 1753) Xylokastro earthquakes are separated by only 11 years. In order to assess whether the earthquake occurrence time on the same segments in the synthetic catalogs behaves as a Poison process or not, we carried out a statistical analysis of the interevent times for the entire 100,000 years simulation. In this respect, Figure 9 shows the interevent time distribution of the simulation. Table 4 displays the mean interevent time, the standard deviation, and the coefficient of variation for each segment. The relatively short average interevent times of the simulations can be justified by the circumstance that often two or more segments rupture simultaneously in a single earthquake. Along with the above mentioned temporal parameters, Table 4 also reports the results of the difference between the log likelihood computed by the Brownian Passage Figure 10. Magnitudes of the earthquakes reported in the synthetic catalog Time renewal model and the Poisson versus the time elapsed after each earthquake of magnitude equal to or time-independent model (dlogL). For larger than 6.0.

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the likelihood estimation we have adopted the values obtained for Tr and Cv reported in Table 4 for each fault segment. Both Figure 9 and Table 4 show, as expected, that the most active segments are those characterized by larger size and higher slip rate (such as Psathopyrgos, Aigion, Eliki, and Xylokastro). The simulation also shows that especially for the less active segments (offshore Perachora, Skinos, and Alepochori), interevent times of several hundreds of years are possible. The coefficient of Figure 11. Number of earthquakes reported in the synthetic catalog versus variation Cv is typically close to 0.6, the time elapsed after each earthquake with M ≥ 6. which would be associated to a moderately time predictable behavior of the seismicity. The log likelihood difference denotes an outstanding better performance of the renewal model against the time-independent hypothesis. The exception to this pseudo-periodical behavior is presented by segment #4 (Offshore Akrata), which exhibits a coefficient of variation slightly larger than 1 and a modest log likelihood difference. We conclude this analysis of the temporal features of the synthetic catalogs looking at the phenomenon of short-term clustering. Figure 10 displays the magnitudes of all the earthquakes reported in the synthetic catalog versus the time elapsed after each earthquake of magnitude equal to or larger than 6.0. The timescale spans the first 0.1 years (36 days). Clustering is evident in the first days after the main shock, as expected in real cases. Figure 11, showing the histogram of the number of earthquakes reported in the catalogs versus the time after all the previous earthquakes of M ≥ 6.0, confirms the clustering effect visible in Figure 10 and puts in evidence a sort of Omori law of the aftershock sequences during the first days after the main shock. The fact that day #1 displays less earthquakes than day #2 is an artifact due to the discretization of the timescale in steps of 0.001 years in the synthetic catalog.

6. Discussion and Conclusions One of the main ingredients of our simulation algorithm is the imposition of an average slip rate released by earthquakes to each one of the segments recognized in the investigated fault system. This slip rate is derived from a combination of geological and geodetic observations, and in particular comparison of GPS measurements with old triangulations, as described in section 3.1. Although no constraint is made to the propagation of the fracture across different segments during an earthquake, the result of the long-term slip released by the simulated seismic activity matches the imposed slip rate quite well (Figure 6). There are no intrinsic limitations in the model to adopt a continuous slip rate distribution instead of introducing discontinuities imposed by the fault system segmentation. The frequency-magnitude distribution of the earthquakes reported in our synthetic catalogs is consistent with the frequency-magnitude distribution obtained from real observations, which shows a nonlinear trend, due to a lack of moderate events in the range 5.6 ≤ M ≤ 6.2. In section 3.1 we considered historical evidences for earthquakes the rupture of which extended over more than a single segment of those recognized in the study area, and we concluded that ruptures involving more than one fault segment have to be considered in our modeling. It may have large impact on the earthquake hazard assessment in the area. Here we want to present a more in-depth analysis of the multisegmented ruptures obtained in our simulations. In this analysis, the results of which are reported in Tables 4 and 5, we have assumed the rules introduced in section 5 to assign an earthquake to one or more

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Journal of Geophysical Research: Solid Earth Table 5. Number of Simulated Earthquakes Rupturing a Different Number of Segments Number of Segments 1 2 3 4 5 6 7 8

Number of Events 3112 947 691 43 21 2 0 0

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specific segments. These rules are necessary only for the classification made in our analysis, but they do not constitute a constraint to the location and size of earthquake ruptures.

Table 5 shows the distribution of the number of simulated earthquakes with respect to the number of segments ruptured simultaneously in each one of them. We may see that roughly half of the events appear produced by the rupture of more than one segment. Considering the magnitudes reported in Table 1 for the observed seismicity during the latest three centuries, and taking into account that an M = 6.5–6.7 earthquake can extend its rupture to cover more than one individual segment, the results of our simulations appear in fairly good agreement with the observations. Another kind of statistics on the simulation results is reported in Table 6, where for each segment of the Corinth fault system the number of cases of single-segment rupture is compared with the number of cases when the rupture of this segment is associated to the rupture of at least one more segment in the same earthquake. Table 6 shows that the number of single-segment ruptures is smaller than the number of multisegmented ruptures for segments #1, #2, and #3, characterized by the largest slip rate. This case is particularly evident also for segment #4, which is the one with the smallest size in the fault system. The simulations show that as expected, this segment is unlikely to produce a characteristic earthquake of M ≥ 6.0 by its own rupture, but it is often associated with the rupture of adjacent segments. Different is the case of segments #5, #6, #7, and #8, for which the number of single-segment ruptures is larger than the number of multisegmented ruptures, with particular evidence regard to segment #6. The application of our simulation algorithm to the CGFS, based on an unsegmented model of earthquake generation, has shown quite satisfactory results both in the magnitude and in the time-space behavior of the seismicity. The main conclusions drawn on these aspects can be resumed in the following: 1. The magnitude distribution of the simulated seismicity is consistent with observations, which support a characteristic earthquake hypothesis. 2. The calculated average repeat times of strong earthquakes for each segment appear consistent with those inferred from the historical seismic catalog. 3. The long period of simulations has allowed obtaining the statistical distribution of repeat time—an indispensable component for any seismic hazard analysis, which cannot be obtained from real observations, due to their short duration. The statistical distribution of earthquakes with M ≥ 6.0 on single segments exhibits a fairly clear pseudo-periodic behavior, with a coefficient of variation Cv of the order of 0.6. 4. We have found clustering of the stronger events (multiplets) —a feature that can be inferred even from the limited time period covered by the observations. 5. The synthetic catalog obtained from the simulations clearly shows the effect of smaller events clustering near to stronger ones (aftershocks). This effect appears to be very short in time—a peculiarity of the study area also observed in the evolution of real aftershock sequences. 6. None of the above reported conclusions need a segmented rupture model, but Table 6. Number of Simulated Earthquakes Rupturing a Single they are all consistent with a fully Segment or With Several Segments Associated to the Same Rupture unsegmented seismogenic fault model. Segment 7. The statistical features of the seismicity Number Single Segment Rupture Multisegment Rupture obtained from the simulation 1 266 944 algorithm, easily computable from the 2 175 1095 long interevent time series, can provide 3 513 1000 useful information for the seismic hazard 4 32 326 assessment in the Corinth Gulf area, in 5 845 371 6 604 77 terms of occurrence probability of 7 412 232 earthquakes exceeding a given magnitude 8 265 211 for a given period of time in the future.

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Appendix A: Relations Among Source Parameters Adopted in the Simulation Model This section provides the theoretical framework of the model adopted in the simulation algorithm applied in this study. Because the magnitudes of the earthquakes of the synthetic catalog generated by the algorithm are drawn from the Gutenberg-Richter distribution, and the number of these earthquakes per unit time must fit the constraint of the slip rate assigned to any fault segment of the model, it is necessary to adopt relationships between the magnitude and both the rupture area and the average slip of each event. A1. Physical Framework The scalar seismic moment of an earthquake is defined as M0 ¼ μ D S

(A1)

where μ is the shear modulus of the elastic medium, D is the average slip on the fault, and S is the rupture area that for a rectangular shape is the product of the length L by the width W. From the theory of elasticity, the energy released by a fracture through elastic waves is given by 1 E s ¼ ΔσDS 2

(A2)

where Δσ is the static stress drop of the earthquake. From (A1) and (A2), we obtain Es ¼

1 Δσ M0 2 μ

(A3)

Two widely used formulas link the seismic moment and the seismic energy of an earthquake with magnitude logE s ðjouleÞ ¼ 4:8 þ 1:5M

(A4)

logMo ðN mÞ ¼ 9:1 þ 1:5M

(A5)

[Gutenberg and Richter, 1956]

[Hanks and Kanamori, 1979] By substitution of (A4) and (A5) into (A3), we obtain Δσ ¼

2μ ≅ μ104 104:3

(A6)

and adopting a value μ = 33.1010 Pa for rocks in the Earth’s crust Δσ ¼ 3:3106 Pa

(A7)

For a rectangular rupture, in analogy with the theoretical formulas introduced for a circular fault by Keilis–Borok [1959], the following relations were proposed by Console and Catalli [2006]: Δσ 2 pffiffiffiffiffiffi Dðx; y Þ ¼ μ wL

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s " #ffi u w 2 u L 2 x2 t y2 2 2

Δσ pffiffiffiffiffiffi Δσ pffiffiffi wL ¼ S 2μ 2μ π 2 Δσ pffiffiffi π 2 S ¼ Dmax D¼ 32 μ 16

Dmax ¼ Dð0; 0Þ ¼

(A8)

(A9) (A10)

where x and y are the coordinates on the fault plane, counted from the center of the rectangular source, D(x, y) is the displacement on the point x and y coordinates, and Dmax is the displacement on the fault center.From the definition of seismic moment (A1), Mo ¼

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π2 3 Δσ S =2 34


(A11)

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Combining (A1), (A5), (A10), and (A11), we have logS ¼ 6:37

2 logΔσ þ M 3

(A12)

and logD ¼ 2:68 logμ þ

2 logΔσ þ 0:5M 3

(A13)

Dividing equation (A10) by the average interevent time, we obtain a relation between the stress rate and the slip rate: σ˙ ¼ μ

32 D˙ pffiffiffi π2 S

(A14)

A2. Comparison With Empirical Relations Several authors have found empirical relations among fault parameters based on sets of observations collected for earthquakes on global or regional scale. In most cases, their studies were distinguished between different faulting types, such as between strike-slip and dip-slip (normal or reverse) mechanisms. Dowrick and Rhoades [2004] pointed out that there are statistically significant differences between the regressions of different regions, as well as between single regions and multiregion data, suggesting that rupture styles differ with geological region. Here we refer to the well-known study of Wells and Coppersmith [1994] and the more recent one of Papazachos et al. [2004] (Unless explicitly stated, in this paper the International System of Units (SI) is adopted. The relations expressed in centimeter-gram-second (CGS) units, available in the past literature, have been converted into the SI units.). Wells and Coppersmith [1994], for their entire data set including all faulting types, found logLðkmÞ ¼ 2:44 þ 0:59M logw ðkmÞ ¼ 1:01 þ 0:32M

logS km2 ¼ 3:49 þ 0:91M logDðmÞ ¼ 4:80 þ 0:69M

ðσ ¼ 0:16Þ ðσ ¼ 0:15Þ ðσ ¼ 0:24Þ ðσ ¼ 0:36Þ

Wells and Coppersmith [1994], for the set of data including only normal source mechanisms, also found logLðkmÞ ¼ 1:88 þ 0:50M logw ðkmÞ ¼ 1:14 þ 0:35M

log S km2 ¼ 2:87 þ 0:82M log DðmÞ ¼ 4:45 þ 0:63M

ðσ ¼ 0:17Þ ðσ ¼ 0:12Þ ðσ ¼ 0:22Þ ðσ ¼ 0:33Þ

Wells and Coppersmith [1994] noted that the all-slip-type regression for rupture area versus magnitude is appropriate for most applications. In contrast, regressions for displacement relationships show larger differences as a function of slip type. Papazachos et al. [2004], for the dip-slip (both normal and reverse) mechanism in continental areas, found logLðkmÞ ¼ 1:86 þ 0:50M

ðσ ¼ 0:13Þ

logw ðkmÞ ¼ 0:70 þ 0:28M

log S km2 ¼ 2:56 þ 0:78M

ðσ ¼ 0:21Þ

log DðmÞ ¼ 4:82 þ 0:72M Note that the formula between w and M in Papazachos et al. [2004] is just the arithmetic consequence of the relations obtained for L and S, assuming a rectangular fault. It is interesting to try a comparison between the above mentioned relations obtained empirically by Wells and Coppersmith [1994] and Papazachos et al. [2004] and the relations that have been reported in the previous

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Table A1. Empirical and Theoretical Source Parameters for a Magnitude 7.0 Earthquake 2

Log S(km )

Log D

2.88 3.22 2.90 3.02

0.03 0.04 0.22 0.01

Wells and Coppersmith [1994] (all sources) Wells and Coppersmith [1994] (normal sources) Papazachos et al. [2004] (continental dip-slip sources) Physical model adopted in this study

section, on the basis of physical considerations only. If we adopt the values μ = 3.3 1010 Pa and Δσ = 3.3 106 Pa, equations (A12) and (A13) give respectively

log S km2 ¼ 3:98 þ M log DðmÞ ¼ 3:49 þ 0:5 M where S is expressed in km2 and D in meter as in the empirical formulas. The relations for the rupture length L and width W with M are not included here because these parameters scale with magnitude M for earthquakes of moderate size, but they follow a different behavior for large-magnitude events, when the width W tends to a value limited by the thickness of the seismogenic layer of the crust [Shaw and Scholz, 2001]. For the sake of comparison, Table A1 reports the values of S and D for an earthquake of magnitude 7.0 according to the four different approaches. Note the similarities between the empirical and the model-based values for all the considered cases. The differences are typically within the order of 25% on the examined quantities.

Appendix B: Outline of the Simulation Program Purpose: creating a synthetic earthquake catalog in a seismogenic region described by a rectangular fault, divided in segments of different slip rate. The fault geometry is described by the total along-strike length of the fault system (L) the length and the tectonic slip rate of each segment, a uniform downdip width (W), and the cell lengths (a) and width (b). Assuming a stress drop Δσ = 3.3 × 106 Pa, the slip, seismic moment, and magnitude of an earthquake on a single cell is computed (see Appendix A). The following parameters are used by the algorithm: (1) the average initial stress budget on the fault, (2) the variability of the initial stress budget on each cell (e.g., 5%), (3) the stress threshold necessary for event nucleation (stress_thresh), (4) the value of the strength reduction coefficient (strength_red_coeff) (e.g., 0.05); zero means no strength reduction, (5) the multiplying factor to be used for discouraging the propagation of the rupture on the strike direction (aspect_ratio) (e.g., 2.5); infinity means no limitation at all, (6) the time step of the simulations, (7) the total duration of the synthetic catalog, and (8) a warm-up time before the beginning of the catalog. An initial stress budget is randomly assigned to every cell. The first nucleation point is selected as the cell where the largest stress budget is assigned, if it exceeds the minimum stress budget required for event nucleation. Otherwise, the program proceeds by one time step, adding the tectonic stress rate for one time step to every cell, and the search for the nucleation point is started again. If the nucleation cell is found, the stress budget on the nucleation cell is decreased by a stress drop Δσ = 3.3 × 106 Pa. The stress budget on the other cells is increased on the basis of the stress transfer computed on each cell:

dcff ¼ 105 M0 _cell= 1:26 · 1015 1=dist3 where M0 _cell ¼

π2 Δσ ðabÞ3=2 32

is the seismic moment released by the rupture on a single cell [see Console and Catalli, 2006] and dist is the distance in kilometers between the centers of two cells.

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The procedure for the propagation of the rupture on the neighboring cells is started: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Set the number of ruptured cells of the event (Ncell_ev) to 1. Find the smallest of Ncell_ev and ((W/b)2 · aspect_ratio) and call it Ncell_min. Compute Strength_red = Δσ · ((ab/LW)3/2(Ncell_min)1/2 · strength_red_coeff. Starting from 1 to Ncell_ev, find the cell with the largest stress budget among all those already ruptured in the event with the addition of all bordering those already ruptured. The largest stess budget exceeds the threshold value stress_thresh diminished by Strength_red? If not, go to (10). If yes, go on. Decrease the stress budget of the ruptured cell by a value equal to Δσ. Increase the value of the stress budget of any other cell by dcff computed as described above for the nucleation rupture. Increase Ncell_ev by 1. Go to (2). Store the event parameters. The time, the event sequential number, and other parameters of the event are written on the output file.

A cell can be ruptured more than once in the same event. The program proceeds by one time step, adding the tectonic slip rate for one time step to every cell, and the search for a new nucleation point is started again. The process stops when the time assigned for the output catalog is exceeded.

Acknowledgments The authors are grateful to two unknown reviewers for their relevant and constructive comments that have greatly contributed in improving the first version of the manuscript. Fault plane solutions data used in this paper came from http://www.ldeo.columbia. edu/~gcmt/ and published sources listed in the references. Some plots were made using the Generic Mapping Tools version 4.5.3 (www.soest.hawaii.edu/ gmt) [Wessel and Smith, 1998]. Geophysics Department contribution 833. All the data used for obtaining the results presented in figures and tables of this paper can be requested directly to the authors.

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