On the Occurrence of Large Earthquakes: New Insights From a Model based on Interacting Faults Embedded in a Realistic Tectonic Setting

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL.???, XXXX, DOI: /, On the Occurrence of Large Earthquakes: New Insights From a Model based on Interacting Faults Embedded in a Realistic Tectonic Setting Warner Marzocchi, 1 Jacopo Selva, 2 Francesca Romana Cinti, 1 Paola Montone, 1 Simona Pierdominici, 1 Renata Schivardi, 2 Enzo Boschi, 3 W. Marzocchi, Istituto Nazionale di Geofisica e Vulcanologia, Roma 1, Via di Vigna Murata 605, Roma, Italy. ( warner.marzocchi@ingv.it) J. Selva, Istituto Nazionale di Geofisica e Vulcanologia, Bologna, Via Creti 12, Bologna, Italy. ( selva@bo.ingv.it) F. R. Cinti, Istituto Nazionale di Geofisica e Vulcanologia, Roma 1, Via di Vigna Murata 605, Roma, Italy. ( cinti@ingv.it) P. Montone, Istituto Nazionale di Geofisica e Vulcanologia, Roma 1, Via di Vigna Murata 605, Roma, Italy. ( montone@ingv.it) S. Pierdominici, Istituto Nazionale di Geofisica e Vulcanologia, Roma 1, Via di Vigna Murata 605, Roma, Italy. ( pierdominici@ingv.it) R. Schivardi, Istituto Nazionale di Geofisica e Vulcanologia, Bologna, Via Creti 12, Bologna, Italy. ( schivardi@bo.ingv.it) E. Boschi, Università di Bologna, Alma Mater Studiorum Sezione di Bologna, Via Creti 12, Bologna, Italy. ( presidente@ingv.it)

2 X-2 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES Abstract. Earthquake occurrence stems from a complex interaction of processes that are still partially unknown. This lack of knowledge is revealed by the different statistical distributions that have been so far proposed, and by the different beliefs about the role of some key components as the tectonic setting, fault recurrence, seismic clusters, and fault interaction. Here, we explore these issues through a numerical model based on a realistic interacting fault system. We use an active fault system in Central Italy responsible for moderate to large earthquakes, where geometric and kinematic parameters of each structure can be confidently assessed. Then, we generate synthetic catalogs by modeling different seismogenic processes and allowing co- and post-seismic fault interaction. The comparison of synthetic and real seismic catalogs highlights many interesting features: (i) synthetic seismic catalogs reproduce the short-term clustering and the long-term modulation observed in the historical catalog of the last centuries; (ii) a recurrent model of earthquake occurrence on faults is more effective than a Poisson model to explain such short- 1 Istituto Nazionale di Geofisica e Vulcanologia, Roma, Italy. 2 Istituto Nazionale di Geofisica e Vulcanologia, Bologna, Italy. 3 Università di Bologna, Italy. DRAFT October14,2008,12:46pm DRAFT

3 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES X-3 term and long-term time features; (iii) a realistic fault pattern is a key component to generate stochasticity in the seismic catalog, preventing a systematic time synchronization of strongly coupled faults; (iv) such a stochasticity may put strong limits to the forecasting capability of models based on fault interaction, even though the latter is a key component of the process. Finally, the model allows explicit predictions on future paleoseismological observations to be made.

4 X-4 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES 1. Introduction The occurrence of a large earthquake is the result of a complex combination of different physical processes in the Earth s lithosphere. Besides the intrinsic scientific value, the comprehension of such processes has also a practical importance, being the primary ingredient for building reliable earthquake forecasting models. Nonetheless, we are still far from a satisfactory and comprehensive understanding of the earthquake occurrence process. This is one of the main reasons that stand behind the use of different, if not antithetical, models in earthquake forecasting [2007 Working Group on California Earthquake Probabilities, 2008]. From a physical point of view, many issues of earthquake occurrence process are still open, such as the relative importance of the physical mechanism of fault rupture, elastic and viscoelastic interaction, geometry of the fault system, tectonic setting, etc. The solution of all these problems represents a formidable task to be accomplished, both because of the extreme complexity of the processes involved and the scarcity empirical observations. For the time being, too few earthquake occurrence data on single faults are available to constrain model s reliability, and only regional seismic catalogs (with reasonable timemagnitude window extensions) supply some useful information. On the other hand, the continuous increase of the computer capabilities in the last years has opened new perspectives in this field. For instance, it is now possible to model the compound picture of the processes involved through mathematical/numerical models using so-called simulators [e.g., Goes and Ward, 1994; Ward, 1996, 2000; Lynch et al., 2003; Marzocchi et al., 2003; Michael, 2005; Rundle et al., 2006; Yakovlev et al., 2006; Zoeller et al., 2007].

5 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES X-5 These new opportunities have also a counterbalance consisting of the almost uncontrolled proliferation of models based on different subsets of physical ingredients. In general, as for any kind of geophysical modeling, earthquake occurrence modeling usually evolves proposing new models that are almost always the extension of old ones, obtained by merely adding extra terms and/or extra parameters. An implicit assumption of this way to proceed is the existence of a true model, and any attempt has to represent a more close approximation of it. We argue that this procedure, despite that it is usually strongly constrained by a background theory, has some important shortcomings; these limitations, usually neglected, deserve a careful examination in order to give a right perspective of the analyses carried out in this paper. Any conceivable model will be always a rough exemplification of reality, with effectively a countless number of parameters that are impossible to account for. In order to bound this infinite search, it is necessary to consider the goal of the model, i.e., which observation has to be best described by the model. Since a specific observable depends on each component of the model with a different weight, a model must consider only the most relevant ones. In this perspective the right model may not exist, because different kind of observations may require very different models. The inclusion of more adjustable parameters will usually improve the fit. This means that a complicated model may result in overfitting the observations (i.e., fitting the noise and not only the observable), and in making the evaluation of the significance of each single component of the model more difficult. These above considerations are the roots of the famous postulation known as Ockham s razor, which states that entities are not to be multiplied beyond necessity. Along the same

6 X-6 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES line, Popper [1959] states that, if the main goal is the knowledge of a system, a simple model is more informative than a complex one, because it carries out a larger empirical meaning. In practice, even though a more complicated model may apparently improve the fit, we argue that extra terms added to the model do not very often count as beyond necessity, and they make the model difficult to interpret. In this perspective, our model is purposefully simple. We aim to identify the few basic components that are able to explain the time features observed in seismic catalogs, such as the short-term clustering and the long-term modulation. In particular, here we present a numerical model that allows seismic synthetic catalogs to be generated. Then, we compare them with a real catalog in order to check if the model is able to reproduce the main temporal features observed, and to investigate the importance of the different components of the model. The model has three main components, whose effects are explored in detail. The first is a realistic tectonic setting; Central Italy is chosen because the tectonic setting is well known and the real seismic catalog is complete over the last 7-8 centuries for M The other important components are quantitative rules for earthquake generation on every singe fault, and for fault interaction. 2. The model 2.1. Step 1. Set up of a realistic tectonic setting In order to set up a realistic system of active seismogenic faults in Central Italy, we refer to the available Quaternary fault catalogs and merge these data with historical earthquake information. Since knowledge of faults depends strongly on the size of past and likely future earthquakes, our dataset refers to faults that can produce earthquakes with M 5.4 or larger. Specifically, we use as basic source of faults and fault parameters the

7 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES X-7 Database of Individual Seismogenic Sources, version [DISS Working Group, 2005; see Table 1 and Figure 1a]. This new resource may be not complete yet. Thus, in a second Table 1 Figure 1a wider dataset, we also include faults adding those structures indicated within other fault datasets [Barchi et al., 2000; Galadini et al., 2000; 2001], but unaccounted for the DISS database. The merged catalog (see Figure 1b and Table 1) is more complete, although Figure 1b the quality of fault parameters varies strongly. If we plot the historical earthquakes reported in the CPTI catalog [CPTI Working Group, 2004], we note that there are orphans, i.e., earthquakes that cannot be associated to the mapped faults because they are distant from them and/or are too close in time (much less than the typical recurrence times). This evidence indicates a likely under-reporting of faults in both datasets. Most of the mapped faults in the two considered datasets have assigned a most recent event which appears in the historical catalog (see Table 2), as inferred from paleoseismic studies (in a few cases), or from macroseis- Table 2 mic data and epicentral locations (most cases). Other than these events for which the activated fault is reported, 23 moderate to large earthquakes since 1000 A.D. (being in that way conservative on the accuracy of the event data) have unknown source faults. We attempt to infer fault parameters for each of these orphan seismic events (Figure 2) us- Figure 2 ing information describing historical events, such as the epicentral location and intensity, the local seismic and tectonic characteristics, and similarity with adjacent known faults and empirical laws. In summary, the result of this procedure is the achievement of three compilations of faults capable for producing earthquakes with a maximum magnitude of 5.4 or higher; these earthquakes form synthetic seismic catalogs that are used for the statistical analysis:

8 X-8 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES 1. DISS 3.0.1: 38 faults from DISS Working Group [2005] (Figure 1a and Table 1); 2. DISSPLUS: 38 faults from DISS plus 8 faults from Barchi et al. [2000] and Galadini et al. [2000; 2001] (Figure 1b and Table 1); 3. SSD, Stretched Structure Dataset: 46 faults from DISSPLUS and 23 new inferred faults from historical seismic events for which no responsible faults were previously assigned and mapped (Figure 2 and Table 1). In Table 1 we list the geometrical and kinematical parameters of the faults available for the first two datasets, including the maximum magnitude expected. For the SSD dataset we assign parameters consistent with the magnitudes of the orphan events. We use all of these datasets in order to check the effects of possible fault catalog incompleteness. From the inferred map of Figure 2 and Figure 3, we note different processes that are Figure 3 acting, at the same time and in close proximity within this portion of the Peninsula. The normal faults result from the dominating crustal extension orthogonal to the Apennines, where earthquakes concentrate at shallow (<40 km) depth. On the contrary, widespread seismicity and major thrusts occur along the eastern margin of the belt and along the northern Adriatic coast where convergence is ongoing with maximum compression axis perpendicular to the arc curvature. Among the recent papers, for additional information we suggest Castello et al. [2005], Chiarabba et al. [2005] and references therein for an extensive description of the Italian seismicity, Frepoli and Amato [2000], Montone et al. [2004] and Pondrelli et al. [2006] for stress data analysis, Carminati et al. [2002], Piromallo and Morelli [2003] and Ventura et al. [2007] for geodynamic interpretations of the Italian seismicity.

9 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES X Step 2. The mechanism for the earthquake generation on a fault In this section, we describe the mechanism leading to an earthquake occurrence on each fault. We assume that earthquakes on each fault have the same magnitude (the values are reported in Table 1) assuming therefore a characteristic model for the size [Schwartz and Coppersmith, 1984]. Here, we do not explore the effect of imposing a Gutenberg-Richter law instead of a characteristic size for each specific fault, choosing, as mentioned in the introduction, the simplest model for a fault. Anyway, from Table 1, we can see that the magnitudes of each synthetic catalog generated by the model will approximately be distributed as a power law, having 35 faults with characteristic magnitudes in the range , 19 in the range , 14 in the range , and one larger than 6.8. In the past literature many different models have been proposed to describe the time behavior of a seismogenic fault [e.g. Matthews et al., 2002; Yakovlev et al., 2006; Zoeller et al., 2007]. All of these models have different characteristics and statistical properties, but one feature is particularly relevant, namely the degree of periodicity, i.e., the variability of the recurrence time observed between consecutive earthquakes on the same seismogenic structure. Among the range of possible models, two important benchmarks are the purely random Poisson process (POI hereinafter), and the purely regular recurrence model (CHA hereinafter) of the conceptual characteristic earthquake, as defined by Reid [1910], and more recently by Schwartz and Coppersmith [1984]. Almost all the other models so far proposed for the earthquake occurrence on a single fault, such as Brownian Passage time, Weibull, Gamma, have a degree of periodicity between these two limiting cases. One possible way to quantify the degree of periodicity is through the parameter coefficient of variation, C.V., defined as the ratio between the standard deviation and the average of the

10 X-10 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES recurrence times. In particular, for POI C.V. = 1, while CHA has C.V. =0. Itisworth remarking also the existence of a family of distributions having C.V. > 1. This family shows a seismicity clustered in time; while it is widely used to describe the seismicity reported in a catalog (see below), it is almost never used to describe the occurrence of large earthquakes on a single fault. While some models may seem preferable on theoretical or numerical bases [Yakovlev et al., 2006; Zoeller et al., 2007], there is not yet an objective and rigorous empirical corroboration of any model, due to the limited number of earthquake sequences related to each fault. Here we use these two limit distributions, POI and CHA, in order to quantify the importance of the degree of periodicity on the earthquake statistical distribution. For the CHA model, we set each fault loaded by a constant stress rate of MPa/yr, and an earthquake occurs when the accumulated stress reaches the maximum yielded stress σ M = 3 MPa. After the event the stress on the fault is set to zero. If fault interaction is not allowed, each fault of the catalog produces earthquakes with a constant recurrence time of 2000 years. In summary, for CHA we set the stress drop to 3 MPa, the stress rate σ = MPa/yr, and the recurrence time T = 2000 yr; the accumulated stress at time t (in years) since the last event at time t is σ(t) = σ (t t ) (1) For the POI model, we set the average recurrence rate of the Poisson process to λ = σ σ M = 1 T (2) In the unperturbed case, λ =1/2000 yr 1. In Figure 4 we report the earthquake generation mechanism for CHA with and without Figure 4

11 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES X-11 fault interaction. The plots do not refer to a specific fault of the system, but they describe the general behavior of each seismogenic structure. The details about how fault interaction perturbs these systems will be explained in the next section Step 3. Rules for fault interaction: calculation of stress rate variations The occurrence of an earthquake induces a perturbation in the stress field at every point on the earth s surface. Generally speaking, there are three different types of perturbations: the dynamical stress variations due to the passage of the seismic waves, the co-seismic stress variations due to the elastic residual deformation of the lithosphere, and the postseismic stress variations due to the visco-elastic readjustment of the lower-crust and/or asthenosphere and mantle. From an observational point of view, these three perturbations are characterized by different attenuation of the stress as a function of distance from the epicenter, and different characteristic times. The dynamical stress variation lasts only few minutes (at maximum), and its maximum amplitude attenuates with distance slowly, compared to the co- and post-seismic stress variations [e.g. Gomberg et al., 1998]. The coseismic stress variation is approximately instantaneous (being due to the elastic rebound) and it does not vary with time; its maximum perturbation decreases drastically with distance [see e.g. Stein et al., 1992; King et al., 1994; Stein et al., 1994]. The post-seismic stress variation reaches its maximum effect after a few decades or centuries [e.g. Thatcher, 1983, Piersanti et al., 1997; Pollitz et al., 1998; Piersanti, 1999; Kenner and Segall, 2000), depending on the viscosity of the lower crust and mantle, and it decays with respect to the distance less rapidly than the co-seismic one. In this paper, we are mainly interested in estimating possible interaction over time intervals larger than a few minutes, therefore we model only the co- and post-seismic stress

12 X-12 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES variations. In particular, the stress perturbation at time t due to the i-th earthquake (the source) on a j-th fault (the receiver) is written as σ j (t) = i Mo i [ co (d ij,φ ij )H(t t i )+ post (d ij,φ ij )Ω(t t i ) ] (3) where the summation includes all previous events on surrounding faults. In equation 3, Mo i and t i are the seismic moment and the time of occurrence of the i-th earthquake, co (d ij,φ ij ) and post (d ij,φ ij ) are the co- and maximum post-seismic stress variation induced by the i-th earthquake and the j-th fault, d ij and φ ij are the distance and the geometric coupling between the i-th earthquake and the j-th fault, Ω(t t i ) is a time function that takes into account the relaxation of the viscous layers in the earth, and H(t t i ) is a sort of Heaviside function. In particular, the function co (d, φ) results from the Coulomb Failure Function (CFF hereinafter) obtained by Okada s model [Okada, 1992] that estimates the stress variation on the fault induced by the i-th earthquake in an elastic semi-space accounting for the geometry and mechanism of the source and receiver faults. Such a model requires a parameter µ that represents the apparent friction coefficient; here, we use µ = 0.4. The function post (d, φ) can be approximated as [Marzocchi et al., 2003] post (d, φ) = co (d, φ)(0.012δ +1) (4) where δ is a dimensionless number which coincides numerically with distance in km. Equation 4 shows that the relative importance of the post- compared to the co-seismic stress variation increases with distance [see discussion in Marzocchi et al., 2003], and that post-seismic stress variation is, in the long-term (the so-called fluid limit), always equal to or larger than co-seismic stress variation at any distance. Such empirical rule has been

13 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES X-13 obtained by Piersanti et al. s [1997] model, but this feature is shared by other similar post-seismic models [see, e.g., Pollitz et al., 2008]. The temporal evolution is governed by the functions H(t t i ) and Ω(t t i ). The first one reads H(t t i )= { 0 if t ti < 0ort t i t t 1 otherwise (5) where t is the time of the previous earthquake on the j-th fault. In brief, this means that t t i has to be positive, and that the occurrence of an earthquake on the j-th fault sets to zero the accumulated co-seismic stress. The temporal evolution of the post-seismic stress variation in equation 3 is given by Ω(t t i ), and it is approximated by Ω(t t i )= { 1 exp[ (t ti )/τ] Ω if (t t i ) 0 0 if (t t i ) < 0 (6) where t t i is the elapsed time from the occurrence of the i-th earthquake that generates post-seismic relaxation, and Ω is the value of Ω calculated at the time of the previous earthquake occurred on the j-th fault. Subtracting Ω means that each earthquake sets to zero the accumulated post-seismic stress up to that time. This model is a simplification of more sophisticated models, where Ω(t t i )consists of a sum of functions similar to equation 6, each one representing distinct modes of relaxation of the viscous layers. Our simplification assumes that one mode prevails over the others. The relaxation time τ mainly depends on the viscosity of the mantle. Indirect estimations of the asthenosphere viscosity provide quite different values, ranging from Pa s [e.g., Pollitz et al., 1998] to Pa s [e.g., Piersanti, 1999]. Since τ is not well constrained, calculations are performed for two different values, namely τ 1 =30 yr (corresponding to a viscosity of the asthenosphere of about Pa s) and τ 2 =300

14 X-14 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES yr (corresponding to a viscosity of the asthenosphere of about Pa s). Finally, we remark that such a simplification is not penalizing in the present analyses, because the main interest is to check the importance of different components of the earthquake generating process, rather than to estimate the exact perturbation of an earthquake on other faults. To summarize, equation 3 quantifies the stress perturbation of an earthquake on each selected fault. This perturbation acts on the faults modifying the time to the next event, and, more in general, the average recurrence time. For the CHA model, the value obtained by equation 3 is algebrically added to the stress given by equation 1 σ(t) = σ (t t )+ σ (7) For the POI model, the stress perturbation has to increase, in some way, the probability of earthquake occurrence. This is modeled as a sort of time advance [Working Group on California Earthquake Probabilities, 1990] λ = σ (σ M σ) = 1 (T T ) (8) In practice, this means that the stress perturbation increases the rate of occurrence, diminishing the recurrence time of an amount proportional to the stress perturbation. Quantitatively, from equations 2 and 8 we have σ σ M = T T (9) 2.4. Generating synthetic catalogs In order to build a synthetic catalog, we first assign a random initial stress value in the range of 0-3 MPa at each faults of the dataset. Then each fault is loaded by a constant tectonic stress rate σ (see equations 1 and 2). Each time that an earthquake occurs, we

15 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES X-15 calculate the stress variations induced through time on the whole set of faults. In this way, we obtain synthetic catalogs of the desired length that, in our case, we set at one million of years. In this period of time the stress variation given by equation 3 has a constant mean for each fault; a positive (negative) average implies that a fault will have a higher (lower) earthquake frequency compared to the unperturbed state. The stationarity guarantees the validity of the analysis carried out later on, avoiding monotonic continuous acceleration (or decelaration) of the earthquake frequency with time. It is also worth remarking that such a long extrapolation assumes that the mechanism behind the earthquake generating process remains constant in this period of time. This might be questionable, but it is not a problem here. We remark that we have to take caution about very long extrapolations only when we use them to make some real forecasting of the future seismic activity. Here, instead, we want to study the statistical distribution of the synthetic catalog and the comparison with the real one in the last centuries. We produce twelve synthetic catalogs, whose main features are reported in Table 3. For Table 3 the sake of conciseness, in the following we use the numbering reported in this Table to characterize the synthetic catalogs. The first six are relative to the CHA fault mechanism (see equation 1), while the catalogs from 7 to 12 are relative to a POI earthquake generation mechanism (see equation 2). For the sake of clearness, we do not use all possible parameter combinations, but we select the synthetic catalogs that permit to explore the different contribution of: i) faults datasets; ii) the earthquake occurrence process on a fault; iii) fault interaction process.

16 X-16 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES 3. Comparing real and synthetic catalogs 3.1. Statistical features of the real catalog In the last years, the spatio-temporal distribution of the Italian seismicity (see Figure 3) has been worked out by the following two quite different approaches. In one case, the spatio-temporal distribution has been defined by hypothesizing a time behavior for each fault of the DISS dataset, neglecting all possible interaction among structures [Pace et al., 2006]. There are doubts about the validity of this approach [Marzocchi, 2007], but overall this model has never been tested against real data. The other kind of approach is based on a nonparametric statistical modeling of the M 5.5+ earthquakes (occurred since 1600 AD) in a regular grid [Faenza et al., 2003] and in seismotectonic areas [Cinti et al., 2004]. In this case, the use of a regular grid and of a seismotectonic zonation accommodates the epistemic uncertainty linked to the very likely incompleteness of the faults catalog. Both models have the merit to be tested on the past seismicity, and provide explicit forward forecasting for the next earthquakes in Italy ( earthquake/italy/forecasting/m5.5+/). This will give the opportunity to make an independent evaluation of the reliability of the model by following the RELM and CSEP philosophy [Schorlemmer et al., 2007]. The Faenza et al. s [2003] and Cinti et al. s [2004] models show that M 5.5+ earthquakes occurred in Italy in the last four centuries tend to cluster in time for few years, a time larger than the typical length of aftershock sequences in Italy [Faenza et al., 2004]. This clustering is the most clear and statistically significant departure from the Poisson distribution that is still used in seismic hazard assessment [Gruppo di Lavoro, 2004;

17 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES X-17 The seismic catalog used here is the CPTI [CPTI, Working Group, 2004], that is the evolution of the previous version used by Faenza et al. [2003], and Cinti et al. [2004]. The catalog is complete for M 5.5+ in the last four centuries, and it does not contain typical aftershocks, since all events in a time-space interval of 3 months and 30 km were removed. In Figure 5, we report the empirical cumulative distribution of the interevent Figure 5 times of the seismic catalog and of a theoretical exponential (Poisson) distribution. The interevent time is the time between two consecutive earthquakes in a region; note that in previous sections we use a different term for single faults, namely recurrence time. This distinction is made to emphasize the physical difference of the two variables: recurrence time describes the time distribution of earthquakes on single faults, while interevent times has the same meaning but on a population of faults in a region. From Figure 5, the excess of small interevent times for the real catalog that stands for a time clustering of events is clear; note that this clustering is larger than typical aftershocks duration. The coefficient of variation C.V. for such a catalog is about 1.1. An interesting long-term feature of the seismicity in the Italian Peninsula has been reported by Faenza and Pierdominici [2007]. They consider a restricted region of Central Italy, the Umbria region where the record guarantees to go back up to the thirteen century with a complete historical seismic catalog for M5.8+. Figure 6 shows the Gutenberg- Figure 6 Richter law for earthquakes occurring since 1250 in the Umbria region reported in CPTI catalog [CPTI, Working Group, 2004]; the plot shows a straight line with a slope of almost one, corroborating the completeness for such a portion of the seismic catalog. Here, we evaluate the significance of rate variations looking for a trend in the interevent times (see Figure 7) through a nonparametric Runs test [e.g., Gibbons and Chakraborti, 2003]. Figure 7

18 X-18 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES The Runs test seeks for a persistence into the sequence, or, in other words, it checks if long/short interevent times are more likely associated to similar interevent times, as expected if the seismicity rate undergoes significant changes. The details of the test can be found in the Appendix. The results show a significant persistence in the time series (significance level equal to 0.01), i.e., long periods of time with different earthquake rates. Specifically, the seismicity rate shows two change points identified by the algorithm proposed by Mulargia and Tinti [1985]. These two change points mark the existence of three different periods lasting few centuries and having a seismic rate of 0.036±0.005 yr 1, ± yr 1, and ± yr 1, respectively. Note that comparable long-term modulations have been found also in other parts of the world like in California [Selva and Marzocchi, 2005; Lombardi and Marzocchi, 2007] Statistical features of synthetic catalogs In the previous section we show that the real catalog of Central Italy has two main basic features: a short-term clustering of few years [Faenza et al., 2003; Cinti et al., 2004], and a long-term modulation on time scale of centuries [Faenza and Pierdominici, 2007; see also above]. In this section we analyze the synthetic catalogs looking for similar features, and identifying the most important parameters of the model to explain them. In Figure 8, we report the empirical cumulative distribution for synthetic catalogs and, Figure 8 for the sake of comparison, of the real one. The different plots check the sensitivity of the results to different choices of the faults dataset, of the mechanism for earthquake generation imposed on a fault, and of the different kind of interaction. Basically, we see that all catalogs based on a periodic generating mechanism (the CHA catalogs) and allowing fault interaction show a very realistic short-term clustering. In this respect, the

19 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES X-19 number of faults (varying from 38 to 69) does not seem a relevant parameter to explain the short-term clustering; for instance, catalogs CAT1 and CAT6 differ only for the number of faults, and have a quite similar behavior. The presence of post seismic relaxation makes the short-term clustering less marked than models allowing only co-seismic interaction. All synthetic catalogs based on a pure random generating mechanism (POI catalogs) and/or not allowing fault interaction are not able to reproduce short-term clustering. In Table 4, Table 4 we report the coefficient of variations, and the results of a Kolmogorov-Smirnov one sample goodness-of-fit test [e.g. Gibbons and Chakraborti, 2003] with a Poisson distribution. Here, the null hypothesis is that the synthetic inter-event times have an exponential (Poisson) distribution. Notably, only the CHA catalogs allowing fault interaction show significant departures from the null hypothesis. The search for nonstationarity and/or long-term modulation in the synthetic catalogs has been carried out through the Runs test applied to grouped inter-event times. In this case, we group IETs in order to achieve a robust estimation of the seismic rate variation as a function of time [see Cox and Lewis, 1966]. We proceed as follows: let y 1 be the observed time from the first to the l-th event, y 2 the time from the l-th to the 2l-thevent,andso on. Here l is an integer such that no appreciable change in the rate of occurrence arises in any set of l events; an optimal choice is l 4 [cf. Cox and Lewis, 1966]. In our case, we look for time modulations of few centuries. Therefore, considering that the average recurrence time for each catalog is 2000/N years where N is the number of faults (in our case, 38, 46 and 69 depending on the catalog used), we set l = 5 and 10, corresponding to average periods of about 200 and 400 years, respectively. In Table 5, we report the results of the Runs test. All the CHA catalogs allowing fault Table 5

20 X-20 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES interaction show a clear and statistically significant time modulation. The higher number of runs compared to the expected one (see the Appendix) puts in evidence an almost regular alternation of high and low periods of seismicity. The values of l used indicate that these periods have a length of few centuries, comparable to the ones observed in the real seismic catalog. For the sake of example, we report in Figure 9 the cumulative number of earthquakes Figure 9 in a portion of the synthetic catalogs. The plot illustrates qualitatively the similarity of such empirical cumulatives with the one obtained from real data (see Figure 7). As for the real data, the plot shows marked changes in earthquake rate with a characteristic time scale of centuries. It is worth remarking that also previous simulators [Goes and Ward, 1994; Ward, 1996] were able to produce synthetic catalogs with apparent short-term clusters and long-term modulations; in those cases, these time features, as well as the departures from a stationary Poisson distribution, were not statistically significant. These temporal features were clear only in few specific cases. Nonetheless, the complexity of the model makes difficult to identify the most important parameters of the model responsible for such features Looking at the recurrence on each fault In the previous section we have reported the comparison among synthetic and real catalogs. Such a comparison is made possible by the availability of a reliable seismic catalog for the region. Besides that, the model is also able to envision the behavior of generic single faults, not necessarily belonging to Central Italy. In this case, however, the few empirical paleoseismological evidence do not allow a robust statistical validation to be performed. For this reason, these results can be seen as explicit general prognostications

21 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES X-21 of our model that may be empirically checked as long as more paleoseismological data on faults will become available. Note that such results may be generalized to other similar tectonic settings. In an unperturbed system (no fault interaction) each fault of the CHA catalogs has a perfect periodicity of 2000 years. Fault interaction changes significantly such a simple distribution. In Figure 10 we report, for the sake of example, the distribution of the Figure 10 recurrence times for some selected faults that depict the variability observed in the whole range. The graphs show that fault interaction produce a significant increase of earthquake frequency on some faults, and a decrease on others, compared to the unperturbed state. Another important feature is the remarkable multi-modal distribution of the recurrence times. This result means that faults are not longer simply recurrent, but that they can have different recurrence time modes [cf. Lynch et al., 2003; Marzocchi et al., 2003]. Moreover, this also indicates that even in presence of a constant tectonic loading rate, faults can show quite different recurrence time distributions due to fault interaction. In Figure 11, we report the same graphs of Figure 10, but relative to the POI catalogs. It Figure 11 is obvious that the discrepancies between the unperturbed case and the catalogs with fault interaction are much less significant than the case reported above for the CHA catalogs. 4. Discussion of the results In this section, we discuss the implications of three main findings that come out of the previous analysis: i) the role of fault interaction and a recurrent mechanism on each fault to produce short-term clustering and long-term modulation; ii) the limits of fault interaction mechanism to improve our forecasting capability; iii) the compound statistical distribution of large earthquakes on faults.

22 X-22 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES With regards to the first point, the model has three basic components: a realistic tectonic setting (i.e., geometry and focal mechanisms), a mechanism for earthquake generation on each seismogenic structure (pure recurrent or pure random), and a physical process mimicking fault interaction (co- and post-seismic). The last two parameters are particularly important to reproduce the short-term clustering, and the long-term modulation observed in the real Italian seismic catalog for this area [see also Goes and Ward, 1994; Ward, 1996]. While the role of fault interaction appears obvious in this respect, much less obvious is the fact that a recurrent fault mechanism, rather than a purely random one, seems to be more effective to explain the same temporal features. This can be explained with a simple example. Let us assume an hypothetical and simplified case where, at time t, an earthquake occurs producing a stress perturbation σ in a short time interval t on all N faults. Let us discuss what happens if the fault mechanism is recurrent (case I; see equation 1), or Poissonian (case II; see equation 2). In case I, immediately before the earthquake, each structure has a state of stress σ t randomly selected from a uniform distribution [0,σ M ]. Then, if we add a stress perturbation σ to the initial conditions, M = N σ σ M faults will have a stress that exceeds the thresholdσ M and produce an earthquake; in other terms, there are M faults that satisfy the condition σ t + σ σ M. The number of triggered earthquakes in a short time interval t is therefore M, and the difference with the expected ones without stress perturbation is N σ N t [ σ σ M T = N t ] σ M T (10) In case II, the number of triggered earthquakes in t is not a fixed value but it derives from a Poisson distribution with a rate of occurrence equal to λ =1/(T T )(see equation 8), where T accounts for the time advanced due to the positive fault interaction

23 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES X-23 through equation 9. In this case, the expected average number of triggered earthquakes is M = N λ t, and the difference with the expected ones without stress perturbation is Nλ 1 t Nλ t = N T T t N 1 T [ σ ] t σ t = N M T 1 σ σ M (11) If we set realistic values for the short-term clustering and for the stress perturbation, i.e., t equal to a few years, and σ equal to a few tenths of bars, we have that t/t is one order of magnitude less than σ/σ M, i.e., the number of triggered earthquakes on case I is one order of magnitude larger than in case II. In other terms, it is more likely to observe a short-term clustering for recurrent mechanism on a fault, than for a random mechanism. A similar argument can be applied to explain the long-term modulation. The example reported above brings out another interesting feature regarding the second issue to discuss. After a selected earthquake, the short-term clustering (and the long-term modulation as well) is composed by the same set of faults only if the stress on faults before each event is approximately the same. This usually never happens, due to the complex interaction pattern emerged by the realistic tectonic setting. In Figure 12 we report the Figure 12 normalized average of interevent times and the CFF among each couple of faults. A value close to zero in the y axis stands for a synchronization of the earthquakes on these faults. Hereafter, we use the term synchronization to indicate a couple of faults that produce earthquakes close in time, i.e., with interevent times much smaller than the average of interevent times in a system without interaction. The definition is very similar to the one of time cluster, but here we prefer to use the term synchronization instead of time cluster in order to emphasize the different physical meaning of the two quantities. In particular, we refer to a time cluster when we have short interevent times produced by earthquakes

24 X-24 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES on some undefined faults randomly drawn from a population; the term synchronization is used when we consider just a selected couple of faults. If the short-term clustering were due to the same set of faults we would expect to see more values close to zero, indicating short interevent times among couple of faults. The plot, instead, shows the contrary; that is, except for very few cases, almost all the normalized average of interevent times are along an horizontal line y = 1. This points to an almost negligible effect of CFF perturbation on the interevent times between each couple of faults. This may appear surprising because the model is effectively based on fault interaction. We argue that the realistic tectonic setting and fault geometry of all faults break the determinism of fault interaction, because they act in a complex way on the stress history of each fault. In order to further understand this issue, we report, as an example, the case of two major faults of Central Italy, Fucino and Ovindoli Pezza (see Figure 1). The first one was responsible for a M 7.0 event in 1915, and the other associated with a comparable earthquake possibly in In Figure 13, we show the CFF induced by all faults of the Figure 13 DISSPLUS catalog (46 structures) on these two structures. Despite the fact that these faults are clearly positively coupled in terms of CFF (the Ovindoli Pezza and Fucino are the numbers 1 and 2 respectively), other structures of the system have significantly different coupling with them, leading to different stressing history for them. This means that, if we consider a system consisting only of these two faults, they tend to be synchronized in time, because they have a positive CFF coupling; however, the existence of surrounding (even much smaller) faults, acting differently on Ovindoli Pezza and Fucino, prevents this synchronization.

25 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES X-25 This fact has a paramount importance for earthquake forecasting based on fault interaction [Stein et al., 1997; Michael, 2005]. In practice, fault interaction suggests that an earthquake on a fault causes an earthquake on a nearby fault if the stress perturbation is positive (and not negligible) and the elapsed time since the last event on the latter structure is long enough to allow tectonic loading to push the state of stress close to the maximum yielded value. In this case, the two earthquakes would appear synchronized in time. The results reported here show that such a time synchronization between two faults is not systematic, even in a case where fault interaction is a key component of the earthquake generating process. In other words, two strongly coupled faults do not always synchronize in time, because of the complex interaction with surrounding (even smaller) structures. In our model, we do not consider events smaller that 5.4; Helmstetter et al. [2005] and Marsan [2005] show that also small events (M <5.4) close to the main fault also may contribute significantly to randomize the occurrence of larger event on that fault. Clearly, their results and the ones reported here highlight both the limits of model-based forecasting. In practice, this means that we might use fault interaction for earthquake forecasting only if we have a very good knowledge of the state of stress on a fault. We do not measure directly this quantity, that is usually estimated through a statistical stationary and unimodal distribution that accounts for the elapsed time [Matthews, 2002; Yakovlev et al., 2006]; as we will discuss in the next point, the use of an unimodal and stationary statistical distribution could be a very rough approximation of the real situation. We have shown that also a recurrent process on a fault does not produce clear recurrent earthquakes if fault interaction is allowed, even in the presence of regular and stationary

26 X-26 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES tectonic loading. In particular, even if we assume that the tectonic loading is constant in time and space, we may observe different recurrence distributions due to fault interaction. Note that, also in this simple scheme, the statistical distribution of recurrence time on a single fault may be much more complicated than that is usually assumed; for instance, we often observe multimodal distributions, i.e., different time recurrence modes [see also Lynch et al., 2003; Marzocchi et al., 2003]. This prediction of our model can explain periods of clusters and quiescence and similar time features found by some researchers working on real faults [e.g., Rockwell et al., 2000; Friedrich et al., 2003; Hubert-Ferrari et al., 2005; Daeron et al., 2007; Yeats, 2007]. 5. Final remarks The main goal of this paper is to investigate the physical mechanism that causes the temporal features of real seismicity. We argue that simplicity or parsimony in modeling are of paramount importance (if not mandatory) to understand the importance and the role of the key components of a process (in a nutshell: complex is not necessarily better than simple ). Under this perspective, we list some issues emerged from our analyses. - The comparison of synthetic catalogs generated by the model and the real seismic catalog of Central Italy shows that the short-term time clustering and the long-term modulation (with characteristic times of few centuries) can be explained by a set of recurrent and interacting faults. Remarkably, a random mechanism for earthquake occurrence on each fault tends to lower drastically the effects of fault interaction. This result suggests that the temporal features observed for regional seismic catalog might be easier explained by recurrent models.

27 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES X-27 - The fault pattern plays a basic role in generating stochasticity in a seismic catalog. In particular, deterministic fault interaction and earthquake generating processes produce a stochastic seismic catalog if applied to a realistic tectonic setting. The stochasticity is due to the composite effects of interacting faults that produce a compound stressing history for each structure. This stochasticity prevents the synchronization of earthquake occurrence on strongly coupled faults because of the unequal effects on them of the other (even minor) faults. Thus, even models that include fault interaction may be of limited use to forecasting earthquakes on adjacent faults if the stressing history is not known accurately. - Our model allows explicit predictions on future observables. In particular, we anticipate that fault interaction may lead to different statistical distributions of recurrence time on almost isolated faults and faults embedded in a complex network, even though the earthquake generating process is the same. Again, fault interaction may drive single faults to have more than one recurrence mode and may show significant differences with the adjacent structures, even though the tectonic stressing rate is constant in time and space.

28 X-28 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES 6. Appendix: The Runs test The Runs test can be used to test if a process is stationary and not autocorrelated (null hypothesis). In any time sequence of real numbers, a run is an uninterrupted subsequence of consecutive numbers with the same sign, immediately preceded and followed by numbers with opposite sign. In particular, in our case we use the residuals of the interevent times, i.e., the interevent times minus the average; in this case, a positive (negative) residual indicates an interevent time larger (smaller) that the average. If we have N data, of which p are positive and n are negative (n + p = N), the probability P R of obtaining a number of runs less or equal to observed number R, under the null hypothesis, is: ( )( ) ( )( ) ( )( ) n 1 p 1 R i 1 i 3 + n 1 p 1 n 1 p 1 i 3 i 1 R i P R = ) i 2) 1 (12) i=3,5,... ( n+p n i=2,4,... If p and n are both > 10, the distribution of R can be approximated by a normal distribution with mean R and variance σ 2 R equal to ( n+p n R = 2np n + p σ 2 R = 2np (2np n p) (n + p) 2 (n + p 1). (13) In this case we can carry out a Z-test, which consists in testing a standard normal distribution for the statistic [see Gibbons and Chakraborti, 2003]. Z = R R σ R (14) Acknowledgments. This work was partially funded by the Italian Dipartimento della Protezione Civile in the frame of the Agreement with Istituto Nazionale di Geofisica e Vulcanologia - INGV. We thank Joan Gomberg for improving significantly the readability of this paper. The paper also benefits from Jochgem Gunneman s suggestions.

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36 X-36 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES Table 1. Geometrical and kinematical parameters of the faults in the three datasets (DISS 3.0.1, DISSPLUS, SSD). The first column reports the identification number of each fault as used along the text. DISS Id. Fault name Length Width Min-Max Strike Dip Rake Slip Max M [Km] [Km] depth [Km] [deg] [deg] [deg] [m] [Mw] 1 Ovindoli-Pezza Fucino Basin Aremogna-Cinque Miglia Montereale Basin Norcia Basin Colfiorito North Colfiorito South Sellano Mondolfo Campotosto Amatrice Sulmona Basin Barrea Conero Offshore Senigallia Fano Ardizio Pesaro San Bartolo Rimini offshore South Rimini offshore North Rimini Val Marecchia Gubbio South Gubbio Middle Gubbio North Cagli Fabriano Camerino Sarnano Velletri Bastia Foligno Trevi Monterchi Anghiari Selci Lama Offida Poppi Tocco da Casauria DISSPLUS Id. Fault name Length Width Min-Max Strike Dip Rake Slip Max M [Km] [Km] depth [Km] [deg] [deg] [deg] [m] [Mw] 39 M. Vettore Rieti C. Imperatore-Assergi-M.Cappucciata Media Valle Aterno nord Media Valle Aterno sud Alta Valle Sangro Sora S. Pietro Infine

37 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES X-37 SSD Id. Fault name Length Width Min-Max Strike Dip Rake Slip Max M [Km] [Km] depth [Km] [deg] [deg] [deg] [m] [Mw] 47 Anconetano (1269) Riminese (1672, Apr 14) Tosco-emiliano-Appennino (1584) Abruzzo meridionale (1881, Sep 10) Gran Sasso (1950, Sep 05) Maiella (1706, Nov 03) Maiella (1933, Sep 26) Bagnoregio (1695, Jun 11) Bocca Serriola (1389) Città di Castello (1458) Gualdo Tadino (1751) Fiuminata (1747) Valnerina-a (1838) Spoleto (1277) Norcia (1328) Rocca d Evandro (1120) Ceccano (1170) Sora bis (1922) Marsica (1904) Norcia (1730) Valnerina-b (1979) Cascia (1599) Viterbese-Umbria (1349, Sep 09)

38 X-38 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES Table 2. Table 2. Most recent events and active faults of the three datasets (ID numbers refer to faults as in Figures 1 and 2) DATASET 1 DATASET 2 DATASET 3 ID LATEST ETQ ID LATEST ETQ ID LATEST ETQ A.D Aug Sept Jan Jun Apr B.C-1030 A.D. 41 Unknown Sept Feb Nov Sept Jan Oct Sep Sep May Nov Sep Jul Sept Oct Sept Jun Jan Oct Unknown Apr Oct Jul Dec Apr May Sept Dec Oct Dec Unknown Mar Unknown May Aug Dec May Feb Dec May Mar Sept Apr Nov Unknown Sept Unknown Jun Apr Jul Mar Aug Feb Jan Sep Apr Jan Sep Oct Unknown Dec 1456

39 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES X-39 Table 3. Synthetic catalogs: models and dataset used Synthetic Fault Earthquake Fault catalog dataset mechanism interaction CAT1 DISS CHA Co- & Post-seismic (τ = 30yr) CAT2 DISSPLUS CHA None CAT3 DISSPLUS CHA Co-seismic CAT4 DISSPLUS CHA Co- & Post-seismic (τ = 30yr) CAT5 DISSPLUS CHA Co- & Post-seismic (τ = 300 yr) CAT6 SSD CHA Co- & Post-seismic (τ = 30yr) CAT7 DISS POI Co- & Post-seismic (τ = 30yr) CAT8 DISSPLUS POI None CAT9 DISSPLUS POI Co-seismic CAT10 DISSPLUS POI Co- & Post-seismic (τ = 30yr) CAT11 DISSPLUS POI Co- & Post-seismic (τ = 300 yr) CAT12 SSD POI Co- & Post-seismic (τ = 30yr) Table 4. Goodness-of-fit test. The null hypothesis is that the earthquake occurrence has a Poisson distribution. The first column reports the catalog used, the second the significance level of the test, and the third the coefficient of variation. Catalog Sign. level C.V. CAT1 < CAT2 < CAT3 < CAT4 < CAT5 < CAT6 < CAT CAT CAT CAT CAT CAT

40 X-40 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES Table 5. Runs test (two tails). The null hypothesis is that earthquake occurrence is stationarity with time. The first column reports the catalog used, the second and third columns the significance level of the test for different l (see text). Catalog α(l =5) α(l = 10) CAT1 < 0.01 < 0.01 CAT2 < 0.01 < 0.01 CAT3 < 0.01 < 0.01 CAT4 < 0.01 < 0.01 CAT5 < 0.01 < 0.01 CAT6 < 0.01 < 0.01 CAT CAT CAT CAT CAT CAT

41 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES X-41 Figure 1. Maps of seismogenic faults associated to M5.4+ earthquakes in Central Italy: a) DISS compilation; b) DISSPLUS compilation. Faults are numbered as in Tables 1 and 2 where the parameters of each specific fault are listed. The earthquakes since 1000 A.D. are also plotted. Figure 2. Map of seismogenic faults as compiled in the Stretched Structure Dataset (SSD). Faults are numbered as in Tables 1 and 2 where the parameters of each fault are listed. We plot the earthquakes that we associate to each single fault, that do not appear on DISS and DISSPLUS compilations. Figure 3. Italian seismicity [CPTI Working Group, 2004; Castello et al., 2005] and regional tectonic lineaments [Meletti et al., 2000]. Figure 4. Accumulated stress on a fault versus time. The graph show the evolution for an isolated structure (no interaction; purple color), and for a structure interacting with others (blue color). The plot is related to a generic fault in a generic time interval. An earthquake occurs when the accumulated stress reaches 3 MPa. Figure 5. The plot reports the empirical cumulative distribution function of the inter-event times obtained by the real historical catalog (solid blue line), and the same distribution for a Poisson process (red dotted line). We also report the coefficient of variation (C.V.) for the real catalog. Figure 6. Gutenberg-Richter relationship for earthquakes with M 5.5+ occurred in Umbria region since The magnitudes are grouped with M =0.3. The plot indicates that the completeness of the catalog is for M 5.8+, when the data can be described by a straight line. Figure 7. Time evolution of the seismicity of Umbria region with M 5.8+ since The graph shows two change points (indicated by arrows) that mark significant variations of the seismicity rate.

42 X-42 MARZOCCHI ET AL.: ON THE OCCURRENCE OF LARGE EARTHQUAKES Figure 8. Cumulative distributions for real and synthetic catalogs (from CAT1 to CAT12). The characteristics of each synthetic catalog can be found in Table 3. Figure 9. Time evolution of the seismicity for a generic time window of the synthetic catalog CAT4 (DISSPLUS dataset, co- and post-seismic interaction, CHA mechanism; see Table 3). Figure 10. Histograms of the recurrence times for some selected faults. The earthquake synthetic catalog is CAT4. Figure 11. The same as Figure 10, but relative to the CAT10 synthetic catalog. Figure 12. Plot of the normalized average inter-event time versus a function of CFF. The y-axis reports the average inter-event times between two structures normalized with the value obtained when no interaction are allowed. The x-axis reports the common logarithm of CFF, with the CFF sign. Figure 13. Plot of the CFF induced by surrounding structures on (a) Ovindoli-Pezza and (b) Fucino fault. The y-axis reports the common logarithm of CFF, with the CFF sign. The x-axis reports the number of the interacting fault (the numbering is the same as reported in Table 1).

43 11 40' 13 20' 15 0' Trasimeno Lake Bolsena Lake DISS n. 38 faults simplified 3D representation of the fault plane normal thrust strike slip seismicity 5.0 <= M < <= M <= 6.0 M > 6.0 Adriatic Sea 44 10' 43 20' 42 30' 11 40' 13 20' 15 0' Trasimeno Lake Bolsena Lake DISSPLUS n. 46 faults simplified 3D representation of the fault plane normal thrust strike slip seismicity 5.0 <= M < <= M <= 6.0 M > 6.0 Adriatic Sea 44 10' 43 20' 42 30' Tyrrhenian Sea Rome Tyrrhenian Sea Rome a) 0 Km 100 b) 0 Km 100

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