Abruzzo, Italy, Earthquakes of April 2009: Heterogeneous Fault-Slip Models and Stress Transfer from Accurate Inversion of ENVISAT-InSAR Data

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1 Bulletin of the Seismological Society of America, Vol. 101, No. 5, pp , October 2011, doi: / E Abruzzo, Italy, Earthquakes of April 2009: Heterogeneous Fault-Slip Models and Stress Transfer from Accurate Inversion of ENVISAT-InSAR Data by Giuseppe De Natale, Bruno Crippa, Claudia Troise, and Folco Pingue Abstract The seismic sequence that occurred in the Abruzzo Apennines near L Aquila (Italy) in April 2009 caused extensive damage and a large number of casualties (more than 300). The earthquake struck an area in the Italian Apennines chain where several faults, belonging to adjacent seismotectonic domains, create a complex tectonic regime resulting from the interaction among regional stress buildup, local stress changes caused by individual earthquakes, and viscous-elastic stress relaxation. Understanding such complex interaction in the Apennines can lead to a large step forward in the seismic risk mitigation in Italy. The Abruzzo earthquake has been very well recorded by interferometric synthetic aperture radar (InSAR) data, much better than the first Italian earthquake ever recorded by satellites, namely, the 1997 Umbria Marche earthquake. ENVISAT (ENVIronmental SATellite) data for the Abruzzo earthquake are, in fact, very clear and allow an accurate reconstruction of the faulting mechanism. We present here an accurate inversion of vertical deformation data obtained by ENVISAT images, aimed to give a detailed reconstruction of the fault geometry and slip distribution. The resulting fault models are then used to compute, by a suitable theoretical model based on the elastic dislocation theory, the stress changes induced on the neighboring faults. The correlation of the subsequent mainshocks and aftershocks of the Abruzzo sequence with the volumes undergoing increasing Coulomb stress clearly evidence the triggering effect of coseismic stress changes on further seismicity. Moreover, this analysis put in evidence which seismotectonic domains have been more heavily charged by stress released by the Abruzzo mainshocks. The most important faults significantly charged by the Abruzzo sequence belong to the Sulmona and Avezzano tectonic domains. Taking into account the average regional stress buildup in the area, the positive Coulomb stress changes caused by this earthquake can be seen as anticipating the next earthquakes in the neighboring domains of yr. Online Material: Digital version of the best fitting fault-slip model. Introduction The Apennine chain in Italy is characterized by active tectonics, presently extensional, in contrast to previous compressional phases (Pantosti and Valensise, 1995). Extension in the Apennines is somewhat recent (in some cases, a few hundred-thousand years old), which represents a serious problem for the interpretation of present tectonics by a geomorphological approach (Galadini and Galli, 2000). The Apennine chain, on the other hand, represents the site of the largest seismic potential in the Italian peninsula, with the southern and central segments capable of generating earthquakes up to magnitude 7. The present counterclockwise rotation of the Adriatic plate around a pole located in the Northern Apennines is the primary driving mechanism of the extensional regime in the Apennines, with a progressively larger opening rate going from north to south (Westaway, 1992). Large earthquakes in the southern and central Apennine segments are, in fact, dominantly affected by such an extensional regime, as testified by slip vectors whose horizontal projections are dominantly oriented perpendicular to the chain, as estimated by Global Positioning System (GPS) coseismic deformation data (Anzidei et al., 2009). Given the mentioned difficulty in quantifying the earthquake risk on the basis of a purely morphological approach, any new, well-observed earthquake in the Apennines represents a 2340

2 Abruzzo, Italy, Earthquakes of April 2009: Heterogeneous Fault-Slip Models and Stress Transfer 2341 unique opportunity to make a significant step in the understanding of this complex seismotectonic regime and associated seismic risk. Research on active tectonics in the central Apennines began in the 1970s (Bosi, 1975), mainly through the application of geomorphological criteria. A subsequent approach based on Plio-Quaternary geological evolution, considered more reliable than pure geomorphology, gained ground with the publication of the Neotectonic Map of Italy (CNR-PFG, 1987). Only recently, starting from the end of the 1980s, the study of active faults in Italy was given a more quantitative approach, by directly associating earthquakes with visible faults (e.g., Westaway and Jackson, 1984) and also by studying them through seismological, geodetic, and paleoseismological techniques (De Natale et al., 1988; Bernard and Zollo, 1989; Pantosti and Valensise, 1995). At the same time, many works have been aimed at defining seismotectonic zonations in the perspective of seismic hazard assessment through the analysis of the deformations since the Neogene and also analysis of the seismicity (e.g., Scandone et al., 1990; Lavecchia et al., 1994; CNR-GNDT, 1996). In the area of the central Apennines, several earthquakes with magnitudes larger than 5 have occurred in the last 30 yr. In 1979, the Norcia earthquake of magnitude 5.9 (Deschamps et al., 1984) occurred about 100 km north of L Aquila. In 1984, two earthquakes of magnitude 5.8 and 5.3 occurred in the Sangro river area (Del Pezzo et al., 1985; Westaway et al., 1989) in the southernmost Abruzzo region; still, in 1984, the Gubbio earthquake (M S 5.2) occurred in the northern part of the Umbria region. In 1997, the Colfiorito sequence (Umbria Marche), occurred about 50 km south of Gubbio, with three shocks between M S 5.5 and M S 5.9. The L Aquila earthquakes occurred almost in the center of this complex tectonic domain, about 100 km north of the Sangro earthquakes and 100 km south of the Colfiorito earthquakes. Other crucial seismotectonic domains in the area are Sulmona and Avezzano, the last one giving rise to the very destructive earthquake that occurred in 1915 (M 7.0; see Ward and Valensise, 1989), the former struck by the 1706 (M 6.6) earthquake. Understanding the seismogenic processes and fault interaction in this very active part of the Apennines is of fundamental importance also for risk-mitigation purposes. In this paper, we present a detailed analysis and reconstruction of the fault model and slip distribution for the first two mainshocks of the L Aquila sequence, namely, the 6 April (M w 6.3) and 7 April (M w 5.6) shocks, from inversion of interferometric synthetic aperture radar (InSAR) data. Furthermore, based on the reconstructed fault model, we compute the Coulomb stress changes on the neighboring faults. We further compute the Coulomb stress changes on the Avezzano and Sulmona domains as due to both the L Aquila mainshocks and the 1984 Sangro earthquakes. Finally, we discuss the implications for earthquake forecast in this part of the Apennines, taking into account the tectonic stress accumulation rate, the stress changes due to fault interaction, and the stress relaxation due to viscous behavior of the lower crust, as recently determined by Della Via et al. (2005). The L Aquila Earthquake Sequence On 6 April, at 01:32 UTC, an earthquake of M w 6.3, as computed by the MEDNET of the Istituto Nazionale di Geofisica e Vulcanologia (INGV), struck the area near the city of L Aquila, killing more than 300 people and leaving 15,000 homeless. The focal mechanism of the L Aquila earthquake has been recognized by various seismological agencies as almost pure dip-slip along a normal fault, striking in the Apennine chain direction. The estimated body-wave seismic moment of this earthquake ranges between 3: N m (Walters et al, 2009) and 3: N m (Pondrelli et al., 2010). The 6 April mainshock was followed on 7 April at 17:47 UTC by another deeper earthquake about 15 km to the southeast, with smaller moment magnitude (M w 5.6) and seismic moment (M 0 2: N m). On 9 April at 00:52 UTC, another mainshock (M w 5.4 and M 0 1: N m) occurred northernmost in the Apennine direction. The earthquake parameters of the three mainshocks are reported in Table 1, together with seismic moment and fault mechanisms. The occurrence of three mainshocks over a few days and of a seismic tail lasting several months, with several shocks of considerable magnitude (up to magnitude 5.1), confirms the complex patterns of earthquake occurrence in the south and central Apennines, with a high degree of interaction and mutual triggering among neighboring faults (Troise et al., 1998). Focal mechanisms and aftershock distributions are consistent with northwest southeast normal ruptures dipping southwest (Fig. 1). This paper presents a detailed model for the faulting mechanism of the April 2009 L Aquila earthquakes, based on the modeling and inversion of InSAR data. InSAR data, in the last years, have shown themselves to represent a very powerful method for inferring details of the fault geometry and mechanism, particularly for earthquakes of magnitude 6 and up, which produce a considerable amount of ground deformation (Massonet et al., 1993; Chang et al., 2004; Crippa et al., 2006). Because these data essentially sense vertical deformation, they are particularly useful for describing dip-slip earthquakes, just like the Apennine ones. Given the relatively short period of availability of these data (since about 1992 in Italy), they could be used for Italian earthquakes before L Aquila sequence only in the case of the Umbria Marche sequence (Lundgren and Stramondo, 2002; Crippa et al., 2006). However, data from the L Aquila earthquakes are considerably better and clearer, basically because of the sensibly higher magnitude of this earthquake. The detailed model for the earthquake faults obtained in this paper is hence used to compute the theoretical static stress changes induced by L Aquila earthquakes on neighboring faults. Induced stress changes, also due to previous earthquakes in the area, are hence compared with the rate of tectonic stress accumulation in order to deduce the level

3 2342 G. De Natale, B. Crippa, C. Troise, and F. Pingue Table 1 Principal Parameters of Three Mainshocks Date* (yyyy/mm/dd) Time* (UTC) Lat. (deg) Long. (deg) M L * M w Depth (km) Seismic Moment (N m) Strike (deg) Dip (deg) Rake (deg) 2009/04/06 01: * * * 3: /04/07 17: * * * 2: # /04/09 00: * * * 1: # *From Italian Seismological Instrumental and Parametric Data-Base (ISIDE) (see Data and Resources). From Chiaraluce et. al. (unpublished manuscript, 2011). From Chiarabba et al., From RCMT catalog (see Data and Resources). From Walters et al., # From Pondrelli et al., at which recently induced stress can anticipate future earthquakes on the neighboring tectonic domains. InSAR Data A few weeks after the earthquake that struck the L Aquila area, the European Space Agency (ESA) made available an online database of images acquired by optical and radar satellites, like PALSAR (Phased-Array-type L-band Synthetic Aperture Radar), European Remote Sensing (ERS), and ENVISAT. The image database was made available to the international scientific community to promote its use for scientific and research purposes. In this work, we used four single-look complex (SLC) SAR images acquired by the ENVISAT satellite. We selected two couples of SLC-SAR images, an ascending and a descending one. For each couple, there is a preevent image and a postevent image. From these images, we calculated two differential interferograms; their main characteristics can be seen in Table 2. The time intervals and the height ambiguities are adequate to analyze the coseismic deformation associated with the earthquakes under analysis. The two interferograms have a high degree of spatial coherence. Their phases clearly show the presence of an area subject to a strong deformation, most probably due to the seismic processes occurring during the observed period, and in particular, due to the seismic events of 6 7 April The interferometric processing was carried out with the software DIAPASON, using a multilook of 1 by 5, getting a m ground-pixel size, and using the NASA Shuttle Radar Topografic Mission-Digital Elevation Model (SRTM-DEM) with a resolution of 3 arcsec (90 m). Figure 2a,d shows the two analyzed differential interferograms: one may notice that the fringes associated with the main deformation area show a similar pattern. In addition to the main deformation fringes, there are other fringes due to atmospheric effects, orbital errors, and, with minor importance, residual topographic errors. Starting from the principal values of the interferometric phases, the whole interferometric phase values were derived by means of a phase-unwrapping procedure. This is the most Figure 1. Seismotectonic setting and seismicity of the L Aquila area. Locations (stars) and focal mechanisms from CMT inversion for the three main events are shown, together with the aftershock distribution, the historical seismicity (red circles), and the active faults from geological maps, including the Paganica San Demetrio fault (after Atzori et al., 2009).

4 Abruzzo, Italy, Earthquakes of April 2009: Heterogeneous Fault-Slip Models and Stress Transfer 2343 Interferogram Table 2 Main Parameters of Generated Differential Interferograms Date of Slave Image (dd/mm/yyyy) Date of Master Image (dd/mm/yyyy) Track (Type of Orbit) Height Ambiguity (m) Incidence Angle ( ) 1 01/2/ /4/ (descending) /12/ /4/ (ascending) critical step of the entire interferometric analysis. In fact, despite the fact that, in literature, several phase-unwrapping algorithms are proposed, none of them provides an optimal solution; this is due to the fact that the phase recovery is an ill-posed problem. In this work, we apply the procedure proposed by Constantini (1998), which works on an irregular set of pixels selected using the coherence. Figure 2b,e shows the unwrapped phase. In both interferograms, a linear phase term is present, which is stronger in the descending interferogram. These linear terms were removed by estimating the parameters of a plane over the phase values located outside the deformation area at hand. The differential phases measure the deformations (Fig. 2c,f) in the so-called radar line of sight (LOS); knowing the radar incidence angle, one can recover the vertical displacement. The two maps of displacements were geocoded in the WGS84 geodetic system. This step is essential for the fault-inversion processing, which requires geocoded data. Displacement Data Inversion for Earthquake Fault Models The Inverse Method Vertical ground displacements derived from InSAR data have been inverted for variable-slip fault models. Complete specification of fault parameters requires the values of eight independent parameters defining the fault geometry and location, plus a parameter defining the dislocation. For our purposes, because we are interested in heterogeneous slip models, the model is specified by a sum of contributions of individual point sources, each one with a given slip value (Okada, 1992). In our modeling, we fix the geometry of the source to be the same for all the source elements, thus implying that all the sources lie on a single fault plane and the slip direction is the same all over the fault. The previous assumptions are in agreement with reconstructions of faulting mechanisms for the mainshocks (e.g., Walters et al., Figure 2. (a,b,c) Descending interferogram full frame (n. 0079), km 2 of the L Aquila area, computed with SAR images acquired 1 February 2009 and 12 April (a) Wrapped phase. (b) Unwrapped phase: an evident linear term is present, probably due to orbit errors. (c) Unwrapped phase with the linear term subtracted. (d,e,f) Ascending interferogram full frame (n. 129), km 2 of the L Aquila area, computed with SAR images acquired 31 December 2008 and 15 April (d) Wrapped phase. (e) Unwrapped phase: a weak linear term is present, probably due to orbit errors. (f) Unwrapped phase with the linear term subtracted.

5 2344 G. De Natale, B. Crippa, C. Troise, and F. Pingue 2009; Pondrelli et al., 2010), and, however, represent a reasonable simplification in our case. This means that each individual mainshock is well approximated by a single fault plane with the same direction of slip at all the points. The long-period fault mechanisms also put in evidence that the first two mainshocks, namely, the 6 April M w 6.3 and the 7 April M w 5.6, have very similar mechanisms, which are furthermore almost pure dip-slip normal faults. This is a very important observation, although common in large Apennine earthquakes (e.g., Bernard and Zollo, 1989; Boncio, Lavecchia, and Pace, 2004; Boncio, Lavecchia, Milana, and Rozzi, 2004) because InSAR data are almost only sensitive to vertical displacements, which are by far the most constraining ones for dip-slip faults. Once the assumption is made of a single fault plane and slip direction, the direct problem for vertical displacements can be written in the form: u k x i XN j 1 A k x i ; x 0j m x 0j i 1;M; j 1;N; k 1; 3 ; (1) in which u k x i is the displacement at (x i ), along the k-th coordinate direction. The functional forms of q x 0j and A k x i ; x 0j depend on the parameterization for the slip distribution and on the adopted mathematical formulation. Choosing a parameterization in terms of point sources, m x 0j represents the seismic moment of the source at x 0j, whereas it can represent the dislocation on the j-th element if finite dimension elements are chosen. A k x i ; x 0j (k 1, 3) is completely determined from the fault geometry and mechanism once m x 0j is specified. A remarkable feature of this method is that it does not need any smoothing constraints, because the assumption of unidirectional slip is general enough to constrain the solution, which makes null the set of exact solutions and calls for least squares solutions. We solve this problem with an iterative technique based on the determination of the direction pointing to minimum residual (De Natale and Pingue, 1991; Crippa et al., 2006). Briefly, the method used to invert (1) consists of a gradient technique (see also De Natale and Pingue, 1991). The model update at the k-th iteration is sketched as follows: the function we want to minimize is At any iteration, if some m j values become less than zero, they are automatically zeroed in order to satisfy the constraint of unidirectional slip (m j > 0 for all is). The process is repeated until a stable minimum is found for E 2 m. Inversion of L Aquila ENVISAT-InSAR Data We applied the inverse method to model the vertical displacements derived from InSAR data collected on 12 April, as compared to previous data collected on 1 February. Figure 3 shows the descending-orbit interferogram built from the comparison of two subsequent passages of InSAR satellites. These data contain the signal from the two mainshocks of 6 April and 7 April, in which the signal of the former is likely dominant, due to the higher magnitude. In InSAR data, there is no clear influence of the 9 April mainshock, which is located about 10 km further north than the northernmost fringes of Figure 3, probably because of the considerably smaller magnitude. In order to invert displacement data for the variable slip model, we must fix the geometry of the fault plane and the faulting mechanism. We constrain the faulting mechanism from those obtained with long-period seismic data for the 6 April and 7 April shocks (Walters et al., 2009; Pondrelli et al., 2010). The two mechanisms, as obtained by various authors, are remarkably similar. We got as a reference model the solution obtained by Pondrelli et al. (2010) and varied by a trial-and-error procedure the strike, dip, and center of the fault. For these sampling steps, we used 5 for strike E 2 m jja 3 m u 3 jj; where u 3 is the observed data and A 3 m m m 1 ;m 2 ;m 3 corresponds to the synthetic data. We first compute the gradient E 2 m 2A T 3 u 3 A 3 m ; and then update our model: m k 1 m k Δm k 1 E 2 m k ; where Δm k 1 is the factor which, multiplied by E 2 m k, determines the magnitude of the correction applied to m k. Figure 3. Geocoded L Aquila interferogram, descending frame 079, images date: 1 February 2009 and 12 April The interferogram is imposed on DEM of the area. The earthquake location (white star) and fault mechanism (Pondrelli et al., 2010) of the 6 April mainshock are shown. The yellow line represents the fault segment, located in correspondence with the field evidence of the Paganica San Demtrio fault, where significant dislocation has been observed after the earthquake (Emergeo Working Group, 2010).

6 Abruzzo, Italy, Earthquakes of April 2009: Heterogeneous Fault-Slip Models and Stress Transfer 2345 Table 3 Variance Sensitivity (σ 2 ) to Dip and Strike Variations Dip (45 ) Dip (50 ) Dip (55 ) Dip (60 ) Dip (65 ) Dip (70 ) Strike (150 ) 1: : : : : : Strike (145 ) 1: : : : : : Strike (140 ) 1: : : : : : Strike (135 ) 1: : : : : : Strike (130 ) 2: : : : : : Strike (125 ) 2: : : : : : Table 4 Variance Sensitivity (σ 2,inm 2 ) to the Fault Middle Point Location (in km 2 ) x x x y : : : y : : : y : : : and dip and 1 km on x and y, the fault center coordinates, and let them vary in a square of 3 3 km 2. The width and length of the fault were fixed, respectively, to 20 and 35 km, values larger than the actually deformed area, large enough to allow for the inverse method to decide without further constraints the location of the slipped areas on the fault (Tables 3 and 4). To allow for heterogeneous slip, the fault plane has been sampled by 91 point sources along strike and 61 point sources along dip. A shear modulus of 3: Pa and a Lamè s first parameter of 3: Pa were used. We have inverted, in a first step, ascending and descending InSAR data separately, and then we have merged the two data sets into a unique inversion of both. We have also used two conceptually different fault models, the first one representing a single fault plane from the surface to the maximum depth and the second one representing a listric fault schematized as a shallower vertical fault, with 2 km of width and a deeper fault plane, starting from the bottom of the vertical fault, described by the mechanism obtained by seismic data. In this second kind of model, strike, dip, and fault center have been varied around the central values exactly the same way described for the single fault. The best values for strike, dip, and fault center can be determined as the ones giving the best fit to the data, or the minimum residual between observed and theoretical data (Table 5). The resulting values of residuals for varying parameter values and for both fault models are shown in Table 6. From this table, it is clear that the minimum residual is obtained for a simple planar fault. Figure 4a shows the surface projection of the fault and Figure 4b shows the best-fitting slip contours on the fault plane. (For a complete list of the seismic moment/slip values over the faultplane elements, see ETable S1 in the electronic supplement to this paper.) The maximum slip on this fault is about 0.72 m, whereas the slipped area is shallower in the northwest and deeper in the southeast. Surface slip is almost absent, except in a zone about 5 km long, which correlates well with the observed mainsurface dislocations and fractures (Emergeo Working Group, 2010). In the northern part, slip is confined between about 3 and 10 km in width, whereas at the southern end, slip reaches about 18 km in width along the fault. The total geodetic moment is 2: N m, which is in good agreement with seismological estimates, giving about N m for the first shock (Walters et al., 2009) and 2: N m for the second one (Pondrelli et al., 2010). We recall, in fact, that given the time of the second InSAR image, namely, 12 April, the data contain the displacement produced by all the shocks occurring in the first 6 d after 6 April and, in particular, the first two mainshocks occurring on 6 April and 7 April are the only ones able to produce measurable ground deformation at these areas. Locations of the two mainshocks are also shown projected on the fault surface in Figure 4b.Itis interesting to note that they appear both located well below the slipped area. For the 6 April mainshock, this result, obtained from the rigorous inversion of displacement data, could be already qualitatively derived from the simple observation that the earthquake epicenter is located just out of the most external fringe of the interferogram (Fig. 3). The comparison between theoretical and observed data is shown in Figure 5. Table 5 Fault Parameters of the Best Fitting Models Inferred from InSAR Data (Ascending Descending) Inversion Length (km) Width (km) Top Depth (km) Dip ( ) Strike ( ) Rake ( ) Slip Max (cm) East* (km) North* (km) σ 2 (m 2 ) One-Fault Model : Two-Faults Model : *Upper extremity of the fault (UTM- Zone 33N).

7 2346 G. De Natale, B. Crippa, C. Troise, and F. Pingue Table 6 Variance Values Estimate for Various Models Model Variance (m 2 ) Single fault, all data Single fault, descending data Single fault, ascending data Two faults (listric), all data Two faults (listric), descending data Two faults (listric), ascending data 9: : : : : : Figure 5a shows unwrapped InSAR data; Figure 5b shows theoretical displacements computed by our model, whereas Figure 5c shows the map with residuals. Errors and Resolution Analysis An estimate of resolution for the inverse method used has been obtained by inverting simulated data from a homogeneous slip distribution on the best fault model. Such a method is conceptually similar to classical spike tests because it tests the ability of the method to retrieve the correct amount of slip on the different point sources that describe the model. Different sensitivity of real displacement data to the various point sources that compose the model reflect different resolutions at the various fault points, causing apparent slip heterogeneity on the fault. Therefore, any resulting heterogeneity of slip, from the inversion of simulated data based on a homogeneous model will represent an indication of lower resolution. For this resolution test, we have inverted simulated data from the best one-fault model reported in Table 5, assuming at each point on the fault a homogeneous seismic moment corresponding to a dislocation of 1 m in each rectangular element with the center at the source element. We computed the displacements at the same points of the real data. The retrieved model, obtained using zero dislocation everywhere as a starting model, is shown in Figure 6. The progressive degradation of resolution with the fault depth is evident. However, except for this obvious slight decrease of sensitivity with depth, the resulting model is remarkably close to the true homogeneous model, so that we can be sure that the sharp slip heterogeneity found from inversion of the real data is not an artifact of lack of resolution. Also, the abrupt termination of slip at a certain depth, generally shallower than the mainshock depths, is not an artifact of resolution, because in the simulated model, slip decreases only slightly with depth. Error estimates have been performed by inverting many noisy data realizations, simply randomizing the data values to within the associated errors. We performed 100 inversions of real data, adding random errors to them, and computed the standard deviation of retrieved slip values over the 100 inversions. In order to estimate the data errors, we have computed the mean deviation of displacement values at groups of points within a radius of 100 m, centered at several points over the sampled area reasonably far from the fault, in order to avoid areas of sharp gradients due to the fault dislocation. In this way, we estimated an average mean deviation of m; in order to allow for an even larger tolerance, we approximated it to the value of 0.01 m. With such a value as random error, we obtained the distribution of standard deviations on slip values shown in Figure 7. Resulting maximum errors are then on the order of 0.06 m, slightly lower than 10% of maximum slip values. Figure 4. (a) Surface projection of the best fault model (one-fault model in Table 5), with the inferred variable dislocation. Also shown are the locations of the three mainshocks (6 April 2009, M w 6.3; 7 April 2009, M w 5.6; 9 April 2009, M w 5.4) as reported by different authors (green, ISIDE [INGV]; white, Chiaraluce et al. [unpublished manuscript, 2011]; red, Chiarabba et al. [2009]; magenta, RCMT catalog). (b) Plane view of the best fault model, with variable slip as inferred from the inverse procedure., together with a vertical cross section showing the fault dip and the mainshocks position (right). The red segment over the fault plane indicates the position of the observed field dislocation along the Paganica fault. The white rectangle shows the best homogeneous fault geometry for the first (6 April) mainshock, used to compute Coulomb stress changes in Figure 10 (see the Stress Transfer on Neighboring Faults section).

8 Abruzzo, Italy, Earthquakes of April 2009: Heterogeneous Fault-Slip Models and Stress Transfer 2347 Figure 5. (a) Map of vertical displacements inferred from unwrapping of InSAR ascending and descending orbit interferograms, obtained by LOS data considering the incidence angle. Data coming from both interferograms have been combined by interpolation on two nonoverlapping grids. (b) Map of theoretical vertical displacements computed from the best-fitting model (one-fault model in Table 5). (c) Map of residual vertical displacements obtained subtracting theoretical data from observed ones. Stress Transfer on Neighboring Faults One of the most important questions linked to the occurrence of earthquakes in the Apennine domain regards the stress changes induced on adjacent tectonic domains and their influence on the earthquake occurrence. From the obtained model for L Aquila mainshocks, we have then computed the static Coulomb stress changes on the neighboring fault zones. The computation of Coulomb static stress changes has been obtained with the method of Troise et al. (1998), based on the formula The stress tensor itself is evaluated in terms of the spatial derivatives of ground displacements associated with fault dislocations. Such derivatives have been calculated using the analytical formulation by Okada (1992) for rectangular faults embedded within a homogeneous elastic half-space. In order to compute Coulomb stress changes due to the heterogeneous slip model, the fault surface has been considered subdivided in 5400 rectangular fault patches, 90 along the strike by 60 along the dip, each one with the resulting slip value assigned. Δσ f Δτ s μ Δσ n ΔP ; which defines the variation of the Coulomb failure stress Δσ f on a fault plane of fixed orientation and mechanism; Δτ s represents the shear stress change, Δσ n is the normal stress change (positive if tensile), μ is the coefficient of friction, and ΔP represents the pore pressure change (e.g., Stein et al., 1992). The friction coefficient value, reduced by the pore pressure, can be arranged in the form μ 0 μ 1 B, where B is the Skempton coefficient and ranges between 0 an 1 (Rice, 1982). Consequently, the previous equation becomes Δσ f Δτ s μ 0 Δσ n : Several values of μ 0 have been tested in the range 0.2 to 0.6, without substantial modifications of the general pattern. Finally, a value of μ 0 0:4 has been assumed, similar to the value used in most of the papers on this subject (see Troise et al., 1998). Normal and shear stresses have been obtained from the stress tensor computed on a 3D grid. Figure 6. Result of the resolution test, obtained by inverting simulated vertical data computed for a homogeneous slip model with constant dislocation of 1 m. The retrieved model, over most of the fault plane, is not far from a homogeneous one, indicating a good resolution except at the edges.

9 2348 G. De Natale, B. Crippa, C. Troise, and F. Pingue Figure 7. Results of the dislocation-error computation test, obtained by inverting 100 random realizations of real data perturbed with Gaussian noise having standard deviation σ 0:01 m. The dislocation error is obtained by computing the standard deviation of obtained dislocations at each source; source points are all over the fault. Zones of apparent null error are an artifact of the procedure because, in zones over the fault where the inverse method always assigns null slip, error computed this way is meaningless. means that our variable slip model, besides fitting grounddeformation satellite data, also gives a coherent explanation to the aftershock occurrence, as mainly triggered by static Coulomb stress changes. Obviously, the northernmost seismicity is not well interpreted in the framework of our model, because it mainly represents aftershocks of the 9 April Campotosto mainshock, which gave very weak or null contribution to the InSAR inferred deformation, so are practically absent in our fault model. We also investigated the influence of Coulomb stress changes on the consecutive occurrence of the three first mainshocks. For this analysis, we wanted to isolate the effect of the first mainshock, occurring on 6 April, on the subsequent two. Because our heterogeneous slip model basically contains the 6 April and 7 April earthquake fault models, we extracted a simplified, homogeneous slip fault model well-representing the 6 April event on the basis of geodetic and seismological data. Based on the obtained The change of shear stress Δτ s is projected in the assumed slip direction, and the sign is taken to be positive if equal to the sign of the assumed slip, negative otherwise. When a background regional stress field is considered, optimally oriented fault planes can be defined as the planes on which the total Coulomb stress (i.e., due to the regional field plus the change due to slip on the fault system) is maximum (Stein et al., 1992). The static stress change can be hence computed on the optimally oriented planes, which, in a homogeneous nonfractured medium, are the planes undergoing the maximum fracture stress loading, incremental plus regional. In our computations, the amount of tectonic stress has been chosen equal to the value of 2 MPa, as computed by Troise et al. (1998) for the southernmost area of the Apennines. However, using values from 1 to 10 MPa, results for maximum Coulomb stress changes show only negligible variation because the effect of tectonic stress on favorably oriented faults is always dominant for such values (see Troise et al., 1998). The strike of tectonic stress has been assumed orthogonal to the strike of the Apennine chain, in other words, about N45 E, with horizontal extension and vertical compression. Static Coulomb stress changes computed this way from the best variable slip model are shown in Figures 8 and 9. Figure 8 shows stress changes on the map at 8 km of depth. Figure 9 shows stress changes on five depth sections distributed along the fault strike and perpendicular to it. Superimposed to such stress maps are the mainshock and aftershock locations, as computed by Chiaraluce et al. (unpublished manuscript, 2011). A high degree of correlation between the aftershock locations and the zones of maximum positive Coulomb stress changes is evident. This Figure 8. Map of Coulomb stress changes, computed from the best variable slip model at a depth of 8 km. The rectangular fault plane used for slip inversion is shown in map projection with violet contouring. Locations of aftershocks with M L > 1:9, occurring in the period 6 April 31 December 2009 as computed by Chiaraluce et al. (unpublished manuscript, 2011), are shown as black dots. Also shown as white dotted lines are the directions and positions of five profiles perpendicular to the fault strike, on which the depth sections shown in Figure 9 have been computed.

10 Abruzzo, Italy, Earthquakes of April 2009: Heterogeneous Fault-Slip Models and Stress Transfer 2349 Figure 9. Coulomb stress changes computed from the variable slip fault model on the depth sections corresponding to the profiles shown in Figure 8. The letters from A to E refer to the corresponding profiles of Figure 8. The locations of aftershocks computed by Chiaraluce et al. (unpublished manuscript, 2011; with M L > 1:9, occurring in the period 6 April 31 December 2009) are shown as black circles, superimposed over the stress changes. In each section, only earthquakes located within 1 km of distance from the section are shown. On each section, the white line indicates the fault trace. geodetic model for the first two mainshocks, we modeled the fault for the first shock as a homogeneous slip plane with parameters of the best geodetic model and fault size compatible with the actually slip area. The fault size and slip have been further constrained to satisfy the condition that seismic moment is almost the same as the one estimated by seismological data: M 0 Aμd N m. Considering the earthquake locations from seismic data (Fig. 1), we know

11 2350 G. De Natale, B. Crippa, C. Troise, and F. Pingue that the second shock occurred about 12 km southeast of the first one, almost aligned on the fault trend we modeled. So the northern part of the inferred fault represents the first, highest-magnitude mainshock. In order to estimate the southeast termination of the first shock fault, we proceeded, in the previous section, to compute distance along the fault at which the total seismic moment becomes almost equal to the seismological estimate. In this way, we selected a rectangular fault about 16-km long and 13-km wide (in order to include the seismic locations at the bottom end), for a total seismic moment of 2: N m. The second, 7 April shocks can be represented by the remaining part of the southernmost fault, with considerably deeper slip. The inferred size of the first main fault is also in agreement with the seismological results obtained by Maercklin et al. (2011), who analyzed accelerometric records using a seismic array located about 250 km south of L Aquila. The resulting model for the first shock is shown as a white rectangle in Figure 4b, superimposed over the best variable slip model. In order to match the seismic model with this fault area, a homogeneous dislocation d 0:5 m has been assigned. Computing the maximum static Coulomb stress changes, using a value of μ 0 0:4, we get the stress pattern shown in Figure 10, computed at a depth of 14 km, close to both the depths of the two subsequent mainshocks. It is evident that the maximum positive stress areas, located at the borders of the fault, have been filled by the subsequent two mainshocks, namely, the 7 April M w 5.6 to the south, occurring probably along the same fault, and the 9 April M w 5.4 to the north, located on the Campotosto fault (Walters et al., 2009). The subsequent two mainshocks thus appear triggered by the first shock through static stress transfer. These observations confirm that, in the Apennines, the effects of static stress transfer are significant, as pointed out for previous earthquake sequences by Troise et al. (1998) and by other authors (e.g., Nostro et al., 1997; Tallarico et al., 2005). However, what is very interesting as a tool to forecast the most likely areas of future earthquakes is to understand how the recent earthquakes in the area modified the stress state and the earthquake cycle. While a complete deterministic answer to this crucial problem is out of our present capabilities, the computation of static stress changes for the last earthquakes, considered together with the tectonic stress accumulation rate in the area, gives information about the relative amount of stress perturbations induced on neighboring tectonic domains. Such perturbations can be hypothesized to advance or delay the next earthquakes in those tectonic domains. The maximum Coulomb stress changes caused by the whole mainshock sequence 6 9 April are shown in Figure 11. We used our best-fit heterogeneous slip model to represent the first and second mainshocks. For the third one, a homogeneous slip fault model has been inferred from the seismological results of Pondrelli et al. (2010). The results shown in Figure 11 make it evident that the three mainshocks of April 2009 caused increased positive Coulomb stress accumulation on the neighboring domains located northwest and southeast Figure 10. Map of Coulomb stress changes generated by the 6 April mainshock over faults having the same mechanism. White closed circles represent, respectively, the locations of the 7 April and of the 9 April further mainshocks. White contouring represents the surface projection of the homogeneous fault model for the first mainshock used for stress computation. The depth of the shown stress map is 14 km, very close to the depth locations of both the mainshocks. These occurred just at the borders of the first fault, in areas of highest positive Coulomb stress changes. along the Apennine chain. To the north, the closest affected domains are the Mt. Vettore and Norcia domains, which are mostly out of the map of Figure 11 (Deschamps et al., 1984; Bagnaia et al. 1996). In the Southern part, the affected domains include the Avezzano and Sulmona faults (Boncio, Lavecchia, and Pace, 2004). The maximum amount of Coulomb stress increase on such faults is around MPa. Due to the importance of seismotectonic domains as Avezzano and Sulmona located to the south, it is very interesting to consider the further effect of other recent earthquakes that have possibly affected their stress state. It turns out that another earthquake occurred in the last 30 yr close to these areas, namely, the 1984 Lazio Abruzzo earthquake. This earthquake has been well described by Westaway et al. (1984) and, subsequently, by Pace et al. (2002). Although

12 Abruzzo, Italy, Earthquakes of April 2009: Heterogeneous Fault-Slip Models and Stress Transfer 2351 the two proposed models differ slightly regarding the exact fault responsible for the earthquake (we used the Pace et al. [2002] model in our stress computation), such difference has negligible effects for the computation of Coulomb stress changes on the Avezzano and Sulmona faults. Figure 11 further shows the resulting maximum Coulomb stress changes obtained considering together the 2009 L Aquila mainshocks and the 1984 Lazio Abruzzo earthquakes. It is clearly evident that the Avezzano and Sulmona faults experienced considerable increase of Coulomb fracture stress both from the north due to L Aquila earthquakes and from the south due to Lazio Abruzzo ones. The total maximum amount of cumulated positive Coulomb stress on Avezzano and Sulmona faults is about MPa. Discussion Figure 11. Map of maximum Coulomb stress changes computed, at 8 km of depth, from the joint occurrence of the April 2009 L Aquila mainshocks and of 1984 Lazio Abruzzo earthquakes. The white rectangle represents, like in Figure 9, the surface projection of the modeled variable slip fault for the first two mainshocks. A schematic picture of the main fault traces of Avezzano and Sulmona tectonic domains is also superimposed. The results of rigorous inversion of InSAR data put in evidence that the best-fitting model is a single fault, striking 145 and dipping about 50 southwest. The slip is considerably shallower, between 3 and 10 km along the width (i.e., between 2 and 6 km of depth) on the northernmost part and deeper, between 10 and 14 km along the fault (i.e., between 6 and 9 km of depth) on the southernmost part. The inferred fault model is consistent with the known surface expression of the Paganica San Demetrio fault, as already noted by several authors (e.g., Atzori et al., 2009; Anzidei et al., 2009; Emergeo Working Group, 2010). Furthermore, the only segment of our fault model where surface slip is retrieved is consistent with the fault segment where surface dislocation of the same order has been observed on the field after the earthquake (Emergeo Working Group, 2010). Another striking feature obtained from the geodetic model is that the locations of both the mainshocks contributing to the ground displacement reconstructed from InSAR data appear slightly deeper than the areas of significant slip on the fault. This discrepancy cannot be ascribed to artifacts of the inverse method, because it is already evident by a simple visual inspection of interferometric fringes on the map (Fig. 3), where the earthquake epicenter clearly appears just over the most external fringes. In this respect, it could be an effect of slight mislocation of the two mainshocks. However, different locations obtained in recent literature for the two shocks show such a discrepancy anyway (see Fig. 4b). The observation that mainshocks are located deeper than the slip patches naturally suggests that fracture propagated from the depth towards the surface, as for many other Apennine earthquakes (e.g., Bernard and Zollo, 1989). Furthermore, it suggests that the first nucleation phase had a low associated slip, which increased during further propagation. This is in agreement with findings coming from seismological data (e.g., Cirella et al., 2009). Detailed insight on the fracture propagation is obviously out of the capabilities of InSAR-derived displacements, which only give the static part of deformation. We can only point out such evidence, which should be clarified by further analysis of seismological data. As mentioned before, given the time intervals of consecutive passages of the InSAR satellites, the derived model merges the information of both the two mainshocks of 6 April and 7 April, where the first, according to seismological estimates of seismic moments, is by far dominant. The analysis of Coulomb stress changes caused by the first mainshock indicates that the second (7 April) and third (9 April) shocks occurred in the areas of maximum positive stress changes, close to the upper and lower ends of the first shock fault (Fig. 10). Close to the fault edges, in fact, the maximum Coulomb stress changes are focused for faults having a similar mechanism to the causative mechanism. This demonstrates that, as noted in other Italian sequences (Troise et al., 1998), the occurrence of multiple mainshocks in earthquake sequences is generally due to the triggering effect of static stress changes. Overall, the Coulomb stress changes computed for our heterogeneous slip model show a very good agreement between zones of maximum stress changes and aftershock clusters. This means that also the aftershock occurrence is dominated by the

13 2352 G. De Natale, B. Crippa, C. Troise, and F. Pingue triggering effect of Coulomb static stress changes due to coseismic slip on the mainshock faults. Finally, the mainshocks of April 2009 that occurred in the Abruzzo region transferred positive Coulomb stress on the neighboring tectonic structures. The maximum amount of transferred positive stress on the neighboring faults has been on the order of MPa. The maximum amounts of positive Coulomb stress change occurred on the seismotectonic domains located southest and northeast of the L Aquila earthquakes. Among such domains, the southernmost ones include the important faults of Avezzano and Sulmona. Avezzano was the fault giving rise to the devasting earthquake of 13 January 1915 (Baratta, 1916; Bonasia et al., 1986; De Natale et al., 1988; Ward and Valensise, 1989). The Sulmona fault, on the contrary, has not been active since the last large earthquake of 1706 (Galadini and Galli, 2000) occurred about 3 yr after an earthquake occurring in the L Aquila area. The mechanism of seismic stress accumulation and release in the Apennine is largely unknown but can be reasonably schematized as the superposition of three main effects. The first, most important effect is thought to be the regional tectonic stress accumulation; this can be thought to likely occur at a constant rate, which can be estimated, in this part of the Apennines, on the basis of the observed geodetic strain rate of = s(anzidei et al., 2001). The resulting estimate of stress rate, as computed by Tallarico et al. (2005) amounts to 0:002 MPa=yr. The second effect in the stress buildup on active faults is the stress transfer from the neighboring faults when slip occurs. This effect sums up to the constant regional stress accumulation. The third effect is given by the partly viscous behavior of the lower crust, which can modulate and focus the stress in the long term, and, mainly, relaxes the accumulated static stress after a period based on the ratio between shear modulus and viscosity (Schowalter, 1978). The rheological behavior of the crustal and mantle rocks is well approximated by the Maxwell viscous-elastic model, in which dε dt σ η 1 dσ G dt ; where ε is the strain, σ indicates the stress, η is the viscosity coefficient, and G represents the shear modulus, or rigidity. In the framework of this model, the stress relaxes, for an applied constant strain, following an exponential decay. The time scale for stress relaxation is controlled by the ratio η=g, where G is the shear modulus and η is the viscosity. After times considerably longer than η=g, all the applied stress is relaxed; for times considerably shorter than η=g the applied stress is not sensibly modified by viscosity, whereas for intermediate times, only a fraction of the originally applied stress holds. This means that the value of viscosity of the crustal and mantle rocks is crucial to estimating the permanence of static stress in the crust, which in turn controls the mechanism of the earthquake cycle. There are few estimates of viscosity values in the lower crust and mantle in the Apennines because such estimates are generally difficult to make and are affected by large errors. The most viable way for reliable estimates of average viscosity values is to observe and model the postseismic deformation after large earthquakes (Pollitz and Dixon, 1998; Khazaradze et al., 2002; Dalla Via et al., 2003; Pollitz et al., 2006). The most recent and reliable estimate obtained on this basis for the Apennines is due to Dalla Via et al. (2005), who analyzed the postseismic deformation of one of the largest Italian earthquake in the last century, namely, the Irpinia (1980) earthquake. They obtained a viscosity value for the lower crust of about Pa s, whereas they demonstrated that the effect of viscosity of the mantle, due to its large depth, is almost negligible on surface deformation and stress state at seismogenic depths except for much larger time scales. With the inferred value of viscosity for the lower crust, the time scale for stress relaxation is τ η=e = yr. This means that applied stress at a certain time is completely relaxed after times considerably higher than 30 yr. Hence, in order to evaluate the stress state on the Apennine faults, we can approximately consider only the stress summed up in the last 30 yr. As shown in the previous section, the Lazio Abruzzo earthquake, which occurred 25 yr ago, released significant positive fracture stress on the important tectonic domains of Avezzano and Sulmona, which also experienced further fracture stress loading from the last L Aquila mainshock. Most of the stress loading from the 1984 earthquakes still holds and sums up to the stress applied after April The total level of Coulomb stress applied to the Avezzano and Sulmona faults is about MPa. In the framework of a model in which an earthquake on a large fault occurs when the Coulomb fracture stress exceeds a given threshold, we can say that, compared with the constant tectonic stress loading of 0:002 MPa=yr, the loading effect from the 1984 and 2009 earthquakes corresponds to an anticipation of yr of the time of occurrence of the next earthquakes on these faults, with respect to a pure tectonic loading. More detailed ways to compute the effects of static stress loading on the neighboring faults, in terms of earthquake probability changes, have been proposed by various authors (e.g., Stein et al., 1997; Toda et al., 1998; Toda and Stein, 2002; Hardebeck, 2004). The application of such methods requires many assumptions and detailed knowledge of the background seismicity rate. However, the evidence and results obtained in this paper represent a good starting step for their future application to Apennine seismicity. Conclusion The results obtained in this paper shed light on the importance of InSAR data for the understanding of earthquake processes in the Apennines. The L Aquila earthquake demonstrated that also medium size earthquakes, typical of the Apennines, can give very clear satellite interferometric images, able to strongly constrain their mechanisms.