Earthquake: Finite- Fault Effects on Intensity Data

The 6 April 2009, Mw 6.3, L’Aquila (Central Italy) earthquake: finite- fault effects on intensity data

Gabriele Ameri (1), Dino Bindi (1,2), Francesca Pacor (1) and Fabrizio Galadini (3)

(1) Istituto Nazionale di Geofisica e Vulcanologia, via Bassini 15, 20133 Milano, Italy. (2) Deutsches GeoForschungsZentrum GFZ and CEDIM, Helmholtzstraße 7, 14467 Potsdam, Germany (3) Istituto Nazionale di Geofisica e Vulcanologia, via di Vigna Murata 605, 00143 Roma, Italy

Corresponding author: Gabriele Ameri, Istituto Nazionale di Geofisica e Vulcanologia via Bassini 15, 20133 Milano, Italy e-mail: [email protected]

Version: Pre-Print published in Geophysical Journal International

1 Summary

We analyse the spatial distribution of the intensity data points surveyed after the Mw 6.3, 2009 L’Aquila (central Italy) earthquake, with the aim to recognize and quantify finite-fault and directivity effects. The study is based on the analysis of the residuals, evaluated with respect to attenuation-with-distance models, calibrated for L’Aquila earthquake. We apply a non-parametric approach considering both the epicentral and the rupture distance, which accounts for the finite extension of the source. Then, starting from a simplified kinematic rupture model of the L’Aquila fault, we compute four directivity predictors proposed in literature, and assess their correlation with intensity residuals. We derive a so-called Intensity Directivity Factor by the correlation between theoretical predictors and observed residuals that allows us to identify and quantify the intensity data points affected by forward and backward directivity during L’Aquila earthquake. We find that the effects are more pronounced in the forward directivity direction and increments up to 1 MCS intensity unit are expected. Moreover, the directivity predictor that accounts for radiation pattern poorly correlates with residuals. These results show that the spatial distribution of the L’Aquila macroseismic field is affected by source effects and in particular that directivity-induced amplification effects can be recognized. We show that the quasi-unilateral rupture propagation along the fault can explain the high-intensity patterns observed along specific direction at relatively large distance from the instrumental epicentre, in accordance with the seismological source models derived from the analysis of instrumental observations.

2 1. Introduction

Finite-fault effects, such as directivity, hanging-wall/foot-wall and radiation-pattern effects, are known to significantly contribute to the large variability of earthquake ground motions at distances comparable with few fault lengths. The near-fault ground motion from moderate-to-large events is strongly affected by the space and time evolution of the rupture along the extended fault, causing complex spatial distribution of the observed shaking.

Although the characteristics of the seismic source are also expected to contribute to the distribution of macroseismic intensity observed for moderate-to-large seismic events, the attenuation of macroseismic data is generally analyzed in terms of isotropic models

(Lee and Kim, 2002; Musson, 2005; Bakun, 2006b; Pasolini et al., 2008, among many others). Deviations from this behavior can be ascribed to several factors, such as inconsistencies affecting the felt report, different attenuation properties at crustal scale

(Carletti and Gasperini, 2003), interaction between the seismic wave field and the shallow geological structure (Cara et al., 2005), finite-fault effects (Berardi et al, 1995;

Sirovich et al., 2009). To date, only few authors investigated the influence of source effects on the macroseismic intensities (e.g. Sirovich et al., 2009; Sirovich and Pettenati,

2009) while most studies aim to assess the possibility of inferring information about source parameters, such as the fault geometry and focal mechanism, from the regional patterns of macroseismic intensity (Gasperini et al., 1999; Bakun and Wentworth, 1997;

Parson et al., 2000; Bakun 2006a; Pettenati and Sirovich, 2007).

In this study, we look at the macroseismic field of the 6 April 2009, Mw 6.3, L’Aquila

(Central Italy) earthquake that struck the Abruzzo region, causing about 300 causalities and widespread damage in L’Aquila city and its neighboring municipalities, searching

3 for finite-fault effects. Evidence of such effects in recorded ground motions are found by various authors. Pino and Di Luccio (2009) supported the evidence of rupture directivity toward southeast by analyzing the relative source time functions of some stations of the National Seismic Network. Ameri et al. (2009) showed that long-period spectral accelerations from strong-motion data recorded by the National Accelerometric

Network (RAN, Rete Accelerometrica Nazionale) stations show a clear dependence on azimuth, that can be attributed to directivity effects. Akinci et al. (2010) showed that the mainshock strong motions present directivity effect towards southeast direction with a systematic decrease of PGA and PGV at sites located in the backward direction of the rupture propagation. Cirella et al. (2009) proposed a rupture model for the Aquila earthquake from joint inversion of GPS and strong-motion data. The authors found that the main slip asperity is located about 8 km south-east to the epicenter, producing, as a consequence, higher ground motions in this area.

The regional pattern of the macroseismic intensities is characterized by an asymmetric shape, with the most damaged area (I ≥ 7.5 MCS degree) extended for about 20 km and elongated in NW-SE direction with a predominance of high damage SE of the earthquake epicenter (Figure 1a). This area includes 16 localities with the highest values

(I ≥ 8) sited above the fault surface, suggesting that source geometry and its kinematic played a role in the damage distribution (Camassi et al., 2009).

We investigate if the evidence of finite-fault effects clearly observed on the recorded ground motion can be also recognized through the treatment of macroseismic intensities. First, we remove from the intensity data the effect of the attenuation with distance. We apply a nonparametric approach considering both the epicentral distance and the rupture distance, which accounts for the finite extension of the source..

4 Second, we investigate the effects of rupture directivity correlating the residuals with two directivity predictors proposed in literature (Berardi et al., 1995; Spudich and

Chiou, 2008), both based on the isochrone theory (Spudich and Frazer, 1984; Bernard and Madariaga, 1984) computed considering a simple kinematic rupture model. In this way, we quantify the contribution of the source directivity effects to the macroseismic intensities surveyed after the L’Aquila earthquake.

2. The 2009 L’Aquila earthquake and the macroseismic intensity data

On April 6, 2009, 01:32:40 UTC, a Mw 6.3 earthquake occurred in the Abruzzo region

(Central Italy), close to L’Aquila, a town of about 70,000 inhabitants. The main seismological features of the event are consistent with the seismotectonic setting of the

Central Appenines, including a long-lasting sequence of foreshocks and aftershocks

(Chiarabba et al., 2009).

The epicentral area corresponds to the upper and middle Aterno valley which is characterized by a complex tectonic evolution reflected by the high variability of the geologic and geomorphologic patterns. Indeed, the investigated region is characterized by intermontane basins, whose Quaternary history has been conditioned by the normal fault activity responsible for the formation and evolution of half-graben basins (e.g.

Basili et al., 1999). In particular, the upper-middle Aterno valley is characterized by three fault-bounded basins filled by lacustrine and alluvial deposits (Messina et al.,

2009). The Arischia-Barete basin is the northernmost one (Figure 1b) and its evolution results from the Quaternary activity of the Mt. Marine fault (Galadini and Galli, 2000).

Based on paleoseismological data, this fault activated during the strong (Mw 6.7; Rovida and Working Group CPTI, 2009) February 2, 1703 earthquake (Moro et al., 2002).

5 Northwest of L’Aquila, the L’Aquila-Scoppito basin has formed due to the activity of the Pettino fault which probably also activated in 1703 (Galadini and Galli, 2000). The southernmost tectonic depression of the area struck by the 2009 earthquake is the

Middle Aterno Valley basin (Messina et al., 2009), related to the Paganica and San

Demetrio ne’ Vestini faults, whose Late Quaternary activity was documented in publications also preceding the 2009 event (Bagnaia et al., 1992; Bertini and Bosi,

1993; Vezzani and Ghisetti, 1998; Boncio et al., 2004). The Paganica fault is considered as the causative source of the 2009 earthquake (e.g. Falcucci et al., 2009).

For the April 6, 2009 earthquake, a number of fault models have been proposed based on inversion of DInSAR displacement (Atzori etal., 2009), GPS (Anzidei etal., 2009) and GPS + strong-motion data (Cirella et al., 2009). All the models reasonably well agree on the fault geometry and location of the main slip asperity and also are in good agreement with aftershocks relocation (Chiarabba et al., 2009) and with field observations along the above mentioned Paganica fault (Falcucci et al., 2009). In this study we adopted the fault model proposed by Cirella et al., (2009) (Figure 1a), whose main fault parameters are summarized in Table 1. Note that the fault dimensions we use correspond to the portion of the fault where significant slip occurs (see Figure 4 of

Cirella et al., 2009).

Severe damage and collapses mainly affected old buildings (unreinforced masonry or stone buildings) but also a number of recent buildings were destroyed. After the earthquake, the QUEST team (QUick Earthquake Survey Team) immediately started the macroseismic survey and more than 70 settlements were surveyed by the evening of the same day (Camassi et al., 2009). The survey was concluded at the end of July 2009 and

6 macroseismic estimates in MCS scale, with intensities ≥ 5, were provided for 314 localities (Figure 1a) (Galli and Camassi, 2009; Galli et al., 2009).

A general trend can be recognized in the macroseismic intensity distribution. Although the instrumental epicenter is located approximately in between the L’Aquila-Scoppito and the Middle Aterno Valley basins, the maximum damage took place southeast to the epicenter, inside the surface projection of the fault. In particular, the highest intensities

(I ≥ 7 MCS degree, colored dots in Figure 1a and b) appear to be distributed in a NW-

SE direction with a substantially larger number of points SE of the epicenter within the

Middle Aterno Valley basin. The maximum intensities (I > 9 MCS) are reported at 6 villages, among them Castelnuovo and Onna (I = 9.5 MCS), scattered in an area of lesser damage (I ≤ 8 MCS). The contribution of the building vulnerability is apparent, since at almost every locality the historical center suffered major damage with respect to the recent suburbs. Nonetheless, the differences in the local site conditions seem to have played an important role in the damage occurred at specific sites (Bergamaschi et al.,

2011; Ameri et al., 2011). A well-known case is given by the settlements of Onna (I =

9.5) and Monticchio (I = 5) in the Middle Aterno Valley, distant less than 2 km each other, located on lacustrine sediments and rock, respectively (Di Giulio et al., 2010).

Evidence of local amplification can be found also very close to the epicenter, where the historical centre of Poggio di Roio (I = 8.5), located on the Roio Basin, was completely destroyed and the neighboring municipalities suffered very high damage. Another example of possible influence of site effects on damage is given by Castelnuovo (I =

9.5), about 20 km far from the epicenter, placed on the top of a small hill, formed by silts overlaying conglomerates (Ameri et al., 2011).

7 Conversely the damage reported NW of the epicenter rarely exceed I=7.5 degree. This asymmetric distribution contrasts the general geological framework. Indeed, as reported above, the area struck by the earthquake is distributed throughout three intermontane basins (Figure 1b) filled by continental deposits having comparable stratigraphic and sedimentological characteristics (e.g. Messina et al., 2009). Thus, large-scale site effects cannot be solely invoked to explain the larger damage reported SE of the epicenter compared to the ones to the NW.

As a consequence of this asymmetric distribution of the largest intensities, the macroseismic epicenter, computed with the methodology proposed by Gasperini et al.

(1999) is located about 10 km far from the instrumental epicenter, in southeast direction

(black star in Figure 1a).

In Figures 1c and 1d, the intensity data points are plotted as a function of epicentral distance and azimuth, respectively. The highest intensities (I ≥ 9) are in the 5-20 km distance range, and cover azimuths between 70° and 130°. In general, high intensity values are found over such azimuthal range even at large distances from the epicenter (>

10 km), while for other azimuths high intensity values are associated with short epicentral distances (< 10 km). In Figures 1c, the intensities predicted, as a function of epicentral distance (Repi), by the empirical equation proposed by Pasolini et al. (2008) for the Italian territory are compared with the reported ones. The attenuation of the observed intensities with distance looks faster than the predicted median and a general overprediction is observed. Only the highest values are fitted by the empirical curve.

The rupture distance (Rrup) distance is commonly used, in place of Repi, to describe the attenuation in ground motion prediction equations in order to partially capture the finite- fault effects for moderate-to-large magnitude events where the finite dimension of the

8 fault cannot be considered negligible (i.e., the point source assumption is not reasonable). In figure 1e, the intensity data points are plotted as a function of Rrup. The macroseismic data follow a more regular decay (compare Figures 1c and 1e), where high intensities (I ≥9) are associated with localities less than 5 km distant from the rupture surface. The attenuation of intensity with Rrup is compared to the model proposed by Faccioli and Cauzzi (2006), based mostly on Italian data. Also in this case, the observed data decay faster than predictions. To investigate the origin of the faster decay of the observed intensities with respect to the empirical models is beyond the scope of the present study. However the comparisons presented in Figure 1c and 1e showed that such overestimation of the empirical models does not depend on the adopted distance metric (either Repi or Rrup) and regional attenuation properties could be involved.

3. The nonparametric attenuation model

In order to properly describe the average attenuation of the 2009 L’Aquila macroseismic intensity with distance, a regression on intensity values is performed, adopting a nonparametric inversion scheme (e.g., Anderson, 1991; Savage and Anderson, 1995).

Following this approach, any a-priori functional form is assumed and the dependence on distance is driven by the data. The epicentral distance interval from 1.5 to 68 km and the rupture distance interval from 0.5 to 55 km are discretized in Nd=5 and Nd=6 bins equally spaced in logarithmic scale, respectively. The attenuation curve is then evaluated at the fixed knots Rn, n=1,…,Nd. Given for the i-th data point the Intensity (Is) at distance R, the index n is chosen such as Rn≤R≤ Rn+1 . The linear system appear as follows:

9 )( ref n 0 n ++= n+ RAaRAaIRIs n+101 )()( , (1) where an=(Rn+1-R)/ΔR, ΔR=(Rn+1-Rn), an+1=1-an. As described in Anderson (1991), the use of the an is a method of linearly interpolating data that are recorded at arbitrary distances. The unknowns to be determined are Iref and A0(Rn) and the system is solved by least-squares regression (Paige and Saunders, 1982). To avoid the trade-off between the source and attenuation contributions, the regression is performed by constraining the attenuation to zero at the reference distance Rref=3 km. Moreover, we contained the attenuation to be a smooth function of distance by imposing the second derivative of the attenuation function to be small.

Figures 2a shows the nonparametric attenuation curves and the intensity data, for epicentral distance (left) and rupture distance (right). At distance larger than about 5 km, the two nonparametric curves show similar rate of decay, with slightly higher values predicted in terms of Repi. In both cases, the curves show a logarithmic decay with distance, in accordance with the functional forms usually adopted to describe the intensity attenuation (Pasolini et al., 2008; Sorensen et al., 2009; Bakun and Scotti,

2006).

At shorter distances, the nonparametric curve for Repi maintains the logarithmic trend, up to I=8.5 at the minimum distance. On the contrary, the curve for Rrup tends to level off and stabilize to a value of Is=7.

The residuals, computed as observations minus predictions (Iobs-Ipre), do not show any trend with distance (Figure 2b) and their standard deviations, σepi=0.71 and σrup=0.67, are in good agreement with values commonly obtained in other studies (Pasolini et al.,

2008; Sorensen et al., 2009). Residuals for epicentral distance present the largest

10 dispersion around 10 km while for rupture distance the largest dispersion is observed over the range 0.5 to 10 km. As distance increases, the dispersion of residuals decreases.

Residuals are generally within ±2 intensity units. Considering Repi, 7 localities are underpredicted by more than 2 intensity units (i.e., Castelnuovo, Onna, San Gregorio,

Sant'Eusanio Forconese, Tempera, Villa Sant'Angelo and Poggio Picenze), being those sites located between 5 and 20 km with intensity values larger than 8. When residuals versus Rrup are considered, 3 localities are underpredicted (i.e., Castelnuovo, Onna and

Poggio di Roio) and 1 locality is overpredicted (i.e., Cerro, I=5) by more than two units.

The residuals are shown as a function of epicenter-to-site azimuth in Figure 2c. The distribution of residuals obtained from the epicentral distance presents a clear trend where the intensity data between 45 and 135° are on average underestimated, while the others are overestimated. Residuals in the third azimuth bin (90°-135°) show the largest dispersion and the highest positive residuals.

On the other hand, the residuals from rupture distance show a slight trend with azimuth and high absolute residuals are scattered over various azimuth sectors. Although the standard deviations for azimuths bins 45°-90° and 90°-135° increase, medians and weighted means are close to zero. Large standard deviations and high positive residuals are also found in the 180°-270° azimuths sector, due to the underestimation of intensity points very close to the epicenter, as better shown in the following figures.

Figure 3 presents the spatial distributions of the residuals: red and blue symbols correspond to intensity values that are underestimated and overestimated by more than

0.5 intensity unit, respectively. The maps confirm the findings observed in Figure 2.

There is a systematic trend in the residuals for Repi: underestimation of the observed intensities appears southeast of the epicenter, whereas overestimation is observed in the

11 opposite direction. The highest positive residuals ( ≥ 2 intensity units) are mainly concentrated close to the northeastern termination of the fault, while the negative residuals are, on average, lower than 2 and mostly located west to the epicenter. The map of Rrup residuals show a much scattered distribution of points close to the fault while, at larger distances, the distribution is similar to what obtained from the Repi model. The rupture distance better explains the attenuation of the intensity data close to the fault as no systematic trend is found in the residuals, showing that, in this case study, the fault geometry affect the macroseismic observations

4. Directivity predictors

Beside the distance to the fault, in this section we investigate whether the directivity effects can be connected to the observed anisotropic distribution of the L’Aquila macroseismic intensities and, in particular, to the high intensity values (> 8) reported at relatively large distances from the epicenter. Note that we refer to “directivity” in a broad sense including finite source extent, radiation pattern and seismic directivity related to the rupture propagation along the fault (Ben-Menahem, 1961). Thus, in this context, “directivity” will not refer solely to a rupture propagation effect but more in general to the azimuthal variation of near-fault intensities.

To evaluate the contribution of the rupture kinematic of an extended source on the intensity data, we implemented two directivity predictors (Berardi et al., 1995; Spudich and Chiou, 2008) and correlate them with the intensity residuals calculated with respect to the mean value of the nonparametric regression. The two directivity predictors are both based on the isochrone theory (Spudich and Frazer, 1984; Bernard and Madariaga,

1984) and are developed to describe and quantify the distribution of directivity-induced

12 amplification of motion close to an extended fault once that a simple kinematic rupture model is specified in terms of rupture geometry, hypocentral location and rupture velocity. Note that the variable slip distribution over the fault is not considered.

Here we briefly describe the directivity parameters used and some minor modifications we tested, referring to the Appendix for further details.

4.1 Ikrn (theoretical source intensity - Berardi et al., 1995)

The Ikrn term is constructed applying the isochrone theory to a simple rupture scenario over an extended fault. The term is a combination of three parameters to relate earthquake intensity with a physical description of the rupture process:

⎛ C ⎞ ⎛ 1 ⎞ Ikrn = ⎜ max ⎟×⎜ ⎟ (2) Δ ⎜ RT ⎟ ⎝ ⎠ ⎝ ptn ⎠ where C represents the maximum isochrone velocity over the fault plane; R max ptn represents the source-to-receiver distance measured from the point on the fault with the maximum isochrone velocity (i.e., from the sub-fault associated with C ); and ΔT max represents the duration of the rupture process as perceived by a site, and computed as the difference between maximum and minimum isochrone values. The term C /ΔT has max the dimensions of acceleration, and basically states that the greater the acceleration of the rupture, as perceived at a given site, the greater the theoretical source intensity at the site. In equation (2), Ikrn decays as 1/Rptn. However, based on the evidence of the logarithmic decay of intensity found in section 4, we also tested the following modification of Ikrn:

⎛ C ⎞ ⎛ 1 ⎞ Ikrn2 = ⎜ max ⎟×⎜ ⎟ (3) Δ ⎜ ln RT ⎟ ⎝ ⎠ ⎝ ptn ⎠

4.2 IDP (Isochrone Directivity Predictor – Spudich and Chiou, 2008)

Spudich and Chiou (2008) and previous authors (i.e., Spudich et al., 2004; Spudich and

Chiou, 2006) developed the IDP parameter aiming to determine a directivity model and relative corrective factors that may be applied to the ground motion prediction equations developed within the PEER-NGA project (Abrahamson et al., 2008). Their predictor of directivity effects is defined as:

= CSRIDP ri (4) where C is a normalized and capped form of c~′(an approximate isochrone velocity ratio, see Appendix); S quantifies the along-strike portion of fault rupture between the hypocenter and the site and Rri is a point-source (i.e., hypocentral) scalar radiation pattern amplitude.

Since the contribution of radiation pattern is not incorporated in the Ikrn term (Berardi et al., 1995) and studies performed to date make difficult to substantiate its contribution on intensity data we also tested a modified version of IDP as:

2 = 2 SCIDP (5) ~ where C2 is a normalized but not capped form of c′. Note that Spudich and Chiou

(2008) decided to cap c~′ at 2.45 based on analysis of synthetic ground motions, which prompted us to test also a variation of IDP with a not capped c~′.

Although based on the same theory, the two approaches are not expected to predict the same directivity around the faults. The implementation of the Ikrn term requires the actual calculation of isochrones (rupture times + travel times) for a given rupture scenario and site location and it has been developed to be directly correlated to

14 macroseismic intensity. On the other hand, the IDP predictor has been thought to be simple and easy-to-calculate with standard geometry, it also incorporates the effect of the S-waves radiation pattern and has been used to define a directivity models with empirically determined coefficients for ground motion prediction equations (Spudich and Chiou, 2008).

5. Results

To compute the directivity predictors for the L’Aquila earthquake at the 314 intensity data points described in section 2, we construct a simplified kinematic rupture model.

The fault parameters are taken from the Cirella et al. (2009), as discussed in Section 2, and are summarized in Table 1. The kinematic source model for the Ikrn calculation assumes that the rupture starts at the hypocenter and propagates radially outward with a constant rupture velocity along the fault plane. The rupture velocity was set to 0.85β

(with β = 3.2 km/s). This rupture scenario is characterized by quasi-unilateral rupture propagation toward southeast, with both along-strike and up-dip components.

Figures 4 illustrate the normalized Ikrn, Ikrn2, IDP and IDP2 predictors as a function of distance and azimuth (see also Figures A1 and A2). The normalization allows a direct comparison of among the different predictors distributions. Ikrn and Ikrn2 terms reach their maximum at distances between 10 and 20 km and for azimuths of 100-110°, but

Ikrn shows a faster attenuation with distance. The distributions as a function of azimuth for both parameters have two amplitude peaks, the first is located between 90 and 145°

(due to the rupture propagation toward the southeastern edge of the fault) and the other, of smaller amplitude, in the opposite direction (due to the rupture propagation toward the northwestern edge of the fault). The hypocentral radiation pattern term (Rri), adopted

15 in IDP (Figure 4, lower panels) prevents high predicted values in the fault-strike direction (where the S-wave radiation pattern for the considered focal mechanism has a minimum). As a consequence, the maximum IDP values are found at large distances and for smaller azimuths. IDP2 shows similar trend to Ikrn2, identifying the maximum directivity effects approximately in the same distance and azimuth ranges.

5.1 Correlation of directivity predictors with residuals

The map distribution of each directivity predictor is plotted in Figure 5, overlaid are the residuals calculated with respect to the nonparametric attenuation function for epicentral distance. We used the epicentral distance because we want to highlight directivity effects (in a broad sense) in the intensity residuals distribution and, in particular, whether the location of the larger intensity data points match the direction of rupture propagation.

Ikrn and Ikrn2 patterns (Figure 5, left panels) are characterized by elongated contour lines in southeast-northwest direction with the highest values located close to the southeastern edge of the fault. These trends agree with the distribution of residuals: most of the points underestimated by more than 2 intensity units are aligned along the direction of maximum directivity. Furthermore Ikrn2 attenuates more slowly, taking into account the increment of the observed intensity at farthest sites. The negative residuals, are generally located in regions of low Ikrn values.

The IDP (Figure 5, top-right panel) term appears poorly correlated with the residuals, suggesting that this term, calibrated on strong-motion data, might be not suitable to describe the directivity effects on the L’Aquila earthquake macroseismic intensities.

The IDP2 parameter provides similar results to Ikrn2 close to the fault and it better correlates to the residuals with respect to IDP; compared to Ikrn2 it produces wider

16 regions of high values both southeast and northeast of the fault. The better performance of IDP2 with respect to IDP is possibly related the not-recognizable effects of radiation pattern on the L’Aquila intensity data points (or, alternatively, to the small water level used by Spudich and Chiou (2008) to fill the radiation pattern nodes).

The correlation between residuals and directivity predictors is assessed by a linear model Y=a+bDpar, where Y are the residuals and Dpar stands for one of the considered directivity parameters; a and b are the regression coefficients estimated by least-squares

(Figure 6). The correlation coefficients (ρ) are reported in Table 2. Ikrn and Ikrn2 show the largest positive correlation while IDP exhibits almost no correlation with residuals.

In order to assess the stability of the regression we used the bootstrap method (Efron,

1979), where the original dataset is replaced with bootstrap samples obtained by randomly resampling n times, with replacement, the original dataset. Table 2 reports the regressions coefficients, with relative standard errors (computed from 1000 bootstrap replications). Although the correlation coefficient is about the same for Ikrn and Ikrn2 the standard errors reveals that regression is more stable using Ikrn2 as explanatory variable.

We thus adopted the linear model based on Ikrn2, to estimate what we will call the

Intensity Directivity Factor (IDF). This term quantify the contribution of the finite-fault effects on the L’Aquila reported intensities that cause an increment/decrement of the intensity values with respect to an isotropic decay. The IDF (Figure 7) assumes positive values up to 1 intensity unit along direction of maximum directivity (about 110°) and at distance of about 20km. On the other hand, it does not exceed -0.5 degree within the azimuth range between 150° and 300°. These zones well agree with the amplitude of residuals, having absolute values larger than 1. In particular, most of the positive

17 residuals (red circle in Figure 7) are located in region, where the directivity effects are expected to increase ground motion (red area).

It is important to stress that the rupture directivity is only one among several effects leading to an increase of the macroseismic intensity. For example, in Figure 7 some large red circles, (residuals larger than 2) correspond to localities (e.g. Onna,

Castelnuovo) where strong site amplification effects are recognized (Bergamaschi et al.,

2011; Ameri et al., 2011) but not considered in the model we have adopted. However, we verified that the omission of these two sites does not change the correlation coefficients between residuals and directivity predictors.

The residuals computed with respect to the rupture distance are poorly correlated with

Ikrn2 (not shown here). Some discussion on this topic is presented in section 6.

5.2 Test for a north-western rupture propagation

In order to further validate the correlation between a south-eastern rupture propagation along the fault and the residuals distribution, we repeated the analysis assuming an hypocenter located on the opposite side of the fault leading to a north-western rupture propagation. Clearly, in this case, the nonparametric attenuation model and the resulting residuals are calculated assuming the distance from another epicenter (which is not the real one) located close to the south-eastern edge of the fault plane. The spatial distribution of residuals and of Ikrn2 parameter (as an example), computed for such rupture model, are reported in Figure 8 (left panel). The correlation between the residual and Ikrn2 is also assessed (Figure 8, right panel).

This test showed that there is no correlation between the residuals and the Ikrn2 parameter for this alternative rupture model. In other words, a rupture propagation in the

18 opposite direction respect to that attributed to the L’Aquila event is not able to explain the large intensities observed above the fault.

6. Discussion

Finite-fault effects (including radiation pattern, slip heterogeneities and directivity) in recorded ground motions are well documented and a relevant literature exists. For

L’Aquila earthquake forward and backward directivity effects have been recognized by the analysis of the instrumental data, showing a systematic amplification of the ground motions southeast of the epicentre (Ameri at al., 2009; Akinci et al., 2010; Pino and Di

Luccio, 2009). On the other hand, finite-fault effects in macroseismic intensity are less studied (Berardi et al, 1995; Sirovich et al., 2009) mainly due to the qualitative nature of the macroseismic scales.

In this study we investigate the intensity data points for the 2009 L’Aquila earthquake with the aim to show to what extent finite-fault effects are present on macroseismic intensity distribution. The asymmetric distribution of the damage pattern cannot be explained exclusively with a peculiar seismic response due to the general geological setting, since most of the intensity data points related to I ≥ 6 MCS are located in an area characterised by the presence of three intermontane basins (form north to south:

Arischia-Barete, L’Aquila-Scoppito, Middle Aterno Valley) filled by continental deposits having comparable sedimentological and stratigraphic characteristics. For these reasons, the asymmetric distribution of the intensity data seems to be explainable also in terms of finite-fault effects responsible for the large intensity values at sites above the fault surface and in the forward directivity region (i.e., the southeast area of the

L’Aquila earthquake fault). Finite-fault effects are only one among several factors

19 leading to the spatial variability of intensity values close to the seismic source as also site-specific amplification effects or building vulnerability affect the damage distribution. For example, we showed that the large residuals, reported at Castelnuovo and Onna (4 and 3 intensity units, respectively), can be partially ascribed to directivity effects (up to 1 degree), but the well recognized amplifications due site effects have to be considered to justify the high reported intensity values (I = 9.5). Anyway, the appropriate way to evaluate the contribution of site response on macroseismic intensity data is a complex and controversial issue (e.g. Cua et al, 2010) and is beyond the aim of this study.

The analyses of residuals discussed in this work showed that when the rupture distance is considered, the intensities close to the fault are better described by the nonparametric attenuation model suggesting that, in this case study, the fault geometry affect the macroseismic observations. This result is important since, whereas the use of the rupture distance is a standard practice in the context of ground motion models, Intensity

Prediction Equations (IPE) in Italy and worldwide are generally derived using epicentral distance (Bakun et al., 2003; Bakun and Scotti, 2006; Pasolini et al., 2008; Allen and

Wald, 2009; Cua et al., 2010).

Directivity effects are recognized in the distribution of residuals computed with respect to the distance from the instrumental epicenter. The correlation with directivity predictors shows that the radiation pattern is not affecting the intensity distribution while the direction of the rupture provides the dominant contribution. It is important to note that the directivity predictors we used are based on a kinematic rupture model where the fault finiteness is implicitly taken into account. On the other hand, the absence of correlation between directivity predictors and rupture distance residuals

20 could be partially related to the character of macroseismic scales, that are expressed by ordinal and discrete number and does not allow refined analyses. The use of rupture distance could be not adequate to study and quantify the rupture directivity on intensity data as otherwise done for ground motion parameters (Spudich and Chiou, 2008)

These findings demonstrate that, despite the moderate size of the L’Aquila earthquake fault (Table 1), both the fault dimension and rupture kinematic substantially contributed to the level and pattern of the reported damage.

7. Conclusions

In this article we studied the macroseismic intensity data surveyed after the Mw 6.3,

2009 L’Aquila (Central Italy) earthquake. This event ruptured a fault about 18 km long, striking in the NW-SE direction, dipping toward SW and characterized by a rupture propagation toward the South-East direction (Cirella et al., 2009; Chiarabba et al.,

2009).

The regional pattern of the macroseismic intensities is characterized by an asymmetric shape. The most damaged area (I ≥ 7.5 MCS degree) extended for about 20 km southeast to the instrumental epicenter. On the contrary, in the northwest direction, at comparable distances to the epicenter, only intensities lower than 7.5 are reported.

We analyzed the intensity residuals with respect to the estimates from an ad-hoc non parametric empirical model calibrated for the area, with the aim to analyze the source- related effects on the macroseismic intensities. The residuals, considering the epicentral distance, show a clear trend with azimuths and large positive residuals are obtained over the range 45° - 135° degrees (clockwise from north direction), which encompass the direction of the fault strike.

21 Following Berardi et al. (1995) and Spudich and Chiou (2008), we used the isochrone theory to quantify the effect of directivity at the location of the macroseismic data points. Starting from the analysis of residuals, we slightly modified the directivity predictors introduced by that authors (called Ikrn and IDP, respectively). In particular, we considered a logarithmic decay in the Ikrn model (renamed Ikrn2) and we eliminate the radiation pattern contribution to IDP (renamed IDP2), since we observed that it weakly correlates with the residual distributions.

We found that the spatial distribution of the residuals resembles the azimuthal variation of three of the directivity predictors, i.e., Ikrn, Ikrn2 and IDP2, computed for the

L’Aquila fault assuming a quasi-unilateral rupture propagation toward SE. In particular, the predicted direction of maximum forward directivity at about 110° well agrees with azimuth range (90°-135°) where the largest dispersion and the higher positive residuals.

Then, we correlated these predictors to the residuals in order to evaluate to what extent the residuals can be explained in terms of directivity effects. We used the Ikrn2 predictor, showing the largest correlation, to derive a linear model that quantify the directivity effects on the intensity residuals. The so-called Intensity Directivity Factor

(IDF), shows that the effects are more pronounced in the forward directivity direction and increments up to 1 intensity unit are expected. The IDF spatial distribution well agrees with the amplitude of residuals: most of the positive residuals larger than 1 are located in forward region, while the negative ones are mainly located in the opposite area.

In conclusion, this study:

- shows that directivity effects influenced the regional pattern of the L’Aquila

macroseismic intensities;

22 - supports the use of macroseismic intensity data to infer some rupture kinematic

parameters for past earthquakes;

- suggests that further studies should be devoted to the analysis of macroseismic

intensity data (related to a large number of events) in order to calibrate generally

applicable IDF that can be used to account for the main features of the rupture

propagation in Intensity Prediction Equations. Such results would be important

for intensity-based hazard assessment in the near-fault distance range.

Acknowledgements

This work has been supported by the INGV-DPC Project S4, 2007-09. We thank the

Associate Editor Massimo Cocco, Frantisěk Gallovič, and an anonymous reviewer whose comments led to improvements to the manuscript. The authors also wish to thank

Massimiliano Stucchi, Antonio Gomez Capera and Andrea Rovida for providing valuable feedback during the development of this article. Andres Mendez provided the original code for the Ikrn calculation.

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Figure Captions

Figure 1. a) Distribution of the macroseismic intensities, MCS scale. (Galli and Camassi, 2009; Galli et al., 2009). Circles denote intensity values larger than or equal to 7, whereas triangles are used for lower intensities. The surface projection of the seismogenic fault (black rectangle) adopted in this study is reported together with the instrumental epicenter (yellow star). The macroseismic epicenter (Stucchi et al., 2009) is shown by the black star. b) zoom of the epicentral area (black rectangle in a)). From north to south the Arischia-Barete, L’Aquila-Scoppito and Middle Aterno Valley basins are shown by white dashed contours. c) Intensity data versus the epicentral distance, compared with the empirical predictive equation from Pasolini et al. (2008) (mean ± 1σ; σ=0.87 intensity unit). d) Intensity data versus epicenter-to-site azimuth (measured clockwise from North) separated by distance bins; e) Intensity data versus distance from the fault plane (rupture distance- Rrup) compared with the predictive equation from Faccioli and Cauzzi (2006).

Figure 2. Top panels: nonparametric attenuation curve (black line) calculated as a function of Repi (left) and Rrup (right). The observed intensities are shown as grey circles.

Middle panels: residuals calculated as observed minus predicted intensity (Iobs-Ipre; gray crosses) as a function of distance (Repi - left and Rrup - right). The median (black square) of the residuals computed over distance bins equally spaced in logarithmic scale is shown together with plus/minus one standard deviation. The horizontal dashed lines represent the total standard deviation of residuals (σRepi=0.71 and σRrup=0.67. Bottom panels: residuals as a function of epicenter-to-site azimuth (measured clockwise from North). The median (black square) of the residuals computed over azimuth bin 45° wide is shown together with plus/minus one standard deviation. Grey squares represent the mean calculated weighting the residuals by their absolute value.

Figure 3. Spatial distribution of the residuals. Residuals (Iobs-Ipre) considering the epicentral distance (upper map) and the rupture distance (lower map). Red circles

29 indicate underestimation of more than 0.5 intensity degree, while blue squares indicate overestimation of more than 0.5 intensity degree. Crosses indicate absolute residuals smaller than 0.5. The yellow star is instrumental epicenter and black rectangle is the surface projection of the seismogenic fault.

Figure 4. Tested directivity parameters as a function of epicentral distance (left panels) and azimuth (right panels) normalized to their maximum values. The black dots represent the IDP as introduced by Spudich and Chiou (2008), the gray squares represent the Ikrn as introduced by Berardi et al. (1995). IDP2 and Ikrn2 are two slightly modified versions of the parameters originally proposed by the respective authors (modifications are described in the text). See also Figures A1 and A2

Figure 5. Maps of the tested directivity parameters (normalized to their maximum values). From top-left to bottom-right: Ikrn, IDP, Ikrn2 and IDP2. Overlaid on each map are the residuals calculated with respect to the nonparametric attenuation function considering the epicentral distance (also shown in Figure 3, upper plot).

Figure 6. Normalized Ikrn, Ikrn2 (upper panel), IDP and IDP2 (lower panel) versus residuals. The regression coefficients of the linear fit and the correlations coefficients are reported in Table 2. Residuals are calculated with respect to the nonparametric attenuation for epicentral distance.

Figure 7. Map of Intensity Directivity Factor (IDF). Absolute residuals larger than 1 are also reported. Red circles indicate underestimation of more than 1 intensity degree, while blue squares indicate overestimation of more than 1 intensity degree. The yellow star is instrumental epicenter and black rectangle is the surface projection of the seismogenic fault. Residuals are calculated with respect to the nonparametric attenuation for epicentral distance.

Figure 8. Ikrn2 parameter and residuals computed assuming an alternative hypocenter position (yellow star), see text for details. Left panel: map of normalized Ikrn2

30 parameter. The residuals are also reported: red circles indicate underestimation of more than 0.5 intensity degree, while blue squares indicate overestimation of more than 0.5 intensity degree. Crosses indicate absolute residuals smaller than 0.5. The black rectangle is the surface projection of the seismogenic fault. Right panel: normalized Ikrn2 versus residuals.

TABLES

Table 1 – focal mechanism and fault geometry epicenter [lon°, lat°] 13.380, 42.348 hypocenter depth [km] 9.5 moment magnitude 6.3 strike [°] 133 dip [°] 54 rake [°] -90 fault length [km] 18 fault width [km] 16.5 top depth [km] 0.5 along-strike position [km] 4.0 (from NW fault edge) down-dip position [km] 11.7

Table 2 – regression coefficients (a, b) with relative standard errors (computed from 1000 bootstrap replications) and correlation coefficients (ρ) for each directivity predictor.

Dpar a b ρ Ikrn -0.34(±0.05) 1.71(±0.30) 0.42 Ikrn2 -0.43(±0.06) 1.31(±0.19) 0.43 IDP -0.14(±0.07) 0.39(±0.12) 0.14 IDP2 -0.46(±0.06) 1.04(±0.15) 0.39

Figure 1

Figure 2

Figure 3

Figure 4.

Figure 5

Figure 6

Figure 7

Figure 8

38 APPENDIX This Appendix describes more in details the two directivity predictors adopted in this study and their constitutive parameters in the implementation for the L’Aquila earthquake fault geometry.

A.1 The Ikrn parameter (Berardi et al.,1995) Berardi et al.(1995) suggest characterizing an otherwise complex and spatially extended rupture process by a combination of simple parameters derived from the isochrone formulation. The authors propose a combination of three parameters to relate earthquake intensity with a physical description of the rupture process:

Cmax, which represents the maximum isochrone velocity;

Rptn, which represents the source-to-receiver distance measured from the point on the fault having the maximum isochrone velocity (i.e., from the sub-fault associated with C ); max ΔT, which represents the duration of the rupture process as perceived by a site, and computed as the difference between maximum and minimum isochrone values. The proposed theoretical source intensity Ikrn is given by: ⎛ C ⎞⎛ 1 ⎞ Ikrn = ⎜ max ⎟⎜ ⎟ (A1.1) Δ ⎜ RT ⎟ ⎝ ⎠⎝ ptn ⎠ The various factors of equation A1.1 are computed for the adopted source model for L’Aquila earthquake (based on Cirella et al., 2009) and presented in Figure A1. The kinematic rupture model is described by a rupture nucleation that starts at 4 km form the NW edge of the fault, 14 from the SE edge and at 9.5 km depth and propagates radially outward with a constant rupture velocity v =0.85β (where β=3.2 km/s). While R r ptn assumes an almost isotropic shape only slightly modified in the rupture direction, C max and ΔT are clearly not isotropic fields. The former assumes the highest values along the fault-strike direction while the latter assumes the highest values in the direction opposite to the rupture propagation (i.e., backward directivity direction). These behaviors confirm that C and ΔT are able to capture the effect of rupture directivity on seismic max radiation, i.e., the seismic moment rate functions, as perceived by each site, have shorter duration and higher amplitude for stations toward which the rupture propagates than

39 those for stations located in the opposite direction (e.g., Aki and Richards, 1980). Furthermore, R can be used to accounts for the decreasing with distance of the source ptn directivity effect. The rate of decay can be linear (as for the original Ikrn term) or logarithmic, as for the modification we proposed (Ikrn2). Combining the three previous terms as described in equation A1.1, the source intensity field Ikrn, tends to be larger and decays more slowly with distance from the fault for those sites towards which the rupture front propagates. The Ikrn2 distribution present a lower attenuation with distance (as the logarithm of distance is used) in the direction of rupture propagation and the difference between sites located in forward and backward directivity direction is larger than for Ikrn (Figure A1). Note that here the values of Ikrn and Ikrn2 are not normalized as in the main text.

A.2 The IDP parameter (Spudich and Chiou, 2008) Spudich and Chiou (2008) and previous papers (i.e., Spudich et al., 2004; Spudich and Chiou, 2006) developed and tested a so-called Isochrone Directivity Predictor (IDP) obtained combining physically-based predictor variables by using isochrone theory. The aim of these studies is to determine a parameter able to predict directivity (or the azimuthally varying distribution of ground motion in the near-fault region). The selected predictor is used to determine correction factors that may be applied to the ground motion prediction equations developed within the PEER-NGA project (Abrahamson et al., 2008). The directivity predictor proposed by Spudich and Chiou (2008) is:

= CSRIDP ri (A2.1) Where C is a normalized and capped form of c~′(an approximate isochrone velocity ratio) lying in the range [0, 1]; S quantifies the along-strike portion of rupturing fault between the hypocenter and the site and Rri is a point-source scalar radiation pattern amplitude. In particular the various terms are calculated as following: min(c~′ − 8.0)45.2, C = (A2.2) − )8.045.2( where the capping value of 2.45 was selected by Spudich and Chiou (2008) based on correlation of C with directive residuals from synthetic ground motions. In this paper

40 we also tested a not capped form of C that we will call C2 (see the main text). Note that

Spudich and Chiou (2008) assumed that Vr=0.8 β. The isochrone velocity ratio c~′ is an approximation of the isochrone velocity (Spudich and Frazer, 1984) calculated as:

−1 ⎛ β − RR )( ⎞ c~′ : ⎜ −= HYP RUP ⎟ , D > 0 ⎜V D ⎟ ⎝ r ⎠ (A2.3) V 0 , r , D == 0 β where D is the distance from the hypocenter to the point on the fault closest to the site

(note that in this study D is always larger than zero), β is the shear-waves velocity, Vr is the rupture velocity and RHYP and RRUP are the hypocentral and rupture distance, respectively.

S = s h))],max(,75ln[min( (A2.4) where s is the along-strike distance in km from the hypocenter to the point on the fault closest to the site, and h is the down-dip distance in km from the top of the rupture to the hypocenter. The capping of S at 75 km is not relevant for the fault dimensions considered in this study. Finally:

2 2 Rri = max( t + RR u ,ε ) (A2.5)

Rt and Ru are the strike-normal (transverse) and strike-parallel hypocentral S-wave radiation patterns, with a water level ε =0.2 filling the nodes. The spatial distribution of the parameters in equation A2.1 adopted to calculate IDP and IDP2 (see main text) is shown in Figure A2.

In principal, Cmax and C (or C2) map distributions should show some similarities, as the two terms quantify the same parameter (i.e., the maximum isochrone velocity for each site). Indeed the terms are somehow similar, though the distribution of C show large values also on the foot-wall of the fault. The main differences between Ikrn and IDP

41 come from the inclusion of a point-source radiation pattern model on the latter predictor and from the distance dependence on the former. The distribution of Rri, predicted by equation (A2.5), cause large directivity effects in the up-dip direction, while, in the along-strike direction, the nodes of radiation patter prevent high values. When this contribution is not included and C2 is considered the resulting IDP2 predictor provides a spatial distribution similar to Ikrn and Ikrn2 terms.

Figure A1 - Theoretical source terms Ikrn (bottom-left panel), Ikrn2 (bottom-right panel) and fields of constituent parameters (equation A1.1) calculated at the intensity data points presented in the main text and for the L’Aquila fault geometry. The rupture nucleates near the northeastern edge (star) of the fault at a depth of 9.5 km and propagates radially outward with a constant rupture velocity of 0.85β. The surface projection of the fault (black rectangle) is also shown.

Figure A2 – Isochrone Directivity Predictors IDP (bottom-left panel), IDP2 (bottom- right panel) and fields of constituent parameters (equation A2.1) calculated at the intensity data points presented in the main text and for the L’Aquila fault geometry. The rupture nucleates near the northeastern edge (star) of the fault at a depth of 9.5 km. The surface projection of the fault (black rectangle) is also shown.