Polarization of Strong Ground Motions: Insights from Broadband. Modeling of Mw5.4 Aftershock of the 2009 L Aquila, Italy,

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1 Manuscript Click here to download Manuscript: LAquila-aftershock-v2-08_edited.docx Polarization of Strong Ground Motions: Insights from Broadband Modeling of Mw5.4 Aftershock of the 2009 L Aquila, Italy, Earthquake 4 5 F. Gallovič 1, F. Pacor 2, J. Zahradník 1, L. Luzi 2, R. Puglia 2, M. D Amico Charles University in Prague, Faculty of Mathematics and Physics, Dept. of Geophysics, Prague, Czech Republic (gallovic@karel.troja.mff.cuni.cz) 2 Istituto Nazionale di Geofisica e Vulcanologia, Milano, Italy Abstract We perform an extensive study of the largest aftershock of the Mw L Aquila, Italy, earthquake, based on low-frequency inversion and broadband simulation of strong-motion data. The Mw5.4 aftershock occurred on 7th April at 17:47:37 UTC at 15km depth and it was recorded by 33 permanent and temporal accelerometric stations located within 50km from the epicenter. We carry out inversion of low-frequency ( Hz) data for centroid moment tensor and simple finite-fault model. The event ruptured a 6x6km normal fault dipping NE at 60 degrees, antithetic to the causative fault of L Aquila mainshock. We build a broadband (0.1-10Hz) composite source model with fractal number-size distribution of overlapping subsources on the identified fault. Fullwavefield synthetic Green s functions are calculated in 1D layered media in the full (0.1-10Hz) frequency range, assuming shallow site-specific velocity profiles, wherever available, and a generic profile for rock stations. At stations with weak site effects, the fit between synthetic and observed data is generally good both in time and Fourier spectral domains. Comparison of observed and synthetic data in terms of S-wave group polarization at high frequencies reveals a particular 1

2 behavior of the recordings. While some stations retain the predominantly linear polarization in accordance with the 1D modeling up to high frequencies, other stations show a peculiar mismatch. It appears in the observed data either as occurrence of chaotic circular polarization, or as angular rotation of still predominantly linear polarization. We further explore these effects by analyzing directional site-effects and particle motions for shallower events. We conclude that the observations can be explained assuming: i) relatively weak scattering properties of the crust at large depths, and ii) stronger scattering at shallow depths with azimuthally dependent effects at specific locations Introduction Broadband ground motion simulation techniques, based on kinematic rupture models, are employed to generate seismograms in a wide frequency range (0-10Hz). In the literature, most methods simulate ground motions by combining the synthetics computed with deterministic and stochastic approaches in the low and high frequency range, respectively (e.g., Hartzell et al., 1999, 2005; Pitarka et al., 2000; Mai and Beroza, 2003; Liu et al., 2006; Gallovič and Brokešová, 2007; Hisada, 2008; Frankel, 2009; Graves and Pitarka, 2010; Mena et al., 2010; Ameri et al., 2012). The stochastic component is required because source radiation and wave propagation become increasingly incoherent at high frequencies (Liu and Helmberger, 1985; Sato and Fehler, 1998; Hartzell et al., 1999). The most common approach to model the incoherent component of the ground motions is using stochastic Green s functions, which are constructed as an artificial timewindowed signal with random phase and prescribed shape of its Fourier amplitude spectrum (Boore, 1983; 2006; Silva and Darragh, 1995; Beresnev and Atkinson, 1997; Motazedian and Atkinson, 2005). Other approaches introduce stochastic features in the deterministic methods through random processes, either in the source (e.g., Liu et al., 2006) or path description (Mai et al., 2010; Mena et al. 2010; etc.). Broadband source simulation techniques are usually employed to simulate strong events (M > 6), because the ground motion close to the causative faults is mainly controlled by the complexity 2

3 of the source mechanism and propagation effects. These techniques are rarely applied to reproduce moderate magnitude events, because the duration of the source is rather short and high-frequency site and propagation effects might dominate the records. Nevertheless, the broadband modeling of a moderate magnitude event can be useful to investigate to what extent the ground motion is coherent with the source kinematics and 1D propagation and to evaluate the level of randomness of highfrequency due to path and site effects. Polarization of strong motions (i.e. of the main S-wave group) carries important information on the complexity of the source, path and site effects. Simple source model in 1D medium results in relatively simple almost linear polarization with direction given by the radiation pattern of the source. Distortion of the radiation pattern at high frequencies as a result of the scattering effect is found in theoretical studies dealing with wave propagation in realistic random media (Takemura et al., 2009; Imperatori and Mai, 2012). Empirical analysis show controversial results: for example, Vidale (1989), who investigated empirical radiation pattern of two individual seismic events, found a persistent radiation pattern up to high frequencies. On the other hand, the studies by Satoh (2002), Takenaka et al. (2003) and Takemura et al. (2009), carried out on a large seismic dataset, concluded that the radiation pattern diminishes with increasing frequency. The observed ground motions are also affected by the structure below the site. Typically, site effect amplifies the ground motion in a broad frequency range. Recently, there is an increasing interest in peculiar site effects that are able to change the polarization of the incoming wavefield. Such directional site effects were introduced by Bonamassa and Vidale (1991) and Bonamassa et al. (1991) and have been since extensively discussed in the literature in relation to site anisotropic effects. In some cases, topographic irregularities are linked with the polarization of ground motion, such as in cases of the Tarzana hill (Spudich et al., 1996), Nocera Umbra (Pischiutta et al., 2010) and Narni (Lovati et al., 2011) ridges, although no general relationship between topography and ground motion directionality has been found (Burjánek et al., 2014). Directional site effects have also been observed in relation to predominant cracking directions, such as in presence of a fault 3

4 zone (Pischiutta et al., 2012; Avallone et al., 2014), on unstable slopes (Burjánek et al., 2010) or in correspondence of a tectonic contact (Marra et al., 2000). In this paper, we present a broadband modeling of the strongest aftershock (Mw 5.4-7th April 2009, 17:47 UTC) of the L Aquila (central Italy) seismic sequence. The broadband modeling is based on a composite source model with fractal number-size distribution of overlapping subsources and deterministic Green s functions calculated in a 1D layered medium over the full frequency range (0.1-10Hz). The high-frequency stochastic component of the ground motion is modeled via the source only, by randomly distributing subsources and perturbing strike, dip, and rake angle of faulting at short length scales (Zeng et al., 1995; Pulido and Kubo, 2004; Liu et al., 2006). This approach has been demonstrated efficient in simulating the high-frequency recordings of the Mw6.3 L Aquila mainshock (Ameri et al., 2012) and of other worldwide events (Ameri et al., 2009; Ameri et al., 2011a; Schmedes et al., 2012; Gallovič et al., 2013). The general aims of our work are: i) to evaluate the performance of the modeling in case of moderate event and ii) to investigate to what extent the 1D linear source-polarization can be preserved in the observed strong-motion data. The studied aftershock is characterized by several interesting features: i) the rupture process involved a fault plane which is antithetic to that of the main shock (Chiaraluce et al., 2011; Valoroso et al., 2013); ii) the focal depth is about 15 km, which is larger than the average depth of the sequence (about 10 km) ; iii) several studies have inferred a relatively high stress drop, on the basis of either generalized inversion of strong motion data (Bindi et al., 2009; Ameri et al., 2011b) or empirical Green s function technique (Calderoni et al., 2013); iv) preliminary analysis of recordings revealed that this event has generally shorter duration of the major strong motion phase compared to other aftershocks of smaller magnitude; v) there is just a single study devoted to this particular event (Pino and Di Luccio, 2009). In this study we setup the broadband source model based on preliminary inversion of strongmotion data in low frequency band ( Hz), fixing the earthquake mechanism, fault plane position and its dimension, and rupture propagation. The broadband simulation (0.1-10Hz) is then 4

5 performed using 1D Green s functions in the full frequency range, assuming shallow site-specific structure or a generic profile for rock stations. The results are validated through the comparison with observed waveforms and against ground motion parameters predicted by empirical relations (Bindi et al., 2011). Then, we investigate frequency-dependent S-wave polarization of the synthetic and observed data. Although we introduce complexity in the source mechanism at small scales, we show that the 1D synthetics preserve the source radiation polarization up to 10Hz. At some stations the observed data at high frequencies retain the predominantly linear polarization in accordance with the 1D modeling, while at other stations the polarizations exhibit a mismatch. The mismatch appears either as an occurrence of chaotic circular polarization, or as a variation of the angle characterizing the linear polarization. We further explore these effects by analyzing directional siteeffects and particle motions for shallower events. We conclude that the observations can be explained assuming, i) relatively weak scattering properties of the crust at large depths, and, ii) stronger scattering at shallow depths with azimuthally dependent effects at specific locations L Aquila earthquake sequence The 2009 L Aquila seismic sequence (Mw 6.3, 6 th April mainshock) is associated with a complex system of normal faults developing in an area previously affected by compression (e.g., Galadini and Galli, 2000; Chiarabba et al., 2009). The seismic sequence that occurred in April 2009 continued for about six months and was characterized by five major normal-faulting earthquakes (Mw > 5.0). The prevailing kinematics of the main earthquakes is extensional with evidence of a minor strike-slip component for the foreshock and the deepest aftershock (Valoroso et al., 2013). From the analysis of up to 561 foreshocks and 2643 aftershocks with ML 1.9, Chiaraluce et al. (2011) recognized two main SW-dipping normal faults, forming an en-echelon system, extending in the NW-SE direction for about 50 km. Valoroso et al. (2013), confirming the findings by Chiaraluce et al. (2011), extended the data set in order to study the key role of aftershocks in fault growth and co-seismic rupture propagation processes. The 16 km long L Aquila fault, associated with the Mw 5

6 mainshock, shows a planar geometry with constant dip ( 48 degree) through the entire upper crust down to 10 km of depth. The authors observe that the strongest and deepest aftershock of the sequence (15km) occurred at the tip of the L Aquila fault where the main fault plane changes its dip, associating the event with an antithetic fault Dataset and data processing The largest aftershock of the L Aquila earthquake is very well recorded because Istituto Nazionale di Geofisica e Vulcanologia (INGV) installed, after the mainshock, a dense temporary network to accurately locate the events of the L Aquila sequence (Margheriti et al., 2011) and to investigate site effects in the epicentral area (Bergamaschi et al., 2011). We selected records from 33 stations within 50 km (Figure 1 and Table 1) from the epicenter belonging to the permanent National Accelerometric Network (RAN, operated by the Department of Civil Protection, DPC, code IT in Table 1), the National Seismic Network (RSN, operated by INGV, code IV in Table 1) and the Mednet network (operated by INGV, code MN in Table 1). The INGV and DPC permanent and temporary strong-motion stations are equipped with Episensor (Kinemetrics), triaxial force balance sensors, with a natural frequency above 50 Hz, set to either 1 or 2 g full-scale, coupled with various digitizers (Reftek , Kinemetrics Etna and Everest, Kinemetrics K2, Quanterra Q330, or the INGV designed GAIA2 (Rao et al., 2010). All digitizers have resolution of 24 bits and a sampling rate of either 100 or 200 Hz. In this study, the uncorrected waveforms are processed in the following way. After the removal of the linear trend, we apply a 4-th order Butterworth band-pass causal filter. The high-pass corner frequency was selected as low as possible through a visual inspection of the Fourier spectrum, in order to obtain valid displacement signals required for centroid moment tensor and slip inversions. The selection of the low-pass corner frequency depends on the actual application and it is specified later. In all cases, the observed data and the synthetic Green s functions are filtered identically. 6

7 Modeling methods In this section we briefly summarize the inversion and simulation techniques adopted to constrain the low-frequency source properties of the 17 April 2009 aftershock and to generate the broad-band synthetic ground-motion Centroid moment tensor (CMT) The CMT solution is calculated by ISOLA (Sokos and Zahradník, 2008, 2013). It is a broadly used software package for inverting full waveforms at local-to-regional distances in the lowfrequency range. The moment tensors are calculated by the least squares method, while the centroid position and time are the result of a grid search. The quality of waveform fit is expressed in terms of variance reduction (VR), given by VR = 1-sum((obs-syn) 2 )/sum(obs 2 ), (1) where obs and syn are the observed and synthetic displacement waveforms, respectively. The sum is performed over all time samples, components and stations Slip inversion The slip distribution and rupture velocity are inferred applying the MuFEx method introduced by Gallovič and Zahradník (2012). In this approach, the starting model is a single rectangular slip patch with homogeneous slip distribution, radial rupture propagation at constant velocity, and impulse slip rate function (i.e. the rise time is assumed smaller than the reciprocal of the maximum investigated frequency). A set of trial nucleation points, rupture velocities and nucleation times are considered. A grid-search over all combinations of the source parameters is used. For each of the trial models, a linear least-squares problem is solved to obtain the slip value. Each model is characterized by its fit with observed data in terms of VR. Neglecting all models with negative slip values, and considering minimum acceptable VR, it is possible to find a set of plausible rupture 181 models. 7

8 Strong motion broad-band modeling The broad-band modeling of strong ground motions is performed using the composite model of the Hybrid Integral-Composite (HIC) approach (Gallovič and Brokešová, 2007; Ameri et al., 2009; Zollo et al., 2009; Ameri et al., 2011a; Chiauzzi et al., 2011). The integral part can be avoided in this application because the minimum source-station distances are larger than the dimension of the source especially due to the 15km depth. HIC is developed for earthquake ground-motion simulations following omega-squared source model with scalar seismic moment M 0 and corner frequency F C, where the latter is determined through the fit with the observed broadband seismograms. For comparison with other studies it is useful to relate the corner frequency with stress drop Δσ (Keilis-Borok, 1959; Brune, 1970) using standard Brune formula F C =49β(Δσ/M 0 ) 1/3, β being the shear wave velocity (3.5km/s in our application). The modeling technique is based on previous works by Andrews (1980), Herrero and Bernard (1994), Zeng et al. (1994) and Gallovič and Brokešová (2004). The source consists of subsources with number-size distribution with fractal dimension D = 2. The decomposition of the source model into subsources is to be considered just as formal representation to introduce a realistic complex source radiation. Details on the source decomposition are given in Appendix. The ground motions are calculated as a sum of contributions of all the subsources. Standard Brune time function of each subsource is delayed according to the respective rupture time (i.e. time at which the rupture front reaches the center of the subsource assuming constant rupture velocity), and convolved with full-wavefield Green s function assuming a double-couple point source in 1D medium. An important consequence of the composite modeling is that the directivity effect is present only at low frequencies, while it disappears at high frequencies due to the incoherent summation of the subsource contributions (Gallovič and Burjánek, 2007). This is in agreement with directivity derived from empirical data (e.g., Somerville et al., 1997). 8

9 To suppress the radiation pattern at high frequencies, Zeng et al. (1995) suggested prescribing random variation of the rake angle. In accordance with the studies of non-planar fault radiation by Käser and Gallovič (2008) and Gallovič et al. (2010), we assume ±30 random variations of the strike, dip and rake angles of the subsources that are smaller than one half of the fault dimension (see Appendix). Due to the scaling of the source time functions of the subsource, the reduction of the radiation pattern is efficient only at high frequencies (at high frequencies the subsource wavefield contribution is proportional to the subsource size, in contrast to low frequencies, where it is proportional to its third power) D crustal models with site-specific subsurface structures Full wavefield Green s functions are calculated by the discrete wavenumber method (DWN, Bouchon, 1981; Kennett and Kerry, 1979; Coutant, 1989). The DWN technique provides full wavefield deterministic Green s functions; no stochastic Green s functions are used throughout the whole study. DWN requires a 1D crustal model composed of homogeneous layers. We use a general 1D velocity model combined with site-specific subsurface layers when available, as specified below. The 1D-velocity model (Table 2) adopted to simulate the strongest L Aquila aftershock derives from the model proposed by Bianchi et al. (2010) and was used to simulate the 2009 L Aquila main shock by Ameri et al. (2012). Although this model was appropriate to reproduce the overall wave propagation in the study area, it caused underestimation of the high-frequency amplitude of the ground motion at rock sites. Indeed, in central Italy sedimentary rocks are generally weathered and fractured, therefore very hard rock sites with shallow shear wave velocity of 1700 m/s are hardly expected (Gruppo di Lavoro MS-AQ, 2010). In order to simulate 1D site effects at generic rock stations, we substitute the uppermost 160m of the regional crustal model by 60m superficial layer with shear wave velocities of 800 m/s above another 100 m thick layer with velocity of 1200 m/s (Table 3, the ROCK profile in Figure 2).The velocity of the first layer (800 m/s) is the value 9

10 prescribed for seismic bedrock by the Italian seismic code (NTC08) and similar values have been measured at several rock stations in central Italy (see AQP, PSC, SCN, MTC among others). In general, site effects are important in the L Aquila dataset, as the epicentral area is located inside the Aterno river valley, an alluvial valley filled by quaternary deposits of various depths (Bergamaschi et al., 2011; Di Giulio et al., 2011; Puglia et al., 2011, Lanzo et al., 2011). Directional site effects are observed at specific sites in fault zone areas (Avallone et al., 2014) and in cases of complex morphology (Puglia et al., 2011). Geologic conditions are complex and, in few tens of meters, shear wave velocities of the shallower soil layers may vary. The subsurface soil-profiles available for some strong-motion stations are collected in the Italian accelerometric archive ITACA. Specific shear wave velocity profiles are used when available (stations AQK, AQG, AQV, MI03, BZZ, GSA, AVZ, see Figure 2). To properly describe the high-frequency spectral decay of synthetics we adopt the kappa factor (k), introduced by Anderson and Hough (1984). We adjust the k value for stations with subsurface velocity profile, while we fix it to 0.01s for the generic rock stations (Table 1) Broadband source modeling: setup In order to build the broadband source model, we have to fix fault geometry and basic rupture propagation characteristics. These are found by inverting strong motion data in the low frequency range (< 0.5 Hz) as explained briefly in this section Centroid moment tensor (CMT) We first invert for the location and fault-mechanism of the largest L Aquila aftershock using the ISOLA software. ISOLA calculates the moment tensor by least-squares fitting of complete observed displacement seismograms with full-wavefield synthetics computed in a 1D regional crustal model (Table 2). 10

11 The position of the centroid is grid-searched in both horizontal and vertical directions. We use low-frequency data filtered in range Hz, i.e. below the corner frequency of the event, thus a delta function can be considered as the moment-rate function. To satisfy the condition of a pointsource approximation, we select stations farther from the source with rather regular azimuthal coverage, namely stations RM13, CLN, CSO, FMG, ANT, MTR, GSA, and SUL (Figure 1). The non-double-couple percentage for the final solution at optimized centroid position is quite small (<10%), therefore we report hereafter only the double-couple focal mechanism (strike: 346, dip: 63, rake: -61 ; scalar seismic moment M 0 = 1.51*10 17 Nm, Mw=5.4).The focal mechanism is very stable within ~5km of the optimal source position, both in the horizontal and vertical direction. The variance reduction over the three-component waveforms is 0.65 (see Equation 1). The centroid position and the corresponding focal mechanism are shown in Figure 1. The CMT parameters are in good agreement with those found by other authors (see Table 4) Homogeneous slip patch model We then invert for a finite-extent rupture model, increasing the upper frequency limit to 0.5Hz and considering all stations available (Table 1 and Figure 1). The low-pass filtering frequency 0.5Hz is limited by our ability to approximate real 3D structure by the 1D layered crustal models in terms of Green s function modeling. We assume a fault plane passing through the centroid with orientation given by the centroid strike and rake. Out of the two nodal planes of the CMT solution we select the plane antithetic to the major L Aquila fault, as suggested by Chiaraluce et al. (2011). We assume a homogeneous rectangle centered in the centroid and setup trial nucleation points, rupture velocities and origin times. Then we perform a grid-search over the trial values of the parameters to find the best-fitting model, as explained in the Methods section. We also try various rectangle dimensions, fault locations (2km steps) and strike and dip angles of the fault plane (5 steps). The optimal solution is located at the same place as the centroid identified by ISOLA, while 11

12 the dip value is modified from 63 to 58, particularly improving the fit at RM01 and RM02 stations (Figure 1). The best model is characterized by 6x6 km large slip patch, rupturing from the fault center at 3km/s, with slip of 9.4cm, and seismic moment M 0 =1.47*10 17 Nm. The model and the fit between observed and synthetic displacements (variance reduction VR=0.53) are shown in Figure 3. The fit is very good especially at close stations. At larger distances the 1D crustal model cannot explain the later arrivals of the observed data. Figure 3 also shows the analyses of the uncertainty of the subsource parameters and the parameter values for all models having VR at least 0.95 times the best VR. In general, while the slip value and nucleation time are relatively stable (8-12 cm and s, respectively), the rupture velocity has the greatest uncertainty (2-3.5 km/s). The uncertainty of the nucleation point also suggests a minor possibility of NW rupture propagation. We note that in the same sense of fit quality, the uncertainty of slip patch size and position on the fault was estimated as ±1km Broadband source parameters We adopt the fault of 6x6km found in the inversion as the strong motion generation area for the broadband modeling (see section Methods and Appendix). We assume a maximum number of subsources N=8, implying a total of 63 subsources. The subsources are distributed randomly over the fault plane with possible overlap, except for the two largest subsources that are placed in the fault center. We assume radial rupture propagation from the hypocenter at constant speed of 3km/s. The subsource distribution together with the resulting source time (moment rate) function and its Fourier (omega-squared) spectrum are shown in Figure 4. We perform the broadband simulations up to 10Hz for 20 stations located within 30 km from the epicenter, having a specific shear wave velocity profiles or generic rock profile in case of limited site effects (Table 1, in bold). We performed the simulations testing different rupture velocities, distribution of subsources, position of nucleation point on the fault, etc., assuming ranges 12

13 as suggested by the preliminary low-frequency inversion. Evaluating model bias against observed data in terms of response spectra and peak values (see below), the trial-and-error approach results in the final setup of source parameters as listed in Table Broadband source modeling: results One of the aims of our study is to test the performance of the 1D broadband modeling for moderate events. Figures 5 and 6 show the comparison between simulated and observed velocity and acceleration waveforms, respectively, for 10 selected stations (the comparison for the other 10 stations can be found in Figures S1 and S2, available in the electronic supplement to this article). Despite of the simplicity of the modeling, the fit in terms of peak values, duration and waveform complexity is generally good (see, e.g., stations RM02, RM03, RM09, FMG). The 1D modeling can reproduce the most relevant features of ground motion, such as direct P and S waves (including their multiples due to the horizontal stratification of the crustal model), and the strong P and SV wave groups observed on the vertical velocity components. On the other hand, 1D modeling cannot reproduce coda and later surface waves. Nevertheless, strong later arrivals are only relevant for the stations located on very soft sites or affected by 2D/3D site effects (e.g. stations AQK, AVZ, RM11). Figure 7a shows the modeling bias in terms of pseudo-spectral acceleration (PSA), as proposed by Mai et al. (2010). The mean bias of the three components is 0.36 (in natural logarithm units), meaning a minor underprediction of the observation. This can be explained by the lack of sitespecific soil profiles for a proper modeling of the broadband amplification. The strongest bias at NS and EW components visible in Figure 7a corresponds to station AQK. The records at AQK contain strong mid-frequency (~1Hz) surface waves of long duration (see Figures S1 and S2, available in the electronic supplement to this article) due to the presence of a deep sedimentary structure (Bergamaschi et al., 2011), which cannot be reproduced by 1D Green s functions. The standard 13

14 deviation (σ) of the model bias is 0.6, which is in agreement with the quality of other modeling results (Hartzell et al., 2011). The peak values (PGA and PGV) decay with distance is also in agreement with the ground motion prediction equation proposed for the Italian territory by Bindi et al. (2011), as shown in Figure 7b. In particular, the broadband modeling explains correctly the observed PGA values at both vertical and horizontal components, although they generally exceed the median GMPE curve by Bindi et al. (2011). Interestingly, our stress drop values, controlling mainly the strength of the high-frequency source radiation, is equal to 10MPa, which is lower than that found by other empirical studies, such as those based on empirical generalized inversion of strong motion data (Bindi et al., 2009; Ameri et al., 2011b), or on empirical Green s function technique (Calderoni et al., 2013). However, the comparison among stress-drop estimates obtained from different approaches is not straightforward due the trade-off among source and attenuation parameters. The comparison with the 1D synthetics documents that observed waveforms are basically dominated by 1D propagation effects in a broad frequency range. In the following, we examine the match and mismatch of the waveforms in order to discriminate source, path and site effects at individual stations Comparison between observed and simulated data in terms of polarizations As shown in the previous section, the synthetics fit well the observed ground motion at low frequencies (displacement waveforms in Figure 3b), where the partitioning of energy between horizontal components is mainly driven by the source radiation pattern with only minor alternation due to the path and site effects. The approach taken in this study, including random perturbations of the focal mechanisms of the subsources, partially reduces the radiation pattern effect at high frequencies and has, in general, a good performance to reproduce the observed ground motion (velocity and acceleration waveforms in Figure 5 and 6, respectively). Nevertheless, in some cases the energy partition between horizontal components at high frequencies cannot be completely 14

15 captured. For example, at GSA station the simulated velocity and acceleration waveforms show a dominant motion in the NS direction, while, in contrast to the simulations, the observed waveforms have similar amplitude at the horizontal components (see Figures 5 and 6). At station RM01, although the NS ground motion direction prevails in the observed acceleration waveforms, the synthetics exhibit similar amplitude for both horizontal components (Figures 5 and 6). To better understand such bias, we analyze the particle motion in five octave frequency bands from 0.3 and 9.6 Hz at the 10 selected stations. Figure 8 shows, for each frequency band, the comparison between synthetic and observed particle motions, relative to the dominant S-wave group. The particle motions are plotted considering a 5s time window of the velocity waveforms, starting from the S-wave arrival. To further highlight the predominant direction of the polarization, Figure 8b shows the polar diagrams of the peak ground velocity within the same time window and in the same frequency bands used to plot the velocity particle motions. In general, the behavior of the observed particle motion is more chaotic than that of the synthetic, especially at high frequencies. This result is not surprising, due to the simplicity of the 1D modeling and suggests that that the random variability of the focal mechanism introduced at small scales (see Methods) is not enough to reproduce the incoherence of the recorded ground motion. Nevertheless, careful comparison reveals that in some cases the synthetics are in agreement with the observations. Based on the shape of the observed particle motions with respect to the synthetic ones, we can group the stations into three classes as outlined in Figure 8. Stations in Class 1, exemplified by AQV, MI03 and RM13 in Figure 8, exhibit a chaotic particle motion with a rather circular pattern at frequencies larger than ~2 Hz, contrary to the linear polarization of the synthetics. Such behavior is typically explained in literature as a consequence of scattering due to wave propagation in random media (Kennett, 1981; Takenaka et al., 2003; Liu et al., 2006; Castro et al., 2006). Stations of Class 2 (see RM13, RM14, and RM03 in Figure 8 as examples) exhibit predominantly linear particle motion in a broad frequency range. In this case the polarization direction is in agreement with the 15

16 simulated wavefield. In Class 3, stations (RM01, RM02 and GSA are examples) have almost linear polarization in a broad frequency range (up to 5 Hz), but with directions diverging from the synthetic one (see Figure 8) Polarization and directional site effects To analyze the effect of site on the ground motion in more detail, we analyze azimuthally dependent H/V spectral ratios from several other aftershocks of the seismic sequence considered in this study. Figure 9 shows mean H/V amplifications at different azimuths (measured from north) for the same stations as in Figure 8, considering either 5s time windows containing the major S wave phases (left panels) or coda wave group (right panels). The coda is composed by scattered waves incoming from all directions, therefore the persistence of a directional amplification in the coda should indicate site effects independent on the back-azimuth of the source. Both shear and coda waves at stations AQV and RM13 reveal rather strong directional amplification at ~40 in range of 2-3Hz and 3-6 Hz, respectively, suggesting a strong site effect. Similar result for AQV stations was revealed also by Puglia et al. (2011). This direction is apparent in the polarization of the aftershock recordings at the two stations in the corresponding frequency range ( Hz in Figure 8). Note that the synthetic (incoming) wavefield is polarized in the same direction as the site effect (see the 1D synthetics in Figure 8), therefore the polarization of the incoming wavefield (~30 ) is not significantly altered and the two effects couples. At higher frequencies (5-10 Hz) the polarizations become circular for both stations. Station MI03 exhibits directional amplification, although with incompatible azimuthal dependence between the S and coda wave groups (see Figure 9). Note that observed MI03 recording has circular particle motion at frequencies larger than 5 Hz (Figure 8). Being located on rock sites, stations RM14, FMG, and RM03 do not show significant directional amplification (Figure 9), indicating that the site contribution of those stations does not alter the incoming source polarization. RM09 is amplified for frequencies larger than ~8Hz with 16

17 maximum in the northern direction. Nevertheless, since even the polarization of the synthetic wavefield is predominantly NS, it is likely that both the source and site effects couple as in the case of RM13 (see above). RM01 has multiple weak amplification maxima for frequencies >~1Hz all occurring in the NS direction (Figure 9), consisting with the polarization direction of the recorded ground motion, as evidenced in Figure 8, while the synthetics are polarized at NE-SW direction (Figure 8). Both RM02 and GSA exhibit either no or rather weak directional site effects (Figure 9). Thus the observed frequency dependent variation of the direction of the linear polarization cannot be fully attributed to the site effect, and can thus be linked to the path effect Discussion A striking result of our study is the persistence of high-frequency linear polarization of the wavefield observed at some stations for the largest aftershock (see the particle motions in Figure 8, Class 2 and 3). A natural question is whether such a polarization behavior can be observed also for other events. This is analyzed in the next section. After that we interpret and discuss the present findings Linear polarization at high frequencies: other aftershocks In order to verify the persistence and the nature of the high-frequency linear polarization at stations RM01 (Class 3) and RM14 (Class 2), we also analyze the behavior of the observed particle motion for other five aftershocks (M ) of the seismic sequence. With respect to the already examined largest L Aquila aftershock, these aftershocks are characterized by similar mechanisms but different back-azimuths and shallower depths (< 15km). 17

18 The polar diagrams of the rotated peak velocity, analyzed in the same frequency bands as for the largest aftershock, are shown in Figure 10 (while in Figure S3, available in the electronic supplement to this article, the plot of the particle motion is also reported). For station RM01 the particle motions of all events are almost linear at high frequencies (2-10Hz) and, independently of the source back-azimuth, they are persistently oriented in the NS direction. This confirms that the directional site-effect dominate in the wavefield polarization over the source and path contributions. On the other hand, RM14 exhibits rather chaotic circular particle motion at high frequencies (2-10Hz, see Figure 10) for the minor aftershocks. Therefore, we interpret the high-frequency linear polarization observed for the largest aftershock (Figure 8) as a prevailing source radiation effect. Moreover, as the linear polarization for the RM14 station is only evident for the main aftershock (15km deep) we also interpret the loss of linear polarization at high-frequency observed in case of the shallower aftershocks (<15km) as an effect associated to the source depth. We hypothesize that since waves radiated by shallower events propagate more horizontally than in case of deep events, the observed wavefield is more affected by the scattering due to the lateral heterogeneities of the medium Linear polarization at high frequencies: interpretation and implications The persistence of high frequency almost linear polarization observed at some stations is apparently in contradiction with empirical and theoretical studies dealing with the significance of the source-radiation pattern in strong ground motions. For example, Satoh (2002), Takenaka et al. (2003), Takemura et al. (2009) and Castro et al. (2006) conclude that the radiation pattern vanishes with increasing frequency. However, those studies are based on averaging over a relatively large number of events, where the averaging procedure could smooth out particular cases and/or trends, such as the dependency of the high frequency polarization on the source depth, distance, or other characteristics. Additional smoothing effect is introduced by analyzing a large number of stations with potential presence of directional site effects at various azimuths. As consequence, the 18

19 peculiarity of an individual event, like the one examined in this study, might be lost in the averaging procedures. Indeed, Vidale (1989), who analyzed radiation pattern of two individual seismic events, found a persistent radiation pattern up to high frequencies, in agreement with our study. The above-mentioned empirical studies invoke wave propagation modeling to explain the distortion of the radiation pattern at high frequencies by means of scattering in random media (Takemura et al., 2009; Imperatori and Mai, 2012). In particular, Imperatori and Mai (2012) prescribed fractal velocity perturbations with standard deviation of 5-10% down to 15km depth, leading to strong reduction of the source effects (radiation pattern, directivity) in the synthetics. Note that conclusions of those studies are again based on averaging over many sources/receivers, with the same undesired smoothing consequences. We hypothesize that the observed persistence of linear polarization at hard-rock sites (RM14, RM03) imply that the path effect in the deeper crust is not enough strong to reduce the highfrequency linear polarization due to source. In particular, the deep crust (~>1km) should be considered relatively homogeneous (the velocity perturbations can have standard deviation <10%) and the 1D deterministic modeling applied in the present study can be considered appropriate. The destruction of the incoming linear polarization we observe at some stations (AQV, MI03) can be then ascribed to rather strong ( >10%) heterogeneous very local subsurface structure. In the same sense, strong directional site resonance can lead to linear polarization at azimuth being independent on the source radiation. Our interpretation has also consequences on the relative importance of source directivity effects. Strength of the directivity effect depends on rupture process complexity (i.e. smoothness of rupture front) and wave propagation features through heterogeneous media (i.e. smoothness of S-wave front). It is still not well established to what extent the directivity effects disappear at high frequencies (Somerville et al., 1997; Day et al., 2008). In the light of the results achieved in this study, we deduce that, in case of not-efficient scattering at large crustal depth, the directivity effects 19

20 at high frequency could be reduced at the source instead of along the propagation path or can persist also at high frequency. We admit that further studies based on observations or modeling are needed to support our conclusions. We defer more detailed empirical study on frequency dependent particle motion, recognizing that a comprehensive study will eventually require systematic analysis of a large number of earthquakes, taking into account their depth and source-to-site geometries Conclusions This study employs high-density strong motion recordings to analyze the largest Mw5.4 aftershocks of the 2009 L Aquila, Italy, seismic sequence. Low-frequency waveforms (< 0.5 Hz) are used to invert the centroid, fault plane solution, and slip distribution in terms of a single homogeneous patch with constant rupture propagation. The optimal fault plane is 6x6 km large and is considered in broadband modeling (up to 10Hz) of strong ground motions at stations for which 1D subsurface velocity profile is known and at other rock-site stations assuming generic 1D rocksite profile (Table 3). Full-wavefield deterministic 1D Green s functions are used in the whole frequency range. Note that broadband modeling of such a moderate magnitude event is challenging, because the duration of the source is rather short and thus the site and propagation effects might dominate some records. The use of stochastic Green s functions is avoided in this paper because it would not allow us to discuss the role of propagation effects in the observed data. The overall goodness of fit between simulated and observed waveforms obtained in this study suggests that the 1D Green s function model can be adopted, keeping in mind some limitations. The modeling performs well in terms of peak ground-motion values. Moreover, in case of rock stations, the strong motions are correctly predicted even in terms of their duration, suggesting that the dominant S wave group is composed of S waves multiples and weak scattered waves. As expected, the 1D Green s functions fail in reproducing the duration and the energy content of the ground 512 motion recorded at sedimentary basins, although peak displacements are still correctly predicted. 20

21 Modeling of the Mw5.4 aftershock of the L'Aquila earthquake using 1D deterministic Green's functions has proved to be surprisingly successful in broad frequency range (up to 10Hz), perhaps due to the relatively large depth (15km) of the event. Careful analysis of S-wave group polarization at high frequencies (HF) has revealed that while some stations retain the predominantly linear polarization in accordance with the 1D modeling, other stations show a peculiar mismatch. The latter is either expressed by chaotic circular polarization or by polarization remaining linear but at different angle. We interpret these observations as a consequence of strongly depth-varying scattering crustal properties, being relatively weak at larger depths. In particular: For the deep event at rock stations with no site amplification the 1D source linear HF polarization is preserved because the waves travel rather short path in the shallow scattering medium. Contrarily, for shallower events with longer path in the heterogeneous subsurface crust, the scattering "destroys" the linear polarization, resulting in the observed circular chaotic particle motion. At stations with strong site effects associated with very heterogeneous subsurface structure, the linear polarization is "destroyed" in any case. In case of a strong azimuthal dependence of the site-effects (associated perhaps with effectively anisotropic heterogeneous structure), the HF particle motion can be linearly polarized in accordance with the maximum amplification direction, irrespectively to the source radiation Data and Resources Waveforms and site classes were provided by the Italian Strong Motion Database (ITACA, Many of the figures were prepared using the Generic Mapping Tools package ( All electronic addresses referenced here were last accessed February

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31 Appendix HIC model is developed for earthquake ground-motion simulations following omega-squared source model with amplitude spectrum: 806 ( ) ( ), (A1) where M 0 and F C are the seismic moment and corner frequency of the target event, respectively. The acceleration spectrum has a plateau described as: ( ) ( ) ( ). (A2) The corner frequency of the target event can be converted to standard Brune stress drop Δσ (Keilis-Borok, 1959; Brune, 1970) as F C =49β(Δσ/M 0 ) 1/3, β being the shear wave velocity (3.5km/s in our application). Stress drop Δσ is determined through the fit with the observed high-frequency seismograms. The source model formally consists of subsources with number-size distribution with fractal dimension D = 2. For simplicity, the subsources are assumed rectangular with length l k and width w k given by integer fractions of the fault length L and width W, i.e., of sizes l k =L/n and w k =W/n, where the level n = 2 N. For the particular number-size distribution the number of subsources at level n equals to 2n-1. The variable size of subsources is advisable in composite source modeling as it overcomes problems with the definition of the size of the subsources and related deficiency in radiation at mid frequencies (Irikura and Kamae, 1994). We assume that the subsources radiate Brune source time functions being described by seismic moment m k 0 and corner frequency f k C with the complex Fourier spectrum 823 ( ) ( ), (A3) where i is the imaginary unit. Assuming that slip is proportional to the subsource length (the constant stress drop scaling), the subsource seismic moment and corner frequency depend on the size of the subsource as m k 0 =c 1 μl 2 k w k and f k C =c 2 v r /l k, respectively, where μ is the shear modulus and v r the rupture velocity. 34

32 Constant of proportionality c 1 for the seismic moment is such that the sum of seismic moments of all subsources is equal to the target seismic moment, i.e (A4) Assuming incoherent summation of the subsource contributions, constant of proportionality c 2, related to corner frequency f C k, is such that the target acceleration power-spectrum plateau matches the plateau of the sum of the subsource acceleration power spectral plateaus, i.e., 834 ( ) ( ) (A5) Let us point out that although the subsources share the same stress drop, its particular value is not the same as the target stress drop. This is so because it is theoretically impossible to create a fully self-similar source model, where both seismic moment and high-frequency plateau of the target omega-squared spectrum would be fitted by subsources following constant stress drop scaling and having omega-squared spectrum (Frankel, 1991). Therefore, the decomposition of the source model into subsources is to be considered just as a formal representation to introduce a complex omega-squared source radiation. We emphasize that the important physical feature of our model is that the fractal decomposition of the source model implies k -2 slip distribution (demonstrated by 843 Gallovič and Brokešová, 2007, or Ruiz et al., 2011 and 2013) and, consequently, k -1 stress distribution. The latter spectral fall-off was shown to be physically plausible on the basis of theoretical considerations by Andrews (1980)

33 848 Figures Figure 1: Map view of accelerometric stations considered in this study and centroid moment tensor inferred by the ISOLA method (low-frequency full-waveform inversion). Rectangles represent the fault models considered in this study; the empty rectangle is considered when searching for a finiteextent homogeneous source model, while the result of this search is represented by the grey-filled fault (the latter fault is also used for broadband modeling). The highlighted side of the fault corresponds to its top side. Relocated seismicity after Valoroso et al. (2013) in the depth range of the grey fault (13-17km) is shown as grey points. The white star represents the event location by Chiaraluce et al. (2011)

34 Figure 2: Subsurface structure, solid VS, dashed VP. The ROCK profile (presented also in Table 3) corresponds to generic rock-site model considered for the rock stations (see Table 1)

35 Figure 3: Finite-extent source inversion considering a rectangular patch of homogeneous slip and constant radial rupture velocity. (a) Best model in terms of rupture times (left) and slip (right) distribution from grid-search over 9 trial nucleation points (numbers 1-9 in the left plot), rupture velocities and nucleation times; the slip value is inferred using linear least-squares method. The fault is shown in map view in Figure 1. (b) Comparison of displacement waveforms for the best model in (a). The amplitudes are normalized to a common value over all components of real data for each station; the normalization value is depicted on right in mm. (c) Uncertainty analysis of the source parameters from the grid-search. Each panel corresponds to a given parameter. Each point represents a successful model (with variance reduction, VR, better than 0.95 of the best VR) and the respective parameter value as a function of its respective VR

36 Figure 4: Composite source model used for simulation of the strong motion recordings. The left plot shows random distribution of fractal subsources composing the whole source. Each subsource is represented by a point source and its source time function is the Brune pulse, characterized by its rupture time, seismic moment and stress drop. The largest subsource has seismic moment of 2.2e16Nm and stress drop of 4.4MPa. The smaller subsources are scaled assuming constant stress drop. For the sake of clarity, the subsource dimensions are three times smaller than their respective Brune radius. The summation of time function contribution of individual subsources results in the source time function (the moment-release rate) shown in the top right plot. The bottom right plot shows its Fourier amplitude spectrum and is compared with the Brune spectrum with seismic moment of 1.5e17Nm and stress drop of 10.6MPa (see Table 3). Note that there are two largest subsources overlapping in the center of the fault

37 Figure 5: Result of the broadband (0.1-10Hz) simulation using the model shown in Figure 4 in terms of velocity waveforms. The amplitudes are normalized to a common value over all components of real data for each station; the normalization value is depicted on right in cm/s. 40

38 Figure 6: Same as Figure 5, but for acceleration waveforms. Normalization amplitudes are given in cm/s 2. 42

39 Figure 7: (a) Modeling bias (see its definition in Mai et al., 2010) in terms of (left) pseudo-spectral acceleration (PSA), and (right) peak ground acceleration (PGA) and peak ground velocity (PGV) for individual stations (gray curves and symbols) and components (rows). Solid black lines and the dashed lines represent the mean model bias and the standard deviation, respectively; in PGA and PGV the mean and standard deviation are plotted by the circle and the vertical bar, respectively. Positive bias means underprediction. (b) Comparison of observed and synthetic data with Ground Motion Prediction Equations (GMPEs) by Bindi et al. (2011) for PGA (top) and PGV (bottom). Geometric mean of horizontal components is considered in consistency with the definition of GMPE

40 Figure 8: (left) Frequency dependent particle motion (velocities) for the largest aftershock and for ten selected stations (rows). In all cases 5s long main S-wave group is tapered and filtered in the given frequency range (depicted above each column). The particle motions are normalized according to the maximum horizontal (vector) amplitude. (right) polar plot of the peak velocity of rotated horizontal component. Note the three basic classes of high-frequency polarization behavior: Class 1 - linear particle motion in the synthetics and chaotic circular behavior in the observations; Class 2 - linear particle motion in both the synthetics and the observations; Class 3 - linear particle motion in the whole frequency range for both synthetics and observations, but with a diverse polarization direction between observations and synthetics. 44

41 Figure 9: Analysis of azimuthal variation of H/V spectral ratios from many aftershocks at the 10 selected stations. Panels show H/V amplification as a function of frequency and azimuth (measured from north) considering 5s long main S-wave group (left) and coda wave group (right). Arrows denote backazimuths of events that were taken into account

42 Figure 10: Observed polarizations for other five strong aftershocks for station RM01 and RM14 plotted in terms of peak velocity of rotated horizontal component. Legend describes the aftershocks and the causative faults. The events are depicted on the map (right) together with the location of the largest aftershock (denoted as Mw5.4) for reference. The mechanisms and locations (including the depth denoted in the legend) are adopted from Herrmann et al. (2011). 46

43 Supplemental Material (Main Page) Click here to download Supplemental Material (Main Page, Tables, Figures): LAquila-aftershock-v2-electronic.supplement.docx Electronic Supplement to Polarization of Strong Ground Motions: Insights from Broadband Modeling of Mw5.4 Aftershock of the 2009 L Aquila, Italy, Earthquake 4 5 by F. Gallovič, F. Pacor, J. Zahradník, L. Luzi, R. Puglia, and M. D Amico Additional waveform fits and particle motion plots Two figures show fit between simulated and observed velocity (Figure S1) and acceleration (Figure S2) at ten additional stations. They represent extensions of Figures 5 and 6 of the main text, respectively. Third figure (Figure S3) shows particle motions for the other five strong aftershocks for stations RM01 and RM14, thus extending Figure 10 of the main text Figure S1: Result of the broadband (0.1-10Hz) simulation using the model shown in Figure 4 in terms of velocity waveforms (extension of Figure 5). The amplitudes are normalized to a common value over all components of real data for each station; the normalization value is depicted on right in cm/s Figure S2: Same as Figure S1, but for acceleration waveforms (extension of Figure 6). Normalization amplitudes are given in cm/s Figure S3: Observed particle motions for other five strong aftershocks at stations RM01 and RM14. Legend describes the aftershocks and the causative faults. The events are depicted on the map (right) together with the location of the largest aftershock (denoted as Mw5.4) for reference. The mechanisms and locations (including the depth denoted in the legend) are adopted from Herrmann 26 et al. (2011). 1

44 Supplemental Material (Figure 1) Click here to download Supplemental Material (Main Page, Tables, Figures): FigureS1.eps

45 Supplemental Material (Figure 2) Click here to download Supplemental Material (Main Page, Tables, Figures): FigureS2.eps

46 Supplemental Material (Figure 3) Click here to download Supplemental Material (Main Page, Tables, Figures): FigureS3.EPS