A station (FAGN) installed on a segment of the fault system that generated the April 2009 L'Aquila earthquakes shows larger ground motions compared to nearby stations. Spectral ratios using 304 earthquakes result in a station amplification significantly varying event by event in the frequency band 1–8 Hz. The resulting pattern of amplitude dependence on causative earthquake location reveals that the strongest (up to a factor of 10) amplifications occur for tightly clustered aftershocks aligned with the fault dip beneath FAGN thus indicating a fault-guided effect. Fault models are investigated in a grid-search approach by varying velocity, Q, width and depth of the fault zone. Although the problem solution is not unique and there are strong trade-offs among the model parameters, constraints from observations yield a deep trapping structure model where the most likely values of velocity reduction, Q and damage zone width are 25%, 20, and 280 m, respectively.
 Starting on April 6, 2009, three earthquakes with magnitudes Mw 6.3, 5.6, and 5.4 occurred within 4 days near the city of L'Aquila [Chiarabba et al., 2009; Di Luccio et al., 2010]. The three beach balls in Figure 1a indicate their epicenter position and focal mechanisms, that are consistent with the ruptures of NW–SE striking normal faults already documented after geological studies [Vezzani and Ghisetti, 1998; Galadini and Galli, 2000]. After April 6, a long sequence of aftershocks was recorded by the Italian seismic network of the Istituto Nazionale di Geofisica e Vulcanologia (INGV).
 This study has originated from the observation of systematic larger amplitudes of ground motion at one (FAGN) of the permanent broadband stations of the Italian Seismic Network run by INGV. A local amplification at a station is not surprising in itself: it is well known that near-site geological variations with a decreasing velocity near the surface can amplify ground motion. Although limestone outcrops no more than a hundred metres from the station, FAGN is not deployed on hard rock as proved by shallow boreholes drilled around the station that show evidence of poorly consolidated rocks below the surface. Moreover, FAGN is located on the San Demetrio normal fault trace as mapped by Vezzani and Ghisetti . The presence of a fault zone beneath the station could favour local amplifications as well [Davis et al., 2000; Cultrera et al., 2003; Karabulut and Bouchon, 2007].
 Due to this site complexity, larger amplitudes at FAGN are not out of the ordinary. What is less usual is that the difference in amplitude, compared to nearby stations, is extremely large for some particular events and negligible for others of the same seismic sequence. This peculiar feature has motivated a systematic analysis using 304 aftershocks. We have estimated an amplification parameter for each event and then analyzed its variation as a function of the location of the causative shock. The strongest amplifications are found whenever source backazimuth and incidence angle favour the wave propagation inside the fault zone beneath the station. For source-to-receiver paths external to the fault zone, the amplification is much smaller: this indicates that the amplification is caused by the wave-guide effect in the fault zone. Trapping structure properties are then investigated in a grid-search approach and, in spite of the strong trade-offs among the model parameters, their variability is confined to narrow intervals: the most likely values result in fault zone widths of 280 m ± 40 m, velocity reductions of 25 ± 5% and Q values of 20 ± 10.
2. Stations and Data
 The L'Aquila seismic sequence was recorded down to small magnitudes by the 24-bit broad-band seismological stations run by INGV. Waveforms and seismic parameters are available online http://iside.rm.ingv.it. This study is based on the analysis of waveforms from three (namely FAGN, AQU, and FIAM) stations installed in the epicentral area (Figure 1a). AQU and FAGN are aligned NW–SE, approximately, parallel to the strike of the causative fault system. AQU is installed in a 20-m deep underground cavity beneath the ancient castle of L'Aquila, a few kilometres from the two strongest shocks. The castle was built on the stiff “Megabrecce” geological unit that characterizes the seismic response of downtown L'Aquila. FAGN is located 17 km southeast of AQU, on the San Demetrio fault [Vezzani and Ghisetti, 1998]. The receiver is installed on a shallow layer of slope debris overlying stiff mudstone. The debris-mudstone interface, as revealed by boreholes drilled at about 50 m from the station is to a depth of 15 m. A comparison of records of FAGN with records of a nearby temporary station (FA00) deployed on mudstone indicates that the impedance contrast at this interface is not responsible for a large local amplification effect (auxiliary material Figure S1). The third station FIAM is installed 25 km west of FAGN. The geological conditions of FIAM are similar to the ones of FAGN: limestone outcrops tens of meters away from the station, and the receiver is installed on a slope debris layer of unknown thickness and geometry.
 After stringent visual inspection, we selected 304 well recorded aftershocks. The constraints for the event selection were i) availability of good-quality (no spikes or lack of samples due to data transmission) digital records at all of the three stations, and ii) occurrence of only one shock in each time window, avoiding simultaneous shocks or earthquakes in the coda of others. The resulting magnitude range was 1.8 ≤ ML ≤ 4.1. The upper limit is constrained by the signal saturation at larger magnitudes. However, because of the implicit assumption of a point source model in the analysis, the source size has to be significantly smaller than source-to-receiver distance, and larger events do not fit this requirement. The lower magnitude limit is imposed by the need of a satisfactory signal-to-noise ratio of records. The selected data set is representative of the entire data set in terms of space and time distribution.
 All the seismograms were deconvolved by the instrument transfer function to get ground displacement in the time domain. The analyzed frequency band was 0.4–10 Hz, although the largest events have a much larger usable bandwidth.
 The basic observation of this study is the large amplitude variation among the three broad-band stations. In particular, FAGN recorded extremely large amplitudes during some aftershocks. Figures 1b and 1c shows an example of the amplitude anomaly. For that event, the source distances of AQU, FAGN, and FIAM are 16, 13, and 32 km, respectively. Both ground displacement amplitudes of Figure 1b and Fourier spectra of Figure 1c were scaled to the same source distance (15 km) assuming a 1/R geometrical spreading.
 The traces in the left-hand side of Figure 1b illustrate to what extent the ground displacement of FAGN exceeds the one of the other two stations. Interestingly, at low frequency (f < 1 Hz), the three stations have recorded comparable amplitudes (Figure 1b, traces in the right hand side). This rules out instrumental problems or a bias due to source radiation pattern which should be most evident in the low-frequency component. The large high-frequency amplification of FAGN begins after direct S-arrival and lasts more than twenty seconds (see also auxiliary material Figure S2), suggesting a complex amplification effect caused by heterogeneities at different scales. Figure 1c shows in what frequency band the ground motion of FAGN exceeds the one of the other stations. Compared to AQU, there is a distinct increment between 1 and 8 Hz. Note that also AQU exceeds FIAM in amplitude but to a smaller extent. FIAM has the most regular spectral shape, it is well fitted by a Brune  model spectrum. In Figure 1c, a stress drop of 0.7 MPa is used, according to the Calderoni et al.  source scaling assessed for the L'Aquila seismic sequence. The quality of this fit rules out an interpretation in terms of high stress drops for the events with large high-frequency content.
Figure 1c suggests that the spectral ratio FAGN/AQU can be a useful tool to assess the amplification of FAGN when amplitudes are compensated, to a zero order approximation, through a 1/R correction. This approach is acceptable considering that hypocentral distances are sufficiently larger than the source size of the selected aftershocks. We therefore have computed the spectral ratio FAGN/AQU for all the selected earthquakes, and compared them with the spectral ratio FIAM/AQU of the same events. Fourier spectra were computed over 10 sec windows of the three components, and smoothed with a 0.2 Hz running box. A geometric mean was computed for the vertical component spectral ratios over the event ensemble; similarly, the geometric mean for the horizontal motions was computed by averaging altogether the NS and EW spectral ratios. The resulting ±1 standard deviation intervals around the mean of vertical and horizontal spectral ratios are shown in Figures 1d and 1e, respectively. Their comparison gives a clear indication of the significantly larger values of the FAGN/AQU spectral ratios compared to the FIAM/AQU ones. The latter depict a substantially flat trend, slightly below unity. Figure 1d stresses the large variability of FAGN, both in horizontal and vertical motions. Note that the maximum amplification of the vertical motions exceeds the one of the horizontal motions.
 To investigate the origin of the large variations as a function of the causative earthquake, for each event we have computed the average of the logarithm of the spectral ratio FAGN/AQU in the amplified frequency band 1–8 Hz. We call AMPi this quantity for the i-th event. Therefore, we have drawn a map where the epicenter of each event is represented in a colour scale which visualizes the individual AMPi values (Figure 2a). The resulting spatial pattern indicates that the amplification observed at FAGN is strongly dependent on the source location. The largest values of AMPi are found for earthquakes occurring in the southernmost portion of the aftershock cluster (those inside the green rectangle of Figure 2a). Figure 2b shows the projection of these events in a vertical plane orthogonal to the NW–SE strike of the normal fault system in the region. The location at depth of events causing the largest amplifications is consistent with a guided-fault propagation according to the 45° to 70° fault dip inferred by Galadini and Galli . The difference in amplification between events inside and outside the green rectangle is evident in Figure 2c where the ±1 standard deviation bands of the two groups show a small overlap.
 Estimates of the wave-guide amplification effect at FAGN of Figure 2a are based on spectral ratios between stations with different source azimuths and distances. Interdistance between stations is not small, and scaling to the same distance through a spherical geometrical spreading model, in principle, could not be precise enough to guarantee the absence of a bias in the amplification estimates. The lack of a compensation of anelastic dissipation could not be negligible when the difference in source distance between stations is large. Therefore, we made an independent check to measure the high-frequency amplification of each event, by computing the local magnitude ML at FAGN and comparing it with the average local magnitude of the seismic bulletin. This new amplification estimate is supposed to be similar to the spectral ratio one: a difference in magnitude is implicitly a ratio of amplitudes, being ML measured through the logarithm of the maximum peak-to-peak amplitude of each station.
 The pattern resulting from the magnitude difference between FAGN and the average value of each event is shown in Figure 2d. The satisfactory consistency between the ground motion amplification of FAGN in the two approaches (compare Figure 2d with Figure 2a) guarantees the reliability of individual event amplification at FAGN through spectral ratios. The FAGN/AQU spectral ratio computed over the events of the largest amplification cluster is then used as the target spectrum in a best fit procedure aimed at determining the geometric, elastic and anelastic parameters of the trapping structure. The fault zone is modeled as a uniform low-velocity channel where the constructive interference of critically reflected waves generates large-amplitude delayed phases at the surface (the so-called trapped- or guided-waves [see Li and Leary, 1990; Li et al., 1990; Ben-Zion and Aki, 1990; Li et al., 1997]). Amplitude, delay time, and frequency content of trapped-waves depend on the geometry and elastic and anelastic parameters of the fault. As exhaustively discussed by Lewis and Ben-Zion , the strong trade-offs among the fault parameters do not yield a unique solution but rather a range for the most likely values of four model parameters: the damage zone width (W), the length (L) of the low-velocity channel, the shear-velocity reduction (ΔVs) and the quality factor (Q) in the fault zone. The target spectrum TS(f) was computed using the spectral ratios of events falling in the green rectangle of Figure 2a. To give greater significance to events with a good coupling with the fault, we applied AMPi as a weight for each spectral ratio SR(f)i used in the average operation
where N=81 is the number of events falling in the green rectangle of Figure 2a. The result is shown in Figure 2e.
 We used the 2-D analytical solutions of Ben-Zion and Aki  and Ben-Zion  to generate synthetic seismograms of the different models. The target spectrum was fitted by varying W, L, ΔVs, and Q in a least-mean-square approach, having fixed shear-velocity and Q of the massive rock walls to 3000 m/s and 200, respectively. For each model, a spectral ratio is computed between the synthetic seismogram in the middle of the fault zone at the surface and the same position signal in a model where the fault zone has no (substantial) contrast with the external rock. From the time-domain waveforms and spectrograms, we infer that the largest-amplitude phases are delayed from direct S-waves (see the auxiliary material Figure S2). This time delay is of the order of 1 s for earthquakes at a source distance of about 10 km and increases linearly, approximately, as a function of source distance (see the auxiliary material Figure S3). The delay between the S and trapped waves could be related either to the length of propagation in the fault zone or, according to Lewis and Ben-Zion , to a velocity contrast between the rocks on the two sides of the fault zone. In our case, on a geological basis, we have no evidence for a different nature of rocks between the two sides of the San Demetrio fault. Therefore, we used the delay between the S and trapped waves as a constraint to limit the solution search to models where L and ΔVs yield the observed time delay. We then varied L, ΔVs being defined by this constraint and searched for the minimum misfit as a function of W and Q in a grid-search approach for different values of L. Increments on the grid were ΔW = 40 m and ΔQ = 10, in the intervals 40 < W < 1000 m and 10 < Q < 50. Figure 2e shows the best fit solutions for different values of L. Shallow models do not reproduce satisfactorily the shape of the target spectrum, whereas larger values of L improve the fit of the target spectrum, with the two model parameters W and Q resulting in stable estimates of 280 ± 40 m and 20 ± 10, respectively. The corresponding velocity reduction is 25%. The misfit variation for the different models is shown in the auxiliary material Figure S4.
5. Concluding Remarks
 This study shows observations of large ground motion variations at FAGN, a station near the normal-fault of San Demetrio, a segment of the fault system that generated the April 2009 L'Aquila earthquakes (http://diss.rm.ingv.it/diss/). This type of effects can have potential implications in earthquake engineering. Although nonlinear effects in the fault zone decrease bandwidth and amplitude at higher levels of strain [Karabulut and Bouchon, 2007], strong effects were already observed during damaging earthquakes [Cormier and Spudich, 1984; Davis et al., 2000; Spudich and Olsen, 2001; Ben-Zion et al., 2003; Lewis et al., 2005]. A previous study case in the Apennine did deal with an inactive fault in the town of Nocera Umbra, where an accelerometric station exceeded the anomalously large value of 0.5 g acceleration during many moderate-magnitude earthquakes of the Umbria-Marche seismic sequence [Rovelli et al., 2002; Cultrera et al., 2003]. Compared to these studies, the spatial variability around the fault near FAGN cannot be documented using a dense array as the closest stations (AQU and FIAM) are tens of kilometres away, and the seismograms of the strongest shocks were saturated. However, the consistent result obtained in terms of spectral ratios and ML anomaly confirms, also in this study, the occurrence of a large (up to a factor of 10 at low strain levels) amplification for earthquakes that travel in the fault zone.
 The authors wish to thank Antonio Fodarella, Gaetano Riccio, Rocco Cogliano, Stefania Pucillo, Giuliano Milana, and Fabrizio Cara that installed the temporary station of FAOO and performed geophysical site investigations. Paola Vannoli helped us in the reconstruction of local geology of FAGN. We have benefitted from useful discussions with Guido Ventura and Yehuda Ben-Zion, who also gave insights for the use of his codes. We thank the Editor Ruth Harris, Yong-Gang Li, and an anonymous reviewer for their very constructive critical comments.