Under the hypotheses that the high-frequency part of the seismic spectrum is controlled by source duration and by peak slip velocity, we applied a recent coda envelope methodology to obtain stable relative source estimates between selected mainshocks and their aftershocks. We computed stable mainshock/aftershock S-wave spectral ratios and used a simple source model in order to quantify the scaling of the seismic sources of the San Giuliano sequence (Southern Italy). From the analysis of the ratios obtained between the main shock of 10/31/2002, and 11 aftershocks, and of those computed between the other main event of the sequence, of 11/01/2002, and 10 aftershocks, we observe that the scaling relationships: M0 ∝ fc−(3+ɛ) holds, with ɛ = 0.89 ± 0.05. Despite the strong discrepancy between the moment magnitude and the high-frequency ground motion excited by the main shocks (ML was much lower than Mw), that would indicate low-stress drop sources, we compute anomalously high stress parameters for both events.By comparison, the same analysis was carried out on seismic data of the Hector Mine seismic sequence (the main event of October 16, 1999, MW = 7.0, and six of its aftershocks). We found: M0 ∝ fc−(3+ɛ), with ɛ ≈ 0.8 ± 0.4.
 Seismic spectra are usually described using the Brune omega-square source model, where the high-frequency seismic waves are interpreted by a quantity called static stress drop (ΔσS), which strongly trades-off with the geometrical and anelastic crustal attenuation, as well as with the spectral distortion induced by the shallow geology.
 Many studies [e.g., Malagnini et al., 2002], have recommended that no physical meaning should be given to the static stress parameter. Instead, a complete excitation/attenuation “package” is to be used in order to completely define the seismic spectra. Such package includes the static stress drop, ΔσS, the specific geometrical spreading, the crustal quality factor Q ≡ Q(f), and the average (or station-specific) site attenuation parameter, κ0. None of these quantities can be extracted from the mentioned set, and be meaningfully used in a different context.
 Some clarification about the physical meaning of the source parameters in the Brune spectrum was given by Beresnev , who argued against the use of the corner frequency (and so of ΔσS) to determine the radius of the earthquake source. In a subsequent study, Beresnev  demonstrated that the ω−2 source spectrum radiated by a displacement discontinuity of a given seismic moment depends only on two quantities: the source rise time and the peak slip velocity, both of which can be determined from either the recorded P- or S-wave spectra.
 In this study we analyze the seismic sequence started on October 31, 2002, when the first San Giuliano earthquake struck Molise, a region of southern Italy. We demonstrate that the two main shocks of this sequence delineate a very strong strike-slip fault, much stronger than the strike-slip structure responsible for the Hector Mine (California) earthquake, for which the same analysis is shown for comparison.
 The very strong coupling of the San Giuliano fault is not in agreement with the weak ground motion that was recorded during the two main events, and we suggest a qualitative explanation for such a discrepancy.
2. A Method for the Investigation of the Source Scaling
 K. Mayeda and L. Malagnini (An evolution of a new spectral ratio technique for the analysis of source scaling: An application to the Chi-Chi sequence, manuscript in preparation, 2008) designed a grid-search algorithm that uses a specific technique called Magnitude and Distance Amplitude Correction (MDAC) [Walter and Taylor, 2002], that was developed in order to discriminate between event types based on the differences observed in the regional body waves, such as the relative high frequency amplitudes of P and S waves (after path and source effects were quantified and accounted for). The mentioned algorithm is used to analyze network-averaged, coda-based spectral ratios, computed between the main event of a sequence, and all its available aftershocks.
 The advantages of using spectral ratios, or an empirical Green's function deconvolution, are that path and site attenuation corrections are not needed since the event pairs share common path and site responses. The coda-based spectral ratio method outlined by Mayeda et al.  improves upon the direct S-wave ratio methods because of the coda's stability. The coda averages over the source-radiation pattern and lateral crustal variations, thus allowing more events to be used in the analysis, resulting in spectral ratios that are 2 to 3 times less scattered than direct waves.
2.1. Apparent Stress Drop
 In the application described here, the MDAC code allowed the computation of the apparent stress drop, Δσa, for each event in the data set, and of its corner frequency, fc. The apparent stress drop is defined as:
(ER is the radiated seismic energy, M0 is the seismic moment, and μ is the rigidity).
2.2. Seismic Moment Versus Corner Frequency
 We use the functional form:
introduced by Kanamori and Rivera  in order to explain the increase of the lower bound of the normalized radiated energy, min, with the size of the earthquake, M0:
A grid-search is carried out on the best scaling parameter for each event (see Mayeda and Malagnini, manuscript in preparation, 2008, for details), in order to obtain an estimate of its corner frequency and apparent stress drop. Once we have a (M0, fc) data point for every earthquake, we can estimate the best ɛ in (2) for the investigated seismic sequence. Spectral ratios are fitted through the calibration of the scaling relationship (2).
2.3. Static Stress Drop
 In the Brune model, the static stress drop may be written as:
In equation (4), M0 is in dyne-cm, Δσs is in bars, and VS is the shear-wave velocity in km/sec.
 For each of the two seismic sequences analyzed in this study, the number of aftershocks is limited through a quality control performed on the available spectral ratios. Specifically, we define a 1.8 minimum bandwidth for each usable spectral ratio (log units, i.e., the ratio of the largest frequency to the lowest one must be larger than 63), and a minimum differential magnitude of 1.0. After this first screening, each average ratio is visually inspected to assure that bad data are not included in the analysis.
2.6. Standard Errors
 Standard errors are obtained by looping through the entire set of available spectral ratios, using the technique described by Mayeda et al.  in an iterative fashion. A different spectral ratio is used, on each iteration, for the calculation of the scaling properties of the main shock, with respect to the specific aftershock to which the ratio is referred. At the end of the procedure, specific distributions are thus available for all the estimated parameters (fc, ΔσS, Δσa, and Vmax), and so their standard errors can be given. Standard errors on ɛ are obtained by using a bootstrap technique.
3. The San Giuliano Seismic Sequence
 This sequence was characterized by two main events (same moment magnitudes, MW = 5.7, and similar, almost pure strike-slip mechanisms, depths, and source kinematics) [see Vallée and Di Luccio, 2005]. The main earthquakes were followed by a relatively small number of aftershocks at depths ranging between 10 and 20 km. Because of the low-level of observed ground shaking, both the main events were believed to be low-stress drop, and a parallel study by G. Calderoni et al. (Low stress drop in the October-November 2002 earthquakes in Molise, central-southern Italy: Evidence for reutilization of Mesozoic faults?, submitted to Journal of Geophysical Research, 2008) explains their low amplitudes at high frequencies as the result of the motion of a weak fault. In fact, there is a discrepancy between ML and Mw for both earthquakes: while Mw was the same for both (Mw 5.7), ML 5.4 and ML 5.0 were estimated, respectively, for the two earthquakes of 10/31/02 and of 11/01/02 (MedNet RCMT catalog).
 Notwithstanding the low amplitudes at high-frequency, the first earthquake will be remembered because of the collapse of a school in the town of San Giuliano di Puglia, where 26 children died along with one of their teachers. The analysis of the aftershock activity [De Gori and the Molise Working Group, 2004] shows that the causal fault had an East-West strike. With respect to the Hector Mine sequence, that will be described and analyzed in a later section, the San Giuliano events took place much deeper (a depth of 5 ± 3 skm was computed for the Hector Mine event, whereas 20 ± 2 km was estimated for both the main shocks of San Giuliano [see Chiarabba et al., 2005]). The map of Figure 1 shows the epicentral locations of the main shocks of October 31, 2002 and of November 1, 2002 (stars). Squares in Figure 1 represent the locations of the 11 aftershocks used for the computation of the spectral ratios for the first main event, and of the 10 aftershocks used for computing the spectral ratios for the second main earthquake. The waveforms used in this study were recorded by two MedNet stations (AQU and CII), and by two accelerometric stations (ARC1 and TORR).
Figure 2 shows the distribution of the Peak Ground Acceleration (PGA) for the ground motion recorded during the first main shock on 10/31/2002. Note that the peak values tend to be lower than the predictions by Sabetta and Pugliese , and by Malagnini et al. . Note also that a number of stations were not even triggered by the earthquake.
4. The Hector Mine Seismic Sequence
 The Hector Mine earthquake occurred on 16 October 1999, at 9:46 GMT, within the Eastern California Shear Zone, in a sparsely populated area of the Mojave Desert. We already mentioned that the hypocentral depth of the event was 5 ± 3 km [Scientists from the USGS, SCEC, and California Division of Mines and Geology, 2000], and a moment magnitude MW = 7.0 was obtained by G. Ichinose from full regional waveform inversion (G. Ichinose, personal communication, 2006). The main event occurred seven years after the 1992 Landers earthquake (MW 7.3), and 30 km east of it.
 In this study we use the recordings of the Hector Mine main event, and of 6 of its aftershocks, from 6 broadband stations located at epicentral distances ranging between a few tens of kilometers to over 600 km.
5. Results and Comparisons
5.1. Moment-Corner Frequency Relationships and Self-Similarity of Sequences
 In the case of the Hector Mine earthquake, there is a fundamental difference between the small (MW ≤ 5.0) and the large earthquakes. Such a statement agrees with the observations described by Izutani and Kanamori , and also with that described by Aki , who, on the basis of the breakdown zones and barrier intervals on a fault plane, argued that small events (MW ≤ 5.0) and large events in California are fundamentally different.
 L1-norm regressions are run on each set of (M0, fc) data points, in order to estimate a best-fit line on each log-log plot. The functional form used for the minimization is the one by Kanamori and Rivera , described in (1). By applying the bootstrap approach to the entire Hector Mine sequence, we obtain ɛ = 0.8 ± 0.4, although the data distribution seems consistent with a stepwise change in the apparent stress, where the static stress drop is constant and lower for events below ∼Mw 5.0. For events larger than Mw 5.0, the apparent stress (and the static stress) is larger. A possibility is that the stress drop for the events beyond that magnitude threshold is still constant.
 Strong departures from self-similarity are evident also for the San Giuliano seismic sequence, for which the bootstrap approach yielded: ɛ ≈ 0.89 ± 0.05. Moreover, it is clear that the San Giuliano sequence (Figure 3a) is characterized by anomalously large values of static stress drop, whereas the Hector Mine sequence (Figure 3b) shows lower values of the same quantity. Oblique lines represent, from left to right in Figures 3a and 3b, the fc−3 scaling, with Brune static stress drop at 0.1, 1, 10, 100 MPa. The steeper lines represent the average scaling; the standard errors associated to the best ɛ's are obtained from bootstrapping the regressions.
 Note that the standard error on ɛ is larger for the Hector Mine data set, even though the model shows a better fit the individual data points of Figure 3b than of Figure 3a (San Giuliano). Such apparent contradiction is due to the fact that the bootstrap method removes one data point at the time, and proceeds to a new calculation of ɛ. Note that, if the main shock of the Hector Mine sequence is removed from the data set, the rest of the sequence shows a nearly perfect self-similar trend (ɛ ≈ 0). On the contrary, if any of the aftershocks is removed, the sequence is clearly non-self-similar, with ɛ ≈ 1. The San Giuliano sequence, having two main shocks with the same characteristics, results in a lesser error bar for ɛ.
5.2. Peak Slip Velocity
 By using equations (4), (5), and (6), we can write out our results also in terms of peak slip velocity, Vmax (see Figures 3c and 3d). When inspecting Figures 3c and 3d, we need to keep in mind that the underlying hypothesis is that the fault behaves like a circular crack [Eshelby, 1957, 1959; Keilis-Borok, 1959]. This assumption is clearly not adequate for the Hector Mine main shock (rupture is no longer circular when the entire seismogenic zone fails, and a rise-time model would better represent the physics of the rupture than the crack model). Nevertheless, our result is very consistent with what can be extracted from the model described by Kaverina et al. : over the entire fault surface, they computed a maximum value of slip velocity Vmax = 0.918 m/s, whereas the average was max = 0.329 m/s (D. Dreger, written communication, 2008). Our estimate of = −0.5 ± 0.3 ( = 0.3 m/s) was computed with the rough assumption of the circular crack model, which is certainly more appropriate for the two main shocks that struck southern Italy. For San Giuliano we calculated the following log averages: = 0.1 ± 0.2 ( = 1.3 m/s) for the first main shock, and = 0.1 ± 0.2 ( = 1.2 m/s) for the second one.
5.3. Apparent Stress
 The other parameter that comes out from our grid-search is the apparent stress. For the seismic sequence, estimates of such parameter computed for every event in both sequences are shown in Figures 3e and 3f.
6. Discussion and Conclusions
 Surprisingly enough, the seismic sequence comprising the two San Giuliano mainshocks of 10/31/2002 and 11/01/2002 was characterized by large values of radiated energy, in spite of the low amplitudes observed for the high-frequency ground motion at surface sites. Although both events were given an MW 5.7, the first event had an ML 5.4, and the second one was given an ML 5.0 (Mednet RCMT catalog). In contrast with such magnitude discrepancy, the corner frequencies of both events, and hence their static stress drops, were anomalously high. Specifically, a log average = 1.3 ± 0.6 ( = 18 MPa) was found for the event of 10/31/02, and = 1.2 ± 0.5 ( = 17 MPa) was found for the event of 11/01/02. In terms of maximum slip velocities, we computed = 1.3 m/s for the first main shock, and = 1.2 m/s for the second one.
 By comparison, a much larger strike-slip event in Southern California, the Hector Mine mainshock, was characterized by much lower values of static stress drop and peak slip velocity: = 0.6 ± 0.8 ( = 4 MPa), which corresponds to a peak slip velocity = 0.3 m/sec. The numbers presented in this study indicate that the San Giuliano fault is a stronger feature than the one responsible for the Hector Mine event, perhaps due to its greater depth and confining pressure, rheological differences, and/or lesser level of maturity.
 Our results suggest that the Hector Mine seismic sequence might be characterized by a stepwise change in the static stress drop that takes place at a threshold of about Mw 5.0. For events below the threshold, the static stress parameter is constant, and of lesser value; for events larger than Mw 5.0, the static stress drop is larger. Large ruptures average over wide portions of the fault surface, where both large and small values of stress drop may exist. A plausible hypothesis is that such averaging action effectively prevents the observed stress parameter to grow beyond a certain value, and thus the stress drop for the large earthquakes stays constant and controlled by the overall stress level of the region. On the other hand, the San Giuliano seismic sequence seems to be characterized by a smooth increase of the static stress drop as the magnitude increases.
 Both sequences show evidence of non-self-similar behavior, but there seems to be a fundamental difference in how the self-similarity breaks down. We hypothesize that the different maturity of the two active faults may be the reason for the differences in the seismic behavior.
 For the San Giuliano seismic sequence, our results of large values of radiated energy strongly conflicts with the observed, low values of ground motion experienced during the two main events. In order to give a plausible explanation for such an apparent contradiction, we point to a strong velocity inversion at a depth just above the two mainshocks [Steckler et al., 2008; Chiarabba et al., 2005], due to the subduction of the fast Apulian platform beneath the Southern Apennines. Such a strong impedance contrast may have reflected downward part of the energy associated with the direct S-waves, effectively removing it from the direct-wave time windows. It is important to note that the same argument holds for all the aftershocks that were used in this study.
 Kevin Mayeda was supported under Weston Geophysical subcontract GC19762NGD and AFRL contract FA8718-06-C-0024.