ALBERT

Description: Although optimal, computing the moment tensor solution is not always a viable option for the calculation of the size of an earthquake, especially for small events (say, below M w 2.0). Here we show an alternative approach to the calculation of the moment-rate spectra of small earthquakes, and thus of their scalar moments, that uses a network-based calibration of crustal wave propagation. The method works best when applied to a relatively small crustal volume containing both the seismic sources and the recording sites. In this study we present the calibration of the crustal volume monitored by the High-Resolution Seismic Network (HRSN), along the San Andreas Fault (SAF) at Parkfield. After the quantification of the attenuation parameters within the crustal volume under investigation, we proceed to the spectral correction of the observed Fourier amplitude spectra for the 100 largest events in our data set. Multiple estimates of seismic moment for the all events (1811 events total) are obtained by calculating the ratio of rms-averaged spectral quantities based on the peak values of the ground velocity in the time domain, as they are observed in narrowband-filtered time-series. The mathematical operations allowing the described spectral ratios are obtained from Random Vibration Theory (RVT). Due to the optimal conditions of the HRSN, in terms of signal-to-noise ratios, our network-based calibration allows the accurate calculation of seismic moments down to M w 〈 0. However, because the HRSN is equipped only with borehole instruments, we define a frequency-dependent Generalized Free-Surface Effect (GFSE), to be used instead of the usual free-surface constant F = 2. Our spectral corrections at Parkfield need a different GFSE for each side of the SAF, which can be quantified by means of the analysis of synthetic seismograms. The importance of the GFSE of borehole instruments increases for decreasing earthquake's size because for smaller earthquakes the bandwidth available for our calculations is consistently shifted towards higher frequencies.

Description: We use previously determined direct-wave attenuation functions as well as stable, coda-derived source excitation spectra to isolate the absolute S-wave site effect for the horizontal and vertical components of weak ground motion. We use selected stations in the seismic network of the eastern Alps. A detailed regional attenuation function derived by Malagnini et al. (2002) for the region is used to correct the vertical and horizontal S-wave spectra. These corrections account for the gross path effects (i.e., all distance-dependent effects), although the source and site effects are still present in the distance-corrected spectra. The main goal of this study is to isolate the absolute site effect (as a function of frequency) by removing the source spectrum (moment-rate spectrum) from the distance-corrected S-wave spectra. Typically, removing the S-wave source spectrum is difficult because of inadequate corrections for the source radiation pattern, directivity, and random interference. In addition to complexities near the source, 2D and 3D structure beneath the recording site will result in an azimuth-dependent site effect. Since the direct wave only samples a narrow range in takeoff and backazimuth angles, multistation averaging is needed to minimize the inherent scatter. Because of these complicating effects, we apply the coda methodology outlined by Mayeda et al. (2003) to obtain stable moment-rate spectra. This methodology provides source amplitude and derived source spectra that are a factor of 3-4 times more stable than those derived from direct waves. Since the coda is commonly thought of as scattered energy that samples all ray parameters and backazimuths, it is not very sensitive to the source radiation pattern and 3D structure. This property makes it an excellent choice for use in obtaining average parameters to describe the source, site, and path effects in a region. Due to the characteristics of the techniques used in this study, all the inverted quantities are azimuthally averaged, since the azimuthal information is lost in the processing. Our results show that (1) all rock sites exhibited deamplification phenomena due to absorption at frequencies ranging between 0.5 and 12 Hz (the available bandwidth), on both the horizontal and vertical components; (2) rock-site transfer functions showed large variability at high-frequency; (3) vertical-motion site transfer functions show strong frequency dependence; (4) horizontal-to-vertical (H/V) spectral ratios do not reproduce the charactersitics of the true horizontal site transfer functions; and (5) traditional, relative site terms obtained by using reference rock sites can be misleading in inferring the behaviors of true site transfer functions, since most rock sites have nonflat responses due to shallow heterogeneities resulting from varying degrees of weathering. Our stable source spectra are used to estimate the total radiated seismic energy and to compare against similar results obtained for different regions of the world. We find that the earthquakes in this region exhibit nonconstant dynamic stress drop scaling, which gives further support for a fundamental difference in rupture dynamics between small and large earthquakes.

Description: A 1D coda method was proposed by Mayeda et al. (2003) in order to obtain stable seismic source moment-rate spectra using narrowband coda envelope measurements. That study took advantage of the averaging nature of coda waves to derive stable amplitude measurements taking into account all propagation, site, and S-to-coda transfer function effects. Recently, this methodology was applied to microearthquake data sets from three subregions of northern Italy (i.e., western Alps, northern Apennines, and eastern Alps). Because the study regions were small, ranging between local-to-near-regional distances, the simple 1D path assumptions used in the coda method worked very well. The lateral complexity of this region would suggest, however, that a 2D path correction might provide even better results if the data sets were combined, especially when paths traverse larger distances and complicated regions. The structural heterogeneity of northern Italy makes the region ideal to test the extent to which coda variance can be reduced further by using a 2D Q tomography technique. The approach we use has been developed by Phillips et al. (2005) and is an extension of previous amplitude ratio techniques to remove source effects from the inversion. The method requires some assumptions, such as isotropic source radiation, which is generally true for coda waves. Our results are compared against direct S-wave inversions for 1/Q and results from both share very similar attenuation features that coincide with known geologic structures. We compare our results with those derived from direct waves as well as some recent results from northern California obtained by Mayeda et al. (2005) that tested the same tomographic methodology applied in this study to invert for 1/Q. We find that 2D coda path corrections for this region significantly improve upon the 1D corrections, in contrast to California where only a marginal improvement was observed. We attribute this difference to stronger lateral variations in Q for northern Italy relative to California.

Description: What can be learned about absolute site effects on ground motions, with no geotechnical information available, in a very poorly instrumented region? In addition, can reliable source spectra be computed at a temporary deployment? These challenges motivated our current study of aftershocks of the 2001 M (sub w) 7.6 Bhuj earthquake, in western India, where we decouple the ambiguity between absolute source radiation and site effects by first computing robust estimates of coda-derived moment-rate spectra of about 200 aftershocks in each of two depth ranges. Crustal attenuation and spreading relationships, based on the same data used here, were determined in an an earlier study. Using our new estimates of source spectra, and our understanding of regional wave propagation, for direct S waves we isolate the absolute site terms for the stations of the temporary deployment. Absolute site terms for each station were determined in an average sense for the three components of the ground motion via an L (sub 1) -norm minimization. Results for each site were averaged over wide ranges of azimuths and incidence angles. The Bhuj deployment is characterized by a variable shallow geology, mostly of soft sedimentary units. Vertical site terms in the region were observed to be almost featureless (i.e., flat), with amplifications slightly 〈1.0 within wide frequency ranges. As a result, the horizontal-to-vertical (H/V) spectral ratios observed at the deployment mimic the behavior of the corresponding absolute horizontal site terms, and they generally overpredict them. This differs significantly from results for sedimentary rock sites (limestone, dolomite) obtained by Malagnini et al. (2004) in northeastern Italy, where the H/V spectral ratios had little in common with the absolute horizontal site terms. Spectral ratios between the vector sum of the computed horizontal site terms for the temporary deployment with respect to the same quantity computed at the hardest rock station available, BAC1, are seriously biased by its nonflat, nonunitary site response. This indicates that, occasionally, the actual behavior of a rock outcrop may be far from that of an ideal, reference site (Steidl et al., 1996).

Description: The determination of regional attenuation (Q (super -1) ) can depend upon the analysis method employed. The discrepancies between methods are due to differing parameterizations (e.g., geometrical spreading rates), employed datasets (e.g., choice of path lengths and sources), and the nature of the methodologies themselves (e.g., measurement in the frequency or time domain). Here we apply five different attenuation methodologies to a Northern California dataset. The methods are (1) coda normalization (CN), (2) two station (TS), (3) reverse two station (RTS), (4) source pair/receiver pair (SPRP), and (5) coda-source normalization (CS). The methods are used to measure Q of the regional phase, Lg (Q (sub Lg) ), and its power-law dependence on the frequency of the form Q (sub 0) (super feta ) with controlled parameterization in the well-studied region of Northern California using a high-quality dataset from the Berkeley Digital Seismic Network. We investigate the difference in power-law Q calculated among the methods by focusing on the San Francisco Bay area, where knowledge of attenuation is an important part of seismic hazard mitigation. All methods return similar power-law parameters, though the range of the joint 95% confidence regions is large (Q (sub 0) = 85+ or -40; eta = 0.65+ or -0.35). The RTS and TS methods differ the most from the other methods and from each other. This may be due to the removal of the site term in the RTS method, which is shown to be significant in the San Francisco Bay area. In order to completely understand the range of power-law Q in a region, we advise the use of several methods to calculate the model. We also test the sensitivity of each method to changes in geometrical spreading, the Lg frequency bandwidth, the distance range of data, and the Lg measurement window. For a given method, there are significant differences in the power-law parameters, Q (sub 0) and eta , due to perturbations in the parameterization when evaluated using a conservative pairwise comparison. The CN method is affected most by changes in the distance range, which is most likely due to its fixed coda-measurement window. Because the CS method is best used to calculate the total path attenuation, it is very sensitive to the geometrical spreading assumption. The TS method is most sensitive to the frequency bandwidth, which may be due to its incomplete extraction of the site term. The RTS method is insensitive to parameterization choice, whereas the SPRP method as implemented here in the time domain for a single path has great error in the power-law model parameters, and eta is strongly affected by changes in the method parameterization. When presenting results for a given method we suggest calculating Q (sub 0) (super feta ) for multiple parameterizations using some a priori distribution.

Description: We used broadband waveforms collected at short hypocentral distances (r〈 or =40 km) during the Umbria-Marche (Italy) seismic sequence of September-November, 1997, in order to calculate the scaling relationships for the ground motion within the meizoseismal area, in the 0.5-16.0 Hz frequency band. Data were collected by a 10-station portable seismic network deployed by the Istituto Nazionale di Geofisica (Rome, Italy) shortly after the occurrence of the first mainshock of the sequence, on 26 September 1997. Among the thousands of events recorded, we selected 142 earthquakes characterized by good signal-to-noise ratios at all frequencies, and by the absence of multiple shocks within the time window spanned by each recording. The data set of the selected waveforms was made of 2030 horizontal-component seismograms. The logarithm of the peak values of narrow bandpass-filtered versions of the velocity time histories are modeled at each frequency as AMP(f, r) = EXC(f, r (sub ref) ) + SITE(f) + D(r, r (sub ref) , f). EXC(f, r (sub ref) ) is the excitation term at an arbitrary reference hypocentral distance, r (sub ref) ; SITE(f) is a site term. The empirical attenuation functional, D(r, r (sub ref) , f), represents an estimate of the average crustal response for the region, at the hypocentral distance r, at the frequency f. It is modeled by using the following functional form: D(r, r (sub ref) , f) = log g(r) - log g(r (sub ref) ) pi f(r-r (sub ref) )/beta Q (sub 0) (f/f (sub ref) ) (super eta ) ; (f (sub ref) = 1.0 Hz, r (sub ref) = 10 km). g(r) = r (super -1) is the body-wave geometrical spreading function; beta = 3.5 km/sec is the shear-wave velocity in the crust. Due to the constraints applied to the system prior to the regressions, the excitation term represents the expected peak ground motion at the reference distance, as it would be observed at a site representative of the average site response of the network. The random vibration theory (RVT) is used to obtain a theoretical prediction of the attenuation functional. For reproducing D(r, r (sub ref) , f) we use the crustal attenuation parameter Q(f) = 130(f/f (sub ref) ) (super 0.10) obtained by Malagnini et al. (2000) from the analysis of a regional data set representative of the entire Apennines, in the (0.24-5.0 Hz) band. Two parameters are used to predict shapes and levels of the seismic spectra, the stress drop Delta sigma , and a high-frequency attenuation parameter kappa (sub 0) . The values used to reproduce the observed velocity spectra are Delta sigma = 200 bars; kappa (sub 0) = 0.04 sec. The indicated stress drop was estimated in this region by Castro et al. (2000), on recordings of the largest shock of the Umbria-Marche sequence.

Description: By using small-to-moderate earthquakes located within approximately 200 km of San Francisco, we characterize the scaling of the ground motions for frequencies ranging between 0.25 and 20 Hz, obtaining results for geometric spreading, Q(f), and site parameters using the methods of Mayeda et al. (2005) and Malagnini et al. (2004). The results of the analysis show that, throughout the Bay Area, the average regional attenuation of the ground motion can be modeled with a bilinear geometric spreading function with a 30-km crossover distance, coupled to an anelastic function exp(-pi fr/[capital greek beta]Q(f), where: Q(f) = 180 f (super 0.42) . A body-wave geometric spreading, g(r) = r (super -1.0) , is used at short hypocentral distances (r〈30 km), whereas g(r) = r (super -0.6) fits the attenuation of the spectral amplitudes at hypocentral distances beyond the crossover. The frequency-dependent site effects at twelve of the Berkeley Digital Seismic Network stations were evaluated in an absolute sense using coda-derived source spectra. Our results show the following. (1) The absolute site response for frequencies ranging between 0.3 Hz and 2.0 Hz correlate with independent estimates of the local magnitude residuals (delta M (sub L) ) for each of the stations. (2) Moment magnitudes (M (sub w) ) derived from our path and site-corrected spectra are in excellent agreement with those independently derived using full-waveform modeling as well as coda-derived source spectra. (3) We use our weak-motion-based relationships to predict motions regionwide for the Loma Prieta earthquake, well above the maximum magnitude spanned by our data set, on a completely different set of stations. Results compare well with measurements taken at specific National Earthquake Hazards Reduction Program site classes. (4) An empirical, magnitude-dependent scaling was necessary for the Brune stress parameter to match the large-magnitude spectral accelerations and peak ground velocities with our weak-motion-based model.

Description: Regressions over a data set of broadband seismograms are performed to quantify the attenuation of the ground motion in the Apennines (Italy), in the 0.25-5.0 Hz frequency band. The data set used in this article consists of over 6000 horizontal-component seismograms from 446 events, with magnitude ranging from M (sub w) nearly equal 2 to M (sub w) = 6.0. Waveforms were collected during recent field experiments along the Apennines. Data from two MedNet broadband stations, located in central and southern Apennines, were also used. Seismograms are bandpass-filtered around a set of sampling frequencies, and the logarithms of their peak values are written as AMP(f, r)-EXC(f, r (sub ref) )+SITE(f)+D(r, r (sub ref) , f). EXC(f, r (sub ref) ) is the excitation term for the ground motion at the hypocentral distance r (sub ref) . SITE(f) represents the distortion of the seismic spectra induced by the shallow geology at the recording site. D(r, r (sub ref) , f) includes the effects of the geometrical spreading, g(r), and of a frequency-dependent crustal attenuation Q. It is determined as a piecewise linear function, allowing to consider complex behavior of the regional attenuation. A first estimate of D(r, r (sub ref) , f) is obtained using a coda normalization technique (Aki, 1980; Frankel et al., 1990) and used as a starting model in the inversion of the peak values. Then, by trial and error, the empirical D(r, r (sub ref) , f) is fitted using a trilinear geometrical spreading, with crossover distances at 30 and 80 km, and the crustal parameter Q(f) = 130 (f/f (sub ref) ) (super 0.10) ; f (sub ref) = 1.0 Hz. These results suggest a low-Q crust in the entire Apennines in the 0.25-5.0 Hz range, implying that the seismic hazard in the region may be dominated by the local seismicity. The final section is devoted to highlight the limitations of the formula proposed by Console et al. (1988) to estimate duration magnitudes M (sub d) in Italy.