Phillips, W. S.

The aim of this study is to improve our knowledge of the attenuation structure in the Southern Apennines using a new amplitude ratio tomography method (Phillips et al., Geophys Res Lett 32(21): L21301, 2005) applied on both direct and coda envelope measurements derived from 150 events recorded by 47 stations of the Istituto Nazionale di Geofisica e Vulcanologia National Seismic Network (Rete Sismica Nazionale Centralizzata). The twodimensional (2-D) analysis allows us to take into account lateral crustal variations and heterogeneities of this region. Using the same event and station distribution, we also applied a simple 1-D methodology, and the performance of the 1-D and 2-D path assumptions is tested by comparing the average interstation variance for the path-corrected amplitudes using coda and direct waves. In general, coda measurement results are more stable than using direct waves when the same methodology is applied. Using the 2-D approach, we observe more stable results for both waves. However, the improvement is quite small, probably because the crustal heterogeneity is weak. This means that, for this region, the 1-D path assumption is a good approximation of the attenuation characteristics of the region. A comparison between Q tomography images obtained using direct and coda amplitudes shows similar results, consistent with the geology of the region. In fact, we observe low Q along the Apennine chain toward the Tyrrhenian Sea and higher values to the east, in correspondence with the Gargano zone that is related to the Apulia Carbonate Platform. Finally, we compared our results with the coda Q values proposed by Bianco et al. (Geophys J Int 150:10–22, 2002) for the same region. The good agreement validates our results as the authors used a completely independent methodology.

The measurement of regional attenuation Q-1 can produce method dependent results. The discrepancies among methods are due to differing parameterizations (e.g., geometrical spreading rates), employed datasets (e.g., choice of path lengths and sources), and methodologies themselves (e.g., measurement in the frequency or time domain). We apply the coda normalization (CN), two-station (TS), reverse two-station (RTS), source-pair/receiver-pair (SPRP), and the new coda-source normalization (CS) methods to measure Q of the regional phase, Lg (QLg), and its power-law dependence on frequency of the form Q0f^η with controlled parameterization in the well-studied region of northern California using a high-quality dataset from the Berkeley Digital Seismic Network. We test the sensitivity of each method to changes in geometrical spreading, 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, Q0 and η, 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 probably due to its fixed coda measurement window. Since, 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 η is greatly affected by changes in the method parameterization. When presenting results for a given method it is best to calculate Q0fη for multiple parameterizations using some a priori distribution. We also investigate the difference in power-law Q calculated among the methods by considering only an approximately homogeneous subset of our data. All methods return similar power-law parameters, though the 95% confidence region is large. We adapt the CS method to calculate QLg tomography in northern California. Preliminary results show that by correcting for the source, tomography with the CS method may produce better resolved attenuation structure.

A merged, high-quality waveform dataset from different seismic networks has been used to improve our understanding of lateral seismic attenuation for Northern Italy. In a revious study on the same region, Morasca et al. (Bull Seismol Soc Am 98:1936–1946, 2008) were able to resolve only a small area due to limited data coverage. For this reason, the interpretation of the attenuation anomalies was difficult given the complexity of the region and the poor resolution of the available data. In order to better nderstand the lateral changes in the crustal structure and thickness of this region, we selected 770 earthquakes recorded by 54 stations for a total of almost 16,000 waveforms derived from seismic networks operating totally or partially in Northern Italy. Direct S-wave and coda attenuation images were obtained using an amplitude ratio technique that eliminates source terms from the formulation. Both direct and early-coda amplitudes are used as input for the inversions, and the results are compared. Results were obtained for various frequency bands ranging between 0.3 and 25.0 Hz and in all cases show significant improvement with respect to the previous study since the resolved area has been extended and more crossing paths have been used to image smaller scale anomalies. Quality-factor estimates are consistent with the regional tectonic structure exhibiting a general trend of low attenuation under the Po Plain basin and higher values for the Western Alps and Northern Apennines. The interpretation of the results for the Eastern Alps is not simple, possibly because our resolution for this area is still not adequate to resolve small scale structures.

The determination of regional attenuation Q^-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 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 (QLg), and its power-law dependence on frequency of the form Q0fη 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. This approximately homogeneous subset of our data lies in a small region along the Franciscan block. All methods return similar power-law parameters, though the range of the joint 95% confidence regions is large (Q0 = 85 ± 40; η = 0.65 ± 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, it is advisable to use several methods to calculate the model. We also test the sensitivity of each method to changes in geometrical spreading, 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, Q0 and η, 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 probably due to its fixed coda measurement window. Since, 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 η is strongly affected by changes in the method parameterization. When presenting results for a given method it is best to calculate Q0f^η for multiple parameterizations using some a priori distribution.

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 assump- tions 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 com- plicated 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 tomo- graphic 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.

We inverted for laterally varying attenuation, absolute site terms, moments and apparent stress using over 460,000 Lg amplitudes recorded by the USArray for frequencies between 0.5 and 16 Hz. Corner frequencies of Wells, Nevada, aftershocks, obtained by independent analysis of coda spectral ratios, controlled the tradeoff between attenuation and stress, while independently determined moments from St. Louis University and the University of California constrained absolute levels. The quality factor, Q, was low for coastal regions and interior volcanic and tectonic areas, and high for stable regions such as the Great Plains, and Colorado and Columbia Plateaus. Q increased with frequency, and the rate of increase correlated inversely with 1-Hz Q, with highest rates in low-Q tectonic regions, and lowest rates in high-Q stable areas. Moments matched independently determined moments with a scatter of 0.2 NM. Apparent stress ranged from below 0.01 to above 1 MPa, with means of 0.1 MPa for smaller events, and 0.3 MPa for larger events. Stress was observed to be spatially coherent in some areas; for example, stress was lower along the San Andreas fault through central and northern California, and higher in the Walker Lane, and for isolated sequences such as Wells. Variance reduction relative to 1-D models ranged from 50 to 90 % depending on band and inversion method. Parameterizing frequency dependent Q as a power law produced little misfit relative to a collection of independent, multi-band Q models, and performed better than the omega-square source parameterization in that sense. Amplitude residuals showed modest, but regionally coherent patterns that varied from event to event, even between those with similar source mechanisms, indicating a combination of focal mechanism, and near source propagation effects played a role. An exception was the Wells mainshock, which produced dramatic amplitude patterns due to its directivity, and was thus excluded from the inversions. The 2-D Q plus absolute site models can be used for high accuracy, broad area source spectra, magnitude and yield estimation, and, in combination with models for all regional phases, can be used to improve discrimination, in particular for intermediate bands that allow coverage to be extended beyond that available for high frequency P-to-S discriminants.