Regional attenuation in northern California: a comparison of five 1-D Q methods

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