Extracting seismic attenuation coefficients from cross-correlations of ambient noise at linear triplets of stations

We develop and apply an algorithm for deriving interstation seismic attenuation from cross-correlations of ambient noise recorded by linear arrays. Theoretical results on amplitude decay due to attenuation are used to form a linear least-square inversion for interstation Q(R) values of Rayleigh surface waves propagating along linear arrays having three or more stations. The noise wave field is assumed stationary within each day and the interstation distances should be greater than the employed wavelength. The inversion uses differences of logarithmic amplitude decay curves measured at different stations from cross-correlation functions within a given frequency band. The background attenuation between noise sources and receivers is effectively cancelled with this method. The site amplification factors are assumed constant (or following similar patterns) in the frequency band of interest. The inversion scheme is validated with synthetic tests using ambient noise generated by ray-theory-based calculations with heterogeneous attenuation and homogenous velocity structure. The interstation attenuation and phase velocity dispersion curves are inverted from cross-correlations of the synthetic data. The method is then applied to triplets of stations from the regional southern California seismic network crossing the Mojave section of the San Andreas fault, and a dense linear array crossing the southern San Jacinto Fault zone. Bootstrap technique is used to derive empirical mean and confidence interval for the obtained inverse Q values. The results for the regional stations yield Q(R) values around 25 for a frequency band 0.2-0.36 Hz. The results for the San Jacinto fault zone array give Q(R) values of about 6-30 for frequencies in the range 15-25 Hz.