We develop a new approach based on the variance of noise cross-correlation to characterize the noise source and wave propagation under the influence of a non-diffuse noise field. Based on the random errors for the Fourier spectra of stacked noise cross-correlation (Liu et al. 2016) and the assumption of diffuse field, we derive an analytical expression for the variance of every time point in the stacked cross-correlation and validate the theory using synthetic diffuse noise data. The ambient seismic noise field in Southern California is, however, not fully diffuse. The observed correlated neighboring frequencies in the noise data – a definitive character of the non-diffuse field (Liu & Ben-Zion 2016), map into the noise cross-correlation, biasing its variances from theoretical predictions under fully diffuse field assumption. For the secondary ocean microseism, we find strong positive correlation between the correlated neighboring frequencies and the deviations from diffuse field theory predicted variances. The ballistic arrivals on average contain more significant bias than the coda segments of the noise cross-correlation, which agrees with previous time-lapse monitoring studies based on ambient seismic noise. In addition, the station pairs having significant bias between actual and diffuse field theory predicted variances are aligned with the strongest source direction and exhibit significant beamforming source fluctuation.

▪ Our attenuation inversion method is based on Liu et al. (2015) using linear triplet of stations ▪ Application to the dense 3C linear array crossing the San Jacinto Fault in Ramona, CA ▪ Clear fundamental mode Rayleigh and Love wave phases are extracted ▪ Attenuation tomography maps reveal new information in addition to velocity tomography ▪ Shear velocity radial anisotropy and possible shear attenuation anisotropy

Cross-correlation of fully diffuse wavefields averaged over time should converge to the Green’s function; however, the ambient seismic field in the real Earth is not fully diffuse, which interferes with that convergence. We apply blind signal separation to reduce the effect of spurious non-diffuse components on the cross-correlation tensor of the ambient seismic field. We describe the diffuse component as having uncorrelated neighboring frequencies and equal intensity at all azimuths, and an independent (i.e., statistically uncorrelated) non-diffuse component arising from a spatially isolated point source for which neighboring frequencies are correlated. Under the assumption of linear independence of the spurious non-diffuse wave outside the stationary phase zone and the constructive interference of noise waves within that zone, we can suppress the spurious non-diffuse component from the noise interferometry. Our numerical simulations show good separation of one spurious non-diffuse noise source component for either non-diffuse Rayleigh or Love waves. We apply this separation to the Rayleigh-wave component of the Green’s function for 136 cross-correlation pairs from 17 stations in Southern California. We perform beamforming over different frequency bands for the cross-correlations before and after the separation, and find that the reconstructed Rayleigh waves are more coherent. We also estimate the bias in Rayleigh wave phase velocity for each receiver pair due to the spurious non-diffuse contribution.