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Several recent studies have used the coherence of seismic noise between stations to retrieve the phase slowness and attenuation. However, there is considerable debate on the feasibility of attenuation retrieval, its interpretation, and its dependence on the noise directionality and has been the subject of several analytical and numerical studies. In this article, we perform a detailed analysis of the various factors that play a role in the estimation of spatial coherence and attenuation from seismic arrays using data from the Southern California Seismic Network. For instance, certain common preprocessing steps such as averaging neighboring frequencies to improve the estimate are sufficient to introduce attenuation-like effects. The presence of first-mode surface Rayleigh wave and P waves in addition to the fundamental mode in Southern California (at frequencies 0.05-0.2 Hz) suggests that the underlying spatial coherence is better modeled as a linear combination of the above wave types. Although this describes the observed coherence better than a simple zeroth-order Bessel function, the resulting phase cancelations due to the multiple seismic waves can be misconstrued as attenuation if not taken into consideration. Using simulations, we show that due to the slowness inhomogeneity, azimuthally averaging the coherence is not equivalent to homogenizing the medium and instead introduces apparent attenuation in the coherence due to interference. Trying to fit an exponential decay model to this apparent attenuation results in an attenuation coefficient which is similar to previously published results.

Cross-correlations of diffuse noise fields can be used to extract environmental information. The influence of directional sources (usually ships) often results in a bias of the travel time estimates obtained from the cross-correlations. Using an array of sensors, insights from random matrix theory on the behavior of the eigenvalues of the sample covariance matrix (SCM) in an isotropic noise field are used to isolate the diffuse noise component from the directional sources. A sequential hypothesis testing of the eigenvalues of the SCM reveals eigenvalues dominated by loud sources that are statistical outliers for the assumed diffuse noise model. Travel times obtained from cross-correlations using only the diffuse noise component (i.e., by discarding or attenuating the outliers) converge to the predicted travel times based on the known array sensor spacing and measured sound speed at the site and are stable temporally (i.e., unbiased estimates). Data from the Shallow Water 2006 experiment demonstrates the effectiveness of this approach and that the signal-to-noise ratio builds up as the square root of time, as predicted by theory.