On the apparent attenuation in the spatial coherence estimated from seismic arrays

Abstract

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.

On the estimation of attenuation from the ambient seismic field: inferences from distributions of isotropic point scatterers

“…This remark also applies to dissipative media however: the assumption that phase velocity and attenuation are laterally invariant throughout the region over which coherency measurements are averaged, should not be violated (Tsai 2011). In fact, the recent analysis by Menon et al (2014) reveals that spatial and azimuthal averaging may result in significant apparent attenuation in case of an anisotropic velocity medium. A third caveat concerns the trade-off between scatterer density and scattering amplitudes: loss of coherency can be due to either few strong scatterers or many weak scatterers (see Fig.…”

“…Finally, the assumption of waves having a single velocity corresponding to one frequency does not hold in a layered Earth: several modes may be observed at one frequency (Aki & Richards 2002;Weemstra et al 2013). In practice, ambient vibrations associated with primary microseisms (0.05-0.1 Hz) are usually dominated by fundamental-mode waves, whereas secondary microseisms (0.1-0.2 Hz) may well contain significant overtone energy (Kimman et al 2012;Menon et al 2014).…”

“…Averaging coherency measurements over a multitude of receiver couples comes at a cost however: one implicitly assumes uniform medium properties for the entire study region and hence only a 1-D attenuation profile is obtained (Prieto et al 2009;Weemstra et al 2013). Moreover, violation of this assumption may result in apparent attenuation (Menon et al 2014).…”

“…Averaging coherency measurements over a multitude of receiver couples comes at a cost however: one implicitly assumes uniform medium properties for the entire study region and hence only a 1-D attenuation profile is obtained (Prieto et al 2009;Weemstra et al 2013). Moreover, violation of this assumption may result in apparent attenuation (Menon et al 2014).A study by Tsai (2011) suggests that assuming the azimuthally averaged coherency to decay exponentially is contingent upon another assumption, that is that noise sources be uniformly distributed. In fact, his results indicate that different attenuation models should be used for different distributions of sources.…”

Minimum variance projection for direct measurements of power-law spectra in the wavenumber domain

“…Examples are laboratory wave experiments for ocean wave breaking (Babanin et al, 2011), tidal interval waves (Dushaw and Worcester, 1998), oceanic Rossby waves (Zang and Wunsch, 1999), atmospheric layer imaging (Chen et al, 2014), seismic waves (Huang and Wu, 2006;Menon et al, 2014), and low-frequency waves in near-Earth space (magnetosheath) (Motschmann et al, 1996;Glassmeier et al, 2001). The wave energy in Capon's method is evaluated from the covariance matrix of the measured data and the fluctuation model (referred to as the steering vector) as E mv (k) = 1 h † Rh .…”