S U M M A R YAt high frequencies, the acceleration spectral amplitude decreases rapidly; this has been modelled with the spectral decay factor κ. Its site component, κ 0 , is used widely today in ground motion prediction and simulation, and numerous approaches have been proposed to compute it. In this study, we estimate κ for the EUROSEISTEST valley, a geologically complex and seismically active region with a permanent strong motion array consisting of 14 surface and 6 downhole stations. Site conditions range from soft sediments to hard rock. First, we use the classical approach to separate local and regional attenuation and measure κ 0 . Second, we take advantage of the existing knowledge of the geological profile and material properties to examine the correlation of κ 0 with different site characterization parameters. κ 0 correlates well with V s30 , as expected, indicating a strong effect from the geological structure in the upper 30 m. But it correlates equally well with the resonant frequency and depth-to-bedrock of the stations, which indicates strong effects from the entire sedimentary column, down to 400 m. Third, we use our results to improve our physical understanding of κ 0 . We propose a conceptual model of κ 0 with V s , comprising two new notions. On the one hand, and contrary to existing correlations, we observe that κ 0 stabilizes for high V s values. This may indicate the existence of regional values for hard rock κ 0 . If so, we propose that borehole measurements (almost never used up to now for κ 0 ) may be useful in determining these values. On the other hand, we find that material damping, as expressed through travel times, may not suffice to account for the total κ 0 measured at the surface. We propose that, apart from material damping, additional site attenuation may be caused by scattering from small-scale variability in the profile. If this is so, then geotechnical damping measurements may not suffice to infer the overall crustal attenuation under a site; but starting with a regional value (possibly from a borehole) and adding damping, we might define a lower bound for site-specific κ 0 . More precise estimates would necessitate seismological site instrumentation.