Epistemic Uncertainty and Limitations of the κ0 Model for Near-Surface Attenuation at Hard Rock Sites

kaplan s. robert;

The determination of near-surface attenuation for hard rock sites is an important issue in a wide range of seismological applications, particularly seismic hazard analysis. In this article we choose six hard to very-hard rock sites (Vs30 1030–3000ms–1) and apply a range of analysis methods to measure the observed attenuation at distance based on a simple exponential decay model with whole-path attenuation operator κr. The κr values are subsequently decoupled from path attenuation (Q) so as to obtain estimates of near-surface attenuation (κ0). Five methods are employed to measure κr which can be split into two groups: broad-band methods and high-frequency methods. Each of the applied methods has advantages and disadvantages, which are explored and discussed through the comparison of results from common data sets. In our first step we examine the variability of the individual measured κr values. Some variation between methods is expected due to simplifications of source, path, and site effects. However, we find that significant differences arise between attenuation measured on individual recordings, depending on the method employed or the modelling decisions made during a particular approach. Some of the differences can be explained through site amplification effects: although usually weak at rock sites, amplification may still lead to bias of the measured κr due to the chosen fitting frequency bandwidth, which often varies between methods. At some sites the observed high-frequency spectral shape was clearly different to the typical
κr attenuation model, with curved or bi-linear rather than linear decay at high frequencies. In addition to amplification effects this could be related to frequency-dependent attenuation effects [e.g. Q( f )]: since the κr model is implicitly frequency independent, κr will in this case
be dependent on the selected analysis bandwidth. In our second step, using the whole-path κr data sets from the five approaches, we investigate the robustness of the near-surface attenuation parameter κ0 and the influence of constraints, such as assuming a value for the regional crustal attenuation (Q).We do this by using a variety of fitting methods: least squares, absolute amplitude and regressions with and without fixing Q to an a priori value. We find that the value to which we fix Q strongly influences the near-surface attenuation term κ0. Differences in Q derived from the data at the six sites under investigation could not be reconciled with the average values found previously over the wider Swiss region. This led to starkly different κ0 values, depending on whether we allowed for a data-driven Q, or whether we forced Q to be consistent with existing simulation models or ground motion prediction equations valid for the wider region. Considering all the possible approaches we found that the contribution to epistemic uncertainty for κ0 determination at the six hard-rock sites in Switzerland could be represented by a normal distribution with standard deviation σκ0 = 0.0083 ± 0.0014 s.