ALBERT

Description: Knowledge of the acceleration spectral shape is crucial to various applications in engineering seismology. Spectral amplitude decays rapidly at high frequencies. Anderson and Hough (1984) introduced the empirical factor to model this attenuation. This is the first time is studied in a vertical array consisting of more than two stations. We use 180 earthquakes recorded at a downhole array with five stations in soils and rock to investigate the effect of soil conditions on . Given that computation processes vary across literature when following the classic Anderson–Hough method, we investigate its variability with the different assumptions that can be made when applying the method. The estimates of 0 range between 0.017 and 0.031 s at the surface and between 0.004 and 0.024 s at rock. This variability due to the assumptions made is larger than the error of each estimate and larger than the average difference in values between sediment and rock. For this data set, part of it can be attributed to the type of distance used. Given this variability, 0 values across literature may not always be comparable; this may bias the results of applications using 0 as an input parameter, such as ground-motion prediction equations. We suggest ways to render the process more homogeneous. We also find that at rock level is not well approximated by surface records from which we deconvolved the geotechnical transfer function. Finally, we compute on the vertical component and find a dependence of the vertical-to-horizontal ratio on site conditions. Online Material: Table of regression parameters and figure showing the regressed lines.

Description: 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 ( Vs 30 1030–3000 m s –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 r . The r values are subsequently decoupled from path attenuation ( Q ) so as to obtain estimates of near-surface attenuation ( 0 ). Five methods are employed to measure r 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 r 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 r 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 r 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 r model is implicitly frequency independent, r will in this case be dependent on the selected analysis bandwidth. In our second step, using the whole-path r data sets from the five approaches, we investigate the robustness of the near-surface attenuation parameter 0 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 0 . 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 0 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 0 determination at the six hard-rock sites in Switzerland could be represented by a normal distribution with standard deviation 0  = 0.0083 ± 0.0014 s.

Description: The 2010–2012 Canterbury earthquake sequence generated a large number of near-source earthquake recordings, with the vast majority of large events occurring within 30 km of Christchurch, New Zealand’s second largest city. We utilize the dataset to estimate the site attenuation parameter, 0 , at seven rock and stiff-soil stations in New Zealand’s GeoNet seismic network. As part of this study, an orientation-independent definition of is proposed to minimize the influence of observed high-frequency 2D site effects. Minimum magnitude limits for the traditional high-frequency fitting method are proposed, based on the effect of the source corner frequency. A dependence of 0 on ground-shaking level is also observed, in which events with large peak ground accelerations (PGAs) have lower 0 values than events with small PGAs. This observation is not fully understood, but if such a trend holds in future investigations, it may influence how 0 is used in hazard assessments for critical facilities. 0 values calculated from Fourier amplitude spectra of acceleration ( 0,AS ) are compared with the native 0 of local, empirical, ground-motion prediction equations (GMPEs), calculated using the inverse random vibration theory method ( 0,IRVT ). 0,IRVT is found to be independent of magnitude and distance and agrees with the average 0,AS for the region. 0,IRVT does not scale strongly with V S 30 , indicating that current GMPEs may be capturing the average kappa effect through the V S 30 scaling. The results from this study are of particular interest for site-specific ground-motion prediction studies as well as for GMPE adjustments between different regions or rock types.

Description: A ground-motion prediction equation (GMPE) specific to rock and stiff-soil sites is derived using seismic motion recorded on high V S 30 sites in Japan. This GMPE applies to events with 4.5≤ M w ≤6.9 and V S 30 ranging from 500 to 1500 m/s (stiff-soil to rock sites). The empirical site coefficients obtained and the comparison with the simulated site functions show that seismic motion on rock and stiff-soil sites does not depend only on V S 30 , but also on the high-frequency attenuation site properties ( 0 ). The effects of the site-specific 0 on site amplification are analyzed using stochastic simulations, with the need to take into account both of these parameters for rock-site adjustments. Adding the site-specific 0 into the GMPEs thus appears to be essential in future work. The rock-site stochastic ground-motion simulations show that the site-specific 0 controls the frequency corresponding to the maximum response spectral acceleration ( f amp 1). This observation is used to link the peak of the response spectral shape to 0 in this specific Japanese dataset and then to add the effects of high-frequency attenuation into the previous GMPE from the peak ground acceleration and up to periods of 0.2 s. The inclusion of 0 allows the observed bias to be corrected for the intraevent residuals and thus reduces sigma. However, this 0 determination is limited to a minimum number of rock-site records with M w ≥4.5 and to distances of less than 50 km.

Description: Site effects for hard-rock sites are typically computed using analytical models for the effect of 0 , the high-frequency attenuation parameter. New datasets that are richer in hard-rock recordings allow us to evaluate the scaling for hard-rock sites (e.g., V S 30 〉1500 m/s). The high-frequency response spectra residuals are weakly correlated with 0 , in contrast to the strong scaling with 0 in the analytical models. This may be due to site-specific shallow resonance patterns masking part of the effect of attenuation due to damping. An empirical model is developed for the combined V S 30 and 0 scaling for hard-rock sites relative to a reference site condition of 760 m/s (i.e., correction factors that should be used for going from soft rock to hard rock, taking into account the net effect of V S and 0 ). This empirical model shows high-frequency amplification that is more similar to the analytical prediction corresponding to a hard-rock 0 of 0.020 s rather than the typical value of 0.006 s, which is commonly used for hard-rock sites in the central–eastern United States. Compared to the current analytical approach, this leads to a reduction of high-frequency (〉20 Hz) scaling of about a factor of 2.

Description: The parameter ( Anderson and Hough, 1984 ), and namely its site-specific component ( 0 ), is important for predicting and simulating high-frequency ground motion. We develop a framework for estimating 0 and addressing uncertainties under the challenging conditions often imposed in practice: (1) low seismicity (limited, poor-quality, distant records); (2) limited-bandwidth data from the Transportable Array (TA; maximum usable frequency 16 Hz); and (3) low magnitudes ( M L  1.2–3.4) and large uncertainty in stress drop (corner frequency). We cannot resolve stress drop within the bandwidth, so we propose an approach that only requires upper and lower bounds on its regional values to estimate 0 . To address uncertainties, we combine three measurement approaches (acceleration spectrum slope [AS]; displacement spectrum slope [DS]; and broadband spectral fit). We also examine the effect of crustal amplification, and find that neglecting it can affect 0 by up to 35%. DS estimates greatly exceed AS estimates. We propose a reason behind this bias, related to the residual effect of the corner frequency on AS and DS . For our region, we estimate a frequency-independent mean S -wave Q of 900±300 at 9–16 Hz, and an ensemble mean 0 over all sites of 0.033±0.014 s. This value is similar to the native 0 of the Next Generation Attenuation-West 2 ground-motion prediction equations, indicating that these do not need to be adjusted for 0 for use in southern Arizona. We find that stress-drop values in this region may be higher compared to estimates of previous studies, possibly due to trade-offs between stress drop and 0 . For this dataset, the within-approach uncertainty is much larger than the between-approach uncertainty, and it cannot be reduced if the data quality is not improved. The challenges discussed here will be relevant in studies of for other regions with bandlimited data; for example, any region where data come primarily from the TA.

Description: At high frequencies, the acceleration spectral amplitude decreases rapidly; this has been modelled with the spectral decay factor . Its site component, 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 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 0 . Second, we take advantage of the existing knowledge of the geological profile and material properties to examine the correlation of 0 with different site characterization parameters. 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 0 . We propose a conceptual model of 0 with V s , comprising two new notions. On the one hand, and contrary to existing correlations, we observe that 0 stabilizes for high V s values. This may indicate the existence of regional values for hard rock 0 . If so, we propose that borehole measurements (almost never used up to now for 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 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 0 . More precise estimates would necessitate seismological site instrumentation.