Empirical estimation of high-frequency ground motion on hard rock

Site effects for hard-rock sites are typically computed using analytical models for the effect of κ0, 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., VS30 > 1500 m=s). The high-frequency response spectra residuals are weakly correlated with κ0, in contrast to the strong scaling with κ0 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 VS30 and κ0 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 VS and κ0). This empirical model shows high-frequency amplification that is more similar to the analytical prediction corresponding to a hard-rock κ0 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

Weak Motion Linear Soil Amplification at Aegion, Greece, and Comparison with Seismic Design Codes

We use 473 weak motion surface records from a relatively soft soil site (CORSSA) and 81 from a relatively stiff soil site (DIM) in conjunction with downhole records obtained in rock in order to study linear seismic soil amplification in Aegion, Greece. We estimate peak ‘soil-to-outcrop’ amplification factors in the time domain for the two sites through linear regression of PGA values. We view the results derived from these very weak motion records as indicative of the entire linear elastic range based on the large dataset size. We compare the peak horizontal soil amplification factors we derive from records with those suggested by design codes based on site classification, and find that they define lower boundaries rather than predictions of the average. We also find that, although the vertical component is assumed unamplified, both datasets show a two-fold amplification in its peak value. The results are also compared with previous finite difference analyses. For CORSSA, the amplification values calculated from 2D analyses are quite similar to those based on records, while for DIM they are 35% lower. Finally, while the elastic response spectra are well within the design spectra due to the small PGA values, we normalize them as to PGA in the context of discussing site effects. Spectral shapes do not infer strong site effects at DIM, but they do so for CORSSA, indicating strong surface waves particularly around the site’s fundamental period

Hard-Site κ0 (Kappa) calculations for Christchurch, New Zealand, and comparison with local ground-motion prediction, models

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, κ0, at seven rock and stiff‐soil stations in New Zealand’s GeoNet seismic network. As part of this study, an orientation‐independent definition of κ 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 κ0 on ground‐shaking level is also observed, in which events with large peak ground accelerations (PGAs) have lower κ0 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 κ0 is used in hazard assessments for critical facilities. κ0 values calculated from Fourier amplitude spectra of acceleration (κ0,AS) are compared with the native κ0 of local, empirical, ground‐motion prediction equations (GMPEs), calculated using the inverse random vibration theory method (κ0,IRVT). κ0,IRVT is found to be independent of magnitude and distance and agrees with the average κ0,AS for the region. κ0,IRVT does not scale strongly with VS30, indicating that current GMPEs may be capturing the average kappa effect through the VS30 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

Taxonomy of κ: A review of definitions and estimation approaches targeted to applications

In a way perhaps not dissimilar to stress drop (Atkinson and Beresnev, 1997), the high-frequency attenuation parameter κ (kappa), introduced by Anderson and Hough (1984), is one of the most used yet least understood or agreed-upon parameters in engineering seismology. It describes the deviation at high frequencies between observed Fourier amplitude spectra calculated from seismograms and an ω−2 source model, such as the Brune (1970) model. Almost 30 years after its introduction, κ is used by seismologists and engineers alike and constitutes an important input parameter for several applications. Perhaps because of its importance, it is estimated, physically explained, and used in many different ways. This note aims to illustrate the multiple approaches to its estimation, and to suggest that, in order to reduce ambiguities, the parameter should always be given a notation consistent with its measurement and application to help avoid inconsistencies in its application of κ scaling to ground-motion models. Hanks (1982) observed that above a given frequency the acceleration spectrum decays sharply. He termed this frequency fmax (e.g., Fig. 1a) and attributed it mainly to local site conditions. Soon after, Anderson and Hough (1984) introduced an alternative parameter to model this decay, which is the one most commonly used today: κ. They measured κ directly from the high‐frequency part of the acceleration Fourier amplitude spectrum of a record. Above a certain frequency (which they named fe but we will call here f1), the overall shape of the spectrum generally decays exponentially with frequency; the decay constant is most easily measured by finding a linear approximation to the spectrum plotted in log–linear space. The slope of the linear approximation is −πκ (e.g., Fig. 1b). In this note we use the notation κr for individual observations of κ, for example, the κ value corresponding to the slope of a particular record; this record may be at any epicentral distance Re≥0. Anderson and Hough (1984) also observed that κr at individual stations increases with distance and concluded that it includes components related both to the local geology of the top few km of crust beneath the station and to the regional structure. They then suggested that the site component of κ (denoted κ0) could be computed by extrapolating the κr values to zero epicentral distance, thus correcting for the regional effect of anelastic Q. In this note, we discuss the use of κ0 in various engineering seismology applications today and why interest in this parameter has been revived. We briefly discuss its possible physical interpretations, and detail the known approaches to estimate κ0 from seismic records. We group these approaches into families according to basic features, such as the range of frequencies over which κ0 is computed and the trade‐off with path effects. We then discuss the alternative option for estimating κ0 when site‐specific records are not available, based on empirical correlations with VS30. We collect previously published correlations and demonstrate the scatter observed across different studies. Finally, we make suggestions as to how κ0 estimation can be made in a more consistent way with the applications that use it, and how existing correlations can be made more consistent to improve both the inference of κ0 in the absence of site‐specific data and the physical understanding of κ0

Variance reduction and signal-to-noise ratio: Reducing uncertainty in spectral ratios

This paper uses an unusually large dataset to study scatter in site-effect estimation, focusing on how the events that increase uncertainty can be removed from the dataset. Four hundred seventy-three weak motion earthquake records from the surface and bedrock of a 178-m-deep borehole in Aegion, Gulf of Corinth, Greece, are used to evaluate spectral ratios. A simple statistical tool, variance reduction (VR), is first used to identify two groups of events that lie closest and farthest from the average, which is considered here as the initial best estimate of the site response. The scatter in the original dataset is found to be due to the group of events with smallest VR. These events can be removed from the dataset in order to compute a more reliable site response. However, VR is not normally used to choose records for site-effect studies, and it cannot be applied to the usual small datasets available. The signal-to-noise ratio (SNR) is normally used to this end, for which reason we investigate whether SNR can be used to achieve similar results as VR. Signal-to-noise ratio is estimated using different definitions. Data selection based on SNR is then compared to that using VR in order to define an SNR-based criterion that discriminates against events that, according to VR, increase scatter. We find that defining the SNR of a surface record as the mean value over a frequency range around the resonant peak (here, 0.5–1.5 Hz) and using a cutoff value of 5 may be used in this case to exclude most events for which VR is small. This process is also applied to the downhole station, where we obtain similar results for a cutoff value of 3

Semi-automated procedure for windowing time series and computing Fourier amplitude spectra (FAS) for the NGA-West2 database

This document introduces and describes the data processing methods developed for computing Fourier amplitude spectra (FAS) in the NGA-West2 project. The products of this study can be used to estimate high-frequency attenuation, kappa (κ), to estimate site amplification through empirical spectral ratios, as well as to aid in the development of ground-motion models (GMMs) based on FAS. To accommodate different potential user objectives, we selected five time windows in the acceleration time series (noise, P-wave, S-wave, coda, and the entire record) for which we compute the FAS. The processing starts with the time-aligned, instrument-corrected, tapered, and filtered acceleration time series. The proposed window selection method is developed through trial and error, and tested against a range of ground motions with different magnitudes and hypocentral distances from different regions. This document summarizes the steps for window selection and FAS computation, and describes the output data format. This report will be accompanied by the final products of the PEER NGA-West2 Project, namely, the published report describing the database [Ancheta et al. 2013] and the flatfile, which can be downloaded in excel format at: http://peer.berkeley.edu/ngawest2/databases/

A continuous map of near-surface S-wave attenuation in New Zealand

Quantifying the near-surface attenuation of seismic waves at a given location can be important for seismic hazard analysis of high-frequency ground motion. This study calculates the site attenuation parameter, κ0, at 41 seismograph locations in New Zealand. Combined with results of a previous study, a total of 46 κ0 values are available across New Zealand. The results compare well with previous t* studies, revealing high attenuation in the volcanic arc and forearc ranges, and low attenuation in the South Island. However, for site-specific seismic hazard analyses, there is a need to calculate κ0 at locations away from a seismograph location. For these situations, it is common to infer κ0 from weak correlations with the shear wave velocity in the top 30 m, VS30, or to adopt an indicative regional value. This study attempts to improve on this practice. Geostatistical models of the station-specific κ0 data are developed, and continuous maps are derived using ordinary kriging. The obtained κ0 maps can provide a median κ0 and its uncertainty for any location in New Zealand, which may be useful for future site-specific seismic hazard analyses

A review towards the design of extraterrestrial structures: From regolith to human outposts

The design of a permanent human habitat on a planetary body other than the Earth is an idea introduced many decades ago, which became even more significant after the landing of the first humans on the Moon with the Apollo missions. Today’s rampant technological advances combined with ambitious missions, such as the Insight mission on Mars and the Artemis program for the Moon, render the vision of space colonization more realistic than ever, as it constantly gains momentum. There is a considerable number of publications across several disciplines pertaining to the exploration of Lunar and Martian environments, to those planets’ soil properties, and to the design of the first habitable modules. The scope of this paper is to present a meticulous selection of the most significant publications within the scientific areas related to: (a) geotechnical engineering aspects, including the mechanical properties and chemical composition of Lunar and Martian regolith samples and simulants, along with elements of anchoring and rigid pads as potential forms of foundation; (b) ground motions generated by different types of Moonquakes and meteoroid impacts; (c) the different concepts and types of extraterrestrial (ET) structures (generic, inflatable, deployable, 3D-printed), as well as overall views of proposed ET habitats. Apart from the details given in the main text of this paper, a targeted effort was made to summarize and compile most of this information in representative tables and present it in chronological order, so as to showcase the evolution of human thinking as regards ET structures

Revisiting the fundamental structural dynamic systems: the effect of low gravity

This paper revisits the fundamental structural dynamic systems with regard to the effect of gravity, and thus self-weight, on their dynamic characteristics and response. Far from being a purely theoretical exercise, as would have been the case in the past, this study is a first step in structural dynamics inspired by—and anticipating—the potential of building under extraterrestrial conditions. More specifically, five basic structural models are considered: (a) the simple pendulum (SP), (b) the rigid inverted pendulum (RIP), (c) the flexural inverted pendulum (FIP), (d) the rigid rocking block (RRB), and (e) the flexural rocking block (FRB). The focus is to identify patterns and regions where low gravity can have a beneficial or detrimental role on the structural response. The paper initially presents the effect of low gravity on the dynamic characteristics of each system and then proceeds with highlighting their self-similar response, along with the differences in response due to low gravity. It is proved that low gravity is detrimental for the SP, while it is beneficial for the RIP and FIP models. Nevertheless, the effect can be both beneficial and detrimental for the RRB and FRB, depending on their parameters as revealed from this investigation. Finally, the main dynamic characteristics of the five cases studied, factorized by the gravitational multiplier (α), are quantified and summarized in the form of a representative table

A methodology for the estimation of kappa (κ) for large datasets. Example application to rock sites in the NGA-East database

This report reviews four of the main approaches (two band-limited and two broadband) currently used for estimating the site κ0: the acceleration slope (AS) above the corner frequency, the displacement slope (DS) below the corner frequency, the broadband (BB) fit of the spectrum, and the response spectral shape (RESP) template. Using these four methods, estimates of κ0 for rock sites in Central Eastern North America (CENA) in the shallow crustal dataset from NGAEast are computed for distances less than 100 km. Using all of the data within 100 km, the mean κ0 values are 8 msec for the AS approach and 27 msec for the DS approach. These mean values include negative κ estimates for some sites. If the negative κ values are removed, then the mean values are 25 msec and 42 msec, respectively. Stacking all spectra together led to mean κ0 values of 7 and 29 msec, respectively. Overall, the DS approach yields 2–3 times higher values than the AS, which agrees with previous observations, but the uncertainty of the estimates in each case is large. The AS approach seems consistent for magnitudes down to M3 but not below. There is large within-station variability of κ that may be related to differences in distance, Q, complexity along the path, or particular source characteristics, such as higher or lower stress drop. The station-to-station differences may be due to site-related factors. Because most sites have been assigned Vs30 = 2000 m/sec, it is not possible to correlate variations in κ0 with rock stiffness. Based on the available profile, the individual spectra are corrected for crustal amplification and only affect results below 15 Hz. Since the AS and DS approaches are applied over different frequency ranges, we find that only the DS results are sensitive to the amplification correction. More detailed knowledge of individual near-surface profiles may have effects on AS results, too. Although κ is considered to be caused solely by damping in the shallow crust, measurement techniques often cannot separate the effects of damping and amplification, and yield the net effect of both phenomena. The two broadband approaches, BB and RESP, yield similar results. The mean κ0_BB is 5±0.5 msec across all NEHRP class A sites. The κ0_RESP for the two events examined is 5 and 6 msec. From literature, the average value of κ0 in CENA is 6 ± 2 msec. This typical value is similar to the broadband estimates of this study and to the mean κAS when all available recordings are used along with all flags. When only recordings with down-going FAS slope are selected from the dataset, the mean value of κAS increases by a factor of 2–3. To evaluate the scaling of high-frequency ground motion with κ, we analyze residuals from ground motion prediction equations (GMPEs) versus κ estimates. Using the κ values from the AS approach, the average trend of the ln(PSA) residuals for hard-rock data do not show the expected strong dependence on κ, but when using κ values from the DS approach, there is a stronger correlation of the residuals, i.e., a κ that is more consistent with the commonly used analytically based scaling. The κDS estimates may better reflect the damping in the shallow crust, while the κAS estimates may reflect a net effect of damping and amplification that has not been decoupled. The κDS estimates are higher than the κAS estimates, so the expected effect on the high-frequency ground motion is smaller than that expected for the κAS estimates. An empirical hard-rock site factor model is developed that represents the combined Vs-κ0 site factor relative to a 760 m/sec reference-site condition. At low frequencies ( 10 Hz), the residuals do not show the strong increase in the site factors as seen in the analytical model results. A second hard-rock dataset from British Columbia, Canada, is also used. This BC hard-rock residuals show an increase in the 15–50 Hz range that is consistent with the analytical κ0 scaling for a hard-rock κ0 of about 0.015 sec. The variability of the PSA residuals is also used to evaluate the κ0 scaling for hard-rock sites from analytical modeling. The scatter in existing κ0 values found in literature is disproportionately large compared to the observed variability in high-frequency ground motions. We compared the predicted ground-motion variability based on analytical modeling to the observed variability in our residuals. While the hard-rock sites are more variable at high frequencies due to the additional κ0 variability, this additional variability is much less than the variability predicted by the analytical modeling using the variability from κ0-Vs30 correlations. This is consistent with weaker κ0 scaling compared to that predicted by the analytical modelling seen in the mean residuals