V S 30 in the NGA GMPEs: Regional Differences and Suggested Practice

Background

Incorporating the effects of near-surface geology into ground motion prediction equations (GMPEs) has seen two significant advancements in the past two decades: first, categorizing sites using a quantitative measure instead of descriptive geotechnical classification, and second, using this measure as a continuous, rather than a discrete, parameter.

Site classification in early GMPEs was typically descriptive, often based on surface geology with or without a depth constraint (Campbell 1985). In some cases, categorization was simply binary, describing the site as being either “soil” or “rock” (e.g, Joyner and Boore 1981, McGuire 1978, Sadigh et al. 1997). This categorization often led to misuse in forward application such that the boundary between soil and rock became very subjective and inconsistent between users. For example, while the rock site category included shallow stiff soils for ground-motion studies, in application it was typically assumed to be only rock. In some cases, subcategories were added, such as dividing the “rock” category into “hard rock” and “soft rock” (Campbell, 1997).

The first quantitative measure of site categories was V_S30, the time-averaged shear-wave velocity in the top 30 m, computed as follows:

V S X = X t t ( X )

(1)

The choice of V_S30 to replace the descriptive geological categorization was based on extensive empirical work done by Borcherdt (1994), Borcherdt et al. (1979), and Fumal (1985), who showed good correlation of V_S30 with local amplification. The first GMPE to adopt V_S30 as a site categorization proxy was Boore et al. (1993) who classified their recording sites into four of the proposed six NEHRP categories. The use of V_S30 as a quantitative measure for site classification into multiple site classes was adopted by the National Earthquake Hazard Reduction Program (NEHRP) and the published site classes for the seismic design provisions for new buildings (Martin and Dobry 1994). The use of V_S30 to categorize between site classes was a significant improvement in that it introduced a quantitative, measureable parameter, leading to consistency between different researchers and leading to unambiguous definitions of sites for applications; however, it limited the available ground motion data set because many sites did not have V_S30 measurements. To allow recordings from sites without measured V_S30 values to be used in developing GMPEs, methods were developed to infer the V_S30 based on site geology and knowledge of measurements from other sites on similar geology.

Although quantitative, the discrete NEHRP classification of soil sites into four or six categories still suffered from significant limitations. For example, very similar sites could be on two sides of a class boundary and, by that, be categorized as having significantly different response. Moreover, measurement and interpretation error themselves would often be responsible for placing a site in either side of a class boundary. One way of addressing such limitations would be to incorporate V_S30 as a continuous parameter, essentially providing a smooth transition between site categories.

The first to use V_S30 as a continuous variable were Boore et al. (1997) in a 1994 USGS report. Following that, V_S30 was fully incorporated as a continuous parameter into western U.S. GMPEs as part of the PEER-based Next Generation Attenuation (NGA) project in 2008 (Chiou et al. 2008). In the NGA-1 database, 24% of the sites had V_S30 values based on measurements, mostly from California and Taiwan. In the NGA-West2 database, this number substantially increased to 49% of the sites, with the greatest increase in number of measured-V_S30 sites shown in California and Japan (Ancheta et al. 2013, 2014). At sites for which V_S30 measurements were unavailable, estimated values were assigned based on a number of proxies, such as topographical slope, surface geology, and terrain (see Ancheta et al. 2013, Seyhan et al. 2014).

The site-response component in recent GMPEs is composed of two parts - linear response for relatively weak input motions and potentially nonlinear response for stronger input motions. The PGA _Rock threshold for nonlinearity depends on the velocity profile and material parameters (e.g., Régnier et al. 2013) but it is generally accepted to assume linear behavior for PGA _Rock < 0.1 g. Both the linear and nonlinear parts are typically a function of V_S30, while the nonlinear part is also a function of the expected ground motion intensity on a rock site at the same magnitude and distance. Because empirical data is generally not sufficient for constraining the nonlinear part of site-response in GMPEs, it is often constrained by one-dimensional (1-D) numerical simulations (e.g., Kamai et al. 2014, Seyhan and Stewart 2014, Walling et al. 2008). Although the GMPEs include nonlinear effects, for applications in which nonlinearity is expected to significantly affect the site response, it is generally recommended to conduct a site-specific response analysis rather than using the nonlinear site response scaling within the GMPE. The discussion presented in this paper will be limited to the linear site-response and its correlation with V_S30. The nonlinear dependence on V_S30 or other site categorization indices is a more complicated issue which is beyond the scope of this paper.

Recent studies have proposed several alternatives or supplemental parameters to V_S30. Below is only a partial list, containing some of the more recent studies and approaches on alternative measures for site response. The use of the predominant or the fundamental site period has been promoted by several researchers, because it is believed to be a more physical parameter than V_S30, accounting explicitly for both shear-wave velocities and profile depths. Zhao et al. (2006), followed by Di Alessandro et al. (2012), characterize their sites based on the predominant site period, estimated from the horizontal to vertical ratio of the 5% damped response spectra of earthquake records at the site, similar to the receiver function method. They classify their sites into discrete site-class categories, by period range. This methodology is appropriate for the purpose of classifying sites as part of a GMPE regression but is limited in its forward applicability, as also noted by Zhao et al. (2006). Castellaro and Mulargia (2014) introduced the VfZ approach, in which V represents the average velocity of the cover layer, f represents the resonance frequency of the subsoil and Z represents the impedance contrast between the cover and the bedrock. What makes this approach attractive for site-specific applications is that it is based on fundamental site-properties which could be obtained generally easily. However, for site-categorization in a GMPE, this approach requires estimation of three separate parameters, which increases the complexity of the GMPE, and leads to additional correlations and tradeoffs between parameters.

Luzi et al. (2011) investigates several parameters that could be related to the seismic site response, such as fundamental frequency, average shear-wave velocity to bedrock, sediment thickness and combinations of thereof. They conclude that V_S30 alone is insufficient to properly describe the response of their Italian data set and propose a classification that is based on the two parameters: V_S30 and f_o, where f_o is the fundamental frequency of the site obtained by horizontal-to-vertical spectra ratio from ambient noise. f_o was also suggested by Regnier et al. (2014) as a supplemental parameter to V_S30, together with B₃₀ – the gradient of the velocity profile in the upper 30 meters. Based on their analysis of the Japanese KiK-net database, they found that adding one of these two parameters to V_S30 reduced the standard deviation of the amplification, especially for sites with a shallow impedance contrast. Cadet et al. (2012) also used the KiK-net database to compare the correlation between the empirical one-dimensional (1-D) surface-to-borehole amplification and different site parameters. They show that the “optimal” parameter to explain site amplification in their database is the pair (V_S30,f₀), but when comparing the effectiveness of a single parameter, f₀ was slightly better than V_S30 in its effectiveness as a site characterization proxies. Zhao and Xu (2013) compare the effectiveness of site period (T _S ) and V_S30 for estimating site amplification. They show that the two parameters yield comparable results for short site periods but that T _S is a better predictor of site amplification for sites with long site periods (T _S > 0.6 s). Finally, Rathje and Navidi (2013) conduct an extensive set of 1-D site response simulations, varying the soil profiles for constant V_S30 and depth to bedrock values. They conclude that site amplification can be better estimated with two additional parameters: V _ratio (the ratio of the average shear-wave velocity from 20 m and 30 m to the average shear-wave velocity in the top 10 m) at short periods; and Z_1.0 (the depth to V _S = 1,000 m/s) at long periods.

While site-period parameters may be considered more physical than V_S30, there is some debate about their applicability. Assuming the shear-wave velocity profile is unavailable, the fundamental frequency can be obtained in one of the following two methods: (1) using ambient noise measurements, and (2) using ground-motion recordings at the site (both micro-seismicity and strong ground motions). Both typically use the ratio of horizontal to vertical response spectra, or horizontal-to-vertical spectral ratio (HVSR), to obtain the characteristic transfer function of the site. In the former case, debate has focused over the appropriateness of the seismic source (noise) and generated wave-types to predict the site-response of vertically-propagating SH waves, but comparison studies have generally shown successful predictions and the method is gaining popularity, mostly outside the United States (e.g., Field and Jacob 1993, Field and Jacob 1995, Nakamura 2000, Zaslavsky et al. 2000). In the latter case, the determination of the site parameter is either conditioned on obtaining ground motion recordings at the site of interest, or alternatively classifying similar sites into discrete site classes based on groups of recordings sites. However, recordings are not always available at the site of future engineering applications and if the method is used for classifying groups of recording stations, the probability of assigning an incorrect site class to a single site may be too large, as noted by Zhao et al. (2006). For purposes of GMPE development, measuring the site proxy has to be done independent of the data used to fit the GMPE; otherwise, their dependency may bias the site-response scaling within the GMPE.

In this paper, we do not seek to judge between the different alternatives or to demonstrate that V_S30 is better or worse than other methods. Instead, we note the fact that no alternative thus far has been suggested for a single, effective, continuous parameter that can work well for a large global data set, and that V_S30 will probably continue to dominate GMPE site classification for the near future. Therefore, we examine the logic and physical reasoning for using V_S30, and provide guidelines and limitations for its use in site-specific seismic hazard evaluations.

The analysis described in following sections of the paper is based on two databases of measured velocity profiles. The Japanese profiles were downloaded directly from http://www.kyoshin.bosai.go.jp/. The database consists of 1,735 velocity profiles that were available as of February 2013. All of the profiles are associated with measurements next to ground-motion stations from both seismic networks (KiK-Net and K-NET). Profiles from California and Taiwan were extracted from the profile database used to develop the NGA-West2 site-database (provided by Pacific Engineering and Analysis, last accessed January 2015). The database contains 499 profiles from Taiwan, which were a contribution of work done by both NCREE (National Center for Research on Earthquake Engineering) and CWB (Central Weather Bureau) in Taiwan (Kuo et al. 2012). The database also contains 1094 profiles from California, 553 of which are associated with ground-motion recording stations. These 553 profiles are the best representation of the V_S30 scaling in the GMPE. Therefore, the analysis of California velocity profiles in this paper relates to this subset only.

In the sections that follow, the PEER NGA GMPEs will be frequently discussed, and as such, we will use the following abbreviations: AS08 (Abrahamson and Silva 2008), ASK14 (Abrahamson et al. 2013, 2014), BA08 (Boore and Atkinson 2008), BSSA14 (Boore et al. 2013, 2014), CB08 (Campbell and Bozorgnia 2008), CB14 (Campbell and Bozorgnia 2013, 2014), CY08 (Chiou and Youngs 2008), CY14 (Chiou and Youngs 2013, 2014), IMI08 (Idriss 2008), and IMI14 (Idriss 2013, 2014).

V_S30: DOES IT WORK?

For the fundamental discussion below, let us define site response as the ratio of the response (either the Fourier or response spectra) on a soil site to the response on an equivalent site with reference conditions. Note again, as mentioned above, that we limit our discussion to the linear site-response; meaning, the response to weak input ground motions, ignoring nonlinear effects. Generally, for weak motions, the observed response on soil sites is amplified with respect to the response on rock sites. This amplification can be caused by a number of different physical phenomena (as reviewed by Anderson 2007), including: (1) amplification due to the decrease of density and shear wave velocities toward the surface (Aki and Richards,2002), (2) resonance of predominantly S-waves in low-velocity layers at a strong impedance contrast near the surface, (3) trapping of surface wave energy in low-velocity layers near the surface, (4) further 3-D effects such as basin response, edge effects, etc.

Keeping the discussion to vertically propagating SH waves such as in forms (1) and (2) above, it is clear that the site amplification represents the physical response of the entire soil column down to bedrock, influenced from both layer thicknesses and the corresponding soil properties. Therefore, site-specific analysis is generally preferred for evaluations of site-effects in places where the full soil profile can be obtained. However, the use of a simple site categorization is required in at least the four following cases: (a) site categorization for regression of ground motion models, (b) forward applications of large spatial coverage, such as seismic hazard maps, (c) site-specific applications for very deep soil sites (greater than ∼300 m), for which 1-D site response analysis may become unreliable, or (d) site specific applications in projects for which the full profile is not available.

As frequently noted by both supporters and objectors of V_S30, it is not a fundamental soil property, but rather it is an index of the velocity profile. As such, it is used to represent the soils’ response to seismic loading. There is also no doubt that to fully and accurately describe site response, individual soil layers should be characterized by their thickness and dynamic soil properties and, hence, one average parameter is not sufficient. Nevertheless, a large body of scientific and engineering literature shows that, in absence of the full soil profile characterization or for cases in which a simplified representation of the profile is needed, much of the amplification can be successfully correlated with geological, topographical, and geophysical proxies (e.g., Borcherdt 1970, Borcherdt and Gibbs 1976, Rathje and Navidi 2013).

In this section, we perform a residual analysis on the 2013 PEER ground-motion database (Ancheta et al. 2013), to demonstrate whether or not V_S30 can be used as a site-response proxy and under which conditions. Amplification factors as a function of V_S30 are presented in Figure 1. These amplification factors were obtained by performing a random-effects regression through the NGA-West2 database, using a simple GMPE (see Equation 2) which is only a function of magnitude and distance (no site dependence). If the site has a lower spectral acceleration than average, its residual will be negative, and if it has a higher acceleration than the predicted average, its residual will be positive. In this way, we test the correlation between amplification and a representative parameter—in this case, V_S30. While the data may include both weak and strong input motions, and hence include nonlinear effects, it can be shown that the NGA-West2 data is dominated by linear motions (e.g., Figure 1 in Kamai et al. 2014). Therefore, we assume that the results of this analysis generally represent the linear site response scaling within the NGA-West2 data set.

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Figure 1.

Amplification ratios for three regions.

The simple GMPE has the following form:

In ( S a ) = a 1 ( M − 6 ) + a 2 ( 8.5 − M ) 2 + ( a 3 + a 4 ( M − 6 ) ) ln ( R r u p + 10 ) + a 5 R r u p + a 6

(2)

The intra-event residuals in Figure 1 were binned into 11 V_S30 bins and normalized by the amplification at V_S30 = 450 m/s for plotting purposes. The amplification factors in Figure 1 are presented for three different regions (California, Taiwan, and Japan), and four different spectral periods (PGA, 0.5 s, 1 s, and 2 s). The symbols represent the median amplification for that V_S30 bin and the error-bars represent the standard error of the mean. Generally, Figure 1 shows a clear trend between amplification and V_S30 for all three regions, but the scaling with V_S30 can be different between regions due to different correlations between V_S30 and the full Vs profile.

At short periods (e.g., PGA), V_S30 captures the general site amplification for both soil and soft rock sites (450 m/s < V_S30 < 800 m/s). The scaling may be different between different regions (e.g., Japan vs. Taiwan at T = 0.5 s and 1.0 s) but there is an overall linear trend of log amplification with log V_S30. Extrapolating this linear trend to hard-rock sites (V_S30 > 800 m/s) may not work because the scaling of amplification with V_S30 at intermediate V_S30 values does not capture the effects of kappa—the high-frequency attenuation parameter (Anderson and Hough 1984), which can be significant for hard-rock sites. At long periods (bottom row), V_S30 captures the general amplification for soil sites, but the linear trend starts to break down at V_S30 of approximately 600 m/s, due to the loss of correlation with the deeper structure: the shallow velocity layers at rock sites are a result of surface weathering and do not correlate with the profile at depth. Therefore, extrapolating V_S30 scaling to hard-rock sites is not recommended and most GMPE developers put an upper limit on the linear V_S30 scaling in their model. For example, in the ASK14 model, the parameter V₁ represents the upper limit of the V_S30 scaling, ranging between 1,500 m/s for short periods and 800 m/s for long periods.

Why Does it Work?

In typical geological environments, the soil stiffness increases with depth due to its geologic age and accompanying effects such as, for example, compaction and cementation. Moreover, assuming that the geologic history of the profile is generally similar across a region, we expect the shear-wave velocity profiles across geologic regions to be largely similar. For example, Boore et al. (2011) examined the correlation between V_S30 and the average shear wave velocity to other depths, less than or greater than 30 m. They inspected more than 1,000 profiles from four regions and concluded that V_S30 is strongly correlated with average velocities to depths less than 30 m and that the correlation is different for different regions. They also found that V_S30 is correlated with velocities to greater depths (up to 400 m), demonstrating that the top 30 meters are correlated with the deeper structure and hence can be used as a proxy for the full profile. We perform a similar analysis on the NGA-West2 profile database, using profiles from California only. The time-averaged velocity to depths of 50 m, 100 m, and 200 m (denoted V _SX to depth X; see Equation 1) is plotted against the V_S30 of the same profiles in Figure 2. As seen in the figure, V_S30 is highly correlated with average velocities to depths of approximately 100 m. The correlation with average velocities at greater depths is weaker, due to the shape of the average velocity profile: strong velocity gradient to a certain depth (∼100 m) followed by much slower increase at greater depths, as described below.

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Figure 2.

Correlation between time-averaged velocities at different depths (50, 100, 200) and V_S30, the time-averaged velocity at 30 m depth. The dashed lines are the 95% confidence intervals on the fit.

For the remainder of the analysis, the profiles are grouped into four V_S30 bins: 270 m/s, 400 m/s, 560 m/s, and 760 m/s. The binning is defined as a range on V_S30, such that all profiles with V_S30 within ±15% from the bin median (270, 400, 560 and 760) are included in the bin, as shown in Figure 3. The profile shapes for the three regions can be seen in Figure 4 for the first bin only (V_S30 = 270 ± 15%m/s). Additional figures, showing profiles from the four bins are plotted in Figure A1 in the online Appendix. The solid and dashed lines on Figure 4 represent the median shear-wave velocity and the corresponding standard deviation at each depth, respectively. While regional differences exist, all velocity profiles in Figure 4 (and its supplementary plots in Figure A1) demonstrate a typical profile shape—the velocity gradient at shallow depth is higher, with a much slower velocity increase at greater depths (with the “transition” depth increasing for increasing V_S30).

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Figure 3.

Range of profiles (by their V_S30) associated with each of the four bins used for analysis.

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Figure 4.

V _S profiles for California, Japan, and Taiwan for the V_S30 bin V_S30 = 270 ± 15%m/s. The solid and dashed lines are the median and standard deviation of the shear-wave velocity at each depth increment, respectively. “CA” relates to the velocity profiles in California which are associated with strong-motion stations only.

This typical shape demonstrates that knowledge of the top-most layers (e.g., 30 m) can, on average, successfully represent the response of the entire profile, due to the correlation of the top part of the profile with the deeper structure for a specific data set. This can explain why V_S30 is generally a good predictor for the average site-response of sites with typical profiles. We acknowledge, however, the large profile variability, and note that the typical shape only explains the average response, while the response of any single profile may sometimes be quite significantly different.

Using the Site-Response Model within the Gmpe

The linear V_S30 scaling in the GMPE represents the range of sites available within the database on which the GMPE is regressed. Because V_S30 is a proxy for the full profile and is not a fundamental parameter of site response, the V_S30 scaling as provided in the GMPE should be used only if the site-specific Vs profile is consistent with the range of profiles used to derive the V_S30 scaling in the GMPE. In the NGA-West2 site database, almost 40% of the sites are from western North America (mostly California, noted herein CA), 30% are from Japan (JP), and 12% are from Taiwan (TW). Three of the five NGA-West2 GMPEs—ASK14, CY14, and CB14—found that the V_S30 scaling between CA and JP is different enough to calculate separate V_S30 scaling for Japan. ASK14 also provides a separate scaling for Taiwan, such that three linear site-response models exist within the GMPEs. As seen in Figure 1, this difference is mostly significant for intermediate periods (0.5 ≤ T ≤ 1).

The median and corresponding standard deviation of the profile range from Figure 4 is plotted separately for the California, Taiwan, and Japan profiles, in Figures 5, 6, and 7, respectively. Also plotted alongside are the number of profiles represented by these medians at each depth and the depth at which less than 10 profiles remain in the bin (represented by the circles) that is used later to constrain regression. Generally speaking, the Japanese profile database starts with the largest number of profiles per bin, with a sharp decrease at 10 m and 20 m, but still remaining well above 10 profiles per bin down to 100 meters for all bins. The California database is also well represented down to 100 m, apart from the V_S30 = 760 m/s bin, which has the smallest number of profiles and is not well represented beyond 30 m. The Taiwanese profile database starts with an overall number of profiles similar to the California database, but more than 90% of the profiles are shallower than 30 m and hence the Taiwanese median profiles can only be considered reliable above 30 m.

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Figure 5.

(a) median velocity profiles for CA, (b) standard deviation, (c) number of profiles in each bin with depth. Symbol represents the depth at which number of profiles falls below 10. “CA” relates to the velocity profiles in California which are associated with strong-motion stations only.

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Figure 6.

(a) median velocity profiles for Taiwan, (b) standard deviation, (c) number of profiles in each bin with depth. Symbol represents the depth at which number of profiles falls below 10.

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Figure 7.

(a) median velocity profiles for Japan, (b) standard deviation, (c) number of profiles in each bin with depth. Symbol represents the depth at which number of profiles falls below 10.

Figure 8 compares the median velocity profile and its range (±1 Std) for California, Japan, and Taiwan. On average, the velocity gradient (defined as the change in velocity with depth) is highest in Japan, lowest in Taiwan, with California profile gradients falling in between those two. In most cases, the difference between the CA and JP medians or the CA and TW medians is not greater than the variability of single profiles with the same V_S30 in each of the regions. For example, the CA median falls within the Japanese range and the JP median falls within the CA range. However, the V_S30 scaling in the GMPE is the average scaling of all recordings from the respective region, and hence the shape of the median profile will determine the scaling rather the shape of individual profiles—that is, the average velocity gradient with depth is more important than the range. While the comparison in Figure 8 shows a clear difference between the median profiles in all three regions, the discussion that follows will focus on the differences between California and Japan, which is represented by three of the five NGA-West2 GMPEs. The median and standard deviation of the binned velocity profiles, as plotted in Figure 8, are provided as supplemental material in an online Appendix provided with this article.

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Figure 8.

Comparison of median and range (±1 Std) of profiles between CA, TW, and JP for all four V_S30 bins. Median profiles are plotted to depth representing profile count of 10 (circles on Figure 4) “CA” relates to the velocity profiles in California which are associated with strong-motion stations only.

For forward application, we will only discuss CA versus JP profiles, as represented by separate V_S30 scaling models in three of the NGA-West2 GMPEs. We recommend testing whether or not the site-specific velocity profile is consistent with either the JP or the CA profile, and if so, using the corresponding scaling in the GMPE, regardless of association with the geographical region. For example, if your site-specific profile is from Utah but is more similar in shape to the Japanese median profile and it is within ±1 Std from the median Japanese profile, then the Japanese V_S30 scaling from the NGA-West2 GMPEs is expected to provide better prediction of site-response than the CA V_S30 scaling, despite closer geographical association. Before testing if the profile is within the acceptable range, smoothing over a depth range of several meters is recommended, especially for borehole measurement techniques which tend to result in short wavelength fluctuations. If the GMPE site-response model also includes a parameter for sediment depth (typically represented by Z_1.0 or Z_2.5, which are also regionalized in the GMPEs), then the sediment depth scaling should be used such that it is compatible with the region selected for the V_S30 scaling (i.e., Japan Z_1.0 with Japan V_S30, etc.). Finally, note that the sediment depth scaling is intended to account for sites with shallower or deeper sediment depth than the average depth for that V_S30 range in the database. Therefore, the V_S30 scaling for shallow sites is mostly contributed by the sediments above the corresponding velocity horizon (1,000 and 2,500 m/s, for Z_1.0 and Z_2.5, respectively), and hence only that part of the profile should fall within the abovementioned range.

Below, we provide a model to calculate the expected median profile for any V_S30 as function of depth, for CA and JP. This can be used to test the site-specific profile as discussed above. The model for the median V _S profile (V_S,median) is based on regression of the four median profiles from Figures 5 and 7, down to a depth representing a sample size of ten profiles. A separate model for the Taiwanese profiles is not provided, for two reasons: (a) separate TW scaling is currently available only in one GMPE, and (b) the TW profiles are limited to 30 m depth and hence such a model is less reliable.

V S , m e d i a n ( z ) = a 0 + a 1 l n ( Z + a 2 a 2 )

(3)

a 0 = b 1 V S 30 + b 2

(3a)

a 1 = b 3 V S 30 + b 4

(3b)

a 2 = b 5 exp ( b 6 V S 30 )

(3c)

S t d V s ( In units ) = a 3

(4)

a 3 = b 7 V S 30 + b 8

(4a)

The coefficients b₁ through b₈ are given in Table 1. The modeled median velocity profiles and their associated standard deviation are plotted in Figures 9 and 10 for California and Japan, respectively. The CA median model seems to fit the data within regression limits (Z_N=10) generally well. The Japanese median model, however, was more difficult to constrain to both the shallow and the deep part, due to the different median shape. This was true for other functional forms as well. We choose to optimize the fit to the shallow part and allow greater misfit in the deep part for two main reasons: (a) the shallow gradient will usually have a greater effect on the amplification than the deeper parts (e.g., Anderson et al. 1996), and (b) the shallow part is better constrained due to the decrease in the number of profiles with depth. Considering all of the above, the Japanese models are considered appropriate to a depth of 100 m. Beyond that depth, the velocity gradient in the model may be too high (the modeled velocity may increase more quickly than the actual measured profiles). Another way of testing the suggested models is to calculate the model V_S30 and compare to the target value, represented by the bin median (i.e., 270, 400, 560, and 760). Note, however, that the measured medians (represented by the symbols in Figures 8 and 9) do not necessarily match the target value, either, and are within 2% and 5% for the CA, and Japan profiles, respectively. In both regions the suggested model is within 5% from the target value for 270 ≤ V_S30 ≤ 760 and within 10% for 250 ≤ V_S30 ≤ 850. We recommend using the model only within these limits. A comparison of the target V_S30 with the raw and smooth model values can be seen in Figure A2 in the online Appendix. The deviations from the target V_S30 values are the result of fitting the entire Vs and depth range with one smooth, simple, continuous, functional form. A better match with the target V_S30 value could have been obtained, at the cost of either not fitting the median shape very well, or not providing a simple continuous model.

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Figure 9.

V _S -Z model for four V_S30 groups, California profiles only. (a) Median. Open circles represent maximum regression depth (b) Std. “CA” relates to the velocity profiles in California which are associated with strong-motion stations only.

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Figure 10.

V _S -Z model for four V_S30 groups, Japan profiles only. (a) Median. Open circles represent maximum regression depth. (b) Std.

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Table 1

Coefficients for calculating median and Std of velocity profiles (Equations 3 and 4)

Coefficient	California-type profile	Japan-type profile
b 1	0.25	0.2
b 2	104	40
b 3	0.22	0.25
b 4	166	260
b 5	53	28
b 6	-0.00388	-0.00296
b 7	0.0002	0
b 8	0.195	0.4

As for the Std _Vs models, also shown in Figures 8 and 9, we choose to make the California model increase linearly with V_S30, but the Japanese Std _Vs model is independent of V_S30 This is because no clear trend was found with respect to V_S30 in the calculated Japanese Std _Vs . The Japanese Std _Vs is higher on average than the California Std _Vs , due to larger variability of profiles which fall into the same V_S30 category.

Note that the calculated Std _Vs is the standard deviation of the measured profiles only, which represent approximately 49% of the NGA-West2 sites (see Figure 11), and 53% of sites in California (Ancheta et al. 2014). If a V _S profile within 300 m from the strong-motion station was not available, V_S30 was estimated based on one of many available proxies, such as surface geology (Wills and Clahan 2006), topographical slope (Wald and Allen 2007), or terrain (Yong et al. 2012). For a V_S30 estimated based on a correlated surface proxy, additional epistemic uncertainty is recommended by Ancheta et al. (2013), due to the uncertainty related with the correlation between the two proxies. In some cases (such as for example the ASK14 model), such epistemic uncertainty was instead added into the aleatory variability associated with the GMPE, for ease of application. For example, Abrahamson et al. (2014) suggest different intra-event variability for cases of measured vs. estimated V_S30.

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Figure 11.

Distribution of measured V_S30 (red) values vs. inferred V_S30 (blue) values in the NGA-West2 site database.

An important question is whether or not the obtained Std _Vs is representative of the variability of the entire database, including sites with inferred V_S30, which are included in the site-response model of the GMPE. To answer this question, we perform a residual analysis, using residuals from the ASK14 GMPE, separating sites with “measured” V_S30 values from those with inferred (or “estimated”) V_S30 values. We first calculate the systematic deviation of the observed amplification at a single site from the median amplification predicted by the model, termed δ_S2S by Al Atik et al. (2010). We do that with a random effects regression, using only sites containing five recordings or more. An example of the δ_S2S values at two representative spectral periods (PGA and T = 1 s) is presented in Figure 12 for sites with measured and estimated V_S30, separately. The standard deviation of δ_S2S is termed ϕ_S2S, representing the variability in the amplification for sites within the same site-class. Following a simple logic, by which increased input variability inherently leads to increased output variability, we expect ϕ_S2S to increase with increasing variability between different V _S profiles having the same V_S30.

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Figure 12.

ASK14 site terms (ϕ_S2S) for CA sites with measured and estimated V_S30 values, at PGA (left) and T = 1 s (right).

ϕ_S2S for measured and estimated profiles is plotted for ten different spectral periods in Figure 13a, showing no significant increase in uncertainty for the estimated profiles. A two-sample f-test performed on the two populations of δ_S2S confirmed they have the same variance for all spectral periods, with the significance level being higher than 10% for all but one spectral period, 0.2 s. If sites having estimated V_S30 values would have had a wider range of V _S profiles or a significant reduction in accuracy, this should have been observed by a higher ϕ_S2S for the estimated sites than that of the measured sites. Referring to an earlier discussion on the recommended added uncertainty for proxy-based V_S30 estimates, this result is counterintuitive and may require further investigation. It could possibly suggest that the estimation provided by a Vs profile which may be up to 300 m away from the recording station is not necessarily a better estimate than a surface-based proxy. Hence, the comparison in Figure 12a suggests that the profile variability, Std _Vs , obtained from the measured V _S profiles, is representative of the entire NGA-West2 site database and that sites with estimated V_S30 do not generally add uncertainty to the model.

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Figure 13.

(a) The variability of site terms (ϕ_S2S) of CA sites, color-coded by sites with estimated (in blue) vs. measured (in red) V_S30 values. (b) Comparison of amplification variability between 1-D site-response simulations (solid lines) and ASK14 residuals (symbols).

A second question is related to propagation of uncertainty through the site-response component in the GMPE. For example, if our site-specific profile is different than the median V _S (Equation 3) but within range of ±1Std _Vs (Equation 4), do we need to add more uncertainty or is the entire site variability already contained within the ergodic GMPE standard deviation? To answer this question, we compare variability from a set of 1-D site-response simulations with variability as captured by the ground motion residuals obtained from the ASK14 model. The simulations are run using the RVT-based 1-D site response model described in Kamai et al. (2013), using the Toro et al. (1995) model to randomize the soil profiles within a given range. The solid lines in Figure 13b show the standard deviation of the amplification, as obtained from a set of simulations with input rock PGA of 0.2 g, using the Peninsular Range soil material model and using five different base velocity profiles with V_S30 of 190, 270, 400, 560, and 760 m/s, respectively. The symbols on Figure 13b represent the amplification variability from the ground motion database, binned into the same five V_S30 bins. As shown in Figure 12b, the variability obtained from the ground motion database is, on average, greater than that obtained from site-response simulations, with a single exception of the V_S30 = 190 m/s profile. The mismatch for this softer profile may suggest either poor modeling or insufficient data in that range. With that exception, this comparison suggests that the variability of the Vs profile about the median V _S profile (as given in Equations 3 and 4) is already captured by the ergodic GMPE standard deviation. As long as the site-specific V _S profile is within the Std _Vs range, the V_S30 scaling within the GMPE can be used to estimate linear site-response at the site. If the V _S profile is outside of this range, additional study is needed to predict site-response at the site.

Using the Gmpe to Compute Rock Motion for Site-Response Analysis

In lieu of using the GMPE to calculate the surface motions, site-specific site response analysis can be performed to account for the unique geotechnical characteristics of a site (such as layering, material properties, etc.). The most common approach for conducting site-response analysis is to model the soil profile as a 1-D soil column, assuming vertically-propagating SH waves (e.g., Matasovic and Hashash 2012, Rathje et al. 2010, Schnabel et al. 1972, Thompson et al. 2012), and use a GMPE to specify the incoming rock motion. The rock motion is then propagated through the full layered profile, to obtain the expected surface motion. The question asked in this case is what shear-wave velocity to use in the GMPE for calculation of the rock motion, or in other words, where (in the soil profile) to input the rock motion.

There is a tradeoff between the accuracy of the site-response analysis and the accuracy of the input motion calculated from the GMPE. The accuracy of the site-response analysis is enhanced if the soil profile is representative of the full layered profile down to competent rock, where site-effects are negligible. Therefore, for the site-response analysis to be accurate, we may prefer to define the reference rock condition as hard rock (e.g., V_S30 = 1,000 – 2,000 m/s). However, sampling of ground motions on hard-rock sites is still sparse (e.g., see Figure 11) and hence the NGA-West2 GMPEs are relatively poorly constrained for sites with V_S30 values of 1000 m/s or higher. Therefore, to reduce the uncertainty associated with the calculation of the reference input motion, we may prefer to define the reference rock conditions as soft rock (e.g., 700–800 m/s) in which there is sufficient sampling to constrain the GMPE, at the cost of neglecting site-specific site-effects that are due to the soil layers with velocities higher than our reference rock condition.

Our suggested guidelines are for two conditions: First, if there is a strong velocity contrast (i.e., a jump to higher velocities by a factor of 2 or more), input the rock ground motion at that point, specifying V_S30 in the GMPE as the shear-wave velocity representative of the top 30 m below the velocity contrast. Second, for smoothly varying profiles, in which there is no obvious point to enter the motion, it is suggested to set the V_S30 for the input-motion within the range in which the V_S30 scaling in the GMPE is well-constrained (upper end typically considered approximately 760 m/s). In both cases, the velocity gradient below the input level should be consistent with the velocity gradient at the surface of the corresponding generic profile. For example, consider the hypothetical profile shown in Figure 14a, with a V_S30 of 250 m/s. Because the velocity profile is smoothly varying with depth, we look for a velocity horizon with V_S30 between 600–800 m/s and find that the 30-meter increment below Z = 80 m yields a V_S30 of 760 m/s. However, the velocity gradient at that depth is significantly different than that represented by the corresponding velocity profile in the GMPE (calculated by equation 3 and represented by the dashed line on Figure 14a). Therefore, we conduct a separate site-response analysis for two profiles, both with V_S30 of 760 m/s, but with different velocity gradients toward the surface (Figure 14b). We take the ratio between the surface motions calculated for those two profiles, and use that ratio to modify the input motion calculated by the GMPE, using V_S30 of 760 m/s. While this procedure requires an additional step, it ensures that the GMPE V_S30 scaling is used appropriately.

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Figure 14.

An example application for entering an input motion for site-response analysis of a smoothly-varying velocity profile. (a) The soil profile (solid line) reaches V_S30 = 760 at a depth of 80 m. The corresponding generic profile (using Equation 3), shown by the dashed line, has a clearly different velocity gradient. (b) A separate site-response analysis is conducted for both profiles with V_S30 = 760 m/sec but different gradients, and the ratio between the surface motions (represented by full circles) is used to adjust the GMPE prediction for the site-response analysis of the soil profile in Figure 14a.

Summary

V_S30 is shown to be a good predictor of site-response for engineering applications, and hence is used in many recent GMPEs as an index parameter for site characterization. The linear V_S30 scaling in the GMPE represents the range of sites available within the database on which the GMPE is regressed. Therefore, the V_S30 scaling as provided in the GMPE should be used only if the site-specific Vs profile is consistent with the range of profiles used to derive such scaling in the GMPE.

To properly evaluate whether or not the V_S30 scaling in the GMPE is applicable to any single site, knowledge of V_S30 alone is insufficient. Additional information about the velocity structure is required—whether it is a site-specific velocity profile to at least 20 m, or a representative velocity profile for similar geologic conditions, based on measured velocity profiles at other sites in the region. Once a representative profile is available, we recommend testing if it is consistent with either the California-type profile or the Japan-type profile, using the parametric model provided in this paper. If the representative profile is consistent with either one of the models, use the respective V_S30 scaling in the GMPE, regardless of geographical association.

We further explore the site-to-site variability, based on residuals from the ASK14 GMPE, and compare variability of sites with measured versus inferred V_S30 values. We conclude that the inferred V_S30 sites do not seem to have any additional uncertainty and hence that the range of profiles we obtain from the measured sites in the database may be generally representative of the entire set, including sites in which no measurements exist.

We compare the site-to-site variability obtained from the GMPE residuals with amplification variability from 1-D simulations. We see that both are on the order of 0.3 (ln units) and conclude that if the only constrained parameter in the site-response analysis is V_S30, we cannot expect a prediction with greater certainty. This part of the variability is most likely due to the variability in the input motions themselves, and therefore is unavoidable.

Some recent GMPEs that are based on large global data sets identify more than the two separate regions for the linear V_S30 scaling mentioned above (i.e., California and Japan). These may include Taiwan, China, Middle East, and Italy (e.g., GKAS2015). However, the methodology proposed herein can only be expanded to more than two regions once additional velocity profile databases for other regions become available. For the time-being, we are limited to the two options presented in this paper because these are the only two regions with large enough profile databases from which representative velocity profiles can be derived.

Finally, we identify several areas for further investigation, such as the effects of the chosen basin depth parameter on the profile response, its variability, and correlation to other parameters.