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«SUBMITTED: November 2014 Eric M. Thompson Geological Sciences San Diego State University 5500 Campanile Dr. San Diego, CA 92182-1020 ...»

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USGS Award No. G13AP00070




SUBMITTED: November 2014

Eric M. Thompson

Geological Sciences

San Diego State University

5500 Campanile Dr.

San Diego, CA 92182-1020


Tel: 858-848-0095

David J. Wald

U.S. Geological Survey Golden, CO AWARD PERIOD: May 2013 to April 2014 Abstract The goal of this project is to process and analyze site-specific empirical amplification factors (EAFs). EAFs are the ratio of the recorded motions to a common reference rock motion in order to best capture the actual site amplifications. EAFs are computed at seismic stations within California that have sufficient earthquake recordings to determine robust amplification factors. As a representation of observed amplification, EAFs have a number of useful applications for understanding and mapping site response as well as analyzing its uncertainty. Site response is more generally estimated through empirical correlations with the average shear-wave velocity to 30 m (VS30). For mapping purposes, a second proxy is then needed to estimate VS30, such as surface geology, topographic slope, or terrain. One promising strategy for improving the accuracy of site response maps is to map the amplification directly, rather than rely on mapped values of VS30 as an intermediate step. In contrast to previous studies that have focused on compiling databases of VS30 measurements, we focus on compiling a database of EAFs. Sitespecific EAFs at stations that have recorded numerous ground motions provide more accurate estimates of site response than approximations based on VS30 and each EAF can be directly compared with amplification factors inferred from VS30. We describe what conditions these simple approximation site factors are valid and show where they break down significantly. In addition to basic understanding of the nature of amplification at California’s seismic stations, EAFs may be important in site response mapping applications. For example, the use of EAFs for correcting recordings to rock conditions will improve the underlying rock reference layer of ShakeMap, which is currently estimated from recorded ground motions that are adjusted to rock conditions with VS30based corrections. Similar factors are subsequently used to modify the reference rock layer to account for site response (VS30 correction factors, where VS30 is estimated from slope or geology). Thus, the proposed research will improve both of these steps.

Introduction The primary goal of this project is to develop new protocols/algorithms for mapping site response. For many purposes, such as ground motion prediction equations (GMPEs), building codes, and earthquake hazard mapping, site response is generally estimated through empirical correlations with the average shear-wave velocity to 30 m depth (VS30).

Though widely employed, VS30 is often described as being very limited is representing observed amplifications (e.g., Castellaro et al., 2008; Cadet et al., 2010; Régnier et al., 2014). Herein we analyze the uncertainty of VS30 as a predictor for site response for a large number of sites in California. Moreover, for mapping purposes a second proxy is needed just to estimate VS30, such as surface geology (Wills and Clahan, 2006) or topographic gradient (Wald and Allen, 2007), or a combination of proxies (Thompson et al., 2014). One of the major challenges of this approach is the limited number of VS30 measurements and the limited distribution of the VS30 measurements across geologic units. This creates a potentially unnecessary “weak link” in statistical models of site response that can be eliminated by creating a model of site response amplification directly from geospatial variables (geology, topography, terrain). For example, in the Next Generation of Attenuation (NGA) project database, only 33% of the stations have measured VS30 values, and most of these are in site class E or D (Chiou et al., 2008). The percentage of stations with measured VS30 values increased to 43% for the NGA-West 2 project (Seyhan et al., 2014). Many stations have recorded years of ground motion data that can be exploited to measure actual site amplifications. Thus, the total number of observations available to develop the geospatial model of site response can be significantly increased if we focus on empirical amplification factors (EAFs).

EAFs are computed as the ratio of the recorded motions to a common reference rock motion. In this project we define the rock motion with existing GMPEs (and an appropriate reference VS30). Thus, the EAFs include all of the variability in the recorded motion that is not accounted for by the GMPE, such as site, basin, and topographic effects.

A key limitation of VS30 for mapping purposes is that very few VS30 measurements are collected in hard rock. An extreme example of this is the VS30 database for the Central and Eastern U.S. (CEUS); the Pacific Engineering and Analysis VS30 database contains only two measurements with VS30 greater than 1.5 km/sec (site class A) for the CEUS, though we expect that much of the region consists of site class A (Silva et al., 2011). There are good reasons for this sampling bias from the perspective of those who typically collect the data: more construction and geotechnical investigations take place in soil environments, drilling is more difficult in hard rock, access can be more difficult in rugged terrain, and little to no site response is expected at these hard rock sites. However, the lack of velocity measurements in hard rock presents a challenge when attempting to differentiate between rock and sediment response in hazard maps. While station locations also suffer from a similar bias, the bias is less severe than for the VS30 measurements because there are many broadband stations that have purposefully been sited on rock. These sampling limitations can be partly mitigated by working directly with EAFs rather than VS30.

Tinsley and Fumal (1985) provided an influential early effort at mapping site response. They presented an index of site amplification that is primarily based on soil type, age, and the average VS range of the geologic unit. Other efforts have built upon this method, and generally focus on correlations of VS30 with some other variable that is easily measured at the scale and resolution of interest. This includes correlations with surficial geology (Wills and Silva, 1998; Romero and Rix, 2001; Wills and Clahan, 2006), topographic slope (Wald and Allen, 2007; Allen and Wald, 2009), and geomorphologic terrain inferred from satellite imagery (Yong et al., 2012). Eliminating the link of VS30 between the geospatial proxy (geology, slope, terrain, or some combination) and site amplification is a promising alternative approach that we investigate in this report.

In contrast to previous studies that have focused on compiling databases of VS30 measurements, we will focus on compiling a database of EAFs. The benefits discussed above pertain to developing a site response model for mapping purposes. Thus the site response must be a function of geospatial parameters. However, an additional benefit of focusing on EAFs (i.e., the repeatable site effects inferred from ground motions) is to achieve the best possible estimate of the site response at the strong motion stations and to characterize where and why some VS30 approximations are sufficient. Site-specific EAFs at stations that have recorded numerous ground motions will provide a more accurate estimate of site response than approximations based on VS30 or correlations of EAFs with geospatial parameters. This latter point is particularly useful for ShakeMap when correcting the recorded motions to a reference rock motion, which is used to interpolate between stations (Worden et al., 2010). This will improve the underlying rock reference layer of ShakeMap, which is currently estimated from recorded ground motions with VS30-based site corrections. Similar VS30-based factors are subsequently used to modify the reference rock layer to account for site response (where VS30 is estimated from slope or geology). Thus, the proposed research will not only improve our basic knowledge of the nature of site amplification at California’s seismic stations and provide a reality check on the use of VS30-based amplification factors, it will better constrain these two important steps in constructing ShakeMaps.

Data and Processing The data that we analyze in this project was compiled and processed for the NGA-West 2 project (Ancheta et al., 2014). The database (or flatfile) includes recordings from around the globe, but we only use the records from California for this project. This database contains extensive information on the earthquake source, the conditions at the recording station, and the different distance measures that are required to evaluate GMPEs.

One important attribute of the ground motion data reported in the NGA-West 2 flatfile is the lowest usable frequency (fmin), which is a function of the high-pass corner frequency used in processing the record. In this project, we only use records for response spectra at periods less than 1/fmin, which means that the number of records available to compute the EAFs decreases as period increases.

Next, we remove records that do not meet some general requirements. The Geomatrix classification is also reported in the flatfile. We use the first letter of the Geomatrix classification to remove records that may exhibit soil-structure-interaction.

Additionally, the flatfile indicates if a record exhibited a late S-wave trigger so we remove records where this was noted. We only use records where the Joyner-Boore distance (RJB) is less than 400 km and records where no concerns have been observed in the spectral quality (see Ancheta et al., 2014, for discussion of spectral quality flags).

We define the EAFs relative to the Boore et al. (2014) reference rock motion (i.e., VS30 = 760 m/sec). Thus, we can only use records where the event terms can be computed. Therefore, we only use records from events with four or more records that meet the previously described criteria. Since the number of records available for a given earthquake will vary by period, whether or not an earthquake can be used will be a function of period as well. A map of the earthquake epicenters, the number available records, and the data distribution in magnitude and distance space (as a function period) that remain after these criteria have been applied is summarized in Figure 1.

VS30-Based Amplifications Site response in GMPEs has traditionally been modeled as a function of VS30 and parameters to approximate basin depth, such as the depth at which the shear-wave velocity profile exceeds 1.0 km/sec (z1) which has been added in recent years. Following the approach of Boore et al. (2014), site amplification is broken up into three terms as


–  –  –

Computing the Empirical Amplification Functions The first step for computing the EAFs is to compute the event terms. This is the average residual for each event, which will vary with period and must be subtracted from the data in order to isolate the site effects. We refer to the recorded ground motion intensity (peak acceleration, peak velocity, or response spectra) as !, which is a function of oscillator period T, but we leave this out of the equations for brevity. In order to compute the event terms, we must adjust the recorded data to a consistent reference site condition. Since we will use the Boore et al. (2014) GMPE, we adopt their definition of reference rock for this purpose, which is a VS30 of 760 m/sec. We refer to the VS30=760-adjusted recorded

intensities as !! = !/!!. This leads to two definitions of residuals:

–  –  –

!! = ! + !! + !!,! !, (4) !,!

where i is the earthquake event index, j is the record index, ! is the mean residual, !! is the mean residual for the ith event (i.e., event term, inter-event residual, or between-event residual), and !!,! is the intra-event (i.e., within event) residual. We estimate the residuals in equation 3 using the mixed effects regression code in R (Pinheiro and Bates, 2000).

The pertinent residual for defining the EAFs is to subtract the event term from the

unadjusted residuals (equation 2):

!!" = !!,! − !! !, (5) !,!

where the “ec” subscript indicates that this is the “event corrected” residual.

With multiple recordings at a site, the EAFs can be estimated as the repeatable component of !!" !,! at that site (e.g., Joyner and Boore, 1993; Lin et al., 2011;

Rodriguez-Marek et al., 2011). Because these factors are estimated from recorded motions, they are not limited by the simplicity of the VS30 proxy or the assumptions in a 1D site response analysis. Thus, the EAFs are able to capture any of the repeatable site effects, including velocity structure that is deeper than 30 m and deviations from 1D behavior such as horizontally propagating surface waves (Graves, 1993) and seismic scattering (Thompson et al., 2009).

EAFs, however, are still subject to epistemic uncertainty because they are estimated from the recorded motions. This epistemic uncertainty decreases as the number of recordings at each station increases. Therefore we only include stations in our analysis for which we can estimate the EAFs with at least five records. There are 1,536 stations with recordings that contribute to the data after the previously described screening criteria were applied (summarize in Figure 1). But there are only 483 stations with at least five recordings for which the Boore et al. (2014) PGA is less than 0.1 g. To summarize this smaller database, Figure 2 reproduces Figure 1 with only the data from these stations.

Additionally, Figure 3 is a map of the station locations. Note that we have not checked the distributions of epicentral distance or backazimuth for the events at each station.

Therefore, it is possible that some stations contain a bias to particular source-to-site

geometries and the uncertainties may be underestimated in such cases. To summarize:

these stations contain at least five recordings that fulfill the following criteria:

1. The Boore et al. (2014) PGA for VS30 = 760 m/sec 0.1 g

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