Effect of near-fault directivity pulses on ground-motion intensity measure correlations from the NGA-West2 data set

Abstract

This article investigates the correlation coefficients of ground-motion intensity measures for ground motions containing near-fault directivity velocity pulses. These correlation coefficients are necessary to quantify conditional multivariate intensity measure distributions and generate realizations from them for ground-motion selection. The empirical correlations between intensity measures representing ground-motion amplitude, frequency content, duration, and cumulative effects are calculated using the RotD50 definition and compared with published models. The impact of intensity measure definition as in RotD50, RotD100, and the geometric mean is also scrutinized. The sensitivity of the results to the considered ground motion set and the reference ground motion model are addressed in the computations. The results are compared with those from only non-directivity and mixed data sets based on the NGA-West2 database. The results indicate that the adopted data set has the largest influence on the variability of the empirically computed correlation coefficients. Given the multiple sources that contribute to uncertainty in these calculations, the authors conclude that existing models for predicting median correlation coefficients based on mixed data sets are sufficient for use with directivity, non-directivity, and mixed ground motions.

Keywords

Ground motion intensity measure correlation directivity near fault NGA-West2

Introduction

Seismic performance assessments via time-domain dynamic response history analyses require the site-specific hazard to be represented using ground-motion ensembles. Correlation coefficients between ground-motion intensity measures (IMs) are an important ingredient in establishing conditional multivariate distributions of IMs and generating realizations of them in ground-motion selection procedures (e.g., Baker and Cornell, 2006b; Bradley, 2012a; Tarbali and Bradley, 2015; Wang, 2011). In addition, they are used in performing vector-valued probabilistic seismic hazard analysis (Baker and Cornell, 2005; Bazzurro and Cornell, 2002; Gülerce and Abrahamson, 2010). These correlation coefficients are generally computed using empirical ground-motion data (e.g., Akkar et al., 2014; Baker and Cornell, 2006a; Baker and Jayaram, 2008; Bradley, 2012b; Goda and Atkinson, 2009; Inoue and Cornell, 1990; Kohrangi et al., 2020; Kotha et al., 2017; Wang and Du, 2012). Conventionally, pseudo-spectral accelerations (SAs) are used to represent the target probabilistic and scenario-based seismic hazards for the purpose of ground-motion selection. The dependence of correlation coefficients on the ground-motion causal parameters, that is, rupture magnitude, distance, and site condition, does not seem substantial (Baker and Bradley, 2017; Kohrangi et al., 2020; Kotha et al., 2017; Wang and Du, 2012). The dependence of correlation coefficients on adopted ground-motion models (GMMs) and their corresponding between-event residuals is also reported to be not significant (Baker and Jayaram, 2008; Bradley, 2012b).

Near-fault ground motions containing forward-directivity velocity pulses—with characteristics such as narrow-band amplifications of long-period SA ordinates, short significant durations, and large peak ground velocities—may impose disproportional demands on engineered systems (Champion and Liel, 2012; Chioccarelli and Iervolino, 2010; Luco and Cornell, 2007). Tarbali et al. (2019) showed that an accurate representation of the near-fault seismic hazard in the presence of forward-directivity pulses can be achieved by considering non-SA IMs such as the significant duration and cumulative absolute velocity (CAV) alongside SA ordinates in ground-motion selection. However, empirical IM correlations have to date been developed based on “mixed” data sets of ground motions with and without near-fault directivity records and naturally dominated by the latter. Thus, it is valuable to investigate whether directivity affects such correlation coefficient estimation in addition to the (lack of) causal parameter dependence noted above. It is noted that ground motions containing pulse-like motions generated by the nonlinear site response or basin-generated waves are not the focus of this study.

This article calculates IM correlation coefficients of the near-fault ground motions containing directivity pulses. Sensitivities to the adopted ground-motion data set and reference GMM are addressed, and the results are compared with existing empirical correlation models. The impact of IM definition in terms of the geometric mean, RotD50,¹ and RotD100 is also scrutinized. In the next sections, the methodology and data sets used to compute the correlation coefficients are described, followed by comparisons and discussions on the computed correlations and their variabilities.

Methodology

The Pearson correlation coefficient that measures the linear dependence between two variables (Ang and Tang, 1975) is computed to obtain the empirical correlation between a given IM pair. Considering the varying number of records from a single event and the linear relationship between the total residual and the prediction from a GMM shown in Equation 1, correlation coefficients are calculated between the total residuals of the given IM pair by separating the between- and within-event residuals, using Equation 2 (Goda and Atkinson, 2009):

\ln I M_{i} = μ_{\ln I M_{i}} (rup, site) + δ B_{I M_{i}} + δ W_{I M_{i}}

(1)

ρ_{ε_{I M_{i}}, ε_{I M_{j}}} = \frac{ρ_{δ B_{I M_{i}}, δ B_{I M_{j}}} τ_{I M_{i}} τ_{I M_{j}} + ρ_{δ W_{I M_{i}}, δ W_{I M_{j}}} ϕ_{I M_{i}} ϕ_{I M_{j}}}{σ_{T_{I M_{i}}} σ_{T_{I M_{j}}}}

(2)

where $\ln I M_{i}$ is the prediction from an empirical model; $μ_{\ln I M_{i}} (rup, site)$ is the mean of the logarithm of $I M_{i}$ as a function of rupture ( $rup$ ) and site ( $site$ ) characteristics; $δ B_{I M_{i}}$ and $δ W_{I M_{i}}$ are the between- and within-event residuals of $I M_{i}$ , respectively, and their sum is the total residual of $\ln I M_{i}$ with respect to $μ_{\ln I M_{i}}$ ; $ρ_{ε_{I M_{i}}, ε_{I M_{j}}}$ , $ρ_{δ B_{I M_{i}}, δ B_{I M_{j}}}$ , and $ρ_{δ W_{I M_{i}}, δ W_{I M_{j}}}$ are the correlation coefficients of the total, between-, and within-event residuals for the $I M_{i} - I M_{j}$ pair, respectively; and $σ_{T_{I M_{i}}}$ , $τ_{I M_{i}}$ , and $ϕ_{I M_{i}}$ are the total, between-, and within-event standard deviations of $I M_{i}$ , respectively. Because $μ_{\ln I M_{i}}$ is obtained from a given GMM, using a different GMM will result in a different $δ B_{I M_{i}}$ and $δ W_{I M_{i}}$ and consequently a different total residual and correlation coefficients (for a given $I M_{i} - I M_{j}$ pair). It is noted that $δ B_{I M_{i}}$ and $δ W_{I M_{i}}$ are calculated for each and every earthquake and ground motion using the mixed effect regression procedure elaborated upon by Jayaram and Baker (2010).

In this article, correlation coefficients are determined for a range of IMs representing the ground-motion amplitude, frequency content, duration, and cumulative effects. Specifically, SAs for 22 vibration periods ( $T$ = 0.01, 0.02, 0.03, 0.04, 0.05, 0.075, 0.1, 0.15, 0.2, 0.25, 0.3, 0.4, 0.5, 0.75, 1.0, 1.5, 2.0, 3.0, 4.0, 5.0, 7.5, and 10.0 s); peak ground acceleration (PGA); peak ground velocity (PGV); acceleration spectrum intensity (ASI)²; spectrum intensity (SI)³; displacement spectrum intensity (DSI)⁴; CAV⁵; Arias intensity (AI)⁶; and 5%–75% and 5%–95% significant durations⁷ (D_s575 and D_s595, respectively).

Because the calculated residuals are conditioned on the adopted GMMs, using different GMMs results in different correlation coefficient estimates (i.e., a source of epistemic uncertainty). Table 1 presents the considered GMMs and their corresponding abbreviated names for each IM. $N_{GMMs}$ is the total number of adopted GMMs for each IM. The epistemic uncertainty associated with the adopted GMMs is quantified by using the combination of considered GMMs in Table 1 for a given $I M_{i} - I M_{j}$ pair. Table 2 presents the number of correlation coefficients calculated based on the combination of considered GMMs.⁸ Note that, with the exception of a large number of available GMMs for SA (Douglas, 2017; Stewart et al., 2015), relatively few GMMs are published for the remaining IMs such as AI, CAV, D_s575, and D_s595. Equal weights were assigned to every GMM combination (Kulkarni et al., 1984) for computing a distribution over this source of epistemic uncertainty. It is noted that, in practice, each GMM should be paired with its corresponding correlation model to determine the target IM distribution (in ground-motion selection) for each and every logic tree branch. The aim here is to estimate the correlation distribution percentiles given the GMM and data set uncertainties and investigate the effects of directivity pulses.

Table 1.

IMs and corresponding GMMs considered in the correlation calculations

IM	$N_{GMMs}$	GMMs—abbreviation
SA, PGA, and PGV	4	Boore et al. (2014)—BSSA14 Chiou and Youngs (2014)—CY14 Campbell and Bozorgnia (2014)—CB14 Abrahamson et al. (2014)—ASK14
ASI	4	Bradley (2010) using BSSA14, CY14, CB14, and ASK14
SI	4	Bradley et al. (2009) using BSSA14, CY14, CB14, and ASK14
DSI	4	Bradley (2011a) using BSSA14, CY14, CB14, and ASK14
CAV	1	Campbell and Bozorgnia (2010)—CB10
AI	3	Travasarou et al. (2003)—TBA03 Foulser-Piggott and Stafford (2012)—FS12 Campbell and Bozorgnia (2012)—CB12
D_s575 and D_s595	2	Afshari and Stewart (2016)—AS16 Bommer et al. (2009)—BSA09

PGA: peak ground acceleration; PGV: peak ground velocity; ASI: acceleration spectrum intensity; SI: spectrum intensity; DSI: displacement spectrum intensity; CAV: cumulative absolute velocity; AI: Arias intensity; GMM: ground-motion model; IM: intensity measure; SA: spectral acceleration.

Table 2.

Number of GMM combinations for each IM_i–IM_j pair. The lower-left portion of the matrix is symmetric with the upper-right portion and duplicates the pairings

	IM_i
IM_j	SA, PGA, and PGV	ASI	SI	DSI	CAV	AI	D_s575	D_s595
SA, PGA, PGV	4	4	4	4	4	12	8	8
ASI	—	—	4	4	4	12	8	8
SI	—	—	—	4	4	12	8	8
DSI	—	—	—	—	4	12	8	8
CAV	—	—	—	—	—	3	2	2
AI	—	—	—	—	—	—	6	6
D_s575	—	—	—	—	—	—	—	2
D_s595	—	—	—	—	—	—	—	—

A source of potential bias in the estimated residuals for ground motions containing directivity pulses is the fact that the existing empirical GMMs for the SA and non-SA IMs are developed based on mixed ground-motion data sets with mostly non-directivity records. Therefore, most GMMs account for the directivity pulse effects in a broad sense (with the exception of the Chiou and Youngs (2014) model for SA). The misfit of the considered GMMs with respect to the directivity ground motions is presented in the Supplementary Appendix of this article. While there are some minor biases in the directivity ground motions, the overall misfit is not substantial. Because of the lack of directivity consideration in the non-SA and most SA models, this article investigates IM correlation coefficients based on the prevalent GMMs for shallow crustal events listed in Table 1 without any specific consideration for directivity effects (i.e., also ignoring the directivity component of the Chiou and Youngs (2014) model). It is noted that existing post hoc models to account for the directivity effects can provide results with significant inter-model uncertainty (Donahue et al., 2019), indicating the need for further research.

The primary IM definition used in this article is RotD50, which considers the median IM amplitude over all horizontal orientations of shaking (Boore, 2010). Results obtained based on the geometric mean definition (i.e., the square root of the multiplication of two horizontal as-recorded IMs) showed no notable numerical differences (see Supplementary Appendix), consistent with the statistical similarity of the geometric mean and RotD50 for SA ordinates (Beyer and Bommer, 2006). However, due to the directionality potential of directivity ground motions, comparisons between correlation coefficients obtained using the RotD50 and RotD100 definitions are examined in Section “Correlation dependence on the directional IM definition.”

Ground-motion data set

The 143 ground-motion records identified by Shahi and Baker (2014a) as containing directivity pulses in the NGA-West2 database are adopted as the directivity data set (which contains records from shallow crustal events of various geographical regions). A subset of the NGA-West2 database containing 6636 records with $M_{w} \geq$ 5.0 and $R_{rup} \leq$ 600 km is used as the non-directivity data set. This is ∼80% of all NGA-West2 data with $M_{w} \geq$ 5.0; hence, we refer to it simply as the NGA-West2 data set herein (the full data set was not available due to download restrictions on the time series, which are needed to compute the non-SA IMs). Figure 1a presents the rupture magnitude ( $M_{w}$ ) and source-to-site distance ( $R_{rup}$ ) distribution of the utilized ground motions along with the site classifications according to NEHRP (2003) for the directivity subset. Ground motions are used in the range of usable frequency for any IM pair that includes SA, PGV, ASI, SI, and DSI. The usable frequency limitations, associated with record noise and processing, result in a smaller number of IM values for longer vibration periods (Figure 1b). PGV is calculated for records with usable periods not smaller than $T_{\max}$ = 4.0 s due to the filtering effects on the processed records (Akkar and Bommer, 2007). SI and DSI are also calculated for records with usable periods greater than $T_{\max}$ = 2.5 and 5.0 s, respectively.

Uncertainty due to the finite number of ground motions used to calculate the correlation coefficients (especially considering the significantly smaller size of the directivity data set) is addressed by generating bootstrapped samples of the calculated residuals. This non-parametric approach is performed by randomly selecting sample sets from a given base data set with replacement (see Efron and Tibshirani (1993) for further details) and is demonstrated by Bradley (2012b) and Wang and Du (2012) to generate results consistent with those from the Fisher transformation (Ang and Tang, 1975). A total of 2000 bootstrapped samples were found to provide stable results across all IMs for both the directivity and non-directivity data sets.

Results

The final output of the correlation coefficient computation for a given $I M_{i} - I M_{j}$ pair is a distribution of $ρ$ generated by the bootstrapped realizations for each GMM combination. Following Bradley (2012b), the percentiles of this distribution are used to illustrate the uncertainty effects and compare different data sets and published models in the following subsections.

Sensitivity to data set and adopted GMM

Figure 2 illustrates the correlation of SA ordinates from $T$ = 0.01 to 10 s periods with SA(3.0) and D_s575 for the considered directivity and non-directivity data sets. For each GMM, the 50th percentile of $ρ$ is shown in solid lines, and the bootstrapped 16th and 84th percentiles are shown in dashed lines. This figure shows that the variation in the median $ρ$ due to the adopted GMM uncertainty is larger for the directivity data set than that for the non-directivity ground motions. Also, for a single GMM, the 16th–84th percentile range for the directivity data set is larger than that for the non-directivity data set. In both instances, this can be attributed to the smaller sample size of the directivity data set and potentially also to their characteristic properties. In addition, most directivity ground motions have $M_{w} \geq$ 6.0 and $R_{rup} \leq$ 30 km for which GMMs have larger misfits and greater between-model differences.

In order to investigate the relative contribution of the potential factors, 20 ground-motion sets from the non-directivity data set, each with 143 records (equal to the directivity data set size), were randomly selected. As shown in the Supplementary Appendix, the variation of $ρ$ for these random sets is on the order of the variation of $ρ$ from the directivity data set. This, therefore, indicates that the data set sample size plays the most significant role in the variability of the obtained correlation coefficients in Figure 2. In terms of the median correlations, the smaller absolute median $ρ$ between long- and short-period SAs and between long-period SAs and significant durations for the directivity ground motions (when compared with the non-directivity counterparts—see Supplementary Appendix) can be related to the inherent characteristics of directivity ground motions (i.e., narrow-band amplifications of long-period SAs, short D_s575 and D_s595, and large PGV).

The D_s575 correlation curves in Figure 2c and d show that the median $ρ$ curves calculated using the Afshari and Stewart (2016) model are separated from those obtained using the Bommer et al. (2009) model. This illustrates the effect of GMM uncertainty on the calculated $ρ$ values that is more pronounced in the case of smaller data sets. This also emphasizes that, for a given D_s575 model, the difference between the four SA models is smaller than the difference between the D_s575 models (which also holds true for SA correlations with D_s595 and AI).

We also scrutinized whether the non-directivity data set provides different results in comparison to a mixed data set (containing 6636 non-directivity and 143 directivity records from the NGA-West2 subset considered here). No differences were observed between the results across all considered IMs (see Supplementary Appendix). This is expected because the directivity ground motions constitute only ∼2% of such a mixed data set; thus, the mixed and non-directivity data sets are 98% identical. Because the published correlation models in the literature have used mixed data sets (containing both directivity and non-directivity ground motions), the rest of this article compares the directivity results with the mixed data set and published models.

Comparison between the correlation coefficients from the directivity and mixed data sets

Figure 3 compares the correlation coefficients of SA ordinates with SA(0.1), SA(0.5), SA(1.5), and SA(4.0) for the directivity-only and mixed data sets. Note that the combined effects of uncertainty due to the sample size and adopted GMMs are presented via percentiles of a single distribution (obtained by pooling the bootstrapped realizations from all GMM combinations with equal logic tree weights) for a given IM pair. The commonly adopted SA correlation model of Baker and Jayaram (2008) is also presented. Figure 3 shows that the trend of the SA correlations for the directivity data set is similar to that from the mixed data set across the vibration period range. The largest difference between the two data sets and the Baker and Jayaram (2008) model occurs when one IM in the $I M_{i} - I M_{j}$ pair represents a long-period IM and the correlation is low (i.e., $| ρ | <$ 0.5). This can be attributed to the smaller number of usable records for the long-period SAs available for the directivity data set as well as Baker and Jayaram (2008) in comparison with the mixed data set. These differences were also reported by Baker and Bradley (2017).

Figure 4 compares the correlation of PGV, CAV, D_s575, and DSI with the SA ordinates for the directivity and mixed data sets as well as the corresponding published models in the literature (specifically, Bradley (2012b) for PGV, Bradley (2012c) and Wang and Du (2012) for CAV, Bradley (2011b) for D_s575, and Bradley (2011a) for DSI). This figure shows high proximities between the mixed data set results and the published models, but larger differences between them and the directivity data set. Figure 4b shows that the CAV–SA correlation of the directivity data set is smaller for the entire period range in comparison with the mixed data set and Bradley (2012c). The Wang and Du (2012) model for the CAV–SA correlation agrees more with the directivity data set results for periods smaller than 0.5 s but follows the mixed data set and Bradley (2012c) trends for periods larger than 0.5 s. They report a standard deviation of less than 0.05 for their SA-CAV correlation using an NGA-West1 subset which is close to the mixed data set results here (see Figure 4b).

As shown in Figure 4c for D_s575, the directivity data set has smaller (median) correlations with long-period SAs in comparison with the mixed data set and Bradley (2011b). This is consistent with the high long-period SAs and short D_s575 (and D_s595) of the directivity ground motions (caused by the superposition of seismic waves in the directivity phenomenon). However, this is not a significant difference as there is relatively no practical difference between $ρ$ = 0 and −0.1 in establishing a multivariate IM distribution and generating realizations from it (as demonstrated by Baker and Bradley (2017) in comparison with GMM uncertainty impacts). The lower correlation of PGV with 0.5–3.0 s period SAs (as well as SAs with periods smaller than 0.2 s) for directivity ground motions (shown in Figure 4a) can also be interpreted similarly.

Figure 4d also shows that the correlation of DSI with short-period SAs is smaller for the directivity data set in comparison with the mixed data set and Bradley (2011b), and similar to the SA(4.0) correlation with SA ordinates shown in Figure 3d. It is noted that DSI represents the medium-to-long period (i.e., 2.0–5.0 s) ground-motion content, which has characteristic differences for the directivity ground motions when compared with non-directivity records.

Figure 5 compares the correlation of PGV, CAV, D_s575, and DSI with other non-SA IMs considered. The published models are the corresponding ones mentioned in Figure 4. As shown, the directivity data set has consistently larger variability for all the considered non-SA IMs in comparison with the mixed data set. Considering this larger variability, the median $ρ$ from the directivity and mixed data sets can be considered close to each other and to the published models. It is noted that the published model values correspond to their 50th percentile and the 16th–84th percentile range can be considered at least 0.1 for the IMs presented in Figure 5.

Correlation dependence on the adopted data set

Using a subset of the NGA-West2 database, Baker and Bradley (2017) showed that there is no apparent systematic dependence on $M_{w}$ , $R_{rup}$ , and $V_{s 30}$ ⁹ for the correlation of SA ordinates with themselves and with D_s575. Similar remarks were made by Kohrangi et al. (2020) regarding the vertical and horizontal ground-motion IMs. Wang and Du (2012) also concluded no dependence of CAV-SA correlation on $M_{w}$ and site condition; however, they showed its dependence on distance and categorization of ground motions as pulse-like motions using the NGA-West1 subset and GMMs. Figure 6 compares the median CAV-SA correlations from the mixed and directivity data sets adopted here with three models of Wang and Du (2012), namely, correlation based on the NGA-West1 subset, pulse-like directivity set containing 91 fault-normal records (identified using the Baker (2007) method), and 0–30 km distance ground motions (according to Tables 1 to 3 in Wang and Du, 2012). As shown, the Wang and Du (2012) model for pulse-like motions has the largest differences with the directivity ground motions considered here, especially for periods larger than 0.2 s. Their model for the 0–30 km records sits in the middle of their pulse-like and the directivity results from this study. Considering the consistency in the methodologies used to obtain the differing results in Figure 6 (i.e., GMM uncertainty consideration and bootstrapping), this figure illustrates that the distribution of ground motions in the adopted data set and its sample size (and to some extent the adopted GMM misfits to a specific directional IM—fault-normal in this case) can affect the correlation results significantly.

In order to scrutinize the dependence of the obtained correlation coefficients on the adopted data set, the 832 non-directivity NGA-West2 ground motions with $R_{rup} \leq$ 30 and $M_{w} \geq$ 5.5 are assembled as a separate “non-directivity near-fault” data set. The upper limit of $R_{rup} \leq$ 30 is used here because 135 of the directivity records are in this range (only 8 have $R_{rup} >$ 30 km). Figure 7 compares the correlation coefficients of this data set with the directivity and mixed data sets. Figure 7a shows that the non-directivity near-fault data set has its median correlations closer to the directivity data set for SA(3.0) (as well as other SA ordinates not shown here for brevity). For CAV-SA correlations, Figure 7b shows that the non-directivity near-fault data set correlations are closer to the mixed data set results and the correlation model of Wang and Du (2012) for the 0–30 km distance ground motions. For PGV correlations with D_s575 and D_s595, Figure 7d shows high proximities between the median $ρ$ of the directivity and non-directivity near-fault data sets.

To further investigate the dependence of obtained correlation coefficients on $R_{rup}$ , the non-directivity NGA-West2 ground motions with $M_{w} \geq$ 5.5 were divided into distance bins of $R_{rup}$ = (0, 30], (30, 60], (60, 90], and (90, 120] km. Each bin contains 761 available records from our subset of the NGA-West2 database (dictated by the number of available ground motions in the (90, 120] km bin). Figure 8 presents the median $ρ$ of SA(3.0), CAV, D_s575, and PGV for each of these bins and shows no apparent systematic dependence of $ρ$ on $R_{rup}$ . Overall, the variability of the median $ρ$ due to $R_{rup}$ binning is similar to the difference between the mixed and directivity data set results shown in Figures 3 and 4. Note that the relatively larger size of these non-directivity subsets results in slightly smaller variability for their correlations across all IMs considered when compared with the directivity data set correlations (as shown in Figure 8d for PGV correlations with other non-SA IMs).

Correlation dependence on the directional IM definition

Considering the high seismic demands that may be imposed by directivity ground motions and the importance of accounting for the maximum directional ground motion in seismic design (ASCE 7-16, 2017), it is worth investigating the correlation coefficients of the maximum directional IMs, that is, RotD100 (Boore, 2010), for the directivity data set. Figure 9 compares the SA-to-SA correlation results based on the RotD50 and RotD100 definitions with the Baker and Jayaram (2008) model. Specifically, for each recorded ground motion, we compute the RotD100 values directly by rotating the 2 horizontal as-recorded components by 1° increments. For the ground-motion prediction (used for computing the residuals), we take the RotD50 prediction from the native GMMs and then apply the RotD50-to-RotD100 adjustment factor from Shahi and Baker (2014b). Ground-motion predictions for the RotD100 definition are not currently available for non-SA IMs.

Figure 9 shows that the SA correlations obtained based on RotD50 and RotD100 for the directivity ground motions are highly close to each other, with less than 0.05 deviation across all considered SA ordinates (observed for SA(0.5) shown in Figure 9b). This was also reported by Baker and Bradley (2017) for the NGA-West2 database. Considering the 16th–84th percentiles variability range due to the GMM uncertainty and the adopted data set sample size, the differences between the RotD50 and RotD100 correlations, and their differences compared with the Baker and Jayaram (2008) model, are not significant.

Uncertainty in IM distributions for ground-motion selection

The computed correlation coefficients between various IMs are affected by the adopted data set and its ground-motion distribution, the sample size of the data set, and the adopted GMMs. The variability in correlation coefficients can affect the target IM distributions for ground-motion selection. As demonstrated by Baker and Bradley (2017), even appreciable changes in the correlation coefficients typically do not have a significant effect (compared with the uncertainty in the adopted GMMs) on the target IM distribution for ground-motion selection. Epistemic uncertainty due to the adopted GMMs and rupture forecast parameters can affect the target IM distribution significantly (e.g., Figure 4 in Tarbali et al. (2018)), resulting in order of magnitude differences in the demand hazard curves (e.g., Figure 6 in Tarbali et al. (2018)). Although the results of this article can be used to account for the correlation coefficient variability in the considered SA and non-SA IMs of the NGA-West2 and directivity data sets, the uncertainty in IM correlation models does not seem to be a predominant contributor among the essential modeling components to establish the target IM distributions for ground-motion selection.

The results presented in this article are computed using GMMs that do not explicitly account for the directivity effects. It is conceptually expected that considering directivity modifications to GMMs may reduce the differences presented between the correlation coefficients of directivity and mixed data sets because most of the inherent properties of directivity records will be reflected in the median estimates of modified GMMs rather than appearing in residual distributions, and consequently correlation coefficients.

Conclusion

This article presented correlation coefficients of the ground-motion IMs representing amplitude, frequency content, duration, and cumulative effects for the near-fault empirical records containing directivity velocity pulses. The results were compared with those from a larger subset of the NGA-West2 database and with published models. The sensitivity of the results to data set sample size and GMMs used to calculate the correlation coefficients was also quantified.

The results indicated that the correlation coefficients from the directivity ground motions are effectively equivalent to those from the NGA-West2 data set and existing published models. The differences between the computed correlations can be attributed mainly to the data set ground-motion distribution and its sample size, rather than the inherent characteristics of the directivity records. Overall, the uncertainty in the correlation coefficients is not a strong contributor to the total uncertainty in establishing the target IM distributions for ground-motion selection. Therefore, the existing published models continue to be a reasonable choice to characterize correlations of IMs in ground motions with directivity pulses.

Supplemental Material

sj-pdf-1-eqs-10.1177_87552930231199059 – Supplemental material for Effect of near-fault directivity pulses on ground-motion intensity measure correlations from the NGA-West2 data set

Supplemental material, sj-pdf-1-eqs-10.1177_87552930231199059 for Effect of near-fault directivity pulses on ground-motion intensity measure correlations from the NGA-West2 data set by Karim Tarbali, Brendon A Bradley and Jack W Baker in Earthquake Spectra

Footnotes

Acknowledgements

The first author dedicates this article to the memory and lifelong mentorship of his father, Mohammad Tarbali. He will forever be missed.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Karim Tarbali

Brendon A Bradley

Jack W Baker

Supplemental material

Supplemental material for this article is available online.

Notes

References

Abrahamson

Silva

Kamai

(2014) Summary of the ASK14 Ground Motion Relation for Active Crustal Regions. Earthquake Spectra 30: 1025–1055.

Afshari

Stewart

(2016) Physically parameterized prediction equations for significant duration in active crustal regions. Earthquake Spectra 32: 2057–2081.

Akkar

Bommer

(2007) Empirical prediction equations for Peak Ground Velocity derived from Strong-Motion Records from Europe and the Middle East. Bulletin of the Seismological Society of America 97: 511–530.

Akkar

Sandıkkaya

BÖ

(2014) Compatible ground-motion prediction equations for damping scaling factors and vertical-to-horizontal spectral amplitude ratios for the broader Europe region. Bulletin of Earthquake Engineering 12: 517–547.

Ang

AHS

Tang

(1975) Probability Concepts in Engineering Planning and Design. New York: John Wiley & Sons.

ASCE 7-16 (2017) Minimum Design Loads and Associated Criteria for Buildings and Other Structures. Reston, VA: American Society of Civil Engineers.

Baker

(2007) Quantitative classification of near-fault ground motions using wavelet analysis. Bulletin of the Seismological Society of America 97: 1486–1501.

Baker

Bradley

(2017) Intensity measure correlations observed in the NGA-West2 database, and dependence of correlations on rupture and site parameters. Earthquake Spectra 33: 145–156.

Baker

Cornell

(2005) A vector-valued ground motion intensity measure consisting of spectral acceleration and epsilon. Earthquake Engineering and Structural Dynamics 34: 1193–1217.

10.

Baker

Cornell

(2006a) Correlation of response spectral values for multicomponent ground motions. Bulletin of the Seismological Society of America 96: 215–227.

11.

Baker

Cornell

(2006b) Spectral shape, epsilon and record selection. Earthquake Engineering and Structural Dynamics 35: 1077–1095.

12.

Baker

Jayaram

(2008) Correlation of spectral acceleration values from NGA ground motion models. Earthquake Spectra 24: 299–317.

13.

Bazzurro

Cornell

(2002) Vector-valued probabilistic seismic hazard analysis. In: 7th U.S. national conference on earthquake engineering, Boston, MA, 21–25 July.

14.

Beyer

Bommer

(2006) Relationships between median values and between aleatory variabilities for different definitions of the horizontal component of motion. Bulletin of the Seismological Society of America 96: 1512–1522.

15.

Bommer

Stafford

Alarcón

(2009) Empirical equations for the prediction of the significant, bracketed, and uniform duration of earthquake ground motion. Bulletin of the Seismological Society of America 99: 3217–3233.

16.

Boore

(2010) Orientation-independent, nongeometric-mean measures of seismic intensity from two horizontal components of motion. Bulletin of the Seismological Society of America 100: 1830–1835.

17.

Boore

Stewart

Seyhan

Atkinson

(2014) NGA-West2 equations for predicting PGA, PGV, and 5% Damped PSA for shallow crustal earthquakes. Earthquake Spectra 30: 1057–1085.

18.

Bradley

(2010) Site-specific and spatially distributed ground-motion prediction of acceleration spectrum intensity. Bulletin of the Seismological Society of America 100: 792–801.

19.

Bradley

(2011a) Empirical equations for the prediction of displacement spectrum intensity and its correlation with other intensity measures. Soil Dynamics and Earthquake Engineering 31: 1182–1191.

20.

Bradley

(2011b) Correlation of significant duration with amplitude and cumulative intensity measures and its use in ground motion selection. Journal of Earthquake Engineering 15: 809–832.

21.

Bradley

(2012a) A ground motion selection algorithm based on the generalized conditional intensity measure approach. Soil Dynamics and Earthquake Engineering 40: 48–61.

22.

Bradley

(2012b) Empirical correlations between peak ground velocity and spectrum-based intensity measures. Earthquake Spectra 28: 17–35.

23.

Bradley

(2012c) Empirical correlations between cumulative absolute velocity and amplitude-based ground motion intensity measures. Earthquake Spectra 28: 37–54.

24.

Bradley

Cubrinovski

MacRae

Dhakal

(2009) Ground-motion prediction equation for SI based on spectral acceleration equations. Bulletin of the Seismological Society of America 99: 277–285.

25.

Campbell

Bozorgnia

(2010) A ground motion prediction equation for the horizontal component of cumulative absolute velocity (CAV) based on the PEER-NGA strong motion database. Earthquake Spectra 26: 635–650.

26.

Campbell

Bozorgnia

(2012) A comparison of ground motion prediction equations for Arias intensity and cumulative absolute velocity developed using a consistent database and functional form. Earthquake Spectra 28: 931–941.

27.

Campbell

Bozorgnia

(2014) NGA-West2 ground motion model for the average horizontal components of PGA, PGV, and 5% damped linear acceleration response spectra. Earthquake Spectra 30: 1087–1115.

28.

Champion

Liel

(2012) The effect of near-fault directivity on building seismic collapse risk. Earthquake Engineering and Structural Dynamics 41: 1391–1409.

29.

Chioccarelli

Iervolino

(2010) Near-source seismic demand and pulse-like records: A discussion for L’Aquila earthquake. Earthquake Engineering and Structural Dynamics 39: 1039–1062.

30.

Chiou

BS-J

Youngs

(2014) Update of the Chiou and Youngs NGA model for the average horizontal component of peak ground motion and response spectra. Earthquake Spectra 30: 1117–1153.

31.

Donahue

Stewart

Gregor

Bozorgnia

(2019) Ground-motion directivity modeling for seismic hazard applications. https://peer.berkeley.edu/sites/default/files/2019_03_stewart_final.pdf

32.

Douglas

(2017) Ground motion prediction equations 1964-2019 (December 2019). SED Report SED/ENSI/R/01/20140911, 19 December. http://www.gmpe.org.uk

33.

Efron

Tibshirani

(1993) An Introduction to the Bootstrap. New York: Chapman & Hall.

34.

Foulser-Piggott

Stafford

(2012) A predictive model for Arias intensity at multiple sites and consideration of spatial correlations. Earthquake Engineering and Structural Dynamics 41: 431–451.

35.

Goda

Atkinson

(2009) Probabilistic characterization of spatially correlated response spectra for earthquakes in Japan. Bulletin of the Seismological Society of America 99: 3003–3020.

36.

Gülerce

Abrahamson

(2010) Vector-valued probabilistic seismic hazard assessment for the effects of vertical ground motions on the seismic response of highway bridges. Earthquake Spectra 26: 999–1016.

37.

Inoue

Cornell

(1990) Seismic Hazard Analysis of Multi-Degree-of-Freedom Structures, Reliability of Marine Structures, RMS-8. Stanford, CA: Stanford University.

38.

Jayaram

Baker

(2010) Considering spatial correlation in mixed-effects regression and the impact on ground-motion models. Bulletin of the Seismological Society of America 100: 3295–3303.

39.

Kohrangi

Papadopoulos

Bazzurro

Vamvatsikos

(2020) Correlation of spectral acceleration values of vertical and horizontal ground motion pairs. Earthquake Spectra 36: 2112–2128.

40.

Kotha

Bindi

Cotton

(2017) Site-corrected magnitude- and region-dependent correlations of horizontal peak spectral amplitudes. Earthquake Spectra 33: 1415–1432.

41.

Kulkarni

Youngs

Coppersmith

(1984) Assessment of confidence intervals for results of seismic hazard analysis. In: Proceedings of the eighth world conference on earthquake engineering, Vol. 1, pp. 263–270. Tokyo, Japan: International Association for Earthquake Engineering.

42.

Luco

Cornell

(2007) Structure-specific scalar intensity measures for near-source and ordinary earthquake ground motions. Earthquake Spectra 23: 357–392.

43.

NEHRP (2003) NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures, Part1: Provisions, FEMA 450. Washington, DC: Federal Emergency Management Agency.

44.

Shahi

Baker

(2014a) An efficient algorithm to identify strong-velocity pulses in multicomponent ground motions. Bulletin of the Seismological Society of America 104: 2456–2466.

45.

Shahi

Baker

(2014b) NGA-West2 models for ground motion directionality. Earthquake Spectra 30: 1285–1300.

46.

Stewart

Douglas

Javanbarg

Bozorgnia

Abrahamson

Boore

Campbell

Delavaud

Erdik

Stafford

(2015) Selection of ground motion prediction equations for the Global Earthquake Model. Earthquake Spectra 31: 19–45.

47.

Tarbali

Bradley

(2015) Ground motion selection for scenario ruptures using the generalized conditional intensity measure (GCIM) method. Earthquake Engineering and Structural Dynamics 44: 1601–1621.

48.

Tarbali

Bradley

Baker

(2018) Consideration and propagation of ground motion selection epistemic uncertainties to seismic performance metrics. Earthquake Spectra 34(2): 587–610.

49.

Tarbali

Bradley

Baker

(2019) Ground motion selection in the near-fault region considering directivity-induced pulse effects. Earthquake Spectra 35(2): 759–786.

50.

Travasarou

Bray

Abrahamson

(2003) Empirical attenuation relationship for Arias intensity. Earthquake Engineering and Structural Dynamics 32: 1133–1155.

51.

Wang

(2011) A ground motion selection and modification method capturing response spectrum characteristics and variability of scenario earthquakes. Soil Dynamics and Earthquake Engineering 31: 611–625.

52.

Wang

(2012) Empirical correlations between cumulative absolute velocity and spectral accelerations from NGA ground motion database. Soil Dynamics and Earthquake Engineering 43: 229–236.

Supplementary Material

Please find the following supplemental material available below.

For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.

For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.

0.00 MB

36.07 MB

3.72 MB