Ground-motion models for predicting vertical components of PGA, PGV and 5%-damped spectral acceleration (0.01–10 s) in Iran

Abstract

This paper presents ground motion models to predict vertical components of peak ground acceleration, peak ground velocity, and 5%-damped response spectral acceleration at periods ranging from 0.01 to 10 s. These models are derived from the comprehensive Iranian strong ground-motion database containing 1350 three-component time-histories recorded during 370 earthquakes with 4.5 ≤ ${\text{M}}_{\text{w}}$ ≤ 7.4. Possible regional dependency of vertical ground-motions to characteristics of three seismo-tectonic regions in Iran was investigated through analysis of variance (ANOVA) technique. Consistent models based on four distance measures; two for point-source (${\text{R}}_{\text{epi}}$ and ${\text{R}}_{\text{hyp}}$) and two for finite-fault (${\text{R}}_{\text{JB}}$ and ${\text{R}}_{\text{rup}}$), were developed. The distribution of inter and intra-event residuals presents satisfactory agreement between actual data and our proposed vertical ground motion prediction equation (GMPE). Furthermore, a detailed comparison between our predictions and four local and global GMPEs is presented, well as horizontal model of Darzi et al. (Bull Seismol Soc Am. https://doi.org/10.1785/0120180196, 2018). In addition, this study provides period-dependent correlation coefficients between epsilons of different GMPEs corresponds to either horizontal, vertical, or vertical-to-horizontal spectral ratio intensity measures as a function of single or two-periods of interest.

Appendix A: Regional dependency test

It is believed that earthquakes from different tectonic regions have a different behavior in terms of source, path and site effects and may invoke discrepancies in ground-motions. As for horizontal GMs by Dea18, the possible regional dependency of vertical components of similar Iranian ground-motion dataset is evaluated through ANOVA. For detailed description of methodology and dataset please refer to Dea18. Due to insignificant influence of SOF on ground-motion amplifications in Iran (Soghrat and Ziyaeifar 2016; Darzi et al. 2018), SOF effect has not been imposed in ANOVA test. In order to avoid the site effect on ground-motions and subsequently regional dependency test’s results, all data with known measured $V_{S30}$ values are adjusted to rock site ($V_{S30} > 750 \;{\text{m}}/{\text{s}}$) and estimated $V_{S30}$ s are used for the remaining data with fundamental frequency $\left( {f_{0} } \right) > 1$ Hz. In this regard $f_{0}$-based prediction equation proposed by Darzi et al. (2019) is used. They determined $f_{0}$ through an automatic technique which is on the basis of horizontal-to-vertical spectral ratio (Nakamura 1989) method.

The null hypothesis of ANOVA is the median ground motions at each bin are equal. If the ratio of the two estimates of the variance of the ground motions is greater than the critical value of F for the significance level (5%), the null hypothesis is rejected, which means that there is high evidence of regional dependency. In this case, earthquake ground motions in regions of comparison are dissimilar and should be kept separate to prevent biased prediction relationships and higher uncertainty in the resulting GMPE. In case of low regional dependency, the resultant combined database can be used in development of future ground motion prediction models to overcome incompleteness of data and reach more reliable prediction model. Additionally, it can enhance the applicable ranges of distance and magnitude in GMPEs and decrease the standard deviation of derived models.

To perform ANOVA, the provided dataset is categorized into three subsets corresponding to three seismo-tectonic regions of Alborz-Azerbaijan-Kopeh dagh (Northern Iran), Zagros, and Central Iran-Makran. Data from each region is separated into intervals of 5 km*0.2 ${\text{M}}_{\text{w}}$ units. Ghasemi et al. (2009) and Sedaghati and Pezeshk (2016) applied ANOVA to 30 number of 5 km*0.25 ${\text{M}}_{\text{w}}$ intervals and 41 number of 10 km*0.5 ${\text{M}}_{\text{w}}$ intervals. They also applied this technique on a limited number of magnitude-distance intervals with minimum magnitude of ${\text{M}}_{\text{w}}$ 5. In present study, almost 6 times larger bins which contain sufficient GM records are used for applying regional investigation test.

We selected data by criterion of earthquake having being recorded by ≥ 2 stations for each bin and afterwards ANOVA is applied to all available bins for which the means of ground motion spectral values has been computed for a certain period for each comparative group. We applied the statistical analysis to 5%-damped vertical response spectral acceleration at five natural periods of 0.01, 0.1, 0.5, 1 and 3 s.

Figure 15 presents 69 bins with sufficient data where at each ANOVA is performed between Zagros (black markers) and Central Iran (red markers). Top intervals are ${\text{R}}_{\text{rup}}$ ranges and the left numbers are ${\text{M}}_{\text{w}}$-intervals for considered bins. If the null hypothesis is rejected, results are shown by plus-signs; otherwise dot-signs present little evidence of regional dependency. Figures 16 and 17 show the ANOVA results between Northern Iran and Zagros, and between Northern Iran and Central Iran, respectively. We used logarithmically transformed ground motions for five couple values of SA which are indicated in vertical axes of bins. The first (leftmost) couple of markers are SAs at 0.01 s, the second couple of markers are SAs at 0.1 s and it continues to the last two points which represents the SAs at 3 s. We found negligible evidence of regional dependence for Zagros and Central Iran ground motions except in one bin of ${\text{M}}_{\text{w}}$ (4.8–5)–${\text{R}}_{\text{rup}}$ (25–30). Note that for distance greater than 80 km although number of analysed bins were decreased, they show no differences in the average ground-motion amplitudes of compared regions. Results from Fig. 16 suggest that ground-motions from Northern Iran supplemented by data from Zagros area as only negligible differences appeared. Similar results were found for Central Iran and Northern Iran as well. It should be noted that the analysis were performed to a vast range of periods as well as PGA and PGV and similar results were revealed. For the sake of brevity results of selected five periods are shown here.

Fig. 15

Graphical outcome of ANOVA results for five SAs at T = 0.01, 0.1, 0.5, 1 and 3 s indicated in five couple of markers, for Zagros (black markers) and Central Iran (red markers) regions for bins with sufficient data. Top right numbers represent number of events at each bin for Zagros (upper) and Central Iran (lower) at specific magnitude-distance interval

Fig. 16

Graphical outcome of ANOVA results for five SAs at T = 0.01, 0.1, 0.5, 1 and 3 s indicated in five couple of markers, for Northern Iran (blue markers) and Zagros (black markers) regions for bins with sufficient data. Top right numbers represent number of events at each bin for Northern Iran (upper) and Zagros (lower) at specific magnitude-distance interval

Fig. 17

Graphical outcome of ANOVA results for five SAs at T = 0.01, 0.1, 0.5, 1 and 3 s indicated in five couple of markers, for Northern Iran (blue markers) and Central Iran (red markers) regions for bins with sufficient data. Top right numbers represent number of events at each bin for Northern Iran (upper) and Central Iran (lower) at specific magnitude-distance interval

Based on the analyses, there seems to be negligible evidence of regional dependency, and accordingly, ground-motions from the considered three regions could be joined together to form one rich dataset and used in regression analysis for development of V-GMPE applicable to the entire parts of Iran. Consistent with the current study, Dea18’s results suggested little evidence of regional dependence of horizontal GMs between the three neighboring seismotectonic regions at all periods.