AN AUXILIARY TOOL TO BUILD GROUND-MOTION LOGIC-TREE FRAMEWORK FOR PROBABILISTIC SEISMIC HAZARD ASSESSMENT

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1 AN AUXILIARY TOOL TO BUILD GROUND-MOTION LOGIC-TREE FRAMEWORK FOR PROBABILISTIC SEISMIC HAZARD ASSESSMENT Ö. Kale 1 and S. Akkar 2 1 Ph. D., Kandilli Observatory and Earthquake Research Institute, Boğaziçi University, İstanbul, Turkey 2 Professor, Kandilli Observatory and Earthquake Research Institute, Boğaziçi University, İstanbul, Turkey ozkankale@gmail.com ABSTRACT: We propose a methodology to build ground-motion logic-trees for site-specific and regional seismic hazard assessment. The methodology aims to select the most proper ground-motion equation set and its weights from a suite of candidate ground-motion prediction equations (GMPEs). The overall process leads to a logictree structure such that none of the GMPEs and the corresponding weights dominate the median hazard. A logic-tree biased towards a particular GMPE would fail to capture the epistemic uncertainty. We present several case studies on site-specific and regional hazard to illustrate the implementation of the proposed methodology. The case studies also show the variations in ground motion amplitudes upon the use of alternative ground-motion logic-trees. The discussions in the paper emphasize the importance of decisions on the final ground-motion logic-tree structure in regional or site-specific hazard assessment. KEYWORDS: Ground-motion prediction equation, probabilistic seismic hazard assessment, ground-motion logic tree, sensitivity analysis 1. INTRODUCTION Empirical ground-motion prediction equations (GMPEs) are developed from regression analyses by using recorded accelerograms from past earthquakes. They predict the ground-motion amplitudes of future earthquakes by ergodic assumption (Anderson and Brune, 1999) relying on large and high quality groundmotion datasets. The nature of ground-motion prediction models introduces two types of uncertainties into probabilistic seismic hazard assessment (PSHA) that are classified as aleatory variability and epistemic uncertainty. The former is known as the intrinsic variability (Toro et al., 1997) and it is represented by the standard deviation (sigma, ) of the predictive model. The epistemic uncertainty emerges as a result of incomplete knowledge and data about the physics of the earthquake process (Toro et al., 1997). Theoretically, epistemic uncertainty can be reduced to zero with sufficient knowledge. This is currently impossible due to insufficient and unreliable metadata information in the ground-motion databases that promote the uncertainties in the explanatory variables utilized by the predictive model (Scherbaum et al., 2005; Bommer, 2012; Douglas, 2012). Consequently, the ground-motion logic-tree (Kulkarni et al., 1984) is frequently implemented in PSHA to capture the epistemic uncertainty. General concepts and implementation details of ground-motion logic-trees are discussed in several papers (e.g., Bommer et al., 2005; Scherbaum et al., 2005; Sabetta et al., 2005; Bommer and Scherbaum, 2008; Scherbaum and Kuehn, 2011; Delavaud et al., 2012; Bommer, 2012). These papers indicate that excessive numbers of GMPEs in the ground-motion logic-tree structure would complicate the hazard calculations and would make the weighting strategies insignificant. This fact implies the improper use of logic trees in addressing the epistemic uncertainty. The aforementioned studies, under the light of these remarks, also emphasized the importance of selecting the most proper suite of GMPEs while developing the groundmotion logic-trees. 1

2 Several tools on the selection of GMPEs have been published in recent years. These tools can be classified under non-data-driven (Cotton et al., 2006; Bommer et al., 2010) and data-driven (Scherbaum et al., 2004, 2009; Kale and Akkar, 2013) categories. The non-data-driven tools (also referred to as pre-selection methods) bring forward the qualitative measures (e.g., quality of strong-motion database used in the development of GMPE, its suitability for the tectonic regime of interest, regression method, number of explanatory variables and the functional form of the model, etc.) in selecting the proper GMPEs. The datadriven models have a mathematical basis and mostly rely on statistics and probability concepts. They rank and select the GMPEs by making use of ground-motion datasets particularly compiled for the specific needs of the hazard project. Implementation of data-driven and non-data-driven tools or their combination would help to identify the proper suite of GMPEs but the challenge in the overall process still remains until finalizing the groundmotion logic-tree structure. In other words, the decision on the final number of GMPEs and their weights on each logic-tree branch are still the most important tasks for proper addressing of epistemic uncertainty. The current practice considers either (a) expert opinions (e.g., Stewart et al., 2015), (b) scores of data-driven tests, (c) preliminary PSHA sensitivity analyses, (d) combinations of (a), (b) and (c) (e.g., Giardini et al., 2014), or (e) methodologies with some mathematical background (e.g., Petersen et al., 2008; Al Atik and Youngs, 2014; Arroyo and Ordaz, 2011). These approaches will be discussed to some detail in the subsequent section. We present an alternative methodology to handle the epistemic uncertainty in ground-motion characterization. The proposed procedure uses the non-data-driven and data-driven tools as well as the sensitivity analysis to decide on the final ground-motion logic-tree structure. The logic-tree is established such that none of the predictive models dominates the hazard. Biased hazard towards a specific GMPE (that is hazard dominated by a particular predictive model) may fail the proper representation of the epistemic uncertainty in ground-motion characterization. The paper first discusses the current strategies used in building the ground-motion logic-trees. This is followed by the description of the proposed methodology. We show some case studies at the end of the paper to illustrate our methodology as well as the variations in ground motion amplitudes upon the implementation of alternative logic-trees. The last point indicates the significance of taking decision on the final ground-motion logic-tree structure for a proper assessment of ground-motion intensity levels. 2. GENERAL PROCEDURES TO ESTABLISH GROUND-MOTION LOGIC-TREE The combinations of non-data-driven tools, data-driven tests, sensitivity analyses as well as expert opinions are frequently applied while establishing the logic-tree structure in PSHA. A typical example to this practice is the ground-motion characterization of the SHARE (Seismic Hazard HARmonization in Europe; Giardini et al., 2014) project that developed seismic hazard maps for Europe and the Euro-Mediterranean region. The predictive model pre-selection criteria set by Cotton et al. (2006) was used to identify the potential GMPEs in SHARE. These predictive models were subjected to the statistical tests proposed in Scherbaum et al. (2009) by using an extended ground-motion databank (Yenier et al., 2010). The test results and limited sensitivity analyses for a few alternative ground-motion logic-tree structures were used as auxiliary information by the experts to decide on the final ground-motion logic-tree weights (Delavaud et al., 2012). The most recent expert-opinion based procedure for structuring the ground-motion logic-tree is described by Stewart et al. (2015). This study reviewed an extensive amount of GMPEs developed for different seismotectonic regimes and recommended a set of GMPEs for each seismotectonic regime by using three main criteria. Stewart et al. (2015) preferred predictive models developed from global databases or internationally reviewed local datasets with complicated functional forms (e.g., magnitude saturation, magnitude dependent geometric spreading etc.) to account for earthquake s physical process as much as possible. The authors also suggest the consideration of dissimilar spectral shapes from candidate GMPEs for dominant earthquake scenarios in the study area to capture the epistemic uncertainty properly. They proposed Trellis plots to visualize and identify the dissimilarly behaving predictive models from the candidates. Needless to say the number of dominant earthquake scenarios would define the practicality of 2

3 using Trellis plots to identify the desired predictive model set for the ground-motion logic-tree. It might be difficult to set the proper GMPE suit for excessive numbers of dominant earthquake scenarios. Stewart et al. (2015) also present the ground-motion logic tree weights from well-known PSHA projects that can be considered as a useful guidance to the seismic hazard expert. Petersen et al. (2008), Arroyo and Ordaz (2011) and Al Atik and Youngs (2014) consider the median and median estimations from a set of GMPEs in their ground-motion logic-tree structure to address the epistemic uncertainty in ground-motion characterization. The computation method of changes in the above papers but it, essentially, accounts for the deficiencies in the ground-motion databases used in the development of GMPEs. It would attain larger values at magnitude, distance and style-of-faulting intervals where predictive model development would suffer due to poor distribution of empirical data (i.e., increased model uncertainty). Our interpretation about these methods is that their implementation requires complete information about the ground-motion databases of GMPEs that are used in the ground-motion logic-tree structure. 3. THEORETICAL FRAMEWORK OF THE PROPOSED METHOD The proposed method combines the non-data-driven procedures and data-driven tools with hazard sensitivity analysis. The first-step constitutes the non-data-driven procedures and data-driven tests to identify the suite of candidate GMPEs that can properly reflect the overall ground-motion characteristics at the area of interest. The last component of the method (hazard sensitivity analysis; second-step ) defines the most proper ground-motion logic-tree structure with the help of simple statistics. The first-step analysis also makes use of Trellis plots (Stewart et al., 2015) while assembling the most proper suite of candidate predictive models. None of the GMPEs in the final logic-tree structure dominates the hazard particularly for the return periods of interest. In our opinion, dominancy of a predictive model in the logic-tree structure is against its conceptual framework. This is because logic-tree integrates the epistemic uncertainty to hazard by a set of weighted models to surmount the modeling uncertainties originating from insufficient scientific knowledge. To this end, the dominance of a single ground-motion predictive model would mean the failure of this concept for ground-motion characterization. The next paragraphs brief the second-step of the proposed procedure as it leads to the final decision on the ground-motion logic-tree structure. Figure 1 shows the flow chart for the second-step analysis. We establish N major GMPE bins from the candidate predictive model suite assembled at the end of first-step. Each major GMPE bin is used to establish different numbers of logic-tree structures (K, L, M, etc.) by varying the logic-tree branch weights of GMPEs in that bin. Since the weights reflect the degree-of-belief in the predictive models, the variations in the branch weights mimic alternative degree-of-belief combinations that can be encountered in actual applications. In essence, P different ground-motion logic-tree patterns (designated as LT 11, LT 12,..., LT NM in the node structure in Figure 1) are established for the sensitivity analyses. As an example consider 3 major GMPE groups (N = 3) and each group is used to assemble 4 alternative logic-tree structures (i.e., K = L = M = 4) with different weighting schemes. This results in 12 ground-motion logic-tree structures (i.e., P = 12). Given a spectral period, a total of P hazard curves are computed from the established logic trees (upper right corner in Figure 1) for the site of interest. Spectral accelerations (SAs) from alternative logic trees corresponding to a specific return period (or mean annual rate of exceedance) are normalized by their median value (SA med ) to obtain P normalized spectral accelerations (NSAs). If the hazard assessment deals with multiple sites (e.g., regional hazard assessment), the procedure is repeated until all sites are completed. NSAs of a single site or multiple sites are binned for each logic tree and the trends in the binned NSAs are evaluated by computing their absolute differences from unity as given in Equation (1). In this expression, i represents the logic tree number and takes values from 1 to P whereas j refers to site number and total number of sites is described by N site. D LT,i is the absolute difference from unity corresponding to the ith logic tree., is the normalized spectral acceleration of the ith logic tree at the jth site. The logic-tree structure with the 3

4 minimum D LT,i is the most suitable one in addressing the epistemic uncertainty of ground-motion characterization for site-specific or regional PSHA., 1, 1 ; 1 (1) Note that the proposed procedure favors the logic-tree structure closer to the median hazard as the hazard curves are normalized with respect to their median. We made this choice deliberately because median hazard trend draws a stable trend regardless of the variations in return period and is frequently used for the seismic performance assessment of structures (Abrahamson and Bommer, 2005). Our procedure can be used by normalizing the hazard curves by their mean that would eventually lead to the preference of logic-tree structure closer to mean. However, we do not recommend it, in particular, for very large return periods as the mean hazard would tend to very large fractiles towards low annual exceedance rates (Abrahamson and Bommer, 2005). Figure 1. Proposed method (second-step). 4. SITE-SPECIFIC AND REGIONAL CASE STUDIES The case studies presented in this section consider a shallow crustal active region along the North Anatolian Fault (NAF) zone (Figure 2). This area has recently been studied by several international 1 and local 1 seismic hazard projects and the GMPEs common in their ground-motion logic-trees are Akkar and Çağnan (2010) - AC10, Akkar et al., (2014) - ASB14, Cauzzi and Faccioli (2008) - CF08, Chiou and Youngs (2008) - CY08 and Zhao et al. (2006) - Zh06. We also used these GMPEs in our case studies and considered them as the end products of the first-step in our procedure (i.e., candidate GMPEs). The Trellis plots given in Figure 3 show the median (top row) and median 2 (middle and bottom rows) PGA estimates of the considered GMPEs for generic rock (V S30 = 760 m/s) in terms of magnitude and distance. We show these plots to illustrate the overall behavior of candidate GMPEs under various earthquake scenarios. In general, AC10 and ASB14 yield lower and center range PGA estimations, respectively. The rest of the GMPEs fluctuate below 1 Earthquake Model of the Middle East (EMME, Erdik et al., 2012); Seismic Hazard Harmonization in Europe (SHARE, Giardini et al., 2014); Revision of Turkish Seismic Hazard Map (Akkar et al., 2014b) 4

5 and above AC10 and ASB14 depending on the earthquake scenario (magnitude and distance combinations) and PGA fractile (i.e., median and median 2 ). In a way, they complement the overall picture in describing the epistemic uncertainty in ground-motion characterization of the selected region. This is discussed in detail in the following paragraph. Figure 2. Region of interest (red rectangle) in the case studies. The site-specific case studies are done for Sites A and B (red and green stars, respectively). The regional case study is done for the entire area covered by the red rectangle. Figure 3. Trellis plots showing the median and median 2 strike-slip PGA trends in terms of distance for different moment magnitudes. The site is a generic rock site with V S30 = 760m/s. As for the second-step of our procedure, we established four GMPE bins from the predictive models presented in the previous paragraph. ASB14 and AC10 permanently exist in these bins because they fairly represent the center and lower bound PGA levels for a wide range of fractiles as given in Figure 3. The first and second groups consider CY08 (Group 1) and Zh06 (Group 2) as the third predictive models. CY08 and Zh06 are closer to the upper PGA bound in many scenarios and they help complementing the full range of epistemic uncertainty (upper, central and lower PGA trends) in ground-motion characterization. The logictree structuring of Groups 3 and 4 follow the same rationale as presented for the first two groups. The third and fourth groups permanently include CY08 as the third GMPE whereas Zh06 (Group 3) and CF08 (Group 4) are the fourth predictive models. Consideration of Zh06 and CF08 as the fourth GMPEs while keeping CY08 permanent in these groups augments addressing the full range of epistemic uncertainty in most of the earthquake scenarios as demonstrated in Figure 3. Three different logic-tree structures are established under each GMPE bin that makes a total of 12 ground-motion logic-trees (from LT 11 to LT 43 ) for sensitivity analysis (Table 1). The number of GMPE bins as well as the number of logic-trees under these bins with alternative weights can be increased to run more detailed analysis for identifying the most proper GMPE set 5

6 and their weights. However, we preferred limiting the size of our analyses in order not to complicate the case studies and to demonstrate (discuss) the essentials in the proposed methodology. Table 1. Weighting schemes applied to the predictive models GMPE Group 1 Group 2 Group 3 Group 4 Acronym LT 11 LT 12 LT 13 LT 21 LT 22 LT 23 LT 31 LT 32 LT 33 LT 41 LT 42 LT 43 AC ASB CF CY Zh Figure 4 shows the normalized PGA hazard curves for the ground-motion logic trees that are described in the previous paragraph. The normalizations are with respect to median PGA at each annual exceedance rate for reasons explained in the previous section. The logic trees pertaining to each major GMPE bin (Group 1 to Group 4) are given in different colors. The logic trees under each GMPE bin (e.g., LT 11, LT 12 and LT 13 for Group 1) are shown with different line styles. The hazard calculations are done using the OpenQuake platform (Pagani et al., 2014). The area seismic sources (Figure 2) are taken from the EMME project. The normalized hazard curves indicate that the logic trees of Groups 1, 2 and 4 are sensitive to the changes in the weighting schemes whereas Group 3 logic trees are less sensitive to the variations in the logic-tree weights. The observed trends in Groups 1 and 2 indicate that the change of weights in Zh06 and CY08 would trigger significant variations in the hazard curves. The weighting scheme of CF08 in the fourth GMPE bin would make the behavior of hazard curves even more delicate (The sensitivity of hazard to the changes in CF08 weights is more noticeable towards lower annual exceedance rates). Note that the level of sensitivity to the weighting schemes changes with the site locations. Confined to the case studies in this paper, Site B (closer to the major fault branch along the NAF zone) is more sensitive to the logic-tree weighting strategies with respect to Site A. This observation is more visible in Group 4 logic trees. Our methodology can emphasize such critical points that would help the hazard expert to decide on the optimum ground-motion logic-tree structure for the site of interest. In essence, under the logic-trees given in these case studies, our methodology would prefer the logic-tree structures of Group 3 for Sites A and B as the pertaining normalized hazard curves are closer to unity and are less sensitive to the weighting schemes. For example, our procedure would prefer LT 31 for 475-and 2475-year return periods for site A. LT 31 and LT 32 would be selected for 475- year and 2475-year return periods, respectively for PGA hazard at Site B. These GMPE logic-trees are identified from the computations of D LT,i (Equation 1) for each site and for each return period of interest. Figure 4. Normalized PGA hazard curves (with respect to median PGA at each mean annual exceedance) for a) Site-A and b) Site-B. If the hazard expert s interest is a spectral period range instead of a specific period, the same analysis should be repeated for N discrete spectral periods covering the period range of interest. The sum of scores from 6

7 discrete periods,, (k = 1 N) for the ith logic tree is,. The minimum of, among the alternative GMPE logic trees would give the preferred logic-tree structure for ground-motion characterization. The mathematical expression for this process is given in Equation 2., 7, (2) Figure 5 shows the implementation of Equation (2) for sites A and B for 2475-year generic rock (V S30 = 760 m/s) design spectra computed from the short-period (S S ; T=0.2s) and 1-second (S 1 ; T = 1.0s) spectral ordinates. We followed the procedure provided in ASCE-SEI 7/10 (ASCE, 2010) to plot the smoothed spectra. The preferred logic tree structures are indicated as LT 31 and LT 32 for sites A and B, respectively. The resulting spectra are given in black in the left (Site-A) and right (site-b) panels in Figure 5. The spectra computed form the alternative GMPE logic trees are given in gray in these panels. The differences between the spectral ordinates of preferred and alternative logic trees reach up to 17%. This observation emphasizes the significance of ground-motion logic trees in design or performance assessment of structures because the level of forces (or deformation demands) would certainly affect the section dimensions and other design details. Differences in earthquake demand given in this case study would even become more important as the structural category shifts towards critical facilities (e.g., base isolated hospitals or airport terminals, nuclear power plants etc.). Sa (g) Site-A, 2475-year Period (s) Sa (g) Period (s) Figure 5. Comparison of 2475-year smoothed spectra computed from the preferred and alternative GMPE logic trees. Left and right panel plots show the results for Site-A and Site-B, respectively. Figures 6 and 7 show the implementation of the proposed procedure to regional scale. This time the calculation of PGA hazard is extended to the red rectangular area (Figure 2) for 475- and 2475-year return periods. The normalized PGA distributions in these figures are computed from the normalized hazard curves at 880 discrete sites that are discretized by mesh gridding the rectangular area in Figure 2. The normalized hazard curves are obtained from the GMPE logic-trees that are presented in Table 1. Each panel in Figures 6 and 7 shows the distribution of normalized PGAs extracted from one of the 12 logic trees. The x-axes in these panels depict the site IDs ranging from 1 to 880. Following the basic idea introduced in the site-specific case studies, the fluctuation of the scatter points about unity refers to the lesser dominancy of the individual GMPEs to the hazard. To help visualizing the biased trends in the scatter plots, the panels in Figures 6 and 7 show red lines crossing the unity. The scatters in Figures 6 and 7 reveal similar observations to those observed of site-specific case studies. The GMPE logic-trees of Groups 1, 2 and 4 are sensitive to the weighting schemes. They tend to yield PGA hazard either above or below unity which indicates biased hazard towards a particular GMPE. The logic-tree patterns of Group 3 seem to be less affected by the weighting strategies as the normalized PGAs are closer to unity when their trends are compared with the other logic trees. In fact,, score of LT 31 is the lowest among the other logic trees for both 475- and 2475-year PGA hazard. Figure 8 shows the 2475-year PGA contour maps for the region of interest computed from LT 31 and LT 42. The latter GMPE logic-tree yields higher PGA hazard with respect to LT 31 as the normalized PGAs are well over unity (Figure 7). The differences (particularly in the vicinity of NAF) between the contour maps emphasize the effect of groundmotion logic-tree in the hazard amplitudes Site-B, 2475-year Spectra - LT 11 to LT 43 Spectra - Preferred

8 Figure 6. Distribution of normalized 475-year PGA scatters for the rectangular region given in Figure 2 that is mesh gridded into 880 sites. The presented logic-trees are those listed in Table 1. Figure 7. Distribution of normalized 2475-year PGA scatters for the rectangular region given in Figure 2 that is mesh gridded into 880 sites. The presented logic-trees are those listed in Table 1. Figure 8. PGA contour maps of LT 31 (left panel) and LT 42 (right panel). 8

9 5. SUMMARY AND CONCLUSIONS Epistemic uncertainty in ground-motion characterization cannot be overlooked for deficiencies in the modeling of ground-motion estimations. Thus, GMPE logic trees are indispensable tools in PSHA. The challenge is the realistic assessment of epistemic uncertainty in ground-motion characterization without introducing exhaustive numbers of GMPEs. Such an attempt would increase the computational effort and would reduce the efficiency of logic tree as weighting strategies lose their significance. We introduced a simple methodology to establish a GMPE logic-tree from a suite of candidate GMPEs. The GMPEs and their weights are configured such that the final hazard is not dominated by any one of the GMPEs in the preferred ground-motion logic-tree. Balanced contributions from the predictive models would prevent bias in the hazard due to a dominancy of a particular GMPE. In our opinion, the epistemic uncertainty would not be fairly addressed if the resultant hazard is dominated by a specific GMPE. This fundamental feature of our methodology can make it as an alternative approach among the others while establishing site-specific or regional ground-motion logic trees. An advantage of our methodology is its visual strength because the behavior of normalized hazard curves in site-specific PSHA or the distributions of NSAs in regional PSHA would yield a useful view for a quick assessment of alternative logic trees. Note that we prefer ground-motion logic trees that are closer to median hazard but the normalization can be done to any fractile of hazard depending on the decisions taken by the utility and hazard experts. The methodology would then prefer the ground-motion logic-tree structure that imposes balanced contributions of GMPEs to the target hazard fractile. ACKNOWLEDGEMENTS The first author of this proceeding is granted by the Department of Science Fellowships and Grant Programs of TUBITAK for conducting his post-doctoral research studies in KOERI, Istanbul. The work presented in this article has been developed during the course of the Earthquake Model of the Middle East Region (EMME) project funded by the Global Earthquake Model (GEM) organization. REFERENCES Abrahamson, N. A., and Bommer, J. J., Probability and uncertainty in seismic hazard analysis, Earthquake Spectra 21, Akkar, S., Eroğlu Azak, T., Çan, T., Çeken, U., Demircioğlu, M. B., Duman, T., Erdik, M., Ergintav, S., Kadirioğlu, F. T., Kalafat, D., Kale, Ö., Kartal, R. F., Kekovalı, K., Kılıç, T., Özalp, S., Altuncu Poyraz, S., Şeşetyan, K., Tekin, S., Yakut, A., Yılmaz, M. T., Yücemen, M. S., Zülfikar, Ö., 2014b. Türkiye sismik tehlike haritasının güncellenmesi projesi, UDAP-Ç-13-06, AFAD, Ankara, Turkey. Akkar, S., and Çağnan, Z., A local ground-motion predictive model for Turkey and its comparison with other regional and global ground-motion models, Bull. Seismol. Soc. Am. 100, Akkar, S., Sandıkkaya, M. A., and Bommer, J. J., Empirical ground-motion models for point- and extended-source crustal earthquake scenarios in Europe and the Middle East, Bull. Earthquake Eng. 12, Al Atik, L., and Youngs, R. R., Epistemic Uncertainty for NGA-West2 Models, Earthquake Spectra 30, American Society of Civil Engineers (ASCE) Minimum design loads for building and other structures (ASCE-SEI 7/10), ASCE, Reston, VA, USA. Anderson, J. G., and Brune, J. N., Probabilistic seismic hazard analysis without the ergodic assumption, Seism. Res. Lett. 70, Arroyo, D., and Ordaz, M., On the Forecasting of Ground-Motion Parameters for Probabilistic Seismic Hazard Analysis, Earthquake Spectra 27, Bommer, J. J., Challenges of Building Logic Trees for Probabilistic Seismic Hazard Analysis, Earthquake Spectra 28, Bommer, J. J., Douglas, J., Scherbaum, F., Cotton, F., Bungum, H., and Fäh, D., On the Selection of Ground-Motion Prediction Equations for Seismic Hazard Analysis, Seism. Res. Lett. 81,

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