Erratum to: Compatible ground-motion prediction equations for damping scaling factors and vertical-to-horizontal spectral amplitude ratios for the broader Europe region

Abstract

In a companion article Akkar et al. (Bull Earthq Eng, doi: 10.1007/s10518-013-9461-4 , 2013a; Bull Earthq Eng, doi: 10.1007/s10518-013-9508-6 , 2013b) present a new ground-motion prediction equation (GMPE) for estimating 5 %-damped horizontal pseudo-acceleration spectral (PSA) ordinates for shallow active crustal regions in Europe and the Middle East. This study provides a supplementary viscous damping model to modify 5 %-damped horizontal spectral ordinates of Akkar et al. (Bull Earthq Eng, doi: 10.1007/s10518-013-9461-4 2013a; Bull Earthq Eng, doi: 10.1007/s10518-013-9508-6 , 2013b) for damping ratios ranging from 1 to 50 %. The paper also presents another damping model for scaling 5 %-damped vertical spectral ordinates that can be estimated from the vertical-to-horizontal (V/H) spectral ratio GMPE that is also developed within the context of this study. For consistency in engineering applications, the horizontal and vertical damping models cover the same damping ratios as noted above. The article concludes by introducing period-dependent correlation coefficients to compute horizontal and vertical conditional mean spectra (Baker in J Struct Eng 137:322–331, 2011). The applicability range of the presented models is the same as of the horizontal GMPE proposed by Akkar et al. (Bull Earthq Eng, doi: 10.1007/s10518-013-9461-4 2013a; Bull Earthq Eng, doi: 10.1007/s10518-013-9508-6 , 2013b): as for spectral periods $$0.01 \hbox { s}\le \,\hbox {T}\le \,4\hbox { s}$$ as well as PGA and PGV for V/H model; and in terms of seismological estimator parameters $$4\le \hbox {M}_\mathrm{w} \le 8, \hbox { R} \le 200 \hbox { km}, 150\hbox { m/s}\le \hbox { V}_\mathrm{S30}\le $$ 1,200 m/s, for reverse, normal and strike-slip faults. The source-to-site distance measures that can be used in the computations are epicentral $$(\hbox {R}_\mathrm{epi})$$ , hypocentral $$(\hbox {R}_\mathrm{hyp})$$ and Joyner–Boore $$(\hbox {R}_\mathrm{JB})$$ distances. The implementation of the proposed GMPEs will facilitate site-specific adjustments of the spectral amplitudes predicted from probabilistic seismic hazard assessment in Europe and the Middle East region. They can also help expressing the site-specific design ground motion in several formats. The consistency of the proposed models together with the Akkar et al. (Bull Earthq Eng, doi: 10.1007/s10518-013-9461-4 2013a; Bull Earthq Eng, doi: 10.1007/s10518-013-9508-6 , 2013b) GMPE may be advantageous for future modifications in the ground-motion definition in Eurocode 8 (CEN in Eurocode 8, Design of structures for earthquake resistance—part 1: general rules, seismic actions and rules for buildings. European Standard NF EN 1998-1, Brussels, 2004).