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Relationships between Median Values and between Aleatory Variabilities for Different Definitions of the Horizontal Component of Motion

DOI:10.1785/0120050210
Authors:
Katrin Beyer at École Polytechnique Fédérale de Lausanne
Katrin Beyer
Julian Bommer at Imperial College London
Julian Bommer
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Abstract

Ground-motion prediction equations (GMPE) for horizontal peaks of acceleration and velocity, and for horizontal response spectral ordinates, have employed a variety of definitions for the horizontal component of motion based on different treatments of the two horizontal traces from each accelerogram. New definitions have also recently been introduced and some of these will be used in future GMPEs. When equations using different horizontal-component definitions are combined in a logic-tree framework for seismic-hazard analysis, adjustments need to be made to both the median values of the predicted ground-motion parameter and to the associated aleatory variability to achieve compatibility among the equations. Because there is additional aleatory variability in the empirical ratios between the median values for different components, this uncertainty also needs to be propagated into the transformed logarithmic standard deviation of the adjusted equations. This study provides ratios of both medians and standard deviations for all existing component definitions with respect to the geometric mean of the two horizontal components, which is currently the most widely used in prediction equations. The standard deviations on the ratios of the medians are also reported. This article also discusses the issue of the ratios of different horizontal component definitions in relation to the specification of seismic input for dynamic structural analyses, highlighting the importance of consistency between the component definition used to derive the elastic design-response spectrum and the way that biaxial dynamic loading input is prepared.
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1769
Bulletin of the Seismological Society of America, Vol. 97, No. 5, p. 1769, October 2007, doi: 10.1785/0120070128
ERRATUM
Bulletin of the Seismological Society of America
Vol. 96, No. 4A, pp. 1512–1522, August 2006
Relationships between Median Values and between Aleatory Variabilities
for Different Definitions of the Horizontal Component of Motion
by Katrin Beyer and Julian J. Bommer
In Beyer and Bommer (2006), the definition of MaxD
in Table 1 (page 1515) was printed incorrectly. The defini-
tion should read as follows:
MaxD: At each period the maximum spectral ordinate from
all possible orientations of the horizontal axis system is de-
termined. MaxD is hence defined as the 100th percentile of
the spectral ordinates obtained.
Reference
Beyer, K., and J. J. Bommer (2006). Relationships between median values
and between aleatory variabilities for different definitions of the hor-
izontal component of motion, Bull. Seism. Soc. Am. 96, no. 4A, 1512–
1522.
ROSE School
Via Ferrata 1
Pavia, 27100, Italy
(K.B.)
Department of Civil and Environmental Engineering
Imperial College London
London SW7 2AZ, United Kingdom
j.bommer@imperial.ac.uk
(J.J.B.)
Manuscript received 13 May 2007.
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