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

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.