The influence of magnitude range on empirical ground-motion prediction

A key issue in the assessment of seismic hazard in regions of low-to-moderate seismicity is the extent to which accelerograms obtained from small-magnitude earthquakes can be used as the basis for predicting ground motions due to the larger-magnitude events considered in seismic hazard analysis. In essence, the question is whether empirical ground-motion prediction equations can be applied outside their strict range of applicability as defined by the magnitude and distance ranges covered by the datasets from which they are derived. This question is explored by deriving new spectral prediction equations using an extended strong-motion dataset from Europe and the Middle East covering the magnitude range M-w 3.0-7.6 and comparing the predictions with previous equations derived using data from only M-w 5.0 and above events. The comparisons show that despite their complex functional form, including quadratic magnitude-dependence and magnitude-dependent attenuation, the equations derived from larger-magnitude events should not be extrapolated to predict ground motions from earthquakes of small magnitude. Moreover, the results suggest not only that ground-motion prediction equations cannot be used outside the ranges of their underlying datasets but also that their applicability at the limits of these ranges may be questionable. Although only tested for smaller magnitudes, the results could be interpreted to suggest that predictive equations also cannot be reliably extrapolated to higher magnitudes than those represented in the dataset from which they are derived, a finding that has important implications for seismic hazard analysis. The conclusion of the study is that empirical derivation of ground-motion prediction equations should be based on datasets extending at least one unit below the lower limit of magnitude considered in seismic hazard calculations. The inclusion of small-magnitude recordings results in a significant increase in the aleatory variability of the equations, although it is yet to be established whether this is due to greater uncertainty in the associated metadata or whether ground-motion variability is genuinely dependent on earthquake magnitude.