Prediction of elastic displacement response spectra in Europe and the Middle East

Empirical equations are presented for the prediction of displacement response ordinates for damping ratios
of 2, 5, 10, 20 and 30% of critical and for response periods up to 4 s, using 532 accelerograms from the
strong-motion databank from Europe and the Middle East. The records were all re-processed and only
employed for regressions at periods within the usable range, defined as a fraction of the filter cut-off
and depending on the instrument type (digital or analogue), earthquake magnitude and site class. The
equations can be applied to predict the geometric mean displacement and pseudo-acceleration spectra
for earthquakes with moment magnitudes (M) between 5 and 7.6, and for distances up to 100 km. The
equations also include style-of-faulting and site class as explanatory variables. The predictions obtained
from these new equations suggest that earlier European equations for spectral displacements underestimate
the ordinates at longer periods as a result of severe filtering and the use of the spectral ordinates at periods
too close to the filter cut-off. The results also confirm that the period defining the start of the constant
displacement plateau in the Eurocode 8 (EC8) spectrum is excessively short at 2 s. The results not only
show that the scaling factor defined in EC8 for estimating the spectral ordinates at damping ratios different
from 5% of critical are a good general approximation, but also that this scaling varies with magnitude and
distance (reflecting the influence of duration) and also displays a mild dependence on response period.
Copyright q 2007 John Wiley & Sons, Ltd.
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