Prediction of earthquake response spectra

We have developed empirical equations for predicting earthquake response spectra in terms of magnitude, distance, and site conditions, using a two-stage regression method similar to the one we used previously for peak horizontal acceleration and velocity. We analyzed horizontal pseudo-velocity response at 5 percent damping for 64 records of 12 shallow earthquakes -in Western North America, including the recent Coyote Lake and Imperial Valley, California, earthquakes. We developed predictive equations for 12 different periods between 0.1 and 4.0 s, both for the larger of two horizontal components and for the random horizontal component. The resulting spectra show amplification at soil sites compared to rock sites for periods greater than or equal to 0.3 s, with maximum amplification exceeding a factor of 2 at 2.0 s. For periods less than 0.3 s there is slight deamplification at the soil sites. These results are generally consistent with those of several earlier studies. A particularly significant aspect of the predicted spectra is the change of shape with magnitude (confirming earlier results by McGuire and by Trifunac and Anderson). This result indicates that the conventional practice of scaling a constant spectral shape by peak acceleration will not give accurate answers. The Newmark and Hall method of spectral scaling, using both peak acceleration and peak velocity, largely avoids this error. Comparison of our spectra with the Nuclear Regulatory Commission's Regulatory Guide 1.60 spectrum anchored at the same value at 0.1 s shows that the Regulatory Guide 1.60 spectrum is exceeded at soil sites for a magnitude of 7.5 at all distances for periods greater than about 0.5 s. Comparison of our spectra for soil sites with the corresponding ATC-3 curve of lateral design force coefficient for the highest seismic zone indicates that the ATC-3 curve is exceeded within about 7 km of a magnitude 6.5 earthquake and within about 15 km of a magnitude 7.5 event. The amount by which it is exceeded for the 7.5 event is largest in the period range from 0.5 to 2.0 s.