Estimation of response-spectral values as functions of magnitude, distance, and site conditions

Open-File Report 82-881




We have developed empirical predictive equations for the horizontal pseudo-velocity response at 5-percent damping for 12 different periods from 0.1 to 4.0 s. Using a multiple linear-regression method similar to the one we used previously for peak horizontal acceleration and velocity, we analyzed response spectra period by period for 64 records of 12 shallow earthquakes in western North America, including the recent Coyote Lake and Imperial Valley, California, earthquakes. The resulting predictive equations show amplification of the response values at soil sites for periods greater than or equal to 0.5 s, with maximum amplification exceeding a factor of 2 at 1.5 s. For periods less than 0.5 s there is no statistically significant difference between rock sites and the soil sites represented in the data set. These results are consistent with those of several earlier studies. A particularly significant aspect of the predictive equations is that the response values at different periods are different functions of magnitude (confirming earlier results by McGuire and by Trifunac and Anderson). The slope of the least-squares straight line relating log response to moment magnitude ranges from 0.21 at a period of 0.1 s to greater than 0.5 at periods of 1 s and longer. 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 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 coefficients for the highest seismic zone indicates that the ATC-3 curve is exceeded within about 5 km of a magnitude 6.5 earthquake and within about 20 km of a magnitude 7.5 event. The amount by which it is exceeded is largest in the period range from 0.5 to 2.0 s.

Additional publication details

Publication type:
Publication Subtype:
USGS Numbered Series
Estimation of response-spectral values as functions of magnitude, distance, and site conditions
Series title:
Open-File Report
Series number:
Year Published:
U.S. Geological Survey,
29 p., ill. ;28 cm.