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Variability in ground motions: Root mean square acceleration and peak acceleration for the 1971 San Fernando, California, earthquake

JACK R. BENJAMIN AND ASSOCIATES, INC., 444 CASTRO STREET, SUITE 501, MOUNTAIN VIEW, CALIFORNIA 94041
THE JOHN A. BLUME EARTHQUAKE ENGINEERING CENTER STANFORD UNIVERSITY, STANFORD, CALIFORNIA
U.S. GEOLOGICAL SURVEY, 345 MIDDLEFIELD ROAD, MENLO PARK, CALIFORNIA 94025

Abstract

Data from the 1971 San Fernando, California, earthquake provided the opportunity to study the variation of ground motions on a local scale. The uncertainty in ground motion was analyzed by studying the residuals about a regression with distance and by utilizing the network of strong-motion instruments in three local geographic regions in the Los Angeles area. Our objectives were to compare the uncertainty in the peak ground acceleration (PGA) and root mean square acceleration (RMS_a) about regressions on distance, and to isolate components of the variance. We find that the RMS_a has only a slightly lower logarithmic standard deviation than the PGA and conclude that the RMS_a does not provide a more stable measure of ground motion than does the PGA (as is commonly assumed). By conducting an analysis of the residuals, we have estimated contributions to the scatter in high-frequency ground motion due to phenomena local to the recording station, building effects defined by the depth of instrument embedment, and propagation-path effects. We observe a systematic decrease in both PGA and RMS_a with increasing embedment depth. After removing this effect, we still find a significant variation (a standard deviation equivalent to a factor of up to 1.3) in the ground motions within small regions (circles of 0.5 km radius). We conclude that detailed studies which account for local site effects, including building effects, could reduce the uncertainty in ground motion predictions (as much as a factor of 1.3) attributable to these components. However, an irreducible component of the scatter in attenuation remains due to the randomness of stress release along faults during earthquakes. In a recent paper, Joyner and Boore (1981) estimate that the standard deviation associated with intra-earthquake variability corresponds to a factor of 1.35.

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