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Bulletin of the Seismological Society of America; December 1981; v. 71; no. 6; p. 2071-2095
© 1981 Seismological Society of America
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The character of high-frequency strong ground motion

THOMAS C. HANKS and ROBIN K. MCGUIRE

U.S. GEOLOGICAL SURVEY, 345 MIDDLEFIELD ROAD, MENLO PARK, CALIFORNIA 94025
ERTEC ROCKY MOUNTAIN, INC., 1746 COLE BOULEVARD, GOLDEN, COLORADO 80401

Abstract

Analysis of more than 300 horizontal components of ground acceleration written by the San Fernando earthquake, eight other moderate-to-large California earthquakes, and seven Oroville aftershocks reveal that these acceleration time histories are, to a very good approximation, band-limited white Gaussian noise within the S-wave arrival window; the band limitation is defined by the spectral corner frequency f0 and fmax, the highest frequency passed by the accelerograph or the Earth's attenuation, and the S-wave arrival window is (0 less double equals tR/ß less double equals Td), where R is distance, ß is shear-wave velocity, and Td is the faulting duration. An examination of the root-mean-square acceleration (arms) characteristics of these records for 0 less double equals tR/ß less double equals Td in terms of the relation


Formula

where {Delta}{sigma} is the earthquake stress drop, yields the surprising result that all 16 earthquakes have stress drops, as determined by record values of arms, very nearly equal to 100 bars (within a factor of 2). The source dependence of arms thus depends solely on the parameter Formula, which increases only as the one-sixth power of seismic moment for constant stress drop earthquakes. Put another way, model and record arms are in agreement within a factor of 2 approximately 85 per cent of the time for {Delta}{sigma} = 100 bars and knowledge of Formula.

On the basis that acceleration time histories are finite-duration, band-limited, white Gaussian noise, for any of which arms is fixed by {Delta}{sigma} = 100 bars and Formula, we can estimate the peak accelerations (amax) for all of these records with considerable accuracy (50 per cent or less). The relation is


Formula

where arms is defined above. With less accuracy, this relation fits the peak acceleration set of Hanks and Johnson (1976) as well, again with {Delta}{sigma} = 100 bars. At a fixed, close distance, we determine the magnitude dependence of amax to be log amax {propto} 0.30 M for Formula, close to that recently determined empirically by Joyner and Boore (1981) for 5.0 less double equals M less double equals 7.7, their coefficient on M (moment magnitude) being 0.25 ± 0.04. In the model presented here, the magnitude dependence of peak acceleration is a function of faulting duration alone; larger earthquakes have larger peak accelerations because they last longer, not because they are intrinsically more powerful at the high frequencies controlling peak acceleration.

These well-behaved characteristics of high-frequency strong ground motion also suggest that the stress differences which develop in the course of crustal faulting are comparably well behaved, both in the average stress release across the characteristic source dimension and in the spectral composition and distribution of stress differences that develop across smaller dimensions.




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Science, June 5, 1992; 256(5062): 1430 - 1432.
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D. A. WALKER, C. S. MCCREERY, and Y. HIYOSHI
T-phase spectra, seismic moments, and tsunamigenesis
Bulletin of the Seismological Society of America, June 1, 1992; 82(3): 1275 - 1305.
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T. C. HANKS and A. C. JOHNSTON
Common features of the excitation and propagation of strong ground motion for North American earthquakes
Bulletin of the Seismological Society of America, February 1, 1992; 82(1): 1 - 23.
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D. M. BOORE and W. B. JOYNER
Estimation of ground motion at deep-soil sites in eastern North America
Bulletin of the Seismological Society of America, December 1, 1991; 81(6): 2167 - 2185.
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J. B. FLETCHER and J. BOATWRIGHT
Source parameters of Loma Prieta aftershocks and wave propagation characteristics along the San Francisco Peninsula from a joint inversion of digital seismograms
Bulletin of the Seismological Society of America, October 1, 1991; 81(5): 1783 - 1812.
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L. HUTCHINGS
"Prediction" of strong ground motion for the 1989 Loma Prieta earthquake using empirical Green's functions
Bulletin of the Seismological Society of America, October 1, 1991; 81(5): 1813 - 1837.
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T. C. HANKS and A. G. BRADY
The Loma Prieta earthquake, ground motion, and damage in Oakland, Treasure Island, and San Francisco
Bulletin of the Seismological Society of America, October 1, 1991; 81(5): 2019 - 2047.
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S. J. GIBOWICZ, R. P. YOUNG, S. TALEBI, and D. J. RAWLENCE
Source parameters of seismic events at the Underground Research Laboratory in Manitoba, Canada: Scaling relations for events with moment magnitude smaller than -2
Bulletin of the Seismological Society of America, August 1, 1991; 81(4): 1157 - 1182.
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M. NIAZI and Y. BOZORGNIA
Behavior of near-source peak horizontal and vertical ground motions over SMART-1 Array, Taiwan
Bulletin of the Seismological Society of America, June 1, 1991; 81(3): 715 - 732.
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P. SOMERVILLE, M. SEN, and B. COHEE
Simulation of strong ground motions recorded during the 1985 Michoacan, Mexico and Valparaiso, Chile earthquakes
Bulletin of the Seismological Society of America, February 1, 1991; 81(1): 1 - 27.
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A. ROVELLI, M. COCCO, R. CONSOLE, B. ALESSANDRINI, and S. MAZZA
Ground motion waveforms and source spectral scaling from close-distance accelerograms in a compressional regime area (Friuli, Northeastern Italy)
Bulletin of the Seismological Society of America, February 1, 1991; 81(1): 57 - 80.
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G.-B. OU and R. B. HERRMANN
A statistical model for ground motion produced by earthquakes at local and regional distances
Bulletin of the Seismological Society of America, December 1, 1990; 80(6A): 1397 - 1417.
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L. WENNERBERG
Stochastic summation of empirical Green's functions
Bulletin of the Seismological Society of America, December 1, 1990; 80(6A): 1418 - 1432.
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P. G. SOMERVILLE, J. P. MCLAREN, C. K. SAIKIA, and D. V. HELMBERGER
The 25 November 1988 Saguenay, Quebec, earthquake: Source parameters and the attenuation of strong ground motion
Bulletin of the Seismological Society of America, October 1, 1990; 80(5): 1118 - 1143.
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S. J. GIBOWICZ, H.-P. HARJES, and M. SCHAFER
Source parameters of seismic events at Heinrich Robert mine, Ruhr Basin, Federal Republic of Germany: Evidence for nondouble-couple events
Bulletin of the Seismological Society of America, February 1, 1990; 80(1): 88 - 109.
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S. K. SINGH, M. ORDAZ, J. G. ANDERSON, M. RODRIGUEZ, R. QUAAS, E. MENA, M. OTTAVIANI, and D. ALMORA
Analysis of near-source strong-motion recordings along the Mexican subduction zone
Bulletin of the Seismological Society of America, December 1, 1989; 79(6): 1697 - 1717.
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D. M. BOORE and W. B. JOYNER
The effect of directivity on the stress parameter determined from ground motion observations
Bulletin of the Seismological Society of America, December 1, 1989; 79(6): 1984 - 1988.
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M. K. SAVAGE and R. P. MEYER
Comment on "Apparent stresses, stress drops, and amplitude ratios of earthquakes preceding and following the 1975 Hawaii MS = 7.2 main shock" by F. R. Zuniga, M. Wyss, and M. E. Wilson
Bulletin of the Seismological Society of America, August 1, 1989; 79(4): 1300 - 1304.
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T. L. Holzer, T. L. HOLZER, T. C. HANKS, and T. L. YOUD
Dynamics of Liquefaction During the 1987 Superstition Hills, California, Earthquake
Science, April 7, 1989; 244(4900): 56 - 59.
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S. H. HARTZELL and T. H. HEATON
Failure of self-similarity for large (M{omega} > Formula) earthquakes
Bulletin of the Seismological Society of America, April 1, 1988; 78(2): 478 - 488.
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J. BOATWRIGHT
The seismic radiation from composite models of faulting
Bulletin of the Seismological Society of America, April 1, 1988; 78(2): 489 - 508.
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A. ROVELLI, O. BONAMASSA, M. COCCO, M. DI BONA, and S. MAZZA
Scaling laws and spectral parameters of the ground motion in active extensional areas in Italy
Bulletin of the Seismological Society of America, April 1, 1988; 78(2): 530 - 560.
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F. SABETTA and A. PUGLIESE
Attenuation of peak horizontal acceleration and velocity from italian strong-motion records
Bulletin of the Seismological Society of America, October 1, 1987; 77(5): 1491 - 1513.
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