The character of high-frequency strong ground motion

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 ≦ t − R/β ≦ Td), where R is distance, β 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 ≦ t − R/β ≦ Td in terms of the relation a rms = 0.85 ( 2 π ) 106 2 Δ σ ϕ R f max f o where Δσ 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 1/fo, 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 Δσ = 100 bars and knowledge of 1/fo. On the basis that acceleration time histories are finite-duration, band-limited, white Gaussian noise, for any of which arms is fixed by Δσ = 100 bars and 1/fo, we can estimate the peak accelerations (amax) for all of these records with considerable accuracy (50 per cent or less). The relation is a max = a rms 2 In ( 2 f max f o ) , where arms is defined above. With less accuracy, this relation fits the peak acceleration set of Hanks and Johnson (1976) as well, again with Δσ = 100 bars. At a fixed, close distance, we determine the magnitude dependence of amax to be log amax ∝ 0.30 M for 4≲M=ML≲612, close to that recently determined empirically by Joyner and Boore (1981) for 5.0 ≦ M ≦ 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.