Magnitude-dependent variance of peak ground acceleration

Abstract

We examine the variability of peak horizontal and vertical accelerations of the large California strong-motion data set for the time period 1957 to 1991 and find a statistically significant dependence of the standard error on earthquake magnitude. Specifically, the standard error decreases with increasing magnitude. The analysis was conducted using a rigorous methodology that examines both earthquake to earthquake (inter-event) variability and within earthquake (intra-event) variability. The magnitude dependence is stronger for inter-event variability than intra-event variability, and stronger for horizontal peak acceleration than for vertical peak acceleration. The data from the recent Landers, Big Bear, and Northridge earthquakes are consistent with these results.

Earthquake Stress Drops From Dynamic Rupture Simulations Constrained by Observed Ground Motions

“…(1) where the intraevent error σ represents the variability among stations for an event, whereas the interevent (or between-event) error τ corresponds to the variability of the event scenarios (Strasser et al, 2009;Youngs et al, 1995). I is the identity matrix, and 1 is the all-ones matrix, both of size N × N, where N is the number of receivers.…”

Estimation of response spectra and peak accelerations from western North American earthquakes; an interim report, Part 2

“…To estimate the standard error of the total variance we use the large-sample expressions given by Searle (1971, p.474) for the variance of <TJ and a\ and the covariance of a\ and o\ , and we assume that o\ is independent of a\ and <TJ, an assumption that may not be strictly correct. The results for peak horizontal acceleration and response spectral values at eight periods are given in Figure 6, which shows the estimate of <7iog y for each magnitude class with error bars corresponding to plus and minus one standard error of <7JL,y-For peak acceleration we, like Youngs et al (1994), find that <7iog y decreases with increasing magnitude and we, like they, find that most of the effect appears below magnitude 6.0. For response spectral values we see no significant dependence of variance on magnitude.…”

“…A number of authors have suggested that the variance of peak horizontal acceleration depends on magnitude (for example, Idriss, 1985, andYoungs et a/., 1994, who show that the dependence is statistically significant). We examine the suggestion for our data, using prediction equations derived by the one-stage maximum-likelihood method to make the results comparable to those of Youngs et al (1994). We divide the data into three magnitude classes, 5.00-5.99, 6.00-6.99, and 7.00-7.99, and take the residuals in each class with respect to the equation determined for the whole data set.…”

On the Testing of Ground-Motion Prediction Equations against Small-Magnitude Data

“…They show that the observations are characterized by a higher variability than the predicted distributions, which is expected as motions from small earthquakes have proved to be more variable than motions from larger earthquakes (e.g. Youngs et al 1995). The origin of this aleatory variability is not identified yet (either a true physically--based uncertainty or an uncertainty due to metadata, Bommer et al 2007).…”

“…In low--seismicity regions such as France, the bulk of the data consists in low magnitude recordings (Mw<4.5). Several studies showed that, due to magnitude--scaling problems, equations based on low--magnitude datasets are not able to correctly predict the ground motions of moderate--to--large magnitudes (Mw ≥ 5, see Youngs et al 1995, Cotton et al 2008. The solution proposed up to now is to select the GMPEs among published equations established from strong motions recorded in higher seismicity regions (either global or region--specific models, Bommer et al 2010).…”