An empirical significant duration relationship for stable continental regions

Abstract

An empirical predictive relationship correlating significant duration to earthquake magnitude, site-to-source distance, and local site conditions (i.e., rock vs. stiff soil) for stable continental regions is presented herein. The correlations were developed from data derived from 620 horizontal motions for stable continental regions (e.g., central and eastern North America: CENA), consisting of 28 recorded motions and 592 scaled motions. The data set encompasses the earthquake magnitude from 4.5 to 7.6 and the distance from 0.1 to 199 km. The non-linear mixed-effects regression technique was used to fit a predictive model to the significant duration data. Similar to the trend observed from active shallow crustal region motions, significant durations predicted for stable continental region motions increased with increasing earthquake magnitude and increasing site-to-source distance. In comparing the predicted durations for CENA motions with those for motions from active shallow crustal regions (e.g., western North America: WNA), it is shown that the differences in significant durations for the two regions are relatively minor for site-to-source distances less than about 100 km. Lastly, the significant durations predicted by the proposed model are shown to be in good agreement with durations of the motions recorded during the Mineral, Virginia earthquake of August 23, 2011.

Appendix: Scaling procedure for CENA motions

The scaling procedure used by McGuire et al. (2001) consists of the following computation processes: (1) determination of response spectral transfer function, (2) computation of response spectrum for a given ground motion, (3) determination of target response spectrum, and (4) spectral matching of the time history. A response spectral transfer function was obtained by first using the single-corner frequency point source model (Brune 1970, 1971) to compute smoothed Fourier amplitude spectra (FAS) for both the CENA and WNA. The values of the point source model parameters used are listed in Table 4, where $\kappa$ is a parameter that represents damping in the shallow crust directly below the site; $\Delta \sigma$ represents the stress drop at the source;$Q_{0}$ and $n$ are regional dependent parameters for the frequency dependent quality factor, $Q(f)$; $\rho _{0}$ is crustal density in the source region; and $\beta _{0}$ is shear wave velocity of the crust at the source. Next, random vibration theory (RVT) was used to generate response spectra from the FAS (e.g., Boore 1983; Boore and Joyner 1984; Silva and Lee 1987). The ratio of these two response spectra is the spectral transfer function. The response spectral transfer functions were generated for each site condition; horizontal/vertical component; earthquake magnitudes of 5.5, 6.5, and 7.5 (i.e., center value of magnitude bins); and distances of 1, 5, 30, 75, and 130 km. A total 60 different transfer functions were therefore developed. Example transfer functions for M6.5 cases are shown in Fig. 17. The response spectrum (5 % damping) of a WNA “seed” acceleration time history is then computed. Next, the CENA target response spectrum is obtained by multiplying the “seed” motion’s response spectrum by the appropriate response spectral transfer function. Lastly, the “seed” acceleration time history is scaled to match the target CENA response spectrum (Silva and Lee 1987). In the spectral matching process, a sample time interval $\Delta$t of 0.005 sec (the corresponding Nyquist frequency is 100 Hz) was used to avoid aliasing effects in the frequency range of interest.

Table 4 Point source parameters for WNA and CENA motions (McGuire et al. 2001).

Fig. 17

Response spectral transfer functions for M6.5, rock and soil sites, horizontal and vertical components, and each distance cases (from McGuire et al. 2001)