2.276 Douglas (2007)

• Ground-motion model is:

  Coefficients not reported since purpose is not to develop models for seismic hazard assessments but to derive confidence limits on median PGA and thereafter to examine possible regional dependence of ground motions.

• Rederives models of Joyner and Boore (1981), Boore et al. (1993, 1997), Ambraseys et al. (1996), Ambraseys et al. (2005a), Ulusay et al. (2004), Kalkan and Gülkan (2004b) and Sabetta and Pugliese (1987) to find their complete covariance matrices in order to compute confidence limits of the predicted median PGA.
• Uses same site classifications as original studies. S_i = 1 for site class i and 0 otherwise.
• Adopts a simple linear functional form and standard one-stage regression method so that the covariance matrices can be easily computed.
• Assumes a fixed coefficient of 5km (a rough average value for this coefficient for most models using adopted functional form) inside square root to make function linear.
• Examines 95% confidence limits on PGA since it is standard to use 5% significance levels when testing null hypotheses. Plots predicted median PGAs and their confidence limits for M_w5, 6.5 and 8.0 up to 200km to show effects of extrapolation outside range of applicability of models. Finds that confidence limits for models derived using limited data (Ulusay et al., 2004; Kalkan and Gülkan, 2004b; Sabetta and Pugliese, 1987) are wider than models derived using large well-distributed datasets (Joyner and Boore, 1981; Boore et al., 1993, 1997; Ambraseys et al., 1996, 2005a). Notes that for 5.5 < M_w < 7 and 10 ≤ d_f ≤ 60km the 95%-confidence limits of the median are narrow and within bands 10–30% from the median but for other magnitudes and distances (away from the centroid of data) they are much wider (bands of 100% from the median). Notes that inclusion of data from large magnitude events decreases the width of the confidence limits of the model derived using the data of Boore et al. (1993, 1997) compared with that derived using the data of Joyner and Boore (1981) and similarly that derived with the data of Ambraseys et al. (2005a) compared with that derived using the data of Ambraseys et al. (1996).