This electronic supplement contains figures of ground-motion intensity measure (GMIM) ratios not shown in the main article because of space limitations and because they are not essential for the relations described in the main article; they are given here for completeness. It also has links to two zip files containing tables of average ratios and the coefficients of fits to the ratios, using the function in equation (1) of the main article.
Figure S1. The RotD100/RotD00 ratio for all events and for five magnitude bins. The values shown are the geometric means of the ratios for each record, with the 95% confidence intervals given by the bars. The ratio RotD100/RotD00 is not particularly useful in engineering practice, but of some interest nonetheless. The increase in the ratios with period is probably due to the stronger correlation of the motions between the components, which can lead to pronounced linear polarization, as noted by Boore et al. (2006), Beyer and Bommer (2006), and Boore (2010).
Figure S2. The RotD00/RotD50 ratio for all events and for five magnitude bins. The values shown are the geometric means of the ratios for each record, with the 95% confidence intervals given by the bars.
Figure S3. The Larger/RotD100 ratio for all events and for five magnitude bins. The values shown are the geometric means of the ratios for each record, with the 95% confidence intervals given by the bars. The Larger/RotD100 ratio is always less than unity, because it must be given the definition of RotD100.
Download: average_ratios_of_gmims.zip [Zipped plain text comma-separated value files; ~137 KB]. The magnitude and distance ranges used in computing the averages is given by Mmin and Mmax and Rmin and Rmax in the filename. Each file contains columns of the minimum and maximum magnitude and distance ranges, periods, the number of records used in computing the averages, and then pairs of columns for each GMIM ratio. The first column for each ratio is the geometric mean for each ratio (computed as the antilog of the arithmetic means of the logarithms of the ratios), and the second column is the standard deviation of the natural logarithms (base e) of the ratios. The units of distance and period are in kilometers and seconds, respectively. All other quantities are dimensionless.
Download: m_r_regression_coefficients_ratios_of_gmims.zip [Zipped plain text comma-separated value files; ~122 KB]. This zip file contains coefficients of equation (1) in the main article as the individual comma-separated values files. The file names indicate which ratio of GMIMs is in each file. The names have been abbreviated (e.g., D50GMAR represents RotD50/GMAR) but the meaning should be obvious. Each file contains columns of period, number of records, and then three columns for each of the coefficients in equation (1) in the main article. The first column in each set of three is the coefficient from the regression; the second column is a smoothed version of the coefficients, computed as the running mean of 11 points centered at each frequency (except for the end points, where the number of points is reduced linearly as the end member periods are reached); and the third column is the standard error of the coefficient. The units of period are in seconds. All other quantities are dimensionless.
Beyer, K., and J. J. Bommer (2006). Relationships between median values and between aleatory variabilities for different definitions of the horizontal component of motion, Bull. Seismol. Soc. Am. 96, 1512–1522.
Boore, D. M. (2010). Orientation-independent, non geometric-mean measures of seismic intensity from two horizontal components of motion, Bull. Seismol. Soc. Am. 100, 1830–1835.
Boore, D. M., J. Watson-Lamprey, and N. A. Abrahamson (2006). Orientation-independent measures of ground motion, Bull. Seismol. Soc. Am. 96, 1502–1511.
[ Back ]
