- Ground-motion model is:
μ(M,rjb,V s) is natural logarithm of ground-motion parameter (e.g. ln(PGA) where PGA is in g),
b1,ss = 0.853 ± 0.28, b1,rv = 0.872 ± 0.27, b2 = 0.442 ± 0.15, b3 = -0.067 ± 0.16, b5 = -0.960 ± 0.07,
bv = -0.154 ± 0.14, h = 8.90km, V a = 760m∕s, σ = 0.47 ± 0.02 (intra-event) and τ = 0.23 (inter-event).
Also gives overall σ = (0.93 - 0.10Mw)0.5 for Mw ≤ 7.0 and overall σ = 0.48 for Mw > 7.0.
- Uses six site classes (from Wills et al. (2000)):
- 760 ≤ V s ≤ 1500m∕s. Uses V s = 1000m∕s in regression. 12 records.
- Boundary between B and C. Uses V s = 760m∕s in regression. 36 records.
- 360 ≤ V s ≤ 760m∕s. Uses V s = 560m∕s in regression. 16 records.
- Boundary between C and D. Uses V s = 360m∕s in regression. 166 records.
- 180 ≤ V s ≤ 360m∕s. Uses V s = 270m∕s in regression. 215 records.
- Boundary between D and E. Uses V s = 180m∕s in regression. 2 records.
- Uses data from the SCEC Phase III strong-motion database.
- Uses three faulting mechanism classes:
- Use b1,ss. 14 earthquakes, 103 records.
- Use b1,rv. 6 earthquakes, 300 records.
- Use 0.5(b1,ss + b1,rv). 8 earthquakes, 46 records.
- Notes that data is unbalanced in that each earthquake has a different number of records for each site type
hence it is important to correct observations for the inter-event terms before examining residuals for site
- Plots average site class residuals w.r.t. BC category and the residuals predicted by equation and finds good
- Uses 197 records with basin-depth estimates (depth defined to the 2.5km∕s shear-wave velocity isosurface)
to examine dependence of inter-event corrected residuals w.r.t. basin depth. Plots residuals against basin
depth and fits linear function. Finds that all slopes are significantly different than zero by more than two
sigmas. Finds a significant trend in subset of residuals where basin-depths are known w.r.t. magnitude hence
needs to test whether basin-depth effect found is an artifact of something else. Hence derives Ground-motion
models (coefficients not reported) using only subset of data for which basin-depth estimates are known
and examines residuals w.r.t. basin-depth for this subset. Finds similar trends as before hence concludes
found basin effect is truly an effect of the basin. Notes that basin-depth coefficients should be derived
simultaneously with other coefficients but because only a subset of sites have a value this could not be
- Tests for nonlinearity by plotting residuals for site class D w.r.t. predicted ground motion for BC boundary.
Fits linear equation. Finds slope for PGA is significantly different than zero.
- Notes that due to large number of class D sites site nonlinearity could have affected other coefficients in
equation leading to less of a trend in residuals. Tests for this by plotting residuals for site classes B and
BC combined w.r.t. predicted ground motion for BC boundary. Fits linear equation. Finds non-significant
slopes. Notes that nonlinearity may lead to rock ground motions being underestimated by model but not
enough data to conclude.
- Investigates inter-event variability estimate through Monte Carlo simulations using 250 synthetic databases
because uncertainty estimate of τ was considered unreliable possibly due to limited number of events. Find
that there could be a problem with the regression methodology adopted w.r.t. the estimation of τ.
- Plots squared residuals w.r.t. magnitude and fits linear equations. Finds significant trends. Notes that
method could be not statistically correct because squared residuals are not Gaussian distributed.
- Plots squared residuals w.r.t. V s and does not find a significant trend.
- Provides magnitude-dependent estimates of overall σ up to Mw7.0 and constant overall σ for larger
- Tests normality of residuals using Kolmogorov-Smirnov test and finds that the null hypothesis cannot be
rejected. Also examines theoretical quantile-quantile plots and finds nothing notable.