where y is in g, c1= -1.5065, c1a= 0.1650, c1b= -0.2550, c1c= -0.1650, c1d= 0.2550, c2= 1.06,
c3= 1.9636, c4= -2.1, c4a= -0.5, c5= 6.4551, c6= 0.4908, c7= 0.0352, c7b= 0.0462, c8= 0.0000,
c8a= 0.2695, c8b= 0.4833, c9= 0.9228, c9a= 0.1202, c9b= 6.8607, c11= 0, c11b= -0.4536,
cRB= 50, cn= 16.0875, cM= 4.9993, cHM= 3.0956, cγ1= -0.007146, cγ2= -0.006758, cγ3= 4.2542,
ϕ1= -0.5210, ϕ2= -0.1417, ϕ3= -0.007010, ϕ4= 0.102151, ϕ5= 0.0000, ϕ6= 300, γJp-It= 1.5817
(use for Japan and Italy), γWn= 0.7594 (use for 2008 Wenchuan earthquake), ϕ1Jp= -0.6846 (use for
Japan), ϕ5Jp= 0.4590 (use for Japan) and ϕ6Jp= 800 (use for Japan).
Ground-motion model is (for aleatory variability):
where τ1= 0.4000, τ2= 0.2600, σ1= 0.4912, σ2= 0.3762, σ3= 0.8000 and σ2Jp= 0.4528 (for Japan).
Use Vs,30 (Finferred=1 for inferred values and Fmeasured= 1 for measured values) and depth to 1km∕s
shear-wave velocity horizon (Z1.0) to characterise sites. State model applicable for 180 ≤ Vs,30≤ 1500m∕s.
Estimate Z1.0 for those sites lacking measured value by empirical relations linking Z1.0 and Vs,30.
Use 3 mechanisms:
Rake angle -120 ≤ λ ≤-60∘. 8 Mw< 5.9 Californian events and 3 Mw≥ 6 Italian events. FNM= 1.
Rake angle 30 ≤ λ ≤ 150∘. FRV= 1.
Other rake angles. FNM= FRV= 0.
Use two locations w.r.t. vertical projection of the top of rupture:
Rx≥ 0km. FHW= 1.
Rx< 0km. FHW= 0.
Model derived within NGA West 2 project, using the project database (Ancheta et al., 2014).
Update model of Chiou and Youngs (2008) w.r.t. faulting mechanism, hanging-wall effects, scaling with
the depth to top of rupture (ZTOR), scaling with sediment thickness (Z1.0), fault dip (δ) and rupture
directivity. Also account for regional differences in distance attenuation and site effects.
Since database consists mainly of Californian data initially focus on developing moel for California using
primarily Californian data. Then supplement these data with records from large earthquakes elsewhere to
refine magnitude-scaling and to derive more robust σ for larger events. Examine regional differences.
Use same selection criteria as Chiou and Youngs (2008) except for these changes. Include only free-field
data from 18 well-recorded Mw≥ 6 earthquakes (2587 records) from outside California. Assess maximum
usable distance (Rmax) for each earthquake using truncated regression with truncation level equal to second
lowest PGA for each earthquake. Set Rmax equal to distance where truncation level equals -2.5 standard
deviations below fitted median from a event-specific model. This allows final model to be derived using
non-truncated regression. Older earthquakes with high truncation levels have Rmax< 70km but Rmax for
recent events is relatively large. Exclude Class 2 earthquakes (including 1999 Duzce event) located within
20km of Class 1 earthquake.
Functional form based on stochastic simulations, seismological arguments (e.g. change from body-wave
spreading to surface/Lg-wave spreading) and examination of data for various periods. Mainly unchanged
from Chiou and Youngs (2008).
Assess variation of γ (anelastic attenuation) with T for 3 magnitude intervals. For each T and interval
compute variance-weighted average of fitted values of γ for individual events. Find variation in γ with
T is magnitude dependent. Examine regional differences in γ for non-Californian earthquakes, including
aftershocks not selected for final model. Find γ for New Zealand, Taiwan and Turkey are similar to those
for California, whereas those for Italy and Japan (only use data in range 6 ≤ Mw≤ 6.9) indicate more
rapid far-source attenuation and data for Wenchuan slower attenuation. Include regional differences in γ
in final model.
Exploratory analysis of data indicates mechanism effect weaker for Mw< 5 than for Mw> 6. Find similar
effects for ZTOR. Hence include these effects in final model using term that prevents undue influence on
large-magnitude scaling by small earthquakes whose estimates of Mw, ZTOR and mechanism are more
uncertain than those for larger events.
Develop M-ZTOR relation to centre the ZTOR adjustment.
Preliminary analysis indicates dependence of event terms for Mw< 5 increase with δ but that there is no
effect for Mw> 6.
Note very few observations for region inside surface projection of rupture (rjb= 0). Hence use simulations
of (Donahue and Abrahamson, 2014) to develop hanging-wall model here using Rx, the horizontal distance
from top of rupture measured perpendicular to strike. Foot-wall data for each simulation fit using simple
functional form. Compute residuals at rjb= 0 and plot w.r.t Rx for specific dip angle. Derive model using
Rx trend excluding data for Mw6, which showed different behaviour. Find model matches simulations and
empirical data for rjb> 0.
Include directivity effects using direct point parameter (DPP), centred on its mean, as variable. Use
narrow-band formulation of directivity effects, excluding linear-magnitude dependence which is unstable
w.r.t T and statistically insignificant for many T. Assume directivity for Mw< 5.5 is negligible because
of absence of finite-fault information for Mw< 5.7 but note that this assumption may not be true.
Use centred Z1.0 to investigate de-amplification for shallow sediment sites. Find evidence for differences
in ΔZ1.0 scaling between Japan and California. State model applicable for ZTOR≤ 20km and do not
recommend using large depth for Mw> 7 because of lack of data.
Find nonlinear Vs,30 component does not need updating w.r.t. Chiou and Youngs (2008) but linear scaling
does. Find evidence for difference in linear Vs,30 between Japan and California, which include in model.
Normal-faulting term not well constrained because of limited data hence do not update coefficients of
Chiou and Youngs (2008).
Model developed through iterative process of regression for all Ts with some parts of model fixed, smoothing
a few coefficients w.r.t. T, then repeating regression using smoothed coefficients. Correct for sample bias
at long-periods smooth c1 by imposing smooth variation in the slope of c1 w.r.t. T.
2 earthquakes (2000 Tottori (Mw6.61) and 1999 Chi-Chi (Mw7.6)) have large absolute event terms.
Analysis of event-term distribution using robust regression suggest Tottori may be a outlier so remove it
when assessing τ. Do not remove Chi-Chi event term because may lead to underestimate of τ.
Bin τ and σ in 0.5-magnitude-unit bins. Find magnitude dependency for most T. Use trilinear form. Allow
for discontinuity in σ at Mw5 but not for τ. Find inclusion of data from events with < 5 records inflates τ,
at least for small events, and hence derive aleatory variability model using only events with ≥ 5 records.
Between-event residuals suggest dependence on rrup but this largely explained for small T by nonlinear
site amplification and increased intra-event variability for Japanese data. Observed dependence for large
T may be due to unmodelled basin effects because of lack of Z1.0 for areas outside California and Japan.
Note that useful to include κ in future models because of potential influence on aleatory variability model.
Examine inter-event residuals w.r.t. Mw and do not find significant trends. Some outliers (> 2τ) for
large non-California earthquakes (1999 Chi-Chi, 2000 Tottori and 2008 Wenchuan). Add loess fits to plot
and find 95% confidence limits emcompass zero hence outliers not significant. Also using only California
earthquakes results in similar event terms.
Examine intra-event residuals w.r.t. Mw, rrup, Vs,30 and ΔZ1.0. Find no significant trends except at edges
of data. Using loess fits conclude that trends are not significant.
Plot intra-event residuals without Vs,30 term grouped by yref w.r.t. Vs,30. Compare to predicted site
amplification. Find good agreement. For Vs,30 model overestimates amplification for Japanese data
suggesting deviation from linear lnVs,30 scaling for stronger nonlinearity at Japanese sites.
Note that, because all Mw< 6 earthquakes are from California, model may not be applicable for small
events in other regions.
Note that for application to regions with different anelastic attenuation may adjust γ model using estimates
of Q for regions derived using geometric spreading models consistent with model.
Note that amplification for Vs,30> 1130m∕s constrained to unity. Little data in database to examine
amplification for higher Vs,30, where κ may decrease.
Recommend setting ΔZ1.0= 0 when Z1.0 unknown.
When Z1.0 is much lower than E(Z1.0) recommend checking predictions not lower than predictions for
reference condition of Vs,30= 1130m∕s.