where: Y is in g, Mref= 4.5, Rref= 1km, Vref= 760m∕s, PGAr is median PGA for reference rock
(i.e. Vs,30= Vref), e0= 0.4473, e1= 0.4856, e2= 0.2459, e3= 0.4539, e4= 1.4310, e5= 0.05053, e6=-0.1662, Mh= 5.5, c1= -1.134, c2= 0.1917, c3= -0.008088, h = 4.5, Δc3,China,Turkey= 0.0028576,
Δc3,Italy,Japan= -0.0025500, c = -0.6, Vc= 1500m∕s, f1= 0, f3= 0.1, f4= -0.15, f5= -0.00701,
f6= -9.9 and f7= -9.9.
Ground-motion model is (for aleatory variability):
where: ϕ is intra-event, τ is inter-event variability, R1= 110, R2= 270, ΔϕR= 0.10, ΔϕV= 0.07,
V1= 225, V2= 300, ϕ1= 0.695, ϕ2= 0.495, τ1= 0.398 and τ2= 0.348.
Use Vs30 (both measured and inferred) to characterise sites. Vs,30 between about 100 and 2016m∕s but
state model applicable from 150–1500m∕s. Most data from soil and soft rock sites (NEHRP C and D)
(peak in distribution about 400m∕s).
Use basin depth (from surface to 1.0km∕s shear-wave velocity horizon) z1 to characterise sites. State model
applicable from 0–3km. Recommend that when z1 is unknown to set δz1 to zero to turn off basin-depth
Use 4 faulting mechanisms:
Strike-slip, P-axis plunge ≤ 40∘ and T-axis plunge ≤ 40∘. About 8500 records from about 210 events.
SS= 1. Other mechanism variables are zero.
Normal, P-axis plunge > 40∘ and T-axis plunge ≤ 40∘. About 1000 records from about 40 events.
NS= 1. Other mechanism variables are zero.
Reverse, P-axis plunge ≤ 40∘ and T-axis plunge > 40∘. About 5500 records from about 100 events.
RS= 1. Other mechanism variables are zero.
Unspecified. No records are from unknown mechanism in input data. U = 1. Other mechanism
variables are zero.
Classify based on plunges of P- and T-axes but almost the same classification using rake angle within 30∘
of horizontal for SS and normal and reverse for negative and positive rake angles not within 30∘.
Model derived within NGA West 2 project, using the project database (Ancheta et al., 2014). Data
principally from: California, Taiwan, Japan, China, Italy, Greece, Turkey and Alaska.
Use three-step approach to balance prediction accuracy and simplicity of form and application. After
constraining site response and some additional effects based on initial analysis (Phase 1), perform
regression (Phase 2) to constrain effects of Mw, rjb and mechanism (base-case model). In Phase 3 examine
inter- and intra-event residuals against secondary variables: region, event type (roughly mainshock or
aftershock), source depth and basin depth. Assess whether secondary variables are statistically significant
and practically meaningful. If so include variables as optional adjustments.
Note lack of constraint for Mw> 7 normal-faulting events.
Develop model to overcome limitations with Boore and Atkinson (2008) in terms of predictions for small
magnitudes and regional dependency in anelastic attenuation.
Exclude data without Mw, rjb and site metadata. Use only one record from co-located stations (e.g. in
a differential array) of same earthquake. Exclude records without both horizontal components. Exclude
earthquakes from oceanic crust or stable continental regions. Exclude records thought not to reasonably
reflect free-field conditions due to site-structure interaction. Only use publicly-available data. Exclude
records (based on visual inspection) with: S-wave triggers, second triggers, noisy traces or time-step
problems. Apply magnitude-distance cut-offs based on instrument type to minimise potential sampling
bias because of triggering of instruments by unusually strong shaking. Only consider earthquakes with ≥ 4
records with rjb≤ 80km after applying other criteria.
Secondary variables are: depth to top of rupture Ztor and hypocentral depth Zhypo; basin depth (from
surface to 1.0km∕s shear-wave velocity horizon) z1; event type: class 1 (mainshocks) or class 2 (aftershocks)
using minimum centroid rjb separation of 10km. Do not consider hanging-wall effects because rjb already
accounts for this.
Magnitude range widest for SS and narrowest for NS so magnitude-scaling better determined for SS
earthquakes. Hence assume common magnitude-scaling for all mechanisms.
Note lack of data at close distances from small events and hence model not constrained here.
Select functional form based on subjective inspection and study of nonparametric data plots. Note
magnitude-dependent geometric spreading, anelastic attenuation and strongly nonlinear (and period
dependent) magnitude-dependency of amplitude-scaling at fixed distance.
Use site-response model of Seyhan and Stewart (2014), which was developed in iterative manner alongside
overall ground-motion model.
Note that, due to trade-offs between geometric and anelastic attenuation, regression cannot simultaneously
determine both. Hence use data from California from Mw≤ 5 (to minimise finite-fault and nonlinear site
effects) to constrain c3 in Phase 1. Correct data for linear site effects. Group data into 0.5 magnitude unit
bins and regress using form ν′+c1′ln(R∕Rref)+c3(R-Rref) to find c3. Find c3 is relatively independent
In Phase 2 exclude Class 2 events (aftershocks) and data from rjb> 80km and adjust data to Vref.
Find evidence for apparent oversaturation in source term but this is compensated by the other terms in
Coefficient e0 is a weighted average of coefficients for other faulting mechanisms.
Recompute coefficients excluding 2008 Wenchuan earthquake (Mw7.9) for which some debate over
suitability for model development. Removal has no effect at short periods but long-period motions increase
for large Mw. See no justification for removal of these data hence retain it for final model.
In Phase 3 (based on mixed-effects residual analyses) find need to include Δc3 (for regional anelastic
attenuation effects) and Fδz1 but not source type or depth adjustments.
Plot inter-event residuals against Mw and rake angle and intra-event residuals against rjb and Vs,30. Find
no trends w.r.t. Mw after excluding Class 2 events from China. Find no trends w.r.t rake angle except for
positive residuals for NS for Mw< 5 and positive bias for T > 1s for RS when Mw> 5. Do not consider
trends sufficient to warrant adjustments. Find no trends w.r.t. rjb nor w.r.t. Vs,30.
Examine influence of non-Californian earthquakes on model by considering Class 1 event terms by region
and fault type. No magnitude overlap for NS events so cannot conclude. For SS event terms similar. For
RS find evidence for higher motions in California for T > 1s but because model for global use do not
Plot intra-event residuals w.r.t. rjb split into different regions: California, New Zealand and Taiwan, for
which find no trends (average Q); Japan and Italy, for which downward trends (low Q); and China and
Turkey, for which upward trends (high Q). For low and high Q cases fit model to residuals for rjb> 25km
to find Δc3.
Use z1 because of its greater practicality and lack of evidence that deeper metrics are more useful for
basin effects. Find stronger residuals when using δz1 than z1 directly. Find no clear trends in intra-event
residuals w.r.t δz1 at short periods but non-zero residuals for longer periods so add additional term using
all data. Find regional variations minor and do not include them.
Find correlation in event terms between parent Class 1 and children Class 2 events hence examine difference
between Class 1 event terms and mean of their children Class 2 event terms w.r.t. Mw. Find no systematic
departure from zero meaning average Class 2 events do not have any more bias than parent Class 1 events.
Conclude that model equally applicable to both types of events.
Examine inter-event residuals w.r.t. Ztor and Zhypo. Find no trends for Mw≥ 5. Find trend for smaller
events but since most hazard is governed by Mw≥ 5 did not include extra term.
Derive aleatory variability model based on binned Phase 3 inter- and intra-event residuals.
Note that aleatory variability model may be too high for a more controlled set of region and site conditions.
Check extrapolation to Mw8.5 (beyond observations) using simple stochastic simulations (not shown) and
model appears reasonable.