- Ground-motion model is (for median):
_{ref}= 4.5, R_{ref}= 1km, V_{ref}= 760m∕s, PGA_{r}is median PGA for reference rock (i.e. V_{s,30}= V_{ref}), e_{0}= 0.4473, e_{1}= 0.4856, e_{2}= 0.2459, e_{3}= 0.4539, e_{4}= 1.4310, e_{5}= 0.05053, e_{6}= -0.1662, M_{h}= 5.5, c_{1}= -1.134, c_{2}= 0.1917, c_{3}= -0.008088, h = 4.5, Δc_{3,China,Turkey}= 0.0028576, Δc_{3,Italy,Japan}= -0.0025500, c = -0.6, V_{c}= 1500m∕s, f_{1}= 0, f_{3}= 0.1, f_{4}= -0.15, f_{5}= -0.00701, f_{6}= -9.9 and f_{7}= -9.9. - Ground-motion model is (for aleatory variability):
_{1}= 110, R_{2}= 270, Δϕ_{R}= 0.10, Δϕ_{V }= 0.07, V_{1}= 225, V_{2}= 300, ϕ_{1}= 0.695, ϕ_{2}= 0.495, τ_{1}= 0.398 and τ_{2}= 0.348. - Use V
_{s30}(both measured and inferred) to characterise sites. V_{s,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) z
_{1}to characterise sites. State model applicable from 0–3km. Recommend that when z_{1}is unknown to set δz_{1}to zero to turn off basin-depth adjustment factor. - Use 4 faulting mechanisms:
- SS
- 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. - NS
- Normal, P-axis plunge > 40
^{∘}and T-axis plunge ≤ 40^{∘}. About 1000 records from about 40 events. NS = 1. Other mechanism variables are zero. - RS
- Reverse, P-axis plunge ≤ 40
^{∘}and T-axis plunge > 40^{∘}. About 5500 records from about 100 events. RS = 1. Other mechanism variables are zero. - U
- 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 M
_{w}, r_{jb}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 M
_{w}> 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 M
_{w}, r_{jb}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 r_{jb}≤ 80km after applying other criteria. - Secondary variables are: depth to top of rupture Z
_{tor}and hypocentral depth Z_{hypo}; basin depth (from surface to 1.0km∕s shear-wave velocity horizon) z_{1}; event type: class 1 (mainshocks) or class 2 (aftershocks) using minimum centroid r_{jb}separation of 10km. Do not consider hanging-wall effects because r_{jb}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 M
_{w}≤ 5 (to minimise finite-fault and nonlinear site effects) to constrain c_{3}in Phase 1. Correct data for linear site effects. Group data into 0.5 magnitude unit bins and regress using form ν′+c_{1}′ln(R∕R_{ref})+c_{3}(R-R_{ref}) to find c_{3}. Find c_{3}is relatively independent of M_{w}. - In Phase 2 exclude Class 2 events (aftershocks) and data from r
_{jb}> 80km and adjust data to V_{ref}. - Find evidence for apparent oversaturation in source term but this is compensated by the other terms in the model.
- Coefficient e
_{0}is a weighted average of coefficients for other faulting mechanisms. - Recompute coefficients excluding 2008 Wenchuan earthquake (M
_{w}7.9) for which some debate over suitability for model development. Removal has no effect at short periods but long-period motions increase for large M_{w}. 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 Δc
_{3}(for regional anelastic attenuation effects) and F_{δz1}but not source type or depth adjustments. - Plot inter-event residuals against M
_{w}and rake angle and intra-event residuals against r_{jb}and V_{s,30}. Find no trends w.r.t. M_{w}after excluding Class 2 events from China. Find no trends w.r.t rake angle except for positive residuals for NS for M_{w}< 5 and positive bias for T > 1s for RS when M_{w}> 5. Do not consider trends sufficient to warrant adjustments. Find no trends w.r.t. r_{jb}nor w.r.t. V_{s,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 adjust model.
- Plot intra-event residuals w.r.t. r
_{jb}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 r_{jb}> 25km to find Δc_{3}. - Use z
_{1}because of its greater practicality and lack of evidence that deeper metrics are more useful for basin effects. Find stronger residuals when using δz_{1}than z_{1}directly. Find no clear trends in intra-event residuals w.r.t δz_{1}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. M
_{w}. 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. Z
_{tor}and Z_{hypo}. Find no trends for M_{w}≥ 5. Find trend for smaller events but since most hazard is governed by M_{w}≥ 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 M
_{w}8.5 (beyond observations) using simple stochastic simulations (not shown) and model appears reasonable.