- Ground-motion model is (for median):
_{x}is closest distance to surface projection of top edge of rupture measured perpendicular to its average strike, W is down-dip width of rupture, A_{1100}is median estimated PGA for V_{s,30}= 1100m∕s, c = 1.88, n = 1.18, h_{4}= 1, c_{0}= -4.416, c_{1}= 0.984, c_{2}= 0.537, c_{3}= -1.499, c_{4}= -0.496, c_{5}= -2.773, c_{6}= 0.248, c_{7}= 6.768, c_{8}= 0, c_{9}= -0.212, c_{10}= 0.720, c_{11}= 1.090, c_{12}= 2.186, c_{13}= 1.420, c_{14}= -0.0064, c_{15}= -0.202, c_{16}= 0.393, c_{17}= 0.0977, c_{18}= 0.0333, c_{19}= 0.00757, c_{20}= -0.0055, Δc_{20,JI}= -0.0035, Δc_{20,CH}= 0.0036, k_{1}= 865, k_{2}= -1.186, k_{3}= 1.839, a_{2}= 0.167, h_{1}= 0.241, h_{2}= 1.474, h_{3}= -0.715, h_{5}= -0.337 and h_{6}= -0.270. - Ground-motion model is (for aleatory variability):
_{ln PGA,ln Y }is correlation coefficient between the intra-event residuals of intensity measure of interest and PGA, τ_{1}= 0.409, τ_{2}= 0.322, ϕ_{1}= 0.734, ϕ_{2}= 0.492, ϕ_{ln AF }= 0.300, σ = 0.840 (for M_{w}≤ 4.5), σ = 0.588 (for M_{w}≥ 5.5) and ρ_{ln PGA,ln Y }= 1. - Use V
_{s,30}and depth to 2.5km∕s shear-wave velocity horizon (Z_{2.5}) to characterise sites. State model applicable for 150 ≤ V_{s,30}≤ 1500m∕s and 0 ≤ Z_{2.5}≤ 10km. - Use 3 mechanisms:
- 1.
- Reverse/reverse-oblique. Rake angle 30 < λ < 150
^{∘}. F_{RV }= 1, F_{NM}= 0. - 2.
- Normal/Normal-oblique. Rake angle -150 < λ < -30
^{∘}. F_{NM}= 1, F_{RV }= 0. - 3.
- Strike-slip. Other rake angles. F
_{RV }= F_{NM}= 0.

Use 2 regions:

- Japan
- S
_{J}= 1 - Elsewhere
- S
_{J}= 0

- Model derived within NGA West 2 project, using the project database (Ancheta et al., 2014).
- Update model of Campbell and Bozorgnia (2008b) to include more-detailed hanging-wall model, scaling
with focal depth (Z
_{HY P }) and fault dip (δ), regionally-dependent anelastic attenuation and site effects and magnitude-dependent σ. - Note that NGA West 2 database provides better constraints on scaling of small earthquakes and at further distances.
- Fewer records for 5 ≤ M
_{w}≤ 6. - Apply similar selection criteria as Campbell and Bozorgnia (2008b). Exclude: 1) records with only one
horizontal component, 2) stations with no measured or estimated V
_{s,30}, 3) earthquakes with no rake angle or focal mechanism, 4) earthquakes with focal depths > 20km and those in oceanic plate or stable continental region, 5) unreliable records because of unrealistic spectral shape, late trigger, incorrect but unknown instrument gain, low quality or non-free-field location, 6) aftershocks (Class 2) located in immediate vicinity (centroid r_{jb}< 10km) of mainshock rupture plane and 7) poorly-recorded earthquakes: for M_{w}< 5.5 < 5 records and for 5.5 ≤ M_{w}< 6.5 < 3 records with r_{rup}≤ 80km (no criterion on minimum number of records were applied for M_{w}≥ 6.5 because of limited data). Near-source dataset: 7208 records from 282 events. Use same criteria (except for 7) to select records in range 80 < r_{rup}≤ 500km to derive anelastic attenuation term. Far-source dataset: 8313 records from 276 events. - 11125 records from 245 earthquakes, primarily from California, with 3 ≤ M
_{w}< 5.5 and 4396 records from 77 earthquakes with 5.5 ≤ M_{w}< 7.9. - Develop or confirm functional form using standard data exploration techniques such as analysis of residuals. Undertake numerous iterations to capture trends in observations. Start with form of Campbell and Bozorgnia (2008b) and add or modify terms as required. Use hanging-wall simulations of Donahue and Abrahamson (2014) to update hanging-wall term. If variables missing either estimated using proxies or perform regression using only records were information available.
- Develop model in 2 phases. Firstly, use near-source database to develop model capturing near-source effects,
including geometric attenuation. Use r
_{rup}≤ 80km because the importance of these distances for seismic hazard. Using only this range of distances avoids trade-off between geometric and anelastic terms. Residuals from this phase confirm near-source recordings do not exhibit significant anelastic attenuation. Secondly, use far-source database and residual analysis to develop regionally-dependent anelastic attenuation term. Finally, apply limited smoothing to remove roughness in estimated spectra. - Compute ρ
_{ln PGA,ln Y }from intra-event residuals of near-source regression. Find ρ_{ln PGA,ln Y }is magnitude-dependent. Use values for M_{w}≥ 5 because: these earthquakes are most concern for seismic hazard analysis, 2) correlation coefficient similar for both inter- and intra-event residuals (so can use one set for both types of variability) and 3) only large earthquakes produce significant nonlinear site response, one of the principal uses for ρ_{ln PGA,ln Y }. - Find anelastic attenuation is regional dependent and derive Δc
_{20}to model difference between base region (California, Taiwan and Middle East; Δc_{20}= 0), Japan and Italy (JI, higher attenuation) and eastern China (CH, lower attenuation). - Plot inter- and intra-event residuals w.r.t. independent variables. Find no strong systematic trends or biases.
- Suggest default values for various independent variables (Z
_{HY P }, Z_{TOR}, W, Z_{BOT }(depth to bottom of seismogenic crust) and V_{s,30}and Z_{2.5}for each NEHRP site class. For California find: lnZ_{2.5}= 7.089-1.144lnV_{s,30}(σ = 1.026) and for Japan: lnZ_{2.5}= 5.359-1.102lnV_{s,30}(σ = 1.403), but recommend caution when using them because of large standard deviations. Also present relations between Z_{1.0}and Z_{2.5}. - Suggest that τ might be regionally-dependent.
- State model applicable for 0 ≤ Z
_{TOR}≤ 20km, 0 ≤ Z_{HY P }≤ 20km and 15 ≤ δ ≤ 90^{∘}. - Even those database includes some data from V
_{s,30}< 180m∕s, caution against using model for NEHRP E and F sites because of potentially unusual site conditions that make site effects more complicated than the model suggests and because equivalent-linear simulations used to derive nonlinear site terms are less reliable for high strains. Note that if soil properties deviate significantly from those used in simulations for nonlinear site term then site response under strong shaking may be different than predicted by the model. - Did not include directivity because of large differences between candidate models for reverse and faults with complicated rupture geometry.
- Find shallow site response similar in all regions except California.