- Ground-motion model is (for median):
_{s,30}= 1180m∕s, Dip is fault dip in degrees, W is down-dip rupture width, c_{4}= 4.5, M_{1}= 6.75, M_{2}= 5, a_{1}= 0.587, a_{2}= -0.790, a_{3}= 0.275, a_{4}= -0.1, a_{5}= -0.41, a_{6}= 2.154, a_{8}= -0.015, a_{10}= 1.735, a_{11}= 0, a_{12}= -0.1, a_{13}= 0.6, a_{14}= -0.3, a_{15}= 1.1, a_{17}= -0.0072, V_{Lin}= 660, b = -1.47, n = 1.5, c = 2.4, a_{43}= 0.1, a_{44}= 0.05, a_{45}= 0, a_{46}= -0.05, a_{25}= -0.0015, a_{28}= 0.0025, a_{29}= -0.0034, a_{31}= -0.1503, a_{36}= 0.265, a_{37}= 0.337, a_{38}= 0.188, a_{39}= 0, a_{40}= 0.088, a_{41}= -0.196 and a_{42}= 0.044. - Ground-motion model is (for aleatory variability):
_{1}= 0.754 and s_{2}= 0.520 for estimated V_{s,30}, s_{1}= 0.741 and s_{2}= 0.501 for measured V_{s,30}, s_{3}= 0.47, s_{4}= 0.36, s_{5}= 0.54 and s_{6}= 0.63. - Coefficients in Abrahamson et al. (2013) and Abrahamson et al. (2014) are not exactly the same. Coefficients of Abrahamson et al. (2014) are final values.
- Use V
_{s,30}and Z_{1}(depth to 1km∕s shear-wave velocity horizon) to characterise sites. 9668 records have Z_{1}estimates (for remaining 6082 records set Z_{1}to Z_{1,ref}, the average Z_{1}for given V_{s,30}). Because correlation between V_{s,30}and deeper structure may be regional dependent, allow model-scaling with V_{s,30}to depend on region. Note that Z_{2.5}may be more directly related to long-period site response but choose Z_{1}because closer to traditional geotechnical deep-to-bedrock parameter and easier to measure for specific projects. Note that model applicable for V_{s,30}≥ 180m∕s. - Use 3 faulting mechanisms:
- Strike-slip
- Other rake angles. 221 events. F
_{RV }= F_{N}= 0. - Reverse
- Rake angles between 30 and 150
^{∘}. 79 events. F_{RV }= 1, F_{N}= 0. - Normal
- Rake angles between -30 and -150
^{∘}. 26 events, mostly 4.6 ≤ M_{w}≤ 6. F_{N}= 1, F_{RV }= 0.

Use two earthquake types:

- Class 1
- Mainshocks. F
_{AS}= 0. - Class 2
- Aftershocks. Events with centroid r
_{jb}< 15km (CR_{jb}). F_{AS}= 1.

Use two locations w.r.t. vertical projection of the top of rupture:

- Hanging wall
- F
_{HW }= 1. - Foot wall
- F
_{HW }= 0.

Use three regional terms to adjust model w.r.t. base model (all other regions, dominated by California):

- Taiwan
- F
_{TW }= 1 - China
- F
_{CN}= 1 - Japan
- F
_{JP }= 1

- Model derived within NGA West 2 project, using the project database (Ancheta et al., 2014).
- Update of Abrahamson and Silva (2008) to: extend down to M
_{w}3, better constrain hanging-wall effects and model regional differences in attenuation and V_{s,30}. - Try to use all data from active crustal regions under assumption that median motions at distances < 80km are similar worldwide, which implies similar median stress drops in California (12044 records, 274 events), Alaska (7 records, 2 events), Taiwan (1535 records, 6 events), Japan (1700 records, 5 events), Middle East (43 records, 5 events), Italy (175 records, 25 events), Greece (3 records, 1 event), New Zealand (72 records, 2 events), other European countries (6 record, 1 event) and other region (5 records, 1 event). Account for differences can longer distances, due to crustal structure or Q, through additional terms.
- Exclude earthquakes not representative of active crustal regions. Remove events with questionable
hypocentral depths. Remove events with fewer than 3 records for M
_{w}> 5 and fewer than 10 records with good distance coverage for M_{w}< 5 (because of abundance of small-magnitude data). Remove 2008 Wenchuan aftershocks because of residuals and spectral shapes that were very different than other data, which may be due to unreliable metadata. Remove records not representative of free-field motions. Remove records missing key metadata. Remove questionable data due to apparent incorrect gain or spectral shape. Remove records from distances greater than magnitude-distance censoring distances, which depend on instrument type. - Use 1D finite-fault kinematic simulations to constrain hanging-wall (Donahue and Abrahamson, 2014) and magnitude scaling and equivalent-linear modelling of Peninsula Range soil to constrain site response terms (Kamai et al., 2014).
- Almost all data from M
_{w}< 5 are from western USA. - Use different number of records in Step 1 (less than 4000 from about 130 events) and Step 2 (about 7000 from about 130 events) because of data selection criteria applied. Within these general three stages (Step 1, 2 and, the final step) various regression analysis undertaken to constrain different sets of coefficients.
- Find 2008 Wenchuan (M
_{w}7.9) earthquake has very weak long-period motions, hich are inconsistent with scaling from finite-fault simulations. Therefore, remove this event from Steps 1 and 2 and only include it once magnitude scaling is fixed. - Use four distance measures to model hanging-wall effects: r
_{jb}, R_{x}(horizontal distance from top edge of rupture, measured perpendicular to fault strike), R_{1}(value of R_{x}at bottom edge of rupture) and R_{y0}(horizontal distance off the end of the rupture measured parallel to strike). - Use site-response model of Kamai et al. (2014) based on PSA on reference rock rather than PGA because simplifies aleatory variability model.
- Note correlation between Z
_{TOR}and mechanism: reverse earthquakes tend to be deeper than strike-slip events. - Constrain V
_{1}based on non-parametric models of V_{s,30}scaling. - Note that nonlinear site term not intended to replace site-specific response analysis for nonlinear soils but rather to allow use of data from such sites to help constrain model.
- For hanging-wall terms only a
_{13}is found from regression of empirical data. Other terms found from simulations of Donahue and Abrahamson (2014). - Some evidence for reduction of depth dependency at shallow depths but use linear scaling for simplicity.
Avoid having the small-magnitude data controlling Z
_{TOR}scaling by constraining the scaling when using all data. - Smooth coefficients in a series of steps.
- Examine inter- and intra-event residuals w.r.t. M
_{w}, r_{rup}, V_{s,30}, Sa_{1180}and Z_{1}(raw and binned) and find no trends.