- Ground-motion model is (for median): where: Sa is in g, is median spectral acceleration in g for reference V s,30 = 1180m∕s, Dip is fault dip in
degrees, W is down-dip rupture width, c4 = 4.5, M1 = 6.75, M2 = 5, a1 = 0.587, a2 = -0.790, a3 = 0.275,
a4 = -0.1, a5 = -0.41, a6 = 2.154, a8 = -0.015, a10 = 1.735, a11 = 0, a12 = -0.1, a13 = 0.6, a14 = -0.3,
a15 = 1.1, a17 = -0.0072, V Lin = 660, b = -1.47, n = 1.5, c = 2.4, a43 = 0.1, a44 = 0.05, a45 = 0,
a46 = -0.05, a25 = -0.0015, a28 = 0.0025, a29 = -0.0034, a31 = -0.1503, a36 = 0.265, a37 = 0.337,
a38 = 0.188, a39 = 0, a40 = 0.088, a41 = -0.196 and a42 = 0.044.
- Ground-motion model is (for aleatory variability): where: s1 = 0.754 and s2 = 0.520 for estimated V s,30, s1 = 0.741 and s2 = 0.501 for measured V s,30,
s3 = 0.47, s4 = 0.36, s5 = 0.54 and s6 = 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 Z1 (depth to 1km∕s shear-wave velocity horizon) to characterise sites. 9668 records have Z1
estimates (for remaining 6082 records set Z1 to Z1,ref, the average Z1 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 Z2.5 may be more directly related to long-period site response but choose Z1 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:
- Other rake angles. 221 events. FRV = FN = 0.
- Rake angles between 30 and 150∘. 79 events. FRV = 1, FN = 0.
- Rake angles between -30 and -150∘. 26 events, mostly 4.6 ≤ Mw ≤ 6. FN = 1, FRV = 0.
Use two earthquake types:
- Mainshocks. FAS = 0.
- Aftershocks. Events with centroid rjb < 15km (CRjb). FAS = 1.
Use two locations w.r.t. vertical projection of the top of rupture:
- FHW = 1.
- FHW = 0.
Use three regional terms to adjust model w.r.t. base model (all other regions, dominated by California):
- FTW = 1
- FCN = 1
- FJP = 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 Mw3, 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 Mw > 5 and fewer than 10 records
with good distance coverage for Mw < 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
- 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 Mw < 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 (Mw7.9) 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: rjb, Rx (horizontal distance from top edge of
rupture, measured perpendicular to fault strike), R1 (value of Rx at bottom edge of rupture) and Ry0
(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 ZTOR and mechanism: reverse earthquakes tend to be deeper than strike-slip
- 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 a13 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 ZTOR scaling by constraining the scaling when using
- Smooth coefficients in a series of steps.
- Examine inter- and intra-event residuals w.r.t. Mw, rrup, V s,30, Sa1180 and Z1 (raw and binned) and find