- Ground-motion model for median motions is: where Y is in g, Rref = 1km, Mref = 4.5, e0 = 0.1836, e1 = 0.2337, e2 = 0.01562, e3 = 0.1538, e4 = 1.247, e5 = 0,
e6 = 0.02257, Mh = 5.5, c1 = -1.1750, c2 = 0.1577, c3 = -0.00922, Δc3,China = 0.00475, Δc3,Japan = 0,
h = 5.1, c = -0.329, V ref = 760, V c = 1500, f1 = 0, f3 = 0.1, f4 = -0.05, f5 = -0.00701 and PGAr
is the PGA obtained by evaluating model for V s,30 = 760m∕s. Model for aleatory variability is:
where τ1 = 0.47631, τ2 = 0.37634, ϕ1 = 0.71175 and ϕ2 = 0.53387.
- Characterise sites using V s,30. Recommend model is used for 200 ≤ V s,30 ≤ 1500m∕s. Note modest
over-prediction for V s,30 > 600m∕s for periods < 0.7s.
- Classify events into 4 mechanisms using same criteria as Boore et al. (2013):
- Strike-slip. SS = 1, RS = NS = U = 0.
- Normal. NS = 1, RS = SS = U = 0.
- Reverse. RS = 1, SS = NS = U = 0.
- Unspecified. U = 1. SS = NS = RS = 0.
- Vertical-component NGA-West 2 model corresponding to horizontal model of Boore et al. (2013) (see
Section 2.365 for details of data and approach used to develop model). Use similar database and functional
form but aspects are different.
- Select data having required source, path and site metadata and from active crustal regions. Exclude data
from large structures. Apply screening of data at large distances as a function of Mw and instrument type.
Use data from Class 1 (mainshocks) and class 2 (aftershocks) using the minimum centroid rjb separation of
10km based on subjective interpretation of results from exploratory analysis. Include data only for periods
within usable frequency band for the vertical component and to exclude any records that are questionable
by manual inspection. These two criteria lead to some differences between horizontal and vertical data.
- Did not consider hanging-wall effects because using rjb implicit accounts for larger motions over hanging
wall for dips between 25 and 70∘, which are well represented in database.
- Find no dependence on sediment depth.
- Find that σ is only a function of Mw and not rjb or V s,30, which were required for the horizontal model.
- Develop model in 3 phases. In phase 1 set coefficients in site amplification model and the anelastic
attenuation coefficient c3, which could not be well-constrained by regression. In phase 2 undertake main
regression for event and path terms. In phase 3 undertake mixed-effects regression to check model and
derive σ model (adjust some of the coefficients from phase 1).
- Set site coefficients through mixed-effects residual analysis of 8075 records with rjb < 80km of vertical
data relative to horizontal model of Boore et al. (2013).
- Estimate c3 through mixed-effects regression by using Californian data with Mw < 5.5 binned into 0.5Mw
intervals corrected to V s,30 = 760m∕s. Find c3 is not dependent on Mw.
- For phase 2 adjust data to reference V s,30 = 760m∕s using the site amplification model. Find FE and
FP coefficients (except c3 and Δc3) using mainshock data from events with ≥ 4 records with rjb ≤ 80km
(7001 records). For some periods found slight upward curvature in quadratic function for Mw < Mh. For
these repeated regression using a linear function. Use Mh from horizontal model of Boore et al. (2013),
which check are appropriate. Compute e0 as weighted average of coefficients for other fault types. Smooth
h, re-regress model using smoothed h and then compute 11-point running means of coefficients (and 9-,
7-, 5- and 3-point operators near ends of period range). Also perform some manual smoothing.
- For phase 3 undertake mixed-effects residual analyses to: check model from phase 1 and 2 and remove
any trends; check for possible regional trends for rjb and V s,30; check for trends for source terms not
included (rupture depth, fault dip and rake angle). For this phase use all data. Plot inter-event residuals
against Mw (and binned into small magnitude intervals) and find no trends, although do find some local
fluctuations. Plot intra-event residuals against rjb and find some trends at long distances so adjust c3.
Find positive bias for rjb > 300m and hence conclude model is not applicable at those distances. Plot
intra-event residuals against V s,30 and find need to slightly adjust c. After these changes still find some
minor trends in residuals.
- Plot intra-event residuals against rjb for different countries and find need for non-zero Δc3 for some regions
(Japan and China), which find by regression. Do not find need for regional variations in V s,30 scaling.
- Investigate need to include depth to top of rupture, hypocentral depth and fault dip in model but find no
trends in residuals w.r.t. these parameters.
- Check overall model bias after all phases and find that it is small, although it increases when data from
80–300km is included.
- Bin event terms and intra-event residuals into magnitude bins to evaluate magnitude dependency. Find
evidence for Mw dependency. Also check distance dependency of ϕ for Mw > 5.5 but, although evident
for some periods and distances, no strong trends overall. Believe high τ near 0.1s is site effect.
- Recommend model for mainshocks. Note that model may be applicable for Class 2 events but this is not