- Ground-motion model for median motions is:
_{ref}= 1km, M_{ref}= 4.5, e_{0}= 0.1836, e_{1}= 0.2337, e_{2}= 0.01562, e_{3}= 0.1538, e_{4}= 1.247, e_{5}= 0, e_{6}= 0.02257, M_{h}= 5.5, c_{1}= -1.1750, c_{2}= 0.1577, c_{3}= -0.00922, Δc_{3,China}= 0.00475, Δc_{3,Japan}= 0, h = 5.1, c = -0.329, V_{ref}= 760, V_{c}= 1500, f_{1}= 0, f_{3}= 0.1, f_{4}= -0.05, f_{5}= -0.00701 and PGA_{r}is the PGA obtained by evaluating model for V_{s,30}= 760m∕s. Model for aleatory variability is:_{1}= 0.47631, τ_{2}= 0.37634, ϕ_{1}= 0.71175 and ϕ_{2}= 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):
- SS
- Strike-slip. SS = 1, RS = NS = U = 0.
- NS
- Normal. NS = 1, RS = SS = U = 0.
- RS
- Reverse. RS = 1, SS = NS = U = 0.
- U
- 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 M
_{w}and instrument type. Use data from Class 1 (mainshocks) and class 2 (aftershocks) using the minimum centroid r_{jb}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 r
_{jb}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 M
_{w}and not r_{jb}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 c
_{3}, 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 r
_{jb}< 80km of vertical data relative to horizontal model of Boore et al. (2013). - Estimate c
_{3}through mixed-effects regression by using Californian data with M_{w}< 5.5 binned into 0.5M_{w}intervals corrected to V_{s,30}= 760m∕s. Find c_{3}is not dependent on M_{w}. - For phase 2 adjust data to reference V
_{s,30}= 760m∕s using the site amplification model. Find F_{E}and F_{P }coefficients (except c_{3}and Δc_{3}) using mainshock data from events with ≥ 4 records with r_{jb}≤ 80km (7001 records). For some periods found slight upward curvature in quadratic function for M_{w}< M_{h}. For these repeated regression using a linear function. Use M_{h}from horizontal model of Boore et al. (2013), which check are appropriate. Compute e_{0}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 r
_{jb}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 M_{w}(and binned into small magnitude intervals) and find no trends, although do find some local fluctuations. Plot intra-event residuals against r_{jb}and find some trends at long distances so adjust c_{3}. Find positive bias for r_{jb}> 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 r
_{jb}for different countries and find need for non-zero Δc_{3}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 M
_{w}dependency. Also check distance dependency of ϕ for M_{w}> 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 checked.