### 2.404 Bozorgnia and Campbell (2016b)

• Ground-motion model is the same as for the associated horizontal model Campbell and Bozorgnia (2014) (see Section 2.366) with the following coefficients: h4 = 1, c0 = -4.729, c1 = 0.984, c2 = 0.537, c3 = -1.499, c4 = -0.443, c5 = -2.666, c6 = 0.214, c7 = 7.166, c8 = 0, c9 = -0.230, c10 = 0.759, c11 = -0.356, c12 = 1.019, c13 = 0.373, c14 = -0.117, c15 = -0.097, c17 = 0.1020, c18 = 0.0442, c19 = 0.00784, c20 = -0.0053, Δc20,JI = -0.0018, Δc20,CH = 0.0039, k1 = 865, a2 = 0.167, h1 = 0.241, h2 = 1.474, h3 = -0.715, h5 = -0.337 and h6 = -0.270, c16 = 0.0 (no deep basin effects), k2 = 0.0 (no soil nonlinearity), k3 = 0.0 (no deep basin effects) and c and n are not need because k2 = 0.
• Ground-motion model is (for aleatory variability):
where τ1V = 0.461, τ2V = 0.347, ϕ1V = 0.694, ϕ2V = 0.493, σV = 0.833 for Mw 4.5 and σV = 0.603 for Mw 5.5.
• Characterise sites using V s,30. Because vertical site response behaves linearly in most cases (even when horizontal response may be strongly nonlinear) do not model soil nonlinearity. Do not think that this affects the applicability of the model. Recommend model for V s,30 between 150 and 1500ms (for higher V s,30 recommend setting V s,30 to 1500ms).
• Use 3 mechanisms:
1.
Reverse/reverse-oblique. Rake angle 30 < λ < 150. FRV = 1, FNM = 0.
2.
Normal/Normal-oblique. Rake angle -150 < λ < -30. FNM = 1, FRV = 0.
3.
Strike-slip. Other rake angles. FRV = FNM = 0.

Use 2 regions:

Japan
SJ = 1
Elsewhere
SJ = 0
• Do not include deep basin terms in model because modelling is inconclusive and little evidence from data that basin effects are important for vertical motions.
• Recommend model for depth to top of rupture ZTOR between 0 and 20km, hypocentral depths between 0 and 20km and fault dips δ between 15 and 90.
• Vertical-component NGA-West 2 model corresponding to horizontal model of Campbell and Bozorgnia (2014) (see Section 2.366 for details of data and approach used to develop model). Use similar database and functional form but aspects are different. Use same data selection criteria as Campbell and Bozorgnia (2014) but exclude: records without vertical components, those that triggered on horizontal motion or are of questionable quality. Exclude aftershocks (class 2 events) within immediate vicinity of inferred mainshock fault rupture plane.
• 6989 near-source (rrup 80km) records from 282 events. Use these with 2-stage maximum-likelihood regression to derive near-source model. Use far-source database (80500km) to develop regionally-dependent anelastic attenuation terms. Apply limited smoothing to coefficients.
• From regression fmag predicted oversaturation for PGA and short-period PSA at large Mw and short rrup. Decide to constrain fmag to be constant at Mw > 6.5 and rrup = 0 when regression indicates oversaturation. Find c1, c2 and c3 were not significantly different to those from horizontal model and hence fix them to the horizontal coefficients in final regression.
• Plot inter- and intra-event residuals (individual and binned into small intervals) w.r.t. different variables. Find no significant biases or trends.