- Ground-motion model is:
_{sc}= 6.3, m_{c}= 7.1 (from previous studies), C_{max}= m_{c}, c_{2}= 1.151 (from magnitude-fault length relations), c_{1}= -5.30119, c_{SL1}= 1.44758, c_{SL2}= 0.37625, d_{SL}= 0.42646, b_{SL}= 0.01826, g_{SL}= -1.98471, g_{SLL}= 1.12071, e_{SL}^{v}= -0.01499, e_{SL}= -0.00340, e_{SLH}= -0.00050, γ = -9.880, S_{2}= 0.2320, S_{3}= 0.1437, S_{4}= 0.1470, σ = 0.587 (intra-event), τ = 0.457 (inter-event) and σ_{T }= 0.744 (total). - Use 4 site classes (T is natural period of site):
- SC I
- Rock, NEHRP site classes A+B+C, V
_{s,30}> 600m∕s, T < 0.2s. Note that these sites are neither rock or engineering bedrock sites as many have a layer of stiff soil of thickness ≤ 24m and V_{s}> 200m∕s at the surface. Many sites have strong impedance ratios. Note that nonlinear effects at these sites is limited. 2002 records (2031 in complete dataset). - SC II
- Hard soil, NEHRP site class C, 300 < V
_{s,30}≤ 600m∕s, 0.2 ≤ T < 0.4s. 1292 records (1354 in complete dataset). - SC III
- Medium soil, NEHRP site class D, 200 < V
_{s,30}≤ 300m∕s, 0.4 ≤ T < 0.6s. 414 records (443 in complete dataset). - SC IV
- Soft soil, NEHRP site classes E+F, V
_{s,30}≤ 200m∕s, T ≥ 0.6s. 847 records (882 in complete dataset).

Prefer site classes because useful for design codes and for application of model for sites with no accurate site period or V

_{s,30}. Classify stations for early data and for some K-Net stations from H/V response spectral ratios. Use site terms derived in previous studies that account for nonlinear response (see article for details) — S_{2}, S_{3}and S_{4}are the linear site terms. - Partner model to those of Zhao et al. (2016b) (see Section 2.418) for interface earthquakes and Zhao et al. (2016c) (see Section 2.419) for crustal earthquakes. Derive separate models for three different types of earthquakes because it allows σ (and its components) and site amplification to vary with event type. Sufficient data available for separate models.
- Focal depths between 10 and 170km, which most between 30 and 70km.
- Focal mechanisms: reverse: 98 (95 in dataset 2); strike-slip: 13 (10 in dataset 2); and normal: 25 (20 in dataset 2).
- Data reasonably well distributed w.r.t. M
_{w}and x. 7 earthquakes (539 records) with M_{w}> 7.0 in dataset 1 but fewer large events in dataset 2. - Use maximum log likelihood (MLL), rather than model standard deviation, as the indicator of goodness of fit. Find MLL is useful for identifying biased distribution of residuals when this is strongly influenced by an outlier because if an additional term is included to correct bias the MLL does not change and hence the correction is not necessary.
- Use data up from 1968 to 2012.
- Use dataset 1 (all data) to find magnitude-scaling for events with M
_{w}≥ 7.1 and then dataset 2 (excluding sites with inferred site class) for rest of derivation with magnitude-scaling taken from first dataset. Find removing records from sites with inferred site class improves goodness of fit. - Account for volcanic zone by using an anelastic attenuation term based on horizontal distance within
possible volcanic zones (x
^{v}). x^{v}is capped at 12km for shorter lengths and at 80km for longer lengths. - Use fault-top depth h.
- Plot intra-event residuals w.r.t. site period, T, for SC I sites. Find clear trend, which use to estimate deamplification ratios for a site with T = 0s.
- Smooth the coefficients w.r.t. the logarithm of the period. Note that smooth spectra are not obtained at
all M
_{w}and x. - Plot inter- and intra-event residuals and fit trend lines. Find slopes of trend lines are small.
- Compute intra- and intra-site standard deviations for each site class.
- Check if σ depends on M
_{w}by splitting residuals into 0.5M_{w}unit bins and compute standard deviations in each magnitude bin. Do not find evidence for magnitude-dependent σs.