- Ground-motion model is: where y is in g, msc = 6.3, mc = 7.1 (from previous studies), Cmax = mc, c2 = 1.151 (from magnitude-fault
length relations), c1 = -5.30119, cSL1 = 1.44758, cSL2 = 0.37625, dSL = 0.42646, bSL = 0.01826,
gSL = -1.98471, gSLL = 1.12071, eSLv = -0.01499, eSL = -0.00340, eSLH = -0.00050, γ = -9.880,
S2 = 0.2320, S3 = 0.1437, S4 = 0.1470, σ = 0.587 (intra-event), τ = 0.457 (inter-event) and σT = 0.744
- Use 4 site classes (T is natural period of site):
- 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).
- Hard soil, NEHRP site class C, 300 < V s,30 ≤ 600m∕s, 0.2 ≤ T < 0.4s. 1292 records (1354 in complete
- Medium soil, NEHRP site class D, 200 < V s,30 ≤ 300m∕s, 0.4 ≤ T < 0.6s. 414 records (443 in
- 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)
— S2, S3 and S4 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
- Data reasonably well distributed w.r.t. Mw and x. 7 earthquakes (539 records) with Mw > 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 Mw ≥ 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 (xv). xv 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 Mw 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 Mw by splitting residuals into 0.5Mw unit bins and compute standard deviations
in each magnitude bin. Do not find evidence for magnitude-dependent σs.