where Sa is in g, C_{1}= 7.8, n = 1.18, b = 1.88, C_{4}= 10, V_{lin}= 865.1, b = -1.186, θ_{1}= 4.2203,
θ_{2}= -1.350, θ_{3}= 0.1, θ_{4}= 0.9, θ_{5}= 0.0, θ_{6}= -0.0012, θ_{7}= 1.0988, θ_{8}= -1.42, θ_{9}= 0.4, θ_{10}= 3.12,
θ_{11}= 0.0130, θ_{12}= 0.980, θ_{13}= -0.0135, θ_{14}= -0.40, θ_{15}= 0.9996, θ_{16}= -1.00; for interface
events: ΔC_{1}(central value) = 0.2, ΔC_{1}(lower value) = 0., ΔC_{1}(upper value) = 0.4; for intraslab events:
ΔC_{1}(central value) = -0.3, ΔC_{1}(lower value) = -0.5., ΔC_{1}(upper value) = -0.1; PGA_{1000} is median
PGA for V_{s,30}= 1000m∕s, ϕ = 0.60 (intra-event), τ = 0.43 (inter-event) and σ = 0.74 (total).
Characterise sites by V_{s,30}. Most V_{s,30} from correlations between site class and V_{s,30} and not measured.
Because of insufficient data and because believe should be similar to crustal site amplification adopt slightly
modified Walling et al. (2008) site model.
Classify events into 2 categories:
F_{event}= 0
Interface
F_{event}= 1
Intraslab
Classify sites into 2 locations:
F_{FABA}= 0
Forearc or unknown sites
F_{FABA}= 1
Backarc sites
Use data from Atkinson and Boore (2003) combined with additional data from Japan, Taiwan, South and
Central America, including Mexico. Collect 3557 horizontal pairs of components from 163 interface events
and 6389 horizontal pairs from 129 intraslab events. Some older records are not available so only PGA and
PSA at 0.1, 0.2, 0.4, 1.0, 2.0 and 3.0s are used. Use record for frequencies above 1.2 times the high-pass
corner frequency. Some recent Taiwanese data available in terms of GMRotI50, which assume equivalent
to geometric mean.
Check available classification of earthquakes into interface/intraslab and find some problems. Correct
problematic classifications using available information (often from International Seismological Centre). Use
Global CMT for M_{w} unless not available when use regional CMT. Prefer pP depths if available. Changed
classification of 9 intraslab events to interface.
Classify stations in Japan, Cascadia and Taiwan into forearc (between subduction trench axis and axis of
volcanic fronts) and backarc location. Almost all backarc data from Japan and so differences in backarc
attenuation may be regional rather than global backarc differences.
Note that definition of distances for some records (particularly older ones) is not clear. Adopt distances
without re-evaluation. Note that mixture of r_{rup} and r_{hypo} is used, which could be significant for shallow
large interface events.
Remove questionable data (e.g. clear outliers by a factor of 100 or more and 1992 M_{w}7 Cape Mendocino
event that could be crustal). To focus on large interface and moderate to large intraslab events: exclude
data from interface events with M_{w}< 6 and intraslab with M_{w}< 5.
To avoid upward bias in data at large distances due to triggering apply magnitude-dependent distance
limits based on PGA.
Find that M-scaling for 5–7 for intraslab is similar to scaling for 6–8 for interface with constant offset.
Hence use common scaling. Use numerical simulations for Cascadia to constrain scaling for M_{w}> 8, where
little data. Bin PGAs in 0.5-unit bins and correct to rock site and 100km and compare to scaling from
simulations. Find break in scaling at M_{w}7.8. Find cannot simultaneously find geometric spreading and
saturation from data and hence fix depth term to 10km. Note that another value could be chosen and the
other coefficients would adjust.
Initially did not use focal depth Z_{h} in model. Inter-event residuals showed strong trend with Z_{h} for
intraslab but not for interface. Include Z_{h} term in intraslab model with maximum depth limit of 120km.
Initially did not account for forearc/back arc but intra-event residuals showed trend with distance for
backarc sites. Hence include additional attenuation term.
Find coefficients in steps, smoothing coefficients 1 or 2 at a time and re-computing the others. Only use
events with ≤ 5 records before final regression to avoid poorly-recorded earthquakes strongly impacting
results. First find coefficients θ_{3}, θ_{4} and θ_{5} for PGA and constrain them to these values for other periods.
Run test using different minimum number of records per event. Find results insensitive to inclusion of
poorly-recorded earthquakes.
Examine inter- and intra-event residuals. Find limited evidence for regional dependency in inter-event
residuals except for poorly-sampled regions and Cascadia (5 intraslab events). Find no trends in intra-event
residuals w.r.t. r. Find no trends w.r.t. V_{s,30}.
Use data from 2010 M_{w}8.8 Maule, Chile, and 2011 M_{w}9.0 Tohoku, Japan, earthquakes, which occurred
after data collection, to check model using residual analysis. For PGA find Tohoku data shows much
stronger forearc attenuation than model predicts. Believe that this is a regional effect for Japan and hence
do not modify model. Find evidence for bias in the model for large interface events and hence introduce ΔC_{1}
term that includes epistemic uncertainty. Note that break in intraslab M-scaling is not well constrained
but propose ΔC_{1} term and its uncertainty based on available data and previous models.
Provide estimates of epistemic uncertainty from region-specific event terms that can be used to define logic
tree branches.