- Ground-motion model is:
_{1}= -0.00219, c_{2}= -0.00298, c_{3}= -0.219, h = 60, a = 2.8193 ± 1.006, b = 0.1908 ± 0.130, ϕ = 0.284 (intra-event), τ = 0.196 (inter-event) and σ = 0.345 (total). - Characterise sites using V
_{s,30}(all based on measured profiles, most down to 10--20m. Extend site velocity profiles to 30m using approach of Boore et al. (2011). Note that data are affected by highly-significant shallow soil response that is specific to Japan. Median V_{s,30}is 266m∕s for forearc stations and 313m∕s for backarc stations. - Classify station locations into location relative to volcanic front:
- 1.
- Forearc. F = 1 and B = 0.
- 2.
- Backarc. B = 1 and F = 0.

- Use data from Japanese K-Net. Zero pad records, cosine taper and apply acausal band-pass 4th-order Butterworth filters with cut-offs of 0.04 and 15Hz.
- Only use data from Japan to reduce ambiguity from combining data from different regions.
- Derive event-specific model using only data (> 600 records) from the 2011 Tohoku (Japan) M
_{w}9.0 earthquake. - h is chosen as the value that minimizes the standard deviation and average absolute residual.
- Assume linear site term because previous studies have shown nonlinear effects relatively small for Tohoku earthquake at most stations and because nonlinear part of response trades off against near-source saturation term.
- For Tohoku model, estimate c
_{0}using only forearc records within 200km and then fix c_{0}and compute other coefficients using all data. - Note that the shallow site response affects estimates of ϕ.
- Provide multiplicative factor to adjust predictions for Cascadia (for PGA it is 0.50) because of differences in average site profiles.
- Show residuals from Tohoku model w.r.t. distance.
- Adjust the source term (c
_{0}) by using data from 5 other 7 ≤ M_{w}≤ 8.1 events from Japan. Do this by computing mean residuals of ground motions w.r.t. Tohoku GMPE using only forearc stations (which are the nearest) and exclude records beyond a cut-off where PGA v R_{rup}plot starts to flatten (due to instrument noise and/or non-triggered stations). Find that for some earthquakes the attenuation is less rapid. Hence only use data from ≤ 200km to compute residuals for all events to reduce residuals at shorter distances at the expense of greater over-prediction for > 200km. Plot c_{0}against M_{w}. Then fit these mean residuals with linear function to obtain equation for c_{0}. Consider making h a function of magnitude but do not find strong evidence in data for this. - Find slope of function for c
_{0}is of marginal significance at higher frequencies based on P-value of Student’s t test. - Plot observed and predicted ground motions and residuals w.r.t. distance for all data.
- Compute mean residuals for 60 sites that have all events. Find that some sites show large residuals,
particularly at high frequencies, which relate to shallow site response that is not captured by V
_{s,30}. Conclude that the value of ϕ estimated may not be representative for other regions with more homogeneous conditions nor representative of expected variability at a single site. Hence believe reported variabilities are upper bounds on actual aleatory variability as it includes some epistemic components. - Provide estimates of epistemic uncertainty range (low and high branches) of model based on arguments from recent studies.