- Ground-motion model is: where c1 = -0.00219, c2 = -0.00298, c3 = -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
- Classify station locations into location relative to volcanic front:
- Forearc. F = 1 and B = 0.
- 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) Mw9.0
- 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
- For Tohoku model, estimate c0 using only forearc records within 200km and then fix c0 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 (c0) by using data from 5 other 7 ≤ Mw ≤ 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 Rrup 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 c0 against Mw. Then fit these mean
residuals with linear function to obtain equation for c0. Consider making h a function of magnitude but
do not find strong evidence in data for this.
- Find slope of function for c0 is of marginal significance at higher frequencies based on P-value of Student’s
- 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.