- Ground-motion model is: where PGA is in g. Derive models with and without a6 constrained to zero. Model A6 (least-squares):
a1 = 2.45, a2 = 0.42, a3 = -0.17, a4 = -1.73, a5 = -0.0056, a6 = 0.56, σ = 0.9 (total), τ = 0.48
(inter-event), ϕS = 0.65 (intra-event) and ϕSS = 0.46 (single-station intra-event). Model F5 (the authors’
preferred model): a1 = -4.23, a2 = 1.31, a3 = -0.09, a4 = -1.2 (fixed a priori), a5 = -0.02, a6 = 0,
σ = 0.87, τ = 0.34, ϕS = 0.67 and ϕSS = 0.44. Provide coefficients for 11 other models but these are not
given here due to space limitations.
- Characterise sites by V s,30 (measured at 32 stations and estimated using terrain-based proxies at rest).
V s,30 between about 200 and about 1100m∕s with most 300–700m∕s.
- Data from Anza, San Jacinto Fault Zone, Caltech, UC Santa Barbara and Plate Boundary Observatory
seismic networks from 2013. Most instruments are STS-2s with Quanterra digitizers.
- Vast majority of data from 1 ≤ Mw ≤ 2 and from rrup < 30km. Very few events have Mw > 3.
- Focal depths between about 0 and about 25km with vast majority between 5 and 20km.
- Data from 78 different stations. All events recorded by ≥ 5 stations.
- High-pass filter records with cut-off of 0.5Hz to remove noise but preserve PGAs. Automatically find PGAs
using measured or estimated P- and S-wave arrivals at each station. Compute signal-to-noise ratios between
PGA and maximum-amplitude in noise window before P-wave arrival.
- Because all events are small, consider only linear V s,30 term and assume rrup = rhypo.
- Derive models to investigate the path component of ground-motion variability for building a non-ergodic
- Compare coefficients, residuals and variabilities computed using pooled ordinary least-squares and
mixed-effects maximum-likelihood regression.
- Often find that using mixed-effects regression a4 and a5 are unrealistic because these terms are highly
correlated so fix a priori certain coefficients.
- Find very weak correlation between residuals and V s,30, which relate to homogeneity of site response
in region and perhaps site amplification for this region may be better correlated with deeper structure
than modelled by V s,30. Provide individual average site terms and standard errors from the residuals for
considered stations as believe more useful than V s,30-based term.