- Ground-motion model is:
_{6}constrained to zero. Model A6 (least-squares): a_{1}= 2.45, a_{2}= 0.42, a_{3}= -0.17, a_{4}= -1.73, a_{5}= -0.0056, a_{6}= 0.56, σ = 0.9 (total), τ = 0.48 (inter-event), ϕ_{S}= 0.65 (intra-event) and ϕ_{SS}= 0.46 (single-station intra-event). Model F5 (the authors’ preferred model): a_{1}= -4.23, a_{2}= 1.31, a_{3}= -0.09, a_{4}= -1.2 (fixed a priori), a_{5}= -0.02, a_{6}= 0, σ = 0.87, τ = 0.34, ϕ_{S}= 0.67 and ϕ_{SS}= 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 ≤ M
_{w}≤ 2 and from r_{rup}< 30km. Very few events have M_{w}> 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 r_{rup}= r_{hypo}. - Derive models to investigate the path component of ground-motion variability for building a non-ergodic model.
- Compare coefficients, residuals and variabilities computed using pooled ordinary least-squares and mixed-effects maximum-likelihood regression.
- Often find that using mixed-effects regression a
_{4}and a_{5}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.