- Ground-motion model is:
where Y is in g, for horizontal PGA a = -5.503, b = 0.936, c1 = 0.407, c2 = 0.455, d = -0.816 and
σ = 0.461 and for vertical PGA a = -5.960, b = 0.989, c1 = 0.013, c2 = 0.741, d = -1.005 and σ = 0.551.
- All records from SMART-1 array so essentially identical site conditions and travel paths.
- All records from free-field instruments mounted on 4inch (10cm) thick concrete base mats, approximately
2 by 3feet (60 by 90cm) across.
- Select earthquakes to cover a broad range of magnitude, distance and azimuth and ensuring thorough
coverage of the array. Criteria for selection is: at least 25 stations recorded shock, focal depth < 30km,
hypocentral distance < 50km except for two large earthquakes from beyond 50km to constrain distance
- Focal depths between 0.2 and 27.2km with all but one ≤ 13.9km.
- Azimuths between 60∘ and 230∘.
- Most records (78%) have magnitudes between 5.9 and 6.5. Note magnitude and distance are not
independent (correlation coefficient is 0.6).
- Records have sampling interval of 0.01s. Processed using trapezoidal band passed filter with corner
frequencies 0.07, 0.10, 25.0 and 30.6Hz.
- Not enough information to use distance to rupture zone.
- Source mechanisms of earthquakes are: 4 normal, 2 reverse, 1 reverse oblique and 1 normal oblique with 4
unknown. Do not model source mechanism dependence because of 4 unknown mechanisms.
- Use weighted regression, give equal weight to recordings from each earthquake within each of 10 distance
bins (< 2.5, 2.5–5.0, 5.0–7.5, 7.5–10.0, 10.0–14.1, 14.1–20.0, 20–28.3, 28.3–40.0, 40.0–56.6 and 56.6–130km).
Do this so earthquakes with smaller number of recordings are not overwhelmed by those with a larger
coverage and also to give additional weight to shocks recorded over multiple distance bins. Apply two-stage
regression, because of high correlation between magnitude and distance, excluding 3 earthquakes (M = 3.6,
5.0, 7.8) with 162 records from first stage to reduce correlation between M and R to 0.1. Also do one-stage
regression although do not give coefficients.
- Use mean horizontal component because reduces uncertainty in prediction.
- Examine coefficient of variation for each earthquake using median and normalized standard deviation of
recordings in inner ring of array. Find evidence for magnitude dependent uncertainty (large magnitude
shocks show less uncertainty). Find that main contribution to scatter is inter-event variations again by
examining coefficient of variation; although note may be because using dense array data.
- Examine mean residuals of observations from each earthquake. Find evidence for higher than predicted
vertical PGA from reverse faulting earthquakes and lower than predicted vertical PGA from normal
faulting earthquakes, although due to lack of information for 4 earthquakes note that difficult to draw any
- Examine mean residuals of observations from each station in inner ring. Find mean residuals are relatively
small compared with standard deviation of regression so variation between stations is less than variation
between earthquakes. Find for some stations some large residuals.