- Ground-motion model is:
where F = 1 for reverse or reverse oblique events and 0 otherwise and E = 1 for interplate events and
0 otherwise, a is in g, for horizontal PGA α = -0.62, β = 0.177, c = 0.982, h2 = 0.284, ϕ = 0.132,
b = -0.0008 and σ = 0.277 and for vertical PGA α = -1.15, β = 0.245, c = 1.096, h2 = 0.256, ϕ = 0.096,
b = -0.0011 and σ = 0.296.
- Consider three site classifications, based on Joyner and Boore (1981):
- Rock: corresponds to C, D & E categories of Campbell (1981), 159 records.
- Soil: corresponds to A,B & F categories of Campbell (1981), 324 records.
- Unclassified: 102 records.
Use to examine possible dependence in residuals not in regression because of many unclassified stations.
- Data based on Campbell (1981).
- Fault mechanisms are: strike-slip (256 records from 28 earthquakes), normal (14 records from 7
earthquakes), normal oblique (42 records from 12 earthquakes), reverse (224 records from 21 earthquakes)
and reverse oblique (49 records from 8 earthquakes). Grouped into normal-strike-slip and reverse events.
Weakly correlated with magnitude (0.23), distance (0.18) and tectonic environment (0.03).
- Tectonic environments are: interplate (555 records from 66 earthquakes) and intraplate (30 records from
10 earthquakes) measurements. Weakly correlated with magnitude (-0.26), distance (-0.17) and fault
- Depths less than 25km.
- Use array average (37 instruments are in array) from 10 earthquakes recorded at SMART 1 array in
- Most records from distances less than 100km and magnitude distribution is reasonably uniform but
correlation between magnitude and distance of 0.52.
- Try two-stage technique and model (modified to include fault mechanism and tectonic environment
parameters) of Joyner and Boore (1981), find inadmissable positive anelastic coefficient, so do not use it.
- Use a hybrid regression technique based on Joyner and Boore (1981) and Campbell (1981). A method
to cope with highly correlated magnitude and distance is required. First step: fit data to f2(r) =
clog 10(r + h) and have separate constants for each earthquake (like in two-stage method of Joyner and
Boore (1981)). Next holding c constant find α, β, b and h2 from fitting h = exp(h2M). Weighting based
on Campbell (1981) is used.
- Form of h chosen using nonparametric function, H(M), which partitions earthquakes into 0.5 unit bins.
Plot H(M) against magnitude. Find that H(M) = h1 exp(h2M) is controlled by Mexico (19/9/1985)
earthquake and h1 and h2 are highly correlated, 0.99, although does given lower total variance. Choose
H(M) = exp(h2M) because Mexico earthquake does not control fit and all parameters are well-determined,
magnitude dependent h significant at 90%.
- Try removing records from single-recorded earthquakes and from shallow or soft soil but effect on
predictions and variance small (< 10%).
- Plot weighted residuals within 10km no significant, at 90%, trends are present.
- Find no significant effects on vertical PGA due to site classification.