- Ground-motion model is (following Ambraseys et al. (2005a)):
where (using the preferred 1-stage maximum-likelihood technique): y is in m∕s2, a1 = 1.42397, a2 =
0.00761, a3 = -2.52433, a4 = 0.22046, a5 = 7.43578, a6 = 0.10268, a7 = 0.01468, a8 = -0.05073, a9 =
0.06443, a10 = -0.05634, τ = 0.27410 (inter-event),
ϕ = 0.11514 (intra-event)
and σ = 0.29760 (total)
- Use three site categories:
SS = 1, SA = 0
- Soft soil (S), 180 < V s,30 ≤ 360m∕s. 67 records.
SS = 0, SA = 1
- Stiff soil (A), 360 < V s,30 ≤ 750m∕s. 140 records.
SS = 0, SA = 0
- Rock (R), V s,30 > 750m∕s. 136 records.
Originally include a fourth category, very soft soil (V s,30 ≤ 180m∕s), but only included 7 records so
combined with soft soil records.
- Classify earthquakes using method of Frohlich and Apperson (1992):
- Plunge of T axis > 50∘. 59 records, FT = 1, FN = 0, FO = 0.
- Plunge of P axis > 60∘. 138 records, FT = 0, FN = 1, FO = 0.
- Plunge of B axis > 60∘. 89 records, FT = 0, FN = 0, FO = 0.
- All other earthquakes. 34 earthquakes, 64 records, FT = 0, FN = 0, FO = 1.
- Study the effect of different regression techniques: unweighted (method 1) and weighted (method 2)
least-squares, 1-stage maximum-likelihood (method 3), 3 types of 2-stage methods (unweighted, method
4; Joyner and Boore (1993), method 5; Fukushima and Tanaka (1990), method 6) and using a genetic
algorithm (method 7).
- Use a reduced version of the dataset of Ambraseys et al. (2005a) (see Section 2.235).
- Conduct pure-error analysis (Douglas and Smit, 2001) with bins of size 10km×0.2Mw. Find a significant
(at the 5% level) dependency of the standard deviation from each bin w.r.t. Mw, which model using a
linear equation. Use this equation for the weights in the method 2.
- Compare the fit of the 7 models to the data using histograms of the residuals, quantile-quantile plots and
various statistical measures as well as comparing predictions and observations for different sets of data.
- Find that the predictions of the 7 models are very similar.
- Conclude that the 1-stage maximum-likelihood technique with pure-error analysis being used to obtain
the true variance is the best method.