- Ground-motion model is:
where Y is in cm∕s2; a = 0.787, b = 0.478, c = -1.092, d = -0.0044, e = 0.096, f = 0.146, h = 10.688
and σ = 0.285 including site and mechanism terms; a = 0.829, b = 0.474, c = -1.062, d = -0.004,
e = 0.082, h = 10.772 and σ = 0.291 including only site term; a = 0.881, b = 0.479, c = -1.107,
d = -0.0043, f = 0.142, h = 10.802 and σ = 0.289 including only mechanism term; and a = 0.907,
b = 0.474, c = -1.074, d = -0.004, h = 10.763 and σ = 0.296 including neither term.
- Use 2 site classes:
s = 0
- NEHRP class B (rock).
s = 1
- NEHRP class C and D (stiff and soft soil).
Also consider separate terms for classes C and D.
- Use 2 faulting mechanisms:
m = 0
m = 1
- Strike-slip and thrust.
- Use data from 1973 to 2014. Filter records not already processed using a bidirectional 2nd-order
Butterworth filter with cut-offs of 0.2–0.3Hz and 25–30Hz after zero-padding.
- Use repi because lack of information on rupture planes for most moderate and small events. Note that this
is a limitation of the model but because vast majority of earthquakes have Mw < 6.4 it is not a major
- Do not use rhypo because of poorly-resolved focal depths.
- Split data into training and validation datasets. Regression performed on training datasets, which includes
only earthquakes recorded by > 1 station. Training dataset includes records from 124 different stations.
Validation dataset includes singly-recorded earthquakes plus a few records from training dataset so that
training and validation datasets have same distance range. Validation dataset has 254 records from 123
earthquakes and 45 different stations. No data in validation dataset with repi < 5km.
- Note potential limitation of dataset when using 2-stage regression is number of events with only 2 records,
which provide weak constraints on separation into inter- and intra-event variabilities.
- Note few records from Mw > 6 and repi < 20km so lack of constraint in model for these magnitudes and
- Check significance of coefficients using Student’s t-test and goodness of fit using efficiency coefficient.
- In total consider 24 alternative functional forms. In addition to 4 reported above also consider using h or
not, using d or not and using 3 site classes. Coefficients reported in electronic supplement but not reported
here due to lack of space. Coefficients reported above have the lowest σ and highest efficiency coefficient.
- Consider residuals w.r.t. Mw and repi and the ‘studentized’ residuals w.r.t. predicted PGA, which use
to detect outliers. Find no trends nor outliers. Plot probability density function graphs and normal
quantile-quantile plots. Find that the normality assumption is justified.