- Ground-motion model is:
- Response parameter is acceleration for 5% damping.
- Consider three site conditions but only retain two:
- Rock: ENEA/ENEL S0 classification ⇒ S1 = 0, 49 records.
- Thin alluvium: depth of soil between 5 and 20m,ENEA/ENEL S1 classification ⇒ S1 = 1, 34 records.
- Selected records have de < 60km and focal depth less than 30km. Data selected so that mean and standard
deviation of magnitude and hypocentral distance in each site category are equal, in this case 5.1 and 20km
- All records processed using common procedure. High pass filtered with fl = 0.5Hz, instrument corrected
and low pass filtered with fh = 30Hz.
- Considered three things when choosing method of analysis:
- Attenuation equation must have some physical basis.
- Parameters must be available for original data set.
- Attenuation equation must be easy to use in a predictive manner.
- Hypocentral distance used because rupture not known for most earthquakes. Note that only important for
magnitudes greater than about 6.5 and distances less than about 15km.
- Originally included another set of data (32 records) from thick soil with depth greater than about 20m
(ENEA/ENEL classification S2) but note that results for this category are much more uncertain, possibly
due to diversity of geotechnical characteristics of soils. Therefore excluded.
- Regression was done using two-stage algorithm (Joyner and Boore, 1981) and a weighted one-stage method.
Weight by splitting the magnitude and distance ranges into four intervals and weighting data in each
interval inversely proportionally to number of points in the bin. Thus gives roughly equal weight to each
part of magnitude-distance space.
- Note that results from two-stage regression for this set of data may be misleading because for some periods
it does not bring any ‘explanation’ to the variance of initial data. The two-stage and normal one-stage and
weighted one-stage yield significant changes in predictions.
- Repeat analysis using only S0 subset and using only S1 subset but no significant changes in magnitude or
distance scaling between the two subsets so consider complete set and include a constant scaling between
rock and shallow soil. If set is reduced to 53 records with similar spread of magnitude, distance and sites
then difference between shallow soil and rock is not significant.
- Note that confidence interval should be given by formula in Weisburg (1985) not normal way of simply
using standard deviation.