- Ground-motion model is: where amax is in cm∕s2, log 10A0(R) is an empirically determined attenuation function from Richter (1958)
used for calculation of ML, p is confidence level and v is component direction (v = 0 for horizontal and
1 for vertical). Coefficients are: a = -0.898, b = -1.789, c = 6.217, d = 0.060, e = 0.331, f = 0.186,
Mmin = 4.80 and Mmax = 7.50 (log 10A0(R) not given here due to lack of space).
- Use three site categories:
s = 0
- Alluvium or other low velocity ‘soft’ deposits: 63% of records.
s = 1
- ‘Intermediate’ type rock: 23% of records.
s = 2
- Solid ‘hard’ basement rock: 8% of records.
- Exclude records from tall buildings.
- Do not use data from other regions because attenuation varies with geological province and magnitude
determination is different in other countries.
- Records baseline and instrument corrected. Accelerations thought to be accurate between 0.07 and 25Hz
or between 0.125 and 25Hz for San Fernando records.
- Most records (71%) from earthquakes with magnitudes between 6.0–6.9, 22% are from 5.0–5.9, 3% are
from 4.0–4.9 and 3% are from 7.0–7.7 (note barely adequate data from these two magnitude ranges). 63%
of data from San Fernando earthquake.
- Note that for large earthquakes, i.e. long faults, log 10A0(R) would have a tendency to flatten out for small
epicentral distances and for low magnitude shocks curve would probably have a large negative slope. Due
to lack of data ≲ 20km this is impossible to check.
- Note difficulty in incorporating anelastic attenuation because representative frequency content of peak
amplitudes change with distance and because relative contribution of digitization noise varies with
frequency and distance.
- Note that log 10A0(R) may be unreliable for epicentral distances less than 10km because of lack of data.
- Change of slope in log 10A0(R) at R = 75km because for greater distances main contribution to
strong shaking from surface waves, which are attenuated less rapidly (~ 1∕R1∕2) than near-field and
intermediate-field (~ 1∕R2-4), or far-field body waves (~ 1∕R).
- Note lack of data to reliably characterise log 10a0(M,p,s,v) over a sufficiently broad range of their
arguments. Also note high proportion of San Fernando data may bias results.
- Firstly partition data into four magnitude dependent groups: 4.0–4.9, 5.0–5.9, 6.0–6.9 and 7.0–7.9.
Subdivide each group into three site condition subgroups (for s = 0, 1 and 2). Divide each subgroup into
two component categories (for v = 0 and 1). Calculate log 10a0(M,p,s,v) = M + log 10A0(R) - log 10amax
within each of the 24 parts. Arrange each set of n log 10a0 values into decreasing order with increasing n.
Then mth data point (where m equals integer part of pn) is estimate for upper bound of log 10a0 for p%
confidence level. Then fit results using least squares to find a, …f.
- Check number of PGA values less than confidence level for p = 0.1, …, 0.9 to verify adequacy of bound.
Find simplifying assumptions are acceptable for derivation of approximate bounds.