- Ground-motion model is:
_{max}is in cm∕s2, log_{10}A_{0}(R) is an empirically determined attenuation function from Richter (1958) used for calculation of M_{L}, 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, M_{min}= 4.80 and M_{max}= 7.50 (log_{10}A_{0}(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
_{10}A_{0}(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
_{10}A_{0}(R) may be unreliable for epicentral distances less than 10km because of lack of data. - Change of slope in log
_{10}A_{0}(R) at R = 75km because for greater distances main contribution to strong shaking from surface waves, which are attenuated less rapidly (~ 1∕R^{1∕2}) than near-field and intermediate-field (~ 1∕R^{2-4}), or far-field body waves (~ 1∕R). - Note lack of data to reliably characterise log
_{10}a_{0}(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
_{10}a_{0}(M,p,s,v) = M + log_{10}A_{0}(R) - log_{10}a_{max}within each of the 24 parts. Arrange each set of n log_{10}a_{0}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_{10}a_{0}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.