- Ground-motion model is:
where y is in cm∕s2, a = 0.446, b = 0.00350, c = 0.012, d = 0.446, e = 0.00665, S = 0.941, SR = 0.751,
SH = 0.901, SM = 1.003, SS = 0.995, σT = where σ = 0.135 (intra-event) and τ = 0.203
(inter-event), hc is chosen as 20km because gave positive depth term.
- Use four site categories:
Sk = SR
Sk = SH
- Hard soil
Sk = SM
- Medium soil
Sk = SS
- Soft soil
Note site conditions for many stations are uncertain. S is the mean site term for all data.
- Note ISC focal depths, h, significant reduce prediction errors compared with JMA depths. δh = 1 for
h ≥ hc and δh = 0 otherwise.
- Most Japanese data from x > 50km.
- Use 166 Californian and Chilean (from 2 earthquakes) records to control model in near source.
- Due to lack of multiple records from many sites and because c and d require near-source records use a
maximum likelihood regression method of two steps. Firstly, find all coefficients using all data except those
from sites with only one record associated with them and unknown site class. Next, use individual site
terms for all sites so as to reduce influence of uncertainty because of approximate site classifications and
find a, b, e and site terms using c and d from first step.
- Intra-event and inter-event residuals decrease with increasing magnitude.
- Conclude variation in residuals against distance is due to small number of records at short and large
- Individual site factors means prediction error propagates into site terms when number of records per station
is very small.
- Note model may not be suitable for seismic hazard studies because model prediction errors are partitioned
into σT and mean site terms for a given site class. Suitable model can be derived when accurate site
classifications are available.