where A is in m∕s2, c_{1}= -1.589, c_{2}= 0.561, c_{3}= -0.569, c_{4}= -0.003, c_{5}= 0.173, c_{6}= 0.279 and
σ = 0.80 (for all earthquakes), c_{1}= -1.725, c_{2}= 0.687, c_{3}= -0.742, c_{4}= -0.003, c_{5}= 0.173, c_{6}= 0.279
and σ = 0.83 (for shallow crustal earthquakes) and c_{1}= -0.915, c_{2}= 0.543, c_{3}= -0.692, c_{4}= -0.003,
c_{5}= 0.173, c_{6}= 0.279 and σ = 0.74 (for subduction zone earthquakes).
Use three site categories:
S_{1 }= 0,S_{2}= 0
Rock, 54 records.
S_{1 }= 1,S_{2}= 0
Hard soil, 63 records.
S_{1 }= 0,S_{2}= 1
Soft soil, 83 records.
Most records from SMA-1s with 6 records from SSA-2.
Use PSA at 40Hz (0.025s) as peak ground acceleration.
Records instrument corrected and bandpass filtered with cut-offs of 0.2 and 20Hz.
Use data from shallow crustal earthquakes (133 records) and subduction zone earthquakes (67 records).
Perform regression on combined shallow crustal and subduction zone records, on just the shallow crustal
records using r_{hypo} and using r_{epi} and on just subduction zone records.
Note that distribution w.r.t. distance improves in the near field when epicentral distance is used but only
possible to use r_{epi} for shallow crustal earthquakes because for subduction zone earthquakes hypocentral
distance is much greater than epicentral distance so should use r_{hypo} instead.
For 4 ≤ M ≤ 6 distribution w.r.t. epicentral distance is quite good but for M > 6 no records from
d_{e}< 40km.
Use a two step procedure. Firstly use entire set and both horizontal components and compute two soil terms
(one for hard and one for soft soil). In second step use soil terms to correct motions for rock conditions
and then repeat regression.
Use Bayesian analysis (Ordaz et al., 1994) so that derived coefficients comply with physics of wave
propagation because include a priori information on the coefficients to avoid physically unrealistic values.
Choose initial values of coefficients based on theory and previous results
Cannot find coefficient in r by regression so adopt 6km from previous study.
Examine residuals w.r.t. distance and magnitude and find no trends.