where a_{p} is in g, a_{1}= -1.62, a_{2}= -1.01, a_{3}= 0.246, a_{4}= 0.212, a_{5}= 0.59, a_{6}= -0.29, a_{7}= 0.21 and
σ = 0.29.
Use six local site classifications:
S_{1}
Holocene
S_{2}
Pleistocene soil
S_{3}
Soft rock
S_{4}
Hard rock
S_{5}
Shallow (< 10m depth) soil
S_{6}
Soft soil (e.g. bay mud)
Data from about 800 different stations.
Note that inclusion of subduction-zone events in analysis may affect results with unmodelled behaviour,
particularly with regard to distance scaling although believe use of r_{rup} partially mitigates this problem.
Firstly compute an equation does not include site coefficients. Conduct regression analysis on site-condition
subsets of the residuals using M or logR as dependent variable. Find several regressions are not statistically
significant at the 5% level and/or the predicted effects are small at the independent variable extremes.
Find strongest effects and most significant results are for shallow soil sites and soft soil sites although
because of the high correlation between M and logR in the set used it is difficult to construct unbiased
models.
Use a stochastic random-vibration approach to find theoretical equations for estimating PGA that include
the effect of local site conditions as distance-dependent terms. Using the results from this analysis construct
equation based on the observed PGAs. Try including terms for S_{1}, S_{2}, S_{5}, S_{6} and corresponding logR
terms for each site type but iterate to retain only the significant terms.
Fix magnitude scaling (0.36M) and anelastic attenuation (0.002R). Do not try to optimise the fit other
than using fixed values similar to those given by the stochastic analysis.
Note that anelastic coefficient may be too low but it produces an acceptable geometric spreading term.
Note that because Moho critical reflections can increase amplitudes beyond about 50km the effects of
anelastic or geometric attenuation may be masked.
Allowing all the coefficients in the equation to be free produces a smaller magnitude scaling coefficient, a
smaller geometric spreading coefficient, and a non-significant anelastic attenuation term.
Note that data from S_{5} and S_{6} are sparse.
Compare estimated PGAs with data from within small magnitude ranges. Find that PGAs from Morgan
Hill earthquake are overestimated, which believe is due to the unilateral rupture of this earthquake masking
the effect of the local site conditions.