Chiou and Youngs PEER-NGA Empirical Ground Motion Model for ...

Step 2: Using the smoothed values of φ3, regression analyses were performed to examine the
variation of cn and cM with period. Parameter cn was then smoothed and parameter cM reestimated,
then smoothed.
Step 3: The next step was to assess parameters c5 and c6 which control the shape of the
distance attenuation near the source. With the smoothed values of cn and cM from step 2, the
variation of c5 and c6 with period was examined. Parameter c5 was smoothed, parameter c6
re-estimated, then smoothed. It should be noted that the variation of c5 and c6 with period
and a constant value of c4 accomplishes a similar effect to the variation of c4 with period for
fixed c5 and c6 in Sadigh et al. (1997).
Step 4: The final step in the first phase of the analysis was reassessment of the nonlinear soil
model parameters. With the above model parameters fixed, parameters of φ2 and φ3 were reestimated
from the data. Parameter φ3 was then smoothed, φ2 re-estimated, then smoothed.
Second Phase:
Step 5: In the second phase of parameter development, the hanging wall and footwall data
were included and the hanging wall functional form for fHW was added to the model.
Initially, the inclusion of the hanging wall data resulting in reverse and strike slip faulting
having the same amplitudes (c1a ~ 0). However, it was discovered that this result was largely
due to data from the Chi-Chi main shock. When the Chi-Chi main shock was removed, c1a
increased to approximately 0.1 and the amplitude of the hanging wall coefficient c9 was
reduced. There is a large degree of coupling between these parameters. The value of c1a is
marginally statistically significant (t-values slightly greater than 2). The analysis by Chiou et
al. (2000) found that when the geometric hanging wall effect was removed by using RRMS, a
style of faulting effect remained with reverse faulting earthquakes producing larger ground
motions than strike-slip earthquakes. On this basis, we have assumed that there is a style of
faulting effect for reverse faults. The value of parameter c1a was estimated without the Chi-
Chi main shock data.
The style of faulting effect for normal faults, c1b was found to be statistically significant only
when normal faulting flag FNM was restricted to be 1 for rake angles in the range -120º ≤ λ ≤ -
60º, that is normal-oblique earthquakes have the same level of ground motions as strike-slip
earthquakes. Parameter c1b is also only marginally significant with t-values slightly greater
than 2.
Parameter c1a was found to decrease with increasing spectral period, becoming 0 at a period
of 1.0 seconds and then decreasing to about -0.1 at long periods. This is consisted with the
trends observed in previous empirical models (e.g. Abrahamson and Silva, 1997; Campbell
and Bozorgnia, 2003; the soil model of Sadigh et al., 1997). At high frequency, this is
consistent with an interpretation of higher stress drops (stress parameters) for reverse faulting
earthquakes than for strike-slip earthquakes. However, the negative values of c1a at long
periods is not consistent with this concept, indicating that other factors may also be
influencing the difference between the motions produced by the two styles of faulting. For
normal faulting, the value of c1b was approximately -0.25 and decreased in absolute value as
the spectral period decreased. For spectral periods greater than about 1.0 second, the value of
c1b becomes very uncertain. If one speculates that the negative value of c1a for reverse
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