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

term [ 1 Φ(
y ( θ ) + τ ⋅ z , σ ) ]
− . Maximum likelihood solutions to Equation (18) were
truncation μij i
performed using numerical integration and the general optimization routine optim in R.
The data shown in Figure 27 were fit by maximum likelihood using Equation (18) and a
ground motion model in which all the parameters were fixed except γ and the random effect
for each event. The truncation levels for each case are indicated on the figure. For this
example, γ = -0.013 was obtained from the fit to the full data set and γ = -0.015 was obtained
from the fit to the PEER-NGA data for these three events.
To further evaluate the potential impact of data truncation on the model development, we
developed extended pga data sets for 10 additional California earthquakes. These extended
data sets are described in Appendix D and the earthquakes are listed in Table 4. Additional
pga data for Northridge (EQID 0127) were supplied by Vladimir Graizer (personal
communication, 2006). The remaining data were obtained from the TriNet/ShakeMap
webpages. Only the High Broadband data were used. The PEER-NGA set of earthquakes
was supplemented by data from the Feb 2, 2000 Loma Linda; Dec 23, 2003 San Simeon; and
the Sept 28, 2004 Parkfield earthquake. In addition, an extended data set was developed for
the 1995 Kobe earthquake using the data presented in Fukushima et al. (2000).
For each of these earthquakes, estimates of γ were made using truncated regression and a
ground motion model with fixed values of the other parameters. To remove the influence of
hanging wall effects, hanging wall and footwall sites were removed. Estimates of γ were
obtained using just the PEER-NGA data and using the extended data and these are listed in
Table 4 along with the number of recordings used in each analysis. Figure 28 shows
examples of the results for four of the earthquakes. For the Northridge earthquake, similar
estimates of γ were obtained from the PEER-NGA and extended data set. However, for the
other three earthquakes shown on Figure 28, the estimate of γ obtained from the PEER-NGA
data set were approximately 2/3 of the values obtained from the extended data sets. As
indicated by the results in Table 4, the values of γ computed using only PEER-NGA data are
typically smaller than obtained from the extended data. The few cases where the PEER-
NGA data produced larger (and often unrealistic) values of γ are for earthquakes with very
limited samples in the PEER-NGA database (e.g. San Juan Bautista, Mohawk Valley).
Truncated regression analyses performed using the combined PEER-NGA data for these
earthquakes also produce smaller value for γ than analysis using the combined extended data
sets.
As a short-term solution to this problem, we decided to develop the ground motion model
using the PEER-NGA data truncated at a maximum distance of 70 km. This distance was
selected by visual inspection as the point where, on average, data truncation may begin to
affect the distribution of recordings in the PEER-NGA data base. The regression analyses
were performed using a model for γ determined from the combined extended data sets for
California earthquakes. Figure 29 shows the values of γ for the earthquakes listed in Table 4.
The results indicate that γ decreases in absolute value with increasing magnitude, similar to
results reported by others from analysis of empirical data (e.g. Campbell, 1993) and
stochastic ground motion simulations (e.g. Campbell, 2003).
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