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

EFFECT OF DATA TRUNCATION
The initial analyses of the PEER-NGA data suggested that the anelastic attenuation term γ in
Equation (11) was 50-percent larger in absolute value for earthquakes from Taiwan than for
earthquakes in California or the other active tectonic regions represented in the selected
database (Table 2). For pga the estimated values of γ were approximately -0.006 for
California earthquakes and approximately -0.009 for Taiwan earthquakes. This would imply
that Q for Taiwan was significantly lower than Q for California or the other regions.
However, review of the literature failed to produce studies that confirmed this result. The
comparison of Q estimates was made more difficult by the varying assumptions about
geometric spreading made by the various investigators. In addition, the estimates of γ
obtained from the broadband data for the three southern California earthquakes 0163, 0167
and 0170 were in the range of -0.012 to -0.014 (Figure 13).
These results led us to consideration of the effects of missing response data on the estimation
of ground motion model parameters. There are two forms of missing response data treated in
the literature: censoring and truncation. Censoring occurs when a known set of instruments
is triggered, but the response is only known to be below ytruncation. In this case, the number of
censored observations and predictor variables for these observations (e.g. M, RRUP, and
VS30) are known for the censored sample. Truncation occurs when the observed sample is
truncated at some response level ytruncation such that no responses are reported below this level.
The number of missing values and values of the predictor variables for these observations are
unknown. The two forms of missing response variables lead to different forms of the sample
likelihood function in fitting models by maximum likelihood.
Censoring/truncation of the strong motion database occur due to the occurrence of ground
motions below the trigger threshold for the recording instruments and from the selective
processing of recordings favoring those with larger amplitudes. Censoring/truncation occurs
also from record processing as frequency bands with low signal/noise ratios are filtered out
of the process records. Although the number of possible recordings in a given earthquake is
knowable, some instruments may have malfunctioned and there is not a complete accounting
of the possible instruments available. Therefore, the truncation model is considered the most
appropriate condition.
Some evidence of truncation of the data is seen in Figure 2, but it is more apparent when
examining individual earthquakes. An obvious case is shown in Figure 27 for the three small
southern California earthquakes analyzed previously. The left hand plot shows the 660 pga
values for the three earthquakes obtained from the broad band recordings and the right hand
plot shows the 119 pga values for the processed records that are in the PEER-NGA database
for these earthquakes. Approximate truncation levels are indicated by the dashed horizontal
lines. The curves indicate fits to the data using truncated regression techniques with random
effects as follows.
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