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

and a 2-slope model with the second slope fixed at -0.5:
ln( y) = C + C FBBC
+ C FYL
+ C ln( R ) − 0.
5ln(
R ) + γR
+ φ ln( VS
R
0
=
R
2
1
2
2
+ 6 , R = min( R , C ), R = max( 1,
R
1
3
0
8
4
2
C&Y2006 Page 21
1
0
2
/ C
8
)
1
30
/ 400)
This study was performed before our final decision on the function form for distance
attenuation near the source but alternative forms were found to produce similar results. The
data cannot determine h (insufficient data at small distances) so it was fixed at 6. Dummy
variables FBBC and FYL were used for the intercepts rather than magnitude scaling with
random effects. There is sufficient data for each event (~200 records) that the random effect
should equal the mean residual and the magnitude range is small (4.33 to 4.92). The analysis
was conducted for spectral periods in the range of 0.01 to 5 seconds. Examination of the
recordings (Appendix D) indicated that they could be used without processing to periods at
least as long as 5 seconds.
Figure 13 shows the results of fitting Equations 8 and 9 to the data. At all spectral periods,
the 2-slope models produced slightly smaller standard errors that the single slope model. The
location for the break in slope varied between 40 and 60 km. In addition, use of the singleslope
model produces unrealistic positive values of the anelastic attenuation term γ for longer
period motions, a fact also noted by Atkinson and Silva (1997).
The TRI-Net pga data from many of the better-recorded small magnitude earthquakes display
the change in attenuation rate slope. Tests of the PEER-NGA data also show that a twoslope
model is statistically significant with a slope break also in the range of 45 to 60 km.
Examination of the 1-D rock numerical simulation data also indicate that two-slope model
provides a good fit with a beak in slope at about 60 km.
Based on the above considerations, we adopted the concept of a change in the rate of
attenuation occurring at a distances of approximately 50 km from the source. The
appropriate value of the attenuation rate at distances beyond this point cannot be readily
determined from the data because it is highly correlated with the assessment of the anelastic
attenuation term γ, as had been noted by many previous investigators (e.g. Atkinson, 1989;
Frankel et al., 1990). Therefore, we assume that the rate of attenuation can be modeled by a
slope of -0.5 and will let the anelastic attenuation term γ account for departures from this
value.
The anelastic attenuation parameter γ is likely to have some degree of magnitude
dependence. Boatwright et al. (2003) found magnitude-dependence in the anelastic
attenuation term from their study of pga and pgv from northern California ShakeMap data,
with increasing magnitude producing smaller absolute values of γ (less energy absorption).
In addition, stochastic simulations of ground motions using a magnitude-independent Q
model will produce magnitude-dependence in the resulting anelastic attenuation term γ fit to
response spectra ordinates (e.g. Campbell, 2003). This effect was also noted by us in fitting
ground motions using the Atkinson and Silva (2000) ground motion model. The effect is
likely due to the shift to lower frequencies driving the damped oscillator response (and
driving pga, Boatwright et al., 2003) as the size of the earthquake increases and lower
frequency motions typically display lower values of Q.
(10)