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

1
) ∝ C2
× M + ( C2
− C ) × ln
M T −
C ( T )
ln( y 3
n
n
[ 1+
exp{
C ( T ) × ( C ( ) M)
} ]
In Equation (2) parameter C2 is the slope of the magnitude scaling relationship above the
corner frequency, C3 is the slope of the magnitude scaling relationship below the corner
frequency. Parameter Cn controls the magnitude range over which the transition from C2
scaling to C3 scaling occurs. Parameter CM is the magnitude at the midpoint of this transition
and its value varies with the spectral period of the ground motion parameter y. The function
form of Equation (2) was tested by fitting a set of ground motion response spectra simulated
using the program SMSIM (Boore, 2005) and the Atkinson and Silva (2000) stochastic
ground motion. Figure 8 shows the magnitude scaling obtained from the simulated ground
motions. As indicated on the figure, the functional form of Equation (2) can provide a close
fit to the simulations.
Figure 9 shows peak acceleration data in the distance range of 30 to 50 km and the VS30
range of 300 to 400 m/s from the PEER-NGA database and from the TriNet data (Appendix
D). These values were fit using three alternative scaling relationships. The quadratic form of
Equation (1) uses an exponent n of 2. The Sadigh et al. (1997) form of Equation (1) uses n
equal to 2.5 and mC equal to 8.5. In the magnitude scaling defined by Equation (2),
parameter C3 represents scaling of ground motion spectra below the corner frequency where
the source spectra are directly proportional to seismic moment, M0. Because M ∝ ⅔M0,
theoretically, C3 should equal 1.5×ln(10) or 3.45 and the fit of Equation (2) to the data shown
on Figure 9 used this value of C3. Parameter C2 represents the scaling of the source spectra
above the corner frequency. The source spectral model defined by Atkinson and Silva
(2000) produces scaling of ln(y) ∝ 1.06M. As described in the next section, in the Sadigh et
al. (1997) form of Equation (1), parameter C2 also represents the magnitude scaling of the
source spectra at distances unaffected by extended-source effects and in the Sadigh et al.
(1997) values of C2 were 1.0 to 1.1. The fit of the Sadigh et al. (1997) form of Equation (1)
to the data on Figure 9 also produced C2 equal to 1.0. In fitting Equation (2) to the data on
Figure 9, C2 was constrained to be 1.06, the value obtained from the magnitude scaling of
source spectra above the corner frequency defined by Atkinson and Silva (2000). All three
forms provide essentially equally good fits to the data. We prefer the scaling form of
Equation (2) because we believe that it better represents our current concept of the variation
in earthquake source spectra with earthquake magnitude.
C&Y2006 Page 14
(2)