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

The different forms of distance scaling defined by Equations (3) through (6) also result in
differences in the variation in the scaling of ground motions with magnitude at different
distances. Figure 12 shows the magnitude scaling, defined as ∂ ln(y ) / ∂M
, for the four
ground motion models shown in Figure 10. The steps in the values of ∂ ln(y) / ∂M
occur
where there are changes in the model parameters for different magnitude ranges. The
distance attenuation functional forms that use a magnitude-dependent slope, Equations (5)
and (6) produce continued increases in magnitude scaling with increasing distance. Those
that use a magnitude-dependent near-source adjustment term, c(M), result in a gradual
approach to distance-independent magnitude scaling.
Figure 12: Plots of magnitude scaling at a range of distances produced by the form of the attenuation
curve for the four ground motion models shown in Figure 10. Magnitude scaling is defined as
∂ ln( pga ) / ∂M
.
We examined the alternative forms and their fit to the PEER-NGA data and came to the
conclusion that they all would work equally well given the data distribution. Discrimination
among them would require a great deal more data at distances less than 10 km. The
relationships we are to develop are required to cover the distance range of 0 to 200 km. We
based our selection of the functional form on the behavior over the full magnitude range.
The data show magnitude-dependence in the rate of attenuation at all distances. However,
we believe that the mechanisms that cause this behavior may be different at different
distances. At distances less than ~50 km, magnitude-dependence is due to the effect of
extended sources. This effect can be modeled by all of the form. However, at large
distances, >100 km, we think that another effect may be causing magnitude-dependence in
the attenuation of response spectral ordinates – the interaction of Q with the differences in
source Fourier spectra as a function of magnitude. This concept is explored below. The
magnitude-dependence at large distances may also be modeled by the various functional
forms. We prefer to use a model form that allows for separation of the effect of magnitude at
small and at large distances, and therefore select the form defined by Equation (3). This form
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