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

PATH SCALING
Near-Source Distance Scaling: The scaling or attenuation of ground motion amplitude with
distance from the earthquake rupture involves a number of issues. Foremost of interest for
engineering application in active tectonic regions is the effect of extended sources that leads
to magnitude-dependent attenuation rates at least within the distance range of 0 to 100 km.
The consequence of this effect is what has been termed near-source saturation – less
magnitude scaling at small source-site distances than at large source-site distances. There are
four functional forms that have been used to model this effect in empirical ground motion
models. These forms are shown on Figure 10 in terms of recent applications. The form that
has been used for many years by Ross Sadigh and also by Ken Campbell is defined by
Equation (3):
ln( y)
∝ C M + C
2
c(
M)
= C
5
4
× ln
exp
[ R + c(
M)
]
{ C M}
In this form, magnitude-dependence is introduced by making parameter c a function of
magnitude. Campbell (1993) introduced a modified version of Equation (3):
ln( y)
∝ C M + C
2
4
c(
M)
= C
5
× ln
exp
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6
2
2
[ R + c(
M)
]
{ C M}
Campbell and Bozorgnia (2003) further modified Equation (4) to introduce a quadratic
magnitude term in defining c(M).
The forms defined by Equations (3) and (4) introduce magnitude dependence through the
parameter c(M). An alternative approach is to incorporate magnitude-dependence in the
“slope” term. Idriss (1991) introduced the form
ln( 2
4 5
6
[ R c]
y ) ∝ C M + ( C + C M)
× ln +
(5)
Abrahamson and Silva (1997) introduced a modified version of (5):
2
4
5
2 2 [ R ]
ln( y ) ∝ C M + ( C + C M)
× ln + c
(6)
The attenuation behavior of the four models shown on Figure 10 can be illustrated by
plotting the attenuation rate, defined as ∂ ln( y) / ∂ ln( R)
, versus distance. Figure 11 shows
R + , the rate of attenuation
approaches the value of the parameter C4 or C4+C5M at relatively short distances, allowing
an interpretation of its value as an estimate of the rate of geometric spreading. For those
ln R + c , the attenuation rate approaches the value of C4 or
2 2
the results. For those models that use the term ln[ c ]
models that use the term [ ]
(3)
(4)