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

geometric effect, we expect that smaller overall ruptures would produce less effect than
larger rupture, given the same values of RJB and RRUP. Previous implementations of the
hanging wall effect in empirical models have reduced the effect to 0 for magnitudes less than
M 6. Similarly, as the same size rupture is moved to deeper depths, we would also expect
the hanging wall effect to be reduced. Both smaller rupture sizes and greater depths would
tend to move make RRMS closer to RRUP, and thus, according to the analysis of Chiou et al.
(2000), reduce the hanging wall effect.
We propose a geometric factor, HW* = 2ψ/π, to represent the combined effect of rupture size
and rupture depth. The factor is illustrated on Figure 20. The angle ψ represents the halfangle
of the exposure of the surface to the fault plane and is a function of the rupture width,
W, and the rupture depth, ZTOR. Using the geometry of the fault rupture, HW* is computed
by the relationship:
HW*
2 −1⎛
W cos( δ ) ⎞
= tan ⎜
⎟
τ ⎝ 2(
ZTOR
+ ζ ) ⎠
The factor ζ is included to remove singularities in the calculation and to limit the hanging
wall effect for small magnitudes at shallow depths. Figure 21 show the variation of HW*
with M and ZTOR with ζ set equal to 1 km. The function introduces a decrease in the hanging
wall effect with increasing rupture depth that is magnitude-dependent.
ZTOR
W
ψ
Figure 20: Illustration of the hanging wall geometric factor HW*.
Figure 22 shows that HW* correlates with both magnitude and ZTOR for the data selected for
use in this study.
One additional aspect of the hanging wall effect needs to be addressed. The function
[ 1−
RJB
/ RRUP
] produces the same level of hanging wall effect at locations on top of the
rupture. However, the numerical modeling results presented in Chiou et al. (2000) and those
conducted for the PEER-NGA project (Somerville et al., 2006) show the hanging wall effect
tapering to zero at the fault tip for faults with surface rupture. We model this effect by
multiplying the hanging wall term by tanh(0.5RRUP).
C&Y2006 Page 27
δ
(12)