Geology Reference
In-Depth Information
Figure 4. Radiation spectrum and envelope function, for various M, r
ˆ
ln
f
=
ln
f
+
e
(19)
correlation between the existence of the pulse and
the proximity of the structural site to the seismic
source/fault. For epicentral distances larger than
15-20 km the pulse component according to this
equation is negligible (Bray & Rodriguez-Marek,
2004).
For the rest of the pulse parameters, the phase
and the number of half cycles, no clear link to the
seismic hazard of the structural site has been yet
identified. They need to be considered as indepen-
dent model parameters. The study (Mavroeidis &
Papageorgiou, 2003) provides relevant values for
these parameters by fitting Equation 18 to a suite
of recorded near-fault ground motions.
p
p
f
ˆ
ln
A
=
ln
A
+
e
(20)
v
v
v
where f p and A v are median values (provided
through a regression analysis), and ε p and ε v are
prediction errors following a Gaussian distribution
with zero mean and large standard deviation. For
rock sites the predictive relationships for the
median values are (Bray & Rodriguez-Marek,
2004)
ˆ
ln
f
p =
8 60
.
1 32
.
M
(21)
Near-Fault Excitation Model
ˆ
2
2
ln
A
v =
4 46
.
+
0 34
.
M
0 58
.
ln(
r
+
7
)
(22)
The stochastic model for near-fault motions is
finally established by combining the above two
components through the methodology initially
developed in (Mavroeidis & Papageorgiou, 2003).
The model parameters consist of the seismological
parameters M and r , the additional parameters for
the velocity pulse, ν p , γ p , the white noise sequence
Z w , and the predictive relationships for f p , A v , and
whereas the standard deviation for the predic-
tion errors e f and e v is estimated as 0.4 and 0.39,
respectively. Note that according to Equation 22
the pulse amplitude, which is directly related to
the peak ground velocity (Mavroeidis & Papageor-
giou, 2003), varies almost inversely proportional
to the epicentral distance. This indicates a strong
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