Geoscience Reference
In-Depth Information
Anumberofaccelerograms(121)recordedatsiteswithunknowngroundconditionswas
retained in the dataset; when regressing the data with (2.2), these sites were assumed to
belongeithertoclassBortoclassC,thelatterchoiceprovidingalowerpredictionerror.
Some tests on the spectral ordinate at 10s period, denoted hereinafter as
D
10
,were
performed to investigate whether the statistical significance of the prediction would
be increased to adopt a functional form different from (2.2), e.g. by including a
quadratic dependence on
M
,oradissipative attenuation term, or amagnitude-dependent
attenuation coefficient
a
3
(see Joyner and Boore, 1981; Fukushima, 1996; Ambraseys
etal.,2005).Nosignificantimprovementwasobtainedwithrespecttotheresultsyielded
by(2.2),thathastheadditionaladvantageofallowinganimmediatecomparisonwiththe
theoretical attenuation relation for the far field maximum ground displacement derived
in Faccioli et al. (2004) fromthe Brune model, i.e.
log
d
max
(
cm
)
=−
4
.
46
+
0
.
33log
σ (
MPa
)
+
M
−
log
R
(
km
)
(2.3)
where
d
max
isthemaximumhorizontalgrounddisplacementand
thestressdrop.The
tests with a different functional form of the attenuation relation will be extended also to
the shorterperiod
DRS
ordinates.
σ
The coefficients
a
i
of (2.2) were calculated by the two-stage regression technique first
introduced in Joyner and Boore (1981), allowing to decouple the magnitude and the dis-
tance dependence. The coefficients were determined in the range 0
.
10s
≤
T
≤
20s for
damping 0.05 (listedinTable 2.2), as well as for0.10, 0.20, 0.30 damping.
Note from Table 2.2 that the magnitude and distance dependence of the
DRS
ordinates
is consistent with the theoretical relationship (2.3) at periods between about 6s and 10s,
confirming the soundness of the empirical prediction tool.
Table 2.2. Coefficientsof Eq.(2.2) for the prediction of 5% damped
DRS
(
T
)
T
(s)
a
1
a
2
a
3
a
4
a
5
σ
log
DRS
0.10
−
1
.
7769
0.4974
−
1
.
7479
0.0465
0.042045
0.3935
0.15
−
1
.
757
0.5153
−
1
.
6367
0.0689
0.1379
0.3902
0.2
−
1
.
8922
0.543
−
1
.
5544
0.0844
0.2343
0.3902
0.25
−
2
.
0734
0.5801
−
1
.
5039
0.1004
0.2917
0.3836
0.5
−
2
.
4256
0.6585
−
1
.
416
0.2032
0.4611
0.3689
0.75
−
2
.
6197
0.6964
−
1
.
3616
0.2674
0.5368
0.370
1
−
2
.
7652
0.7499
−
1
.
3796
0.2482
0.5016
0.379
1.25
−
2
.
8531
0.7772
−
1
.
3624
0.2165
0.4463
0.3732
1.5
−
2
.
945
0.8095
−
1
.
3752
0.1856
0.4070
0.3651
1.75
−
3
.
0231
0.8313
−
1
.
3711
0.1643
0.3741
0.3571
2
−
3
.
0489
0.8413
−
1
.
3628
0.1504
0.3450
0.3477
4
−
3
.
7533
0.9544
−
1
.
213
0.1314
0.2578
0.3124
6
−
4
.
3049
1.0321
−
1
.
0915
0.0964
0.2136
0.2896
8
−
4
.
5001
1.0389
−
0
.
9864
0.1089
0.2170
0.2809
10
−
4
.
5621
1.0391
−
0
.
9584
0.1096
0.2157
0.2694
