Civil Engineering Reference
In-Depth Information
1000
900
800
700
600
500
400
300
200
100
0
j
= -17
j
= -10
j
= -2
j
= +4
0
6
12
18
24
30
36
42
T
(s)
Figure 3.1
Wavelet coefficients for four different frequency bands using
Δ
b
= 0.02 s.
shown in Figure 1.2 are plotted in Figure 3.1 for different frequency bands
(
j
= −17, −10, −2 and 4). These coefficients are computed using Δ
b
= 0.02 s.
The same coefficients are computed assuming nonorthogonal properties
(i.e.
j
) for different frequency bands using the same ground motion
and are demonstrated in Figure 3.2. However, in the text and for all exam-
ples used in this topic, we will use Δ
b
= 0.02 s wherever applicable.
Thus, the wavelet coefficients are used to characterize the ground
motions. However, validation should be done to see that this wavelet-based
ground motion characterization works satisfactorily. For this purpose,
b
=
σ
−
j
1
700
j
= -17
j
= -10
j
= -2
600
500
j
= +4
400
300
200
100
0
0
6
12
18
24
30
36
42
T
(s)
j
Figure 3.2
Wavelet coefficients for four different frequency bands using
b
.
=
σ
−
1
j
