Árbók VFÍ/TFÍ - 01.01.1997, Page 233
Simulation of stochastic 231
yi = ._Ljlog,(i^
tr-^y108^1"^0) » yi=yi i+ti .
(23)
The intensity function can be obtained by noting the covariance equivalence between the
amplitude modulated process and the non-homogeneous process using Eq. (10), that is,
v(t) =V0\j/-(t).
Suitable envelope functions vj/(t) for strong earthquake motions have been proposed by inter
al. Amin and Ang [2], in the form
'KO =•
1.0
, Oststj
- t,^tít2
=(i q)
e
t>t.
(24)
The selection of proper constants t,, t2 and c, which completely define vj/(t), has been discuss-
ed by Jennings et al., [12], who point out that the envelope function is dependent on the magni-
tude of the earthquake, the distance from the causative fault and the focal depth. The duration
of the strong motion is characterized by the constant t2 which for the three magnitude values
6, 7 and 8 may be selected of the order 4 sec.,15 sec. and 35 sec. respectively. The constant
t„ is estimated to be of the order 2-4 seconds. Finally, c is selected according to the focal dis-
tance. In Fig. 4, an envelope function for a particular earthquake is shown. The constant vQ in
1.0--
0.5
V'(t)
A B
0.0
IL.
0 2
Earthquake B (M=7.0, D=25km, H = 15km)
O-A: iKtMt/^.O)2
A-B: -v4r(t)=1.0
B-C: ^(t)=Exp(-0.13(t-8.0))
C-D: ■\í'(t)=0.1105Exp(—(0.05(t-25))
8 10
20 25 30
40
50 SEC
Fig. 4 An Amplitude Envelope Function, (after Jennings et ai, 112]).