Characteristics of Ground Motion
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Transcript of Characteristics of Ground Motion
ATL Rule
2 : RMS of displacement ( y ) between two points with a distance L after a time T.
A is site-dependent;10-16~10-21 m/sec.
ATL at Esashi
L = 50m
T=1979.6 ~ 1994.4
A=(0.33±0.05)・ 10-18m/s
National Astronomical Observatory Mizusawa
a random walk(or Brownian) process
GM Model1. 2 dimentional power spectrum
P(,k) = lim lim 1/T 1/L∬x(t,s)e-ite-iks dt ds
P(,k) = A/2/k2 (1-cos(kB/A/ 2)) + Di()Ui(,k)
where, Ui(,k)=2/√k2cut - k2, k2
cut = /vi, vi: phase velociy
Di()=ai/(1+[di(- i)/ i]4), fi=2i
2. Displacement2 = <x(t,s)2> = ∬ P (,k) d dk /(2)2
3. Relative Displacement
2 (T,L) = ∬ P (,k) 2(1-cosT)2(1-coskL) d dk /(2)2
T→∞ L→∞ -T/2 -L/2
T/2 L/2
-∞ -∞
∞ ∞
-∞ -∞
∞ ∞
GM mode (2)l
2 (T,L) = ∫ (,L) 2(1-cosT) d /(2)
(,L) = ∫P(,k)2(1-coskL) dk/(2p)
= AL/ 2 if 0 < < o
= B/ 4 if o < < ∞
where, o = (B/AL)1/2
2 (T,L) = ATL at 0 < < o
(,L) = 2 P() { 1 - Re[N12(,L)]}= 2 P() R (,L)
where, Re(N12(,L)) is correlation;
e.g. N12(,L) = Jo( L/vi) for waves; vi kcut=
-∞
∞
Parameters of P(,k) in ILC-TRCParameter Units Model A Model B Model C
A of ATL m/s 1.0・ 10-19 0.5・ 10-18 1.0・ 10-17
B of ATL m2/s3 0.5・ 10-18 1.0・ 10-18 5.0・ 10-18
f1 Hz 0.001 0.001 0.14
a1 m2/Hz 1.0・ 10-9 1.0・ 10-9 1.0・ 10-11
d1 1 1 5
v1 m/s 3・ 103 vapp(f) vapp(f)
f2 Hz 0.2 0.2 2.5
a2 m2/Hz 3.5・ 10-13 3.5・ 10-9 1.0・ 10-15
d2 3.5 3.5 1.5
v2 m/s 3・ 103 vapp(f) vapp(f)
f3 Hz 5.0 4.5 50.0
a3 m2/Hz 1.0・ 10-21 2.5・ 10-20 1.0・ 10-19
d3 1.3 3.5 1.5
v3 m/s 3・ 103 vapp(f) vapp(f)
Vapp(f) = 450 + 1900 exp(-f/2) m/s