Geology Reference
In-Depth Information
K=12
K=3
0.9
0.8
Carter et al. 1973
0.8
Upper
Lower
0.7
dof
'
s
Bias
K=3
0.333
0.6
0.6
K=4
0.250
K=12
K=3
0.5
K=5
0.200
K=6
0.167
0.4
0.4
K=7
0.143
K=12
K=8
0.125
0.3
K=9
0.111
Scannell
& carter
1978
0.2
K=10
0.100
0.2
K=11
0.091
0.1
K=12
0.080
K=3
0
0
0
0.6
0.2
0.4
0.8
1
0
0.1 0.2
0.3
0.4
0.5
0.6 0.7
0.8
0.9
1
msc
est
msc
est
confidence bounds
(c)
(d)
Phase uncertainty
Bias approximation
0.35
200
0.3
Carter et al. (1973)
0.25
150
Bendat & piersol (1986)
K=3
0.2
100
0.15
K=3
0.1
50
0.05
K=12
K=12
0
0
0
0.2
0.4
0.6
0.8
1
0.2
0.6
0.8
0
0.4
1
msc
est
msc
est
Figure 4.27
Statistics for squared-coherency and cross-phase spectra, computed using
mtmcoherencystats.m
(see
Appendix). As a function of dof K (a) distribution for zero coherence where msc
est
on the horizontal axis can be
related to the probability distribution P on the vertical axis; the table insert indicates the bias for zero coherency
(see also c. at msc
est
= 0.0); (b) 95% CLs, where msc
est
on the vertical axis is related to lower and upper bounds as a
function of K; (c) coherency bias to be subtracted from msc
est
; (d) cross-phase uncertainty σ
ϕ
. Source: Data from
Carter et al. 1973, Scannell & Carter 1978 and Bendat and Piersol 2010.
Table 4.1
CLs and significance levels for zero-squared coherence for K degrees
of freedom
95% confidence limits
Significance levels
K
Lower
Upper
K
90%
95%
98%
99%
3
0.013000
0.84200
3
0.68400
0.77800
0.86100
0.90400
4
0.0080000
0.70800
4
0.53800
0.63500
0.73500
0.79500
5
0.0060000
0.60200
5
0.44000
0.53100
0.63300
0.70000
6
0.0040000
0.45900
6
0.37200
0.45600
0.55400
0.62300
7
0.0040000
0.41000
7
0.33200
0.39900
0.49200
0.56200
8
0.0030000
0.36900
8
0.28300
0.35400
0.44300
0.51200
9
0.0030000
0.33600
9
0.25300
0.31900
0.40300
0.47100
10
0.0030000
0.30800
10
0.22900
0.29000
0.37000
0.43800
11
0.0020000
0.28500
11
0.20900
0.26600
0.34200
0.41000
12
0.0020000
0.26500
12
0.19200
0.24600
0.31800
0.38700
