Geology Reference
In-Depth Information
(a)
1
24
22
Estimated C(f)
2
Lower 95% CL
Upper 95% CL
19
41
0.8
400
17
0.6
99% sig. level
0.4
0.2
0
0.00
0.01
0.02
0.03
0.04
Cycles/kyr
0.05
0.06
0.07
0.08
Figure 4.28
Statistics from
Figure 4.27 and Table 4.1
applied to the coherency (a)
and cross phase (b) spectral
analysis shown in Figure 4.26.
MSC peaks exceeding the
lower 99% CL are considered
to be significantly different
from zero coherence. These
statistics indicate that the MSC
peaks at 1/400 kyr and 1/17 kyr
does not pass this test due to
interference from the noise.
(b)
600
41
24
22
400
400
19
17
5 kyr
200
0
-200
-400
Estimated
ϕ
(f)
±
σ
ϕ
(f)
-60
0.000
0.010
0.020
0.030
0.040
0.050
0.060
0.070
0.080
Cycles/kyr
estimates and are reported as standard deviation σϕ (Bendat & Piersol
1986). Application of these statistics to the example in Figure 4.26 is shown
in Figure 4.28 and reveals that some of the coherency peaks are not signifi-
cantly different from zero.
References
Abe, M. & Smith, III, J.O. (2004) Design criteria for the quadratically interpolated
FFT method (I): Bias due to interpolation, in
Technical Report STAN-M-114
, p. 13.
Department of Music, Stanford University, Stanford.
Bartlett, M.S. (1948) Smoothing periodograms from time series with continuous
spectra.
Nature
,
191
, 686-687. DOI:10.1038/161686a0.
Bartlett, M.S. (1950) Periodogram anlaysis and continuous spectra.
Biometrika
,
37
,
1-16. DOI:10.1093/biomet/37.1-2.1.
Bendat, J.S. & Piersol, A.G. (1986)
Random Data: Analysis and Measurement
Procedures
.
Second Edition
. Wiley and Sons, New York.
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The Measurement of Power psectral from the
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. Dover, New York.
Carter, G.C., Knapp, C.H., & Nuttall, A.H. (1973) Estimation of the magnitude-squared
coherence function via overlapped Fast Fourier Transform processing.
IEEE
Transactions, Audio and Electroacoustics
,
AU-21
, 337-344. DOI:10.1109/TAU.1973.1162496.
