Autocorrelation and Geostatistics - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 201

Fig. 6.10 Power spectra
with m ¼ 100 for
standardized residuals from
linear trend, silt ( solid line )
and clay ( broken line ),
series 4. The coherence
(COH) is also shown
(Source: Agterberg and
Banerjee 1969 , Fig. 12)

From Fig. 6.4 it can be concluded that the lowest frequency waves that form sharp
peaks near the origin of the power spectra in Fig. 6.5 are positively correlated.
Figure 6.10 shows power spectra of the silt and clay residuals. Both have a large
long-period peak that will be discussed later in this section. Clay shows a peak just
below 20 years that was not visible in Fig. 6.5 (series 4). The 14-year peak in the silt
power spectrum also is seen in the silt residual spectrum. The coherence is shown in
Fig. 6.10 as well. It shows local maxima near 20 and 10 years for the sunspot cycle
showing that both clay and silt thicknesses were influenced by this cyclicity. Phase
differences for periods of 9.5 and 10 years were 72 , respectively, that

both represent a 2-year lag of silt with respect to clay. The 2-year lead of clay could
already be seen in the cross-correlogram of Fig. 6.9 . It is interesting that clay did not
participate in the 14-year silt cycle according to the coherence diagram. It would
suggest that, every 15 years, coarser grained material predominated in the annual
turbidity currents that probably took place toward the end of summer. The fine-grained
clay was slowly deposited during the fall and winter. The fact that it led the silt by
about 2 years probably reflects slower response of the coarser grained material. A
greater rate of retreat of the land ice due to an increase in temperature would produce
more melt water and consequently more sediments to be deposited. The clay was
transported across the lake almost immediately, but the silt was delayed. Initially, the
silty material was dumped close to the ice front leaving the thickness profile of varves
in more distal areas relatively unaffected. However, later the steeper profile of
underlying varves, acting as a floor to turbidity currents for later years, helped to
spread the silt farther with the thicker parts moving to more distal areas.

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