Intervals of high SR values along the southwest African coast correlated with intervals of high bioproductivity for the past 1.2 m.y. (Lin et al., 1999). We attributed this and other periods of high SR values to vigorous coastal upwelling in concert with glaciation periods in the Northern and Southern Hemispheres (Keigwin, 1987; Meyers, 1992; Barker, Camerlenghi, Acton., et al., 1999).

We tested our methodology
by designing synthetic density curves using a spectral analysis of both the
depth and time domains. These artificial density curves represent an
accumulative summation over time of a three-component sediment composite
(calcareous, siliceous, and clay), which experiences compaction. We tested
different SR scenarios over depth, including a constant accumulation rate (Fig. **F9A,**
**F9D**), a very
rapid increase in accumulation (Fig. **F9B,**
**F9E**), and a
smooth increase in rates (Fig. **F9C,**
**F9F**).
Experimental studies on various deep-sea marine sediments provided regression
equations for our synthetic compaction curves (Hamilton, 1976). Moreover, we
perturbed our synthetic density curves in the depth domain with five sinusoidal
cycles, equivalent to 100, 41, 23, 19, and 10 k.y. (Fig. **F9**).
One goal of our modeling was to reproduce these five frequencies in the time
domain, utilizing spectral analysis.

At first, we kept
accumulation rates of all three components constant (Fig. **F9A,**
**F9D**) and varied
only the smooth factor, but not the autocorrelation and FFT window length (Fig. **F10A**).
High smooth factors resulted in a better detection of low frequencies.
Consequently, we attempted to choose a smooth factor for the real wet bulk
density data, which prevented the suppression of one Milankovitch component over
the others. Next, we only changed autocorrelation window lengths, which showed
that lower frequencies were enhanced by longer windows (Fig. **F10B**).
In contrast, higher frequencies were not resolved as clearly as with shorter
windows. In addition, they were significantly smeared and displaced over a
certain frequency band, erroneously suggesting cycles that were not part of the
original waveband. This distortion of the original input frequencies could
possibly explain spectral signals in our geologic records that deviated from the
expected Milankovitch periodicity (Figs. **F7,**
**F8**). We point
out that this smearing of frequencies reflected a numerical effect, not one from
orbital forcing. Frequencies were even more distorted when we introduced
broadband frequency noise by incorporating strong high-density contrasts into
the synthetic residual density curve (Fig. **F10C**).

A major goal of our
modeling was to quantify the accuracy of our analysis technique. Therefore, we
tested the behavior of evolutionary spectra in the depth (Fig. **F11**)
and time domain (Fig. **F12**)
for constant and varying accumulation rates (Fig. **F9**).
Moreover, these model studies shed light on possible aliasing effects caused by
undersampling of either synthetic or real-data records. Evolutionary spectra in
the depth domain exhibited a gradual increase in spectral frequencies for
constant accumulation rate values (Fig. **F11A**).
This reflected an apparent increase in cycles per meter (cycles/m) caused by
compaction. A doubling in accumulation of the calcareous component over a short
depth interval caused significant deflections of the spectra (Fig. **F11B**).
The deflections were smoother in the case of a gradual accumulation rate
increase (Fig. **F11C**).
This test provided means to identify significant and subtle changes in SR values
over depth in our geologic records (Fig. **F5**).

Compaction, which
apparently increased frequencies in the depth domain (Fig. **F11A**),
was eliminated in the age domain for constant and varying SR values as long as
their original input rates were reproduced correctly. In the case of constant
deposition, evolutionary spectra in the age domain exhibited an almost constant
frequency value (measured in cycles per million years) over the entire time
range (Fig. **F12A**).
However, the 10-k.y. cycle showed a relatively strong deflection from a straight
spectral path (Fig. **F12A**),
which we attributed to aliasing effects. In general, the difference between
input and output frequencies for constant SR values ranged within an acceptable
1%-3%.

In contrast, drastic
changes in SR values caused significant deflections in some of the evolutionary
spectra from their expected path (Fig. **F12B**).
Consequently, ages obtained from inversion and integration of calculated SR
values were off by 10% and more, depending on the frequency component. A drastic
shift in SR values affected the individual frequency components not only
differently, but also inconsistently (Fig. **F12B**).
Eccentricity (100 k.y.) and the 23-k.y. precessional cycle were deflected less
than obliquity (41 k.y.) and the 19-k.y. precessional cycle, whereas the 10-k.y.
cycle almost disappeared when accumulation rates changed from low to high
values. Below this transition interval, most of the 10-k.y. spectral energy was
folded into the lower frequency range because of the strong aliasing,
superimposing the other input frequencies (Fig. **F12B**).
We interpreted the observed spectral deflections as the combined effect of
aliasing of the various cycles, and of variable autocorrelation window lengths
and smooth factors. Therefore, results from our model studies served as an
important guide on how to interpret deflections of spectra in the depth domain
in order to calculate SR values correctly. Modeling, thus, also improved the
delineation of the individual cycles in the age domain.