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.