Log density was acquired
during Leg 175 with the Schlumberger lithodensity tool (HLDT) at depth intervals
of ~0.15 m (Wefer, Berger, Richter, et al., 1998). GRA bulk density was scanned
on board on unsplit cores every 0.02 to 0.04 m to calculate wet bulk density by
measuring the amount of gamma-ray attenuation within the formation (Boyce, 1976;
Gerland and Villinger, 1995). Density contrasts of as much as 0.8 g/cm^{3}
within thin dolomite horizons at Sites 1081 (Fig. **F3A**),
1082, and 1084 introduced broadband frequency noise into the power spectra. This
noise is similar in character to the Fourier transform of a delta function,
showing equal amplitudes throughout the entire frequency spectrum (Smith, 1997).
By analyzing cyclic perturbations in synthetic density curves, we found that
noise induced by strong density contrasts did not inhibit the correct detection
of spectral peaks. A removal of these maximum peaks was disregarded because it
would have artificially introduced interruptions in the continuous sediment
profile. Subsequent interpolation between all data points and resampling of the
entire profile yielded a data point spacing of 0.1524 m for log density (Fig. **F3A**)
and 0.0400 m for the GRA bulk density profiles in the depth domain. A smooth
factor, similar to a moving average function, was applied to this resampled
density profile (Fig. **F3A**),
which enhanced or reduced certain frequency components. Ideally, the choice of
the smooth factor preserved the contemporaneous coexistence of all main orbital
periods. We then subtracted the interpolated, smoothed data from the nonsmoothed
interpolated profile. We obtained an interpolated residual density record (Fig. **F3B**),
on which we performed our spectral analyses (Fig. **F4**).
Our spectral analysis method consisted of applying a fast Fourier transform (FFT)
on the autocorrelation function (Pisias et al., 1973). In this study, we
calculated the autocorrelation function over a data window of ~40 m in length
(256 points for log density and 1024 points for GRA bulk density records) and
applied the FFT (usually 1024 points for log density and 2048 points for GRA
bulk density profiles) at the midpoint of this window. Autocorrelation and FFT
windows were sufficiently long enough to resolve all main orbital cycles in the
frequency domain. The autocorrelation window was passed over the density
profile, with a step size of 1.125 m. As a result, each step overlapped the
subsequent one to generate a high-resolution profile of evolutionary power
spectra over depth.

We extracted SR values (in
meters per millions of years) from log and GRA bulk density records by dividing
the number of cycles per million years of the individual orbital periods (e.g.,
obliquity at 41 k.y. occurs ~24 times in 1 m.y.) by their corresponding
frequencies (cycles per meter) in our spectra (Fig. **F4**).
We used biostratigraphy as a guide (Berger, Kroenke, Mayer, et al., 1993; Wefer,
Berger, Richter, et al., 1998) to provide a working limit or range of SR values,
and to facilitate in the identification of orbital parameter frequencies (Kronen
and Wilkens, pers. comm., 2000). Calculated SR values were inverted to million
years per meter and integrated over depth to generate a high-resolution SR
profile as a function of time. We then performed spectral analyses on log and
GRA residual bulk density profiles in the time domain to delineate the
individual orbital cycles. Similar to our data preparation in the depth domain,
we resampled the data in the time domain to an equal spacing of 2.0 k.y. The
autocorrelation window, which was at least 400 k.y. long to capture both short
and long cycles, was passed over the residual density records with a step size
of 6 k.y.

For some depth intervals,
biostratigraphic SR and calculated values matched very closely so that spectral
peaks aligned well with most of the Milankovitch periods (Fig. **F4A,**
**F4B**). In cases
when spectral peaks matched only with one of the Milankovitch cycles in the
depth domain (Fig. **F4C**),
we checked whether a different smooth function would enhance other frequencies,
or whether only one frequency component was dominant. If a change in the smooth
factor did not alter our result, autocorrelation windows were expanded in the
depth and time domain to capture more cycles per meter and cycles per million
years. In a last step, SR values were fine-tuned in the depth domain, which in
return improved the alignment of power spectra with Milankovitch cycles in the
time domain. This iterative process optimized the detection of excursions in
calculated SR values that often differed from rates established through
biostratigraphy. We wanted to ensure the validity of our technique, by applying
spectral analyses on synthetic density compaction curves that were perturbed
with known frequencies. These model studies provided an opportunity to test how
the accuracy of our results was affected by variation of the individual analysis
parameters, and will be discussed below.