-
T/T = f/f + SR/SR. (6)
We investigated the downhole logs and core measurements by means of the wavelet transform to identify basic features of the power spectra and to check the fluctuations of their amplitudes and wavenumbers. The wavenumber ranges are, respectively, 0-0.75 and 0-0.8 cycles/m. The wavenumbers, f, found by the wavelet analysis were transformed into periods, T (in kiloyears), using the different sedimentation rates, SR, in centimeters per kiloyear (Fig. F5):
Before dealing with the results, we have to point out the sources for periods uncertainty. Equation 5 allows us to obtain the relative errors as follows:
T/T = f/f + SR/SR. (6)
The wavelet method permits us to constrain the error in defining the wavenumbers (f/f ). As the choice of a suitable wavenumber resolution (f ) is an important issue for the wavelet method, we ran several tests in order to assess the influence of the wavenumber resolution (f) value. We modified this parameter from 0.0005 to 0.1 cycles/m. As mentioned in "Wavelet Transform
Method", the smaller this parameter, the better the resolution of the wavenumbers, but the lower the depth resolution. Figure F7 illustrates this artifact by showing three maps obtained with f = 0.01 cycles/m. If we compare them with the ones obtained for the same signals, but with f = 0.002 cycles/m (Figs. F8B, F9A, F9B), we see that the low wavenumber resolution (f = 0.01) does not resolve wavenumbers that are close to each other. For example, we only note one large feature centered at 0.480 cycles/m on Figure F7A and F7B for the insolation signals, whereas the maps of the wavelet analysis applied to the same signals with f = 0.002 show two precise wavenumbers at 0.474 and 0.500 cycles/m (Fig. F9A, F9B). These examples also allow us to verify that the uncertainty in defining the wavenumbers is about four times the value of the parameter f.
Whereas the depth limits are clear at low wavenumber resolution (Fig. F7), certain dominant wavenumbers appear to extend across intervals in which the sedimentation rate varies at high wavenumber resolution. This is the case for the insolation signals (Figs. F9A, F9B vs. F7A, F7B) or for the core magnetic susceptibility from Hole 1095B (Figs. F8B vs. F7C). We finally chose 0.002 cycles/m for f, the best compromise between the two resolutions. This choice indeed allows us to work at a high wavenumber resolution, with an uncertainty of ±0.008 cycles/m, which means a mean error of ~10%, as well as to distinguish the main limits in depth due to the attenuation of the wavenumber modulus amplitude. However, some dominant wavenumbers may be somewhat smeared when represented in the depth-wavenumber maps (with f = 0.002) and sometimes appear to remain constant across the plot. To facilitate the analysis of these maps, we synthesize the statistically significant wavenumbers (e.g., Torrence and Compo, 1998) and their intervals of appearance more precisely in Tables T1, T2, T3, and T4, for the following results.
The limiting factor is here the uncertainty induced by the differences between the different age models (SR/SR). As mentioned above, we use the geomagnetic reversal age model (Fig. F5) to convert the insolation signal from time to depth and to compute the periods. Confidence in the interpretation of such wavenumber/depth maps is dependent on the accuracy of the age model. The occurrence of the fundamental Milankovitch periods is greatly dependent on the sedimentation rate, as illustrated in Figure F10A; the wavenumbers corresponding to the 20-k.y. period are drastically different, depending on whether we use the geomagnetic reversal, diatom, or radiolarian age models. To give a better idea of these uncertainties, we present in Table T5 some periods computed from the thorium/potassium ratio results (Fig. F10A), using the different age models (Fig. F5). We choose the depth interval 165-195 mbsf, which corresponds to constant sedimentation rates for each model and to one of the main disagreements between the three age models. For this interval, characterized by low wavenumbers (Table T5; Fig. F10A), the sedimentation rates inferred from radiolarian and diatom data are nearly four times higher than the one induced from geomagnetic reversals (Fig. F5). This ratio recurs for the computed periods, leading to very different interpretations. When we use the geomagnetic reversal age model, the periods are long, comparable to the Milankovitch eccentricity period (Table T5). On the contrary, the radiolarian and diatom age models lead to shorter periods, close to the Milankovitch precession and obliquity periods (Table T5). This case, though extreme, shows that this point has to be kept in mind when considering the next results, as it might introduce relative uncertainties in the periods, especially over the intervals where the discrepancies between the different models is important. The uncertainty induced by the age models for Hole 1095B varies from a few percent, when the age models are in agreement, to ~75%.
Before in-depth analysis, we applied the wavelet analyses to the signal previously computed as a function of time (Fig. F4). This preliminary treatment shows how Milankovitch periods are present in the insolation signal at 67°S and how the transition between time/frequency and depth/wavenumber affect the wavelet analysis.
As expected, the annual mean insolation is very sensitive to the 40-k.y. period, the Milankovitch cyclicity related to changes of the Earth's obliquity. This parameter, which affects seasonality and insolation gradient, has greatest effect in high latitudes (e.g., Imbrie and Imbrie, 1979).
This obliquity period is still present on the spectral map of June and December insolation signals, which correspond, respectively, to the minimum and maximum of insolation received by the Earth (Fig. F11A, F11B). This frequency (0.025 cycles/k.y.) presents alternations of its intensity (e.g., stronger between 1.98 and 2.88 Ma, weaker between 2.88 and 3.28 Ma, and stronger between 3.28 and 4.08 Ma). The two maps also reveal very strong frequencies at 0.043 and 0.052 cycles/k.y., the Milankovitch 19- and 23-k.y. cycles, related to precession that affects the radiation intensity for each season. Contrary to the spectral map for December insolation, we observe frequencies different from those of Milankovitch, though much weaker, on the spectral map for June insolation (Fig. F11A): 0.01 cycles/k.y. (100 k.y.; eccentricity that affects total insolation), 0.02 cycles/k.y. (~50/52 k.y.), 0.033 cycles/k.y. (~30 k.y.), 0.067 cycles/k.y. (~15 k.y.), 0.087 cycles/k.y. (~11.5 k.y.), and 0.095 cycles/k.y. (~10.5 k.y.).
To enhance the contribution of other wavenumbers to the spectrum, we truncated the December insolation values by setting those values <510 W/m2 to 0. We speculate that it is the high insolation values that control the extent of the ice sheet and, hence, the supply of glacial sediment to the drifts. The spectral map contains the previous Milankovitch periods but also contains others with significant amplitude (Fig. F11C): 200/330 k.y., 100 k.y.; 50-55 k.y., 30 k.y., 15/16 k.y., and 12/13 k.y. These periods effectively present in the insolation signal (Fig. F11A) (e.g., Laskar, 1993) but with amplitudes much lower than the obliquity and precession periods are better revealed on the truncated December insolation map.
The wavelet analysis was performed for four types of signals: the logs (recorded each 15.24 cm), the core physical properties measurements (recorded each 2, 5, or 15 cm), the bioturbated beds, and the December insolation signals (interpolated each 5 cm). To be able to compare the results, the insolation signals were converted to a depth scale and analyzed on the same depth interval as the logs (165-545 mbsf) (i.e., ~3-9 Ma).
Some representative wavenumber maps are presented in Figures F8 and F10, and all the results are synthesized in Figure F12.
The alternation of glacial-interglacial cycles induces discontinuities in the sedimentary processes. This alternation being related to changes in insolation maxima, we assume that the wavelet analysis of the truncated insolation emphasizes these discontinuities. This truncated form contains the periods present in the total signal, essentially the precession of 19- and 23-k.y. periods. The analysis of this signal also reveals other periods, such as 103, 128, 133, 392, and 439 k.y. in the low wavenumber domain, and 10, 12, and 13 k.y. in the high wavenumber domain.
For this site, we concentrate on the gamma ray and thorium/potassium ratio logs (representative of the different type of clays present in the formation) (e.g., Serra, 1979, 1985; Ellis, 1987), core magnetic susceptibility measurements, and bioturbated interval results (Figs. F8, F10). The complete wavenumber content of all the signals analyzed by wavelet transform is presented in Table T1. As sedimentation rates (SRs) for this site are highly variable, the wavenumbers were transformed into periods using the average SR of the interval where they appear (Fig. F12).
We chose these signals because the comparison of the main periods, recognized in their maps (Figs. F8, F10) allows us to divide the different geological units defined from core description (Shipboard Scientific Party, 1999b) into subunits (Fig. F12). The lower and middle part of Unit II (143-436 mbsf) can be subdivided in five subunits: 140-220, 220-250, 250-320, 320-390, and 390-400 mbsf. Of course, if we look precisely at the maps (Figs. F8, F10), it is clear that the limits are gradual rather than sharp and that the overlap between the wavenumber bands is ~15 m. This is because we favored the high-frequency resolution to the detriment of the spatial resolution; there is a trade-off between the two.
The downhole logs cover the depth interval from 165 to 545 mbsf, from the Miocene (9.6 Ma) to mid-Pliocene (4.3 Ma) time period, according to geomagnetic reversal identification (Shipboard Scientific Party, 1999b). The logs acquired in Hole 1095B do not appear to allow resolution of wavenumbers above ~0.4 cycles/m (Fig. F10). This possibly results from the vertical resolution of the logs, which varies between 30 and 70 cm. The strong heave encountered during logging might also have enhanced the noise that overprints the high wavenumbers domain. In contrast, the information extracted from the core measurements, acquired at a centimeter scale, is much richer in the high-wavenumber domain. In particular, the results correlate very well between the bioturbated beds and core magnetic susceptibility signals for the subunit from 320 to 390 mbsf (Fig. F12). The 24-, 33-, 39-, and 74-k.y. periods are well evidenced, with high modulus (Figs. F8B, F8C; Table T1). The deposit in this subunit was certainly controlled by cyclic processes, some of them being close to Milankovitch precession and obliquity periods. The core magnetic susceptibility allows us to divide this subunit into two parts at the depth of 355 mbsf (Fig. F12). The first interval is mainly characterized by high wavenumbers, contrary to the second one. This shift at ~8 Ma, which corresponds to an abrupt change of low sedimentation rates toward higher ones for the three different age models (Fig. F5), might then be a major transition. The wavenumbers occurring within this particular unit are summarized for the core magnetic susceptibility analysis in Table T2 and again illustrate how different the periods derived from these wavenumbers can be, depending on the age model used. The discrepancies are particularly obvious for the upper part of this subunit, from 320 to 355 mbsf, where the SR is multiplied by ~2.5. For the lower section (355-390 mbsf), the age models are closer. Here, the signal contains the ~41-k.y. period, the Milankovitch cyclicity related to changes of the Earth's obliquity, and is dominated by the ~100-k.y. period (eccentricity).
As previously mentioned, Site 1096 was drilled to sample the shallow part of the stratigraphic section within the drift. It complements Site 1095, where the youngest sediments are thinner. Hole 1096C then allows us to examine at high time resolution the cyclicity in a highly expanded Pliocene-Pleistocene section. If we look at the ages according to geomagnetic reversal identification (Shipboard Scientific Party, 1999b, 1999c), our downhole logging data for Hole 1096C end at ~4.2 Ma (525 mbsf), which corresponds to ~130 mbsf for Hole 1095B. Therefore, we are not able to compare the logs over the same time interval in the two holes.
As for Hole 1095B, the wavelet analysis was performed for the logs, the core physical properties measurements, and the December insolation signals (both truncated and not truncated). For the logs, the analysis was done using two segments of data because of the interruption of logging (Fig. F2). The upper section, from 95 to 325 mbsf, corresponds to the late Pliocene and the early Pleistocene time interval, between ~1.2 and 3.1 Ma. This section encompasses the Unit II/Unit III boundary at 173 mbsf and the geomagnetic Matuyama/Gauss boundary at 216 mbsf (Shipboard Scientific Party, 1999c). Ages of these stratigraphic markers are, respectively, 2-2.1 Ma and 2.6 Ma (Cande and Kent, 1995). The lower section, from 360 to 525 mbsf, corresponds to the early and late Pliocene time interval, between ~3.3 and 4.2 Ma. To compare the results, the insolation signals were also analyzed on these two segments.
Some representative frequency maps are presented for the upper section in Figures F9 and F13, and the main wavenumbers and their corresponding periods are tabulated in Table T3. Note that a drastic change of SR occurs in this first segment: above 215.85 mbsf, the SR averages 8.9 cm/k.y. and below 215.85 mbsf, 20.1 cm/k.y. (Fig. F5).
The 41-k.y. period is present on the spectral map of December insolation signal (Fig. F9A). The map also reveals very strong wavenumbers: from 95 to 235 mbsf, 0.474, 0.500, and 0.592 cycles/m; and from 180 to 325 mbsf, 0.210, 0.218, and 0.264 cycles/m (Fig. F9A). These wavenumbers correspond to the Milankovitch 19- and 23-k.y. cycles (precession). As mentioned in the previous section, the wavenumbers appear to be smeared because of the high wavenumber resolution. Consequently, we list in Table T2 the limit at 216 mbsf (Fig. F7A), instead of 235 mbsf (Fig. F9A). The processing of the truncated signal contains the previous near-Milankovitch periods, especially the main precession periods with very high amplitudes, but also reveals others with significant amplitude (Fig. F9B; Table T3). The discrepancies between the periods evidenced in the signals and the primary Milankovitch periods (e.g., 22 instead of 23 k.y., or 95 instead of 100 k.y.) certainly come from the uncertainty of ±0.008 cycles/m. Contrary to the spectral map for December insolation, the 100-k.y. period is present on the spectral map for December truncated insolation. We also observe periods different from those of Milankovitch, though much weaker (Fig. F9B; Table T3): 7, 10, 11, 12, 15, and 55 k.y. Figure F9C shows that for the reflectance signal the main wavenumbers (with high modulus, represented by the yellow and green colors) approximate all the dominant cycles in the Milankovitch band (19-, 23-, 41-, and 100-k.y. periods), particularly around 100 k.y., but also other periods, very close to the ones already seen in the truncated insolation between 270 and 325 mbsf: 7, 11, 13, and 48 k.y. (Table T3).
Figure F13 shows the maps for three of the logs: porosity, natural gamma ray, and uranium. As for Hole 1095B, the logs acquired in Hole 1096C do not resolve the high wavenumbers. We also note that the periods differ quite markedly from one map to another. In particular, between 95 and 270 mbsf, the strong 79- or 178-k.y. periods identified in the porosity map (Fig. F13A) are absent from the two others (Fig. F13B, F13C; Table T3). However, other periods directly related to Milankovitch cyclicities can be recognized. The near-100-k.y. cycle is present in all the results over the whole interval, although it has various amplitudes depending on the considered log (Table T3). It is also difficult to say whether or not the amplitude becomes lower with depth; for example, the amplitude for the truncated insolation analysis increases with depth, whereas it decreases sharply for the gamma ray (Fig. F13B, F13C; Table T3). Again, there is a good correlation for the 50- to 55-k.y. cycles, and this time the intensities are coherent, being rather high for all the logs. Contrary to the previous results (Fig. F9), the 23- and 41-k.y. periods are not consistent, for they appear only in the uranium map (for the precession cycle) (Fig. F13C) and in the gamma ray map (for the obliquity cycle) (Fig. F13B).
As for the previous section (95-325 mbsf), some representative frequency maps are presented for the lower section (360-525 mbsf) in Figures F14 and F15, and the main wavenumbers and their corresponding periods are tabulated in Table T4. For this second interval, the SR is fairly constant and varies between 15.5 and 24.4 cm/k.y. (Fig. F5).
Again, the Milankovitch 19- and 23-k.y. cycles, related to precession, dominate the spectral map of December insolation signal (Fig. F14A). The 41-k.y. period (obliquity) is still present, with a much lower intensity. As for the upper section, the processing of the truncated signal contains the previous Milankovitch periods but also reveals others with significant amplitude (Fig. F14B; Table T4). For some wavenumbers, two periods are mentioned in Table T4 if their amplitudes are approximately equal across different sedimentation rates. If one period is dominant, we favored the SR corresponding to this interval to convert wavenumbers to periods. The 100-k.y. period shows up on the spectral map for December truncated insolation, and the 41-k.y. cyclicity is enhanced. As for the upper section, we also observe periods different from those of Milankovitch with various strengths (Fig. F14B; Table T4): 10, 11, 14, 16, 33, and 37 k.y.
Figure F15 shows the maps for two different logs: porosity and uranium. For this section, the wavenumber content of the uranium log, which is more complex than that for the upper section (Tables T2, T3), approximates all the dominant cycles in the Milankovitch band (19-, 23-, 41-, and 100-k.y. periods). Some of them are also found in the porosity log, though it is less clear than for the uranium log. The correlation between the various intensities is, however, poor. For example, the 19-k.y. cyclicity is highly represented in the porosity log, whereas it is quite weak in the uranium log (Table T4). The near-100-k.y. cycle is found consistently in all the results with a weak intensity, contrary to the near-41-k.y. cycle (Table T4). This period appears at 430 mbsf for the porosity log analysis, whereas it disappears at 480 mbsf for the uranium log analysis. Again, the 74- and 78-k.y. periods, near the 79-k.y. cycle mentioned above for the upper section, and the 33- and 35-k.y. periods are found in all the results with medium intensities. The 55-k.y. cycle shows up, as well as a near-61-k.y. cycle, but not in both logs.
It is clear that the correlation for the values of all the periods is not possible for the previous results concerning the two sections. Nevertheless, some cycles appear to be dominant in most of the signals. For example, the dominant wavenumbers for the upper section clearly change within the interval 170-270 mbsf (~2.1-2.8 Ma) for all the treated signals (Figs. F9, F13; Table T3). This interval exactly corresponds to a major unconformity between the biostratigraphic data and the geomagnetic reversals. Moreover, this change begins at the transition between lithologic Unit II and Unit III (173 mbsf). Above this transition, in Unit II, near-100-k.y. cycles appear to dominate most of the records (Figs. F9, F13; Table T3). Some signals also exhibit ~41-k.y. and 50- to 55-k.y. periods with high amplitudes. Within the transition interval, the maps show a more complex pattern of the periods, and the results are not well correlated, except for the ~23-k.y. period that appears in the truncated insolation and the gamma ray measurements (Table T3). Below the transition, near-100-k.y. cycles appear again in all the maps (Figs. F9, F13), but, whereas it is the dominant period for the truncated insolation, reflectance, and uranium, the amplitude is much lower for the porosity or natural gamma ray (Table T3). For this lower section, all the maps reveal ~41-k.y. and 50- to 55-k.y. periods with strong amplitudes, whereas the 23-k.y. cycles are only seen in the truncated insolation (dominant period) and in the uranium and reflectance signals with much weaker amplitude. This gradual shift near 2.5 Ma is consistent with discontinuities evidenced in other studies reflecting significant climate changes. For example, a large discontinuity at 3 Ma was evidenced in the oxygen isotope ratios in Atlantic benthic foraminifers (Barker et al., 1999). This 2.5-Ma shift was also pointed out by DeMenocal et al. (1991) in the Arabian Sea, even if the pattern expressed here is different. For the drift Site 1096, this shift probably reflects a change in sediment input related to the history of channel development on either side of the drift, development driven by alternation of glacial-interglacial periods (e.g., Shipboard Scientific Party, 1999a); a northeastern channel, which did not exist for much of Unit III time, was perhaps reactivated, leading to distal turbidites in Unit II.
The differences between the upper and lower section periods (e.g., for the porosity log, 110 instead of 106 k.y. or 55 instead of 52 k.y.) can be explained by uncertainties in the age model and discrepancies in depth position, as the logs were recovered during two separate runs. The main cycles present in the insolation signals for the lower section are 19 and 23 k.y. (precession) with the maximum of amplitude between 400 and 450 mbsf (Fig. F14). The 41- and 100-k.y. cycles are also recognized with medium amplitude. Most of the periods appear to be highly variable in intensity, the contribution of the different periods being either amplified or lowered near 400/450 mbsf (Figs. F14, F15). Some of them disappear or appear at ~450 mbsf, or the intensity diminishes drastically between 400 and 450 mbsf. This limit is coherent with a change in the core observation (Shipboard Scientific Party, 1999c): above 450 mbsf, the laminated silty clay facies dominates, whereas below 450 mbsf, the sediments are mostly massive, bioturbated, more biogenic sandy silty clays. This interval from 3.5 to 3.8 Ma, therefore, appears to be a major change in the sediment supply induced by climate changes, as also evidenced by Weber (submitted [N1]) in the eastern equatorial Pacific.
Although it seems that the sedimentary cyclicity at Site 1096 may have some orbital forcing, other anomalous periods, which do not correspond to primary Milankovitch periods, are also revealed, such as the 50- to 55-k.y. period that is known to be related to eccentricity (e.g., Imbrie and Imbrie, 1979; Imbrie, 1985). In the lower section (Pliocene), a new cycle appears around 33-35 k.y. This period might be related to the 30- to 35-k.y. periods commonly found in Pliocene to Pleistocene eolian time series (Rea, 1994; Lauer-Leredde et al., 1998). Such periods could result from nonlinear responses of the climate system to orbital forcing, most probably interferences of precession and obliquity. We also record periods around 74/80 k.y. for the early Pleistocene and late Pliocene time intervals. These approximate a major peak at 78 k.y. recorded by Robinson (1990) from middle and lower Pleistocene in the tropical Indian Ocean. Ghil (1987) and Robinson (1990) first suggested it might be harmonic or combination tones that reflect nonlinear interactions between primary Milankovitch periods. Transitional states, which have most of their power at a period of ~75 k.y., were also evidenced by Bolton et al. (1995) in climatic records derived from oxygen isotopic ratios of Pliocene-Pleistocene marine sediment cores at ODP Site 677. Liu and Chao (1998) explained an ~80-k.y. cycle, which briefly appeared in the Pleistocene, as a multiple of the obliquity and precession periods. For them, this cycle evolved into the 100-k.y. cycle, these flickers being induced by the amplitude variation of obliquity and precession.
