To construct a timescale for the early Eocene warming events, and their relative position to paleomagnetic boundaries and biozones we follow the metronome approach of Herbert et al.  assuming that each cycle represents a duration equal to the mean period of the orbital parameter that forced its formation. According to Herbert et al.  21-kyr is a good estimate for the mean of the main modern precession periods for cycle counts of more than ∼7 cycles. Previous studies have shown that the main periodicities of precession and obliquity have increased with time because of tidal friction resulting from the gravitational attraction of the sun and moon [e.g., Berger et al., 1992; Dehant et al., 1987; Hinnov, 2000; Laskar, 1999; Laskar et al., 2004; Néron de Surgy and Laskar, 1997]. Although 55 Ma ago the average precession frequency is predicted to have been higher than today (∼1/(20.7 kyr) [Berger et al., 1992]) because the Earth-Moon distance was shorter, and the rotation of the Earth faster [Laskar et al., 2004], we used 21 kyr as the mean duration for the counted precession cycles because of the close correspondence between the ratios of modern eccentricity and precession cycles with those observed in this study. Additionally, this allowed for a more direct comparison with former estimates based on cycle counting [Cramer, 2001; Röhl et al., 2003]. Because we counted more than 200 precession cycles the estimated timescale error by using orbital-forced cycle stratigraphy is less than 2% [Hinnov, 2004].
5.1. Duration of Chrons C24r and C25n
 Chron C24r consists of 148.5 ± 2.5 precession cycles according to our cycle counting and the geomagnetic polarity data for Site 1262, which corresponds with a duration of 3118.5 ± 52.5 kyr (Table 1). A total of 154 ± 6 precession cycles (3234 ± 126 kyr) have been counted at Site 1267, because of the weakly defined top of C24r. Reanalysis of Site 1051 revealed 8 additional precession cycles over the previous counts which were considered to provide “minimum” estimates [Cramer et al., 2003; Ogg and Bardot, 2001; Röhl et al., 2003], resulting in a total of 146 ± 5 precession cycles (or 3066 ± 105 kyr). On average, C24r has a mean duration of ∼3108 kyr, but we consider the estimate on Site 1262 (3118 ± 52 kyr) to be the most reliable (Table S1). This estimate is 260 kyr larger than that presented in the GTS2004 [Gradstein et al., 2004] (see discussion below) which was based on the minimum cycle counting of Röhl et al. . Discrepancies with previous cyclostratigraphies and timescales [Cramer, 2001; Cramer et al., 2003; Ogg and Smith, 2004; Röhl et al., 2003] can be attributed to unrecognized gaps in previously single-cored sites as well as poorly expressed lithological cycles resulting in underestimates of cycles and the durations of specific intervals.
Table 1. Estimates for the Duration of Magnetochrons and the Position of Eocene Events Based on Cycle Countinga
|Site(s)||Study||Eccentricity Cycles||Precession Cycles||Duration, kyr|
|577, 550, 1051, 690||Cramer et al. ||∼24|| ||∼2350 ± 100|
|1051A||Cramer || ||115–157||2856 ± 441|
|1051||Röhl et al. || ||137||2877|
|1051||this study|| ||146 ± 5||3066 ± 105|
|1262||this study|| ||148.5 ± 2.5||3118.5 ± 52.5|
|1267||this study|| ||154 ± 6||3234 ± 126|
|1051, 1262, 1267||this study|| ||148||3108|
|spline||Cande and Kent || || ||2557|
|spline||GTS2004|| || ||2858|
|577, 550, 1051, 690||Cramer et al. || || ||∼450|
|1051||Röhl et al. || ||24 ± 1||504 ± 21|
|Zumaia||Dinarès-Turell et al. || ||22 ± 1||462 ± 21|
|1262||this study|| ||24 ± 1||504 ± 21|
|1267||this study|| ||(12 ± 14)||(252 ± 294)|
|1051, 1262||this study|| ||23||483|
|spline||Cande and Kent || || ||487|
|spline||GTS2004|| || ||515|
|Base C24r to PETM (base of CIE)|
|577, 550, 1051, 690||Cramer et al. || ||∼39–41||850 ± 30|
|1051A||Cramer || ||43 ± 2||903 ± 42|
|1051||Röhl et al. || ||45 ± 1||945 ± 21|
|Zumaia||Dinarès-Turell et al. || ||47||987|
|1262||this study|| ||53 ± 1||1113 ± 21|
|1267||this study|| ||55 ± 2||1155 ± 42|
|1051||this study|| ||53 ± 2||1113 ± 42|
|1051, 1262, 1267||this study|| ||53||1113|
|spline||Cande and Kent || || ||904|
|spline||GTS2004|| || ||865|
|Base C24n to PETM (Base of CIE)|
|577, 550, 1051, 690||Cramer et al. || || ||∼1500|
|1051A||Cramer || ||93 ± 19||1953 ± 399|
|1051||Röhl et al. || ||92||1932|
|1262||this study|| ||95 ± 2||1995 ± 42|
|1267||this study|| ||99 ± 4||2079 ± 84|
|1051||this study|| ||93 ± 3||1953 ± 63|
|1051, 1262, 1267||this study|| ||95||1995|
|spline||Cande and Kent || || ||1653|
|spline||GTS2004|| || ||1992|
|Base C24n to Elmo|
|1262||this study|| ||8 ± 2||168 ± 42|
|1267||this study|| ||11 ± 4||231 ± 84|
|1262, 1267||this study|| ||8||168|
|ELMO to PETM|
|577, 550, 1051, 690||Cramer et al. || || ||1320 ± 30|
|1262, 1267||Lourens et al. ||∼21||-||2035|
|1262, 1263, 1265, 1267||this study||19||87 ± ||1827 ± 11|
 In contrast to magnetochron C24r, the duration of chron C25n is well constrained in both marine- and land-based sections [e.g., Dinarès-Turell et al., 2002; Röhl et al., 2003]. Cycle counting in the record from Site 1262 yields 24 ± 1 (504 ± 21 kyr) precession cycles within chron C25n (Table 1). The top of C25n is well defined in Site 1267, but not its base. Therefore just part of C25n (12 ± 14 precession cycles, = 252 ± 294 kyr) is represented in the Site 1267 record. The duration of C25n as determined at Site 1262, is similar to the estimate for Site 1051 (Figure 4b). Combining the cycle count for both Sites 1262 and 1051 yields an average of 23 precession cycles (or duration of 483 kyr) for chron C25n. This agrees very well with previous estimates from Site 1051 [Röhl et al., 2003] and the land-based Zumaia section [Dinarès-Turell et al., 2002] (Table 1).
5.2. Calcareous Nannofossil Biochronology
 The lowest occurrence (LO) of Tribrachiatus bramlettei was chosen by Martini  to define the base of the calcareous nannofossil zone NP10, which often was used as an approximation of the P/E Boundary. The identity and systematic position of nannofossil marker species in C24r has been discussed by various authors, and their different viewpoints have lead to different interpretations of the same data [see, e.g., Aubry et al., 1996; Berggren and Aubry, 1996; Cramer et al., 2003; Raffi et al., 2005]. For example, the unreliability (diachrony) of T. bramlettei LO biohorizon [e.g., Cramer et al., 2003; Raffi et al., 2005] suggests to consider the LO of Rhomboaster calcitrapa gr. (= LO of Rhomboaster spp.), which defines the base of Bukry's [1973, 1978] subzone CP8b and occurs within the CIE interval, a better biohorizon to approximate the boundary. Moreover, recent results from Leg 199 indicate that the previously proposed subdivision of Martini's  zone NP10 (NP10a–NP10d) [Aubry, 1999] is erroneous, because of differences in stratigraphic relationship between the index species Tribrachiatus contortus and Tribrachiatus digitalis [Raffi et al., 2005]. This finding is confirmed by the results at Site 1262. Because of the needed extensive revision of the late Paleocene and early Eocene biostratigraphy, we here provide information on the relative position of nannofossil events in C24r and 25n as well as their absolute age only (Table 2).
Table 2. Revised Estimates for Calcareous Nannoplankton Biostratigraphic Datum Levels at Site 1262 Relative to the Age of the PETMa
|Event||Nannofossil Marker||Mean Depth, mcd||Mean Age Relative to Onset PETM, kyr||Chron Percentage From Topb|
|HO||T. contortus||118.085 ± 0.105||1740 ± 8||C24r.082|
|Decrease||D. multiradiatus||119.375 ± 0.105||1646 ± 7||C24r.112|
|LO||T. orthostylus||120.665 ± 0.105||1558 ± 7||C24r.140|
|LO||T. contortus||125.615 ± 0.015||1177 ± 1||C24r.263|
|LO||D. diastypus||127.445 ± 0.105||1054 ± 7||C24r.302|
|HO||Fasciculithus spp.||135.865 ± 0.105||403 ± 9||C24r.511|
|HO||R. calcitrapa gr.||139.715 ± 0.005||85 ± 1||C24r.613|
|Abundance crossover||Fasculiths/Z. bijugatus||139.78 ± 0.01||74 ± 2||C24r.616|
|Lowermost specimen||T. bramlettei||139.975 ± 0.005||36 ± 1||C24r.628|
|LO||R. calcitrapa gr.||140.015 ± 0.005||27 ± 1||C24r.631|
|Decrease in diversity of||Fasciculithus||140.1475 ± 0.0025||−5 ± 1||C24r.642|
|LO||D. multiradiatus||154.605 ± 0.105||−1238 ± 7||C25n.226|
|HO||Ericsonia robusta||157.995 ± 0.105||−1500 ± 11||C25n.739|
5.3. Relative Timing of Early Eocene Warming Events
 The pronounced precession cycles within C24r allowed us to define the exact positions of both early Eocene hyperthermal events, the PETM and ETM2 [Kennett and Stott, 1991; Lourens et al., 2005]. For the PETM we defined the onset (P0) as a fixed point, and for the position of ETM2 we chose to use the associated maximum peak in a* values (P88) as a fixed point (= midpoint Elmo horizon). According to our cyclostratigraphy the onset of the PETM is 53 ± 1 (1113 ± 21 kyr) and 55 ± 2 (1155 ± 42 kyr) precession cycles above the C25n/C24r reversal boundary in the Sites 1262 and 1267 records, respectively. The combination of Walvis Ridge sites and Site 1051 yields 53 ± 2 (1113 ± 42 kyr) cycles between the PETM and C25n/C24r (Table 1). This new estimate of 53 precession cycles representing 1113 kyr is ∼160 kyr longer than previous estimates from marine-based sections [Cramer, 2001; Cramer et al., 2003; Röhl et al., 2003]. These latter estimates were based, however, on the incomplete Site 1051 only, which also contains a slumped interval at the base of the PETM [Katz et al., 1999]. Other records (e.g., DSDP Sites 550, 577, and ODP Site 690) clearly possess gaps because of stratigraphic hiatuses or recovery issues [Cramer et al., 2003]. In contrast, a total of only 47 precession cycles have been counted in the Zumaia section between the base of C24r and the PETM [Dinarès-Turell et al., 2002]. The discrepancy with our estimate is likely the result of one or a combination of factors including; (1) the missing interval from −12 to −14 m in the Zumaia outcrop [Dinarès-Turell et al., 2002], (2) less developed precession cycles (overhanging carbonate banks), and/or (3) the duration of the thick clay interval associated with base of PETM.
 In the interval between the PETM and the C24r/C24n reversal boundary we identified 95 ± 2 (1995 ± 42 kyr), 99 ± 4 (2079 ± 84 kyr), and 93 ± 3 precession cycles (1953 ± 63 kyr) for Sites 1262, 1267 and 1051, respectively (Table 1). On the basis of correlation of the three sites we assigned 95 precession cycles (or 1995 kyr) from the PETM to the top of C24r. The difference between our results and those of Röhl et al.  for Site 1051 can be largely explained by the adoption of the new high-resolution paleomagnetic data of Cramer et al. . Our results show, moreover that the interval between the onset of the PETM and the ETM2 spans 87 ± 0.5 precession cycles (1827 ± 11 kyr). This time span is equivalent to ∼19 short eccentricity cycles. Previously, Lourens et al.  estimated 21 short eccentricity cycles for this interval based on the recognition of 18 short eccentricity cycles in the MS and L* records of Sites 1262 and 1267 between the top of the PETM and the base of the Elmo horizon (Figure 5), and the assumption that the PETM consists of 11 precession cycles [Röhl et al., 2000]. They concluded that both the ETM2 and the onset of the PETM are related to maxima of the 405-kyr eccentricity cycle. Spectral analysis of the higher-resolving and higher-quality data presented in this study, however, reveal only 17 short eccentricity cycles between the top of the PETM and the base of the Elmo horizon now (Figure 44). Using the same band-pass filter as given by Lourens et al.  (see auxiliary material Figure S1) the series for Fe (and a*) of Site 1262 reveals one short eccentricity cycle less than that of the MS in the interval of low-amplitude variability around 125 mcd (Figure 5). If we consider the quality (signal-to-noise ratio) of the MS and L* data subordinate to that of the Fe and a* records, this implies that Lourens et al.  overestimated the amount of short-term eccentricity cycles in this interval. Because of the consistency between precession cycle counting and band-pass filtering of proposed short eccentricity cycles in our records, we conclude that the distance between the top of the PETM and the base of the Elmo horizon spans 17 rather than 18 short eccentricity cycles.
Figure 5. Comparison of filter outputs derived from Site 1262 magnetic susceptibility (MS) (black) and Fe intensities (red) between the PETM and Elmo horizon. The same Gaussian filters were applied to extract the 100-kyr component (0.8 ± 0.104 cycles per m) and the 405-kyr component (0.17 ± 0.022 cycles per m) as done by Lourens et al.  to show how the resolution and quality of data have an influence on the filter output. The black numbers represent the number of short eccentricity cycles as proposed by Lourens et al. , whereas the red numbers represent the number of short eccentricity cycles as proposed in this study. The gray box highlights the interval where the filter outputs between MS and Fe intensity give inconsistent results. The resulting mismatch of ∼100 kyr between the two data sets is also present as an offset in the long eccentricity filter output.
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 Secondly, applying the He isotope age model [Farley and Eltgroth, 2003] proposes a much shorter duration (about 90–140 kyr) than the 11 precession cycles assumed for the duration of the PETM [Röhl et al., 2000], even though this method also includes many uncertainties in particular for the recovery interval of the PETM [Farley and Eltgroth, 2003]. Derived from the detailed correlation of Walvis Ridge Fe data to those of Site 690 in the Southern Ocean [Zachos et al., 2005], the interval from the onset of the PETM to the base of eccentricity cycle 19 of Lourens et al.  could alternatively be made up of about 7 to 8 rather than 11 precession cycles. As a consequence, our new results suggest that both the PETM and ETM2 may correspond to short-term eccentricity maxima, but in contrast to previously thought [Lourens et al., 2005], both events are not exactly tied to maxima in the long-term eccentricity (405 kyr) cycle, because they are exactly 4.5 long-term eccentricity cycles apart.
 Finally, we summarized the relative position of the PETM and ETM2 within C24r following the system of Hallam et al.  and the recommendation of Cande and Kent  to use an inverted stratigraphic placement relative to the present. We propose that the duration of chron 24r is 3118 kyr (148 precession cycles) and that the onset of the PETM is 1995 kyr (95 precession cycles) before the chron C24r/C24n boundary. As such, the notation of C24r.64 is assigned to the onset of the PETM indicating that 64% of chron C24r follows the onset of the PETM. Similarly, a compilation of continental sections from the Bighorn Basin yields exactly the same relative stratigraphic position with respect to the chron C24r/C24n boundary [Wing et al., 2000]. The ETM2 is located 8 ± 2 precession cycles or 168 ± 42 kyr at Site 1262 and 11 ± 4 precession cycles or 231 ± 84 kyr at Site 1267 below the chron C24r/C24n boundary. We considered the results from Site 1262 to be more reliable because of the higher quality in paleomagnetic data. Following the same stratigraphic concept, the ETM2 is labeled C24r.05 indication that 5% of chron C24r follows the event.
5.4. Toward an Absolute Timescale for the Late Paleocene and Early Eocene
 The records from the Walvis Ridge display a strong precession signal, which theoretically could be used for orbital tuning in a similar manner to the tuning of the Oligocene and Miocene at the Ceara Rise [Shackleton and Crowhurst, 1997; Shackleton et al., 1999, 1995]. A direct tuning of the late Paleocene to early Eocene records to astronomical solutions is hampered because of the limited precision of the orbital solution [Laskar et al., 2004; Varadi et al., 2003]. In fact, the orbital solution of Laskar et al.  (La2004) is considered to be valid back to 40 Ma [Pälike et al., 2004]. The imprecise knowledge of the solar oblateness term J2 is one of the main sources of uncertainty in the La2004 solution [Laskar et al., 2004]. This limits an accurate age determination of successive minima in the very long eccentricity cycle (∼2.4 Ma), which is the prerequisite to set up a first-order timescale [Hilgen, 1991; Pälike et al., 2004; Shackleton et al., 2000] in the Paleogene. Another eccentricity time series, solution R7 of Varadi et al.  (Va2003), is very similar to La2004 back to ca. 45 Ma, but diverges beyond that age for the same reason. As a consequence, Laskar et al.  recommended that for the construction of an astronomically calibrated timescale in the Paleogene only the very stable 405-kyr-long eccentricity period should be utilized. The period is related to the leading g2-g5 argument in the orbital solution of eccentricity, which has an age uncertainty of about 20 kyr at 50 Ma [Laskar et al., 2004]. Nevertheless, in the following section we will make a tentative comparison between our records and the La2004 and Va2003 solutions to give new insight into currently used absolute age models.
 An effective method to assess the relationship between amplitude modulation in the data and in the hypothetical forcing is complex demodulation [Shackleton et al., 1995]. In order to compare our data with current astronomical solutions we first have to extract the short and stable long eccentricity modulation from the climatic precession signal encoded in the data. We extracted the amplitude modulation of the climatic precession (∼21 kyr) and the main orbital eccentricity signal (∼405 kyr, ∼100 kyr) of the data using the freeware ENVELOPE [Schulz et al., 1999]. ENVELOPE estimates temporal changes in the signal amplitude of unevenly spaced data at a given period using a modified version of the harmonic-filtering algorithm of Ferraz-Mello . To obtain a comparable relative timescale for our records we used the cycle counting age model assuming ∼21 kyr for the precession cycle duration and arbitrarily set an age of 1 Ma for the Elmo horizon. The resulting time series and sedimentation rates for the Fe intensity data from Site 1262 are plotted in Figure 6a. The age model is provided in auxiliary material Table S9. The average sedimentation is 1.2 cm/kyr, though rates seem to vary in a cyclical fashion with lower rates corresponding with the low-carbonate intervals, possibly because of dissolution. Likewise, the PETM and Elmo horizon are characterized by the lowest sedimentation rates (∼0.5 cm/kyr) [Lourens et al., 2005; Zachos et al., 2005].
Figure 6. Comparison of relative cycle counting timescale with present astronomical solutions for orbital eccentricity. (a) Results of relative timescale: Site 1262 detrended Fe intensity data (red line) using a high-pass filter versus relative cycle counting age in Ma. We assume that the mean duration of one precession cycle is 21.0 kyr, and we set the Elmo horizon arbitrarily to 1.0 Ma. The resulting sedimentation rates in cm/kyr show minor variations throughout the record. In contrast, the regions containing the Elmo horizon and the PETM reveal lower than mean sedimentation rates because of strong dissolution of calcium carbonates (for discussion see Lourens et al.  and Zachos et al. ). (b) and (c) Comparison of current astronomical solutions plotted against absolute time and the extracted amplitude modulation of Site 1262 data plotted against relative time. We have shifted the Site 1262 data with respect to the best fit with the 405-kyr cycle; for further explanation, see text. Short eccentricity cycle amplitude modulation of Site 1262 Fe intensity (red) data, a* (dashed black) data, the La2004 [Laskar et al., 2004] (green), and Va2003 [Varadi et al., 2003] (dashed blue) orbital eccentricity solutions (Figure 6b). For comparison the La2004 and Va2003 amplitude modulation have been plotted from 53 to 58 Ma (bottom plot) and 53.4 to 58.4 Ma (middle plot). Climatic precession cycle amplitude modulation of Site 1262 data (Fe in red and a* in dashed black) compared to orbital eccentricity solutions La2004 (green) and Va2003 (dashed blue) from 53 to 58 Ma (bottom plot) and 53.4 to 58.4 Ma (middle plot) (Figure 6c). Additionally, the 2.4 Ma eccentricity minima in Site 1262 data are marked (see text for discussion). The amplitude modulations have been extracted with the program ENVELOPE [Schulz et al., 1999]. Different proposed absolute ages for the onset of the PETM are also shown; for discussion see text.
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 We extracted the amplitude modulation of short and long eccentricity from Site 1262 Fe and a* data using central filter periods of 21 and 95 kyr with ±15% bandwidth, respectively (Figures 6b and 6c). We used a window width factor (wfac) of 4 times the designated filter period, and a Welch taper-type window. The PETM and Elmo horizon were removed from the data set to avoid signal amplitude artifacts. The extracted short and long eccentricity paced signals (Figures 6b and 6c) show prominent amplitude modulations, although slight differences can be identified between the Fe and a* data. Given the higher sampling rate and lower signal-to-noise ratio the Fe data clearly provide a higher-fidelity record of orbital variations. The most important feature is the presence of two minima in the very long eccentricity cycle at ∼1.25 Ma (IV) and ∼3.3 Ma (−I) according to the relative timescale (Figure 6b). These can be easily identified in all data sets as intervals of very low-amplitude modulation of the climatic precession cycles (see Figures 4a and 4b). The second important feature is the lack of a transition in the eccentricity and precession-amplitude-modulation period from ∼2.4 to ∼1.2 Myr between 53 and 58 Ma. The detection of the first transition from a ∼2.4 to ∼1.2 Myr period is though to provide some extreme constraint for the gravitational model of the Solar System and therefore future orbital solutions (for discussion see Laskar et al.  and Pälike et al. ). A final feature is related to the alignment of the onset of the PETM and the ETM2 relative to the short- and long-term eccentricity cycles. While the PETM aligns with a decreasing branch of a 405-kyr eccentricity cycle, the ETM2 falls at a increasing branch, not with a 405-kyr maximum [Lourens et al., 2005] or a 405-kyr minimum [Cramer et al., 2003] as previously speculated. Nevertheless, both events seem to be related to a short eccentricity maximum as proposed by Lourens et al. .
 Subsequently a tentative comparison was made between the extracted amplitude modulations of a* and Fe records, and the current available astronomical solutions (Figure 6b). This may provide a first-order positioning of the Walvis Ridge records with respect to absolute ages. The two solutions, La2004 and Va2003, are almost identical for the 405-kyr component of orbital eccentricity in the period between 58.4 and 53 Ma (Figure 6b), while they differ for both the short-term (∼100 kyr) and the very long-term (∼2.4 Myr) components of eccentricity [Laskar et al., 2004]. For example a minimum in the long-term (∼2.4 Myr) component of eccentricity occurs around 55.7 Ma in La2004, but around 56.1 Ma in Va2003 (Figure 6). The similarity of both solutions in this period might be due to the fact that both are adjusted to the Jet Propulsion Laboratory ephemeris DE406. Because of uncertainties in the astronomical computations [Laskar et al., 2004] and in radiometric dating for this time interval [Machlus et al., 2004], only a floating timescale can be constructed using the stability of the 405-kyr eccentricity cycle as constraint.
 Starting point for tuning is the estimate of 55.3 Ma for the PETM in the Bighorn Basin [Wing et al., 2000] based on the magnetostratigraphy [Tauxe et al., 1994], biostratigraphy [Wing, 1984], and an 40Ar/39Ar age of 52.8 ± 0.16 Ma [Wing et al., 1991] for the base of chron C24n.1n [Tauxe et al., 1994]. To align our records with the stable 405-kyr cycle, however, we have to shift them ∼200 kyr relative to that estimate in either direction. The best fit was obtained by aligning precession cycle 33 to the age datum of 54.850 Ma, which lies close to a maximum in the 405-kyr cycle (Figure 6c). This is reflected in the comparison of the demodulated 405-kyr and 95-kyr amplitude component of the precession cycles in the Fe and a* data with the two eccentricity solutions (Figure 6c). If we assume that the eccentricity solutions La2004 and Va2003 are correct, all other options must be rejected, because the ages of the PETM and reversal boundaries would deviate by more than 1.6 Ma from published estimates [Cande and Kent, 1992, 1995; Lourens et al., 2005; Ogg and Smith, 2004]. Applying the eccentricity solutions La2004 and Va2003 and correlating our data to them we would derive an absolute age of ∼55.53 Ma for the PETM and ∼53.69 Ma for the ETM2 (Table 3). In this case, magnetochron C25n would have lasted from ∼57.16 Ma to ∼56.65 Ma, and C24r from ∼56.65 Ma to ∼53.53 Ma. The error given in Table 3 refers to the uncertainty in cycle counting as discussed above and the position of the reversal boundary in the data sets. In contrast, according to the GTS2004 the age of the PETM is ∼55.8 Ma, thus 300kyr older than our first estimate. In the following section we will discuss some of the uncertainties in estimating the absolute age for the PETM.
Table 3. Estimates of Absolute Age of Magnetochrons and Global Eventsa
|Chron (Event)||Estimated Age, Ma||Duration, Myr|
|Option 1||Option 2|
|C24r|| || ||3.118 ± 0.05b|
|C24r (y)||53.53 ± 0.04c||53.93 ± 0.04c|| |
|C24r (o)||56.65 ± 0.01c||57.05 ± 0.01c|| |
|C25n|| || ||0.511 ± 0.05b|
|C25n (y)||56.65 ± 0.01c||57.05 ± 0.01c|| |
|C25n (o)||57.16 ± 0.04c||57.56 ± 0.04c|| |
|Elmo (ETM-2)||53.69 ± 0.02b||54.09 ± 0.02b|| |
|PETM (ETM-1)d||55.53 ± 0.02b||55.93 ± 0.02b|| |
5.5. Age for the PETM
 An absolute age of the PETM has been in a constant state of flux for the last few decades [e.g., see Aubry et al., 1996; Wing et al., 2000]. The age uncertainties are based on inconsistencies between biochronology and magnetochronology [Aubry et al., 1996; Berggren and Aubry, 1996; Berggren et al., 1995; Norris and Röhl, 1999; Raffi et al., 2005; Wing et al., 2000] and the way the CK95 Geomagnetic Polarity Timescale (GPTS) was constructed [Berggren and Aubry, 1996]. In contrast to CK95 the new GPTS2004 [Ogg and Smith, 2004] utilize radiometric calibration points in the late Paleocene–early Eocene at 52.8 Ma (base of C24n.1n) and 55.07 Ma (C24r.50), and dismiss the calibration point used in CK95 of 55.0 Ma for the Paleocene-Eocene boundary, which was deemed inappropriate [Aubry et al., 1996]. The calibration point C24r.50 is located approximately in the middle of C24r [Ogg and Smith, 2004] constrained by 40Ar/39Ar ages and magnetostratigraphy of DSDP Hole 550 [Swisher and Knox, 1991]. The 40Ar/39Ar date from the middle of polarity chron C24r, which is significantly above the Paleocene-Eocene boundary, is derived from ash −17 with an age of 55.07 ± 0.5 Ma derived by J. D. Obradovich (see postscript given by Berggren et al. ). New 40Ar/39Ar ages for ash −17 (54.96 ± 0.16 Ma [Bird et al., 2003]) support the estimate of ∼55.0 Ma for the middle of chron C24r.
 According to our youngest estimate (option 1, see Table 3), the absolute age of the middle of chron C24r (C24r.50) is ∼55.09 Ma, which is very close to the radiometric dated ages. However, in case the radiometric dates of the −17 and +19 tephra are recalibrated to the Fish Canyon Tuff (FCT) 40Ar/39Ar standard age of 28.02 Ma [Villeneuve, 2004], this would result in an age of 55.3–55.4 Ma for the PETM (2/3 down in C24r). This is close to the estimate of 55.315 Ma (age model 2) by Wing et al.  which does not rely on any marine calibration points in the late Paleocene and early Eocene. More recently, Kuiper et al. [2004, 2005] estimated an older age of 28.21 ± 0.04 Ma for the FCT based on the intercomparison with astronomical-derived ages for Miocene tephra layers. Accordingly, the age of the PETM would be ∼55.75 Ma and that of C24r.50 ∼55.4 Ma. Tuning the Walvis Ridge record one 405-kyr eccentricity cycle older (which theoretically we could do because of the uncertainties of the orbital solutions) would imply an age of the PETM of ∼55.93 Ma (Figure 6c) and C24r.50 of ∼55.49 Ma. If this is correct, this implies that the recalibrated Ar/Ar ages would still be too young by ∼200kyr for the PETM. One explanation for the orbital-radiometric discrepancy that we are struggling with might be the observation that U-Pb and 207Pb/206Pb dates are older than 40Ar/39Ar by <1% (for discussion see Schoene et al. ). Unfortunately, because of the relatively large errors in radiometric dating it is still impossible to verify if U-Pb dates are systematically <1% older than 40Ar/39Ar [Schoene and Bowring, 2006; Schoene et al., 2006].
 If we assume the PETM to be at ∼55.93 Ma (option 2) and compare the demodulated precession signal of the Walvis Ridge record with the two eccentricity solutions (Figure 6b) from 53.4 to 58.4 Ma than the prominent 2.4 Ma minima in the Walvis Records would coincide with intervals of high-amplitude variability in the La2004 and Va2003 solutions. The comparison of the geological data with the eccentricity solutions then would clearly suggest that the La2004 and Va2003 solution, especially the 2.4-Myr modulation, are not correct in the interval from ∼53 to ∼59 Ma. This would simply mean that orbital tuning to precession and eccentricity solutions in this interval is not possible. On the other hand, if we assume that the orbital solutions are correct and the best fit with the geological data gives the correct age for the PETM (∼55.53 Ma), then the recalibrated Ar/Ar ages are too old. Owing to the uncertainty in the determination of the successive minima in the very long eccentricity cycle a direct anchoring of the studied interval to current orbital solutions is not possible. Therefore accurate absolute ages for the PETM and the C24r boundaries cannot be provided in the moment. To establish a robust absolute chronology and further insights in radiometric uncertainties new orbital solutions which are stable beyond 50 Ma are required. In addition, a cyclostratigraphic framework based on the stable long eccentricity cycle for the entire Paleogene has to be constructed, and the exact age of the FCT standard monitor has to be established. Until then, at least two different options for the absolute age of the onset of the PETM should be considered (∼55.53 Ma, ∼55.93 Ma).