Reply on RC1

The geochronology of the Eocene-Oligocene transition remains controversial due to the lack of stratigraphic records. This study presents an astronomically calibrated magnetostratigraphy for this transition. Well-defined magneto-zones help high-resolution correlation between the studied lacustrine record to the deep-sea cores. Time series analysis further refines the geochronology of this study. This paper worth publication after addressing the following major comments:


General comments
The geochronology of the Eocene-Oligocene transition remains controversial due to the lack of stratigraphic records. This study presents an astronomically calibrated magnetostratigraphy for this transition. Well-defined magneto-zones help high-resolution correlation between the studied lacustrine record to the deep-sea cores. Time series analysis further refines the geochronology of this study. This paper worth publication after addressing the following major comments:

Specific comments
This paper aims to investigate whether the cyclic lacustrine deposits are orbitally driven. The analysis, aided with magnetostratigraphic correlation does answer this critical question. However, I would highly recommend the authors considering running statistical tuning methods, either ASM, COCO, or TimeOpt analysis of the gamma-ray data to test the significance level of the null hypothesis of no orbital forcing because the traditional cycle ratio method can generate misleading cycle ratios which lead to misinterpretation. Moreover, the sedimentation rate map is also expected to prove the assumed steady sedimentation rate is robust. The only figure S8 of the evolutive harmonic analysis shows fair results and very unclear implications of sedimentation rate. Therefore, an evolutionary version of ASM, COCO, or TimeOpt would help eliminate this question. Because the original data is unavailable now, so I wouldn't be able to reproduce the results, although the figures provided looks fine.

Reply to Comment #1_ cp-2021-46_ Referee #1:
We agree. As stated by the reviewer, the chronostratigraphic framework from magnetostratigraphic constraints can answer whether the cyclic lacustrine deposits are orbitally-driven. This method is generally used for the Cenozoic cyclostratigraphy. Yet, we agree that statistical approaches to demonstrate the orbital forcing, usually applied to Mesozoic records (without relatively precise age controls), can also provide additional confidence for Cenozoic records.
Accordingly, we now provide statistical methods based on the COCO and the evolutionary COCO analyses in order to test the significance level of the null hypothesis of no orbital forcing, and to estimate the evolution of sedimentation rate throughout the core.
The results are provided in figure 2 for evolutionary COCO results, and in the new figure 3 for the 'single' COCO results. As expected, these results support our previous cyclostratigraphic interpretations based on the preliminary magnetostratigraphic age model and on the manual use of the frequency ratio method.
This paper also aims to refine the Paleogene time scale. It is a great pity that recent advances in the Eocene geochronology were not cited and discussed. Key publications include the GTS2020, Westerhold et al. (2020 Science), andBerggren et al., 2018 (http://orca.cf.ac.uk/117311/1/Chapter_2.pdf). These publications presented the latest ages for the studied magneto-zones. And the GTS suggested a 33.9 Ma EOT, which contradicts the 33.7 or 34.1 Ma EOT age in this paper.

Reply to Comment #2_ cp-2021-46_ Referee #1:
We should have better explained that the latest geological timescale GTS2020 ( GTS2016 (Ogg et al., 2016 and that the GTS2016 and GTS2020 are cited in our paper. We have tried to clarify these points in the associated parts (see Supplementary Table S4, and details in Section 5.1).
Indeed, we had not discussed sufficiently the differences in EOB ages. We are well aware Westerhold et al. (2014) provided an age of 33.89 Ma for the Eocene/Oligocene boundary (EOB) and that a slightly different age of 33.90 Ma is used in all previous geological timescales GTS2012, GTS2016 and GTS2020. Despite significant advances and the apparent agreement in these proposed ages in astronomically calibrated Cenozoic timescale, it should be clear that controversial ages of the EOB unfortunately still exist (discussed in depth in Hilgen andKuiper, 2009, see also Sahy et al., 2017). Thus, we have tested this 33.90 Ma age of the EOB retained by the geological timescales together with all previously suggested ages (see Supplementary Table S4, and details in Section 5.1) to investigate the phase relationship between the sedimentary NGR data and the theoretical orbital eccentricity variations.
We had noted in the caption of Table 1 that: « Note that durations of all these chrons in GTS2020 (Gradstein et al., 2020 are from Westerhold et al. (2014). ».
In addition, to further highlight this note to the reader, we now added some clarifications in the first paragraph of Section 4.5 for the magnetic polarities, and in Section 5.1 for the age of EOB.
We also now cite the interesting paper of Berggren et al. (2018) suggested by the reviewer, focused on chronostratigraphy of planktonic foraminiferal biostratigraphy, and suggested two alternatives for the age of EOB, i.e. 33.70 and 33.90 Ma. These ages are based on previous studies that we extensively discussed in the paper (Section 5.1). In particular, these two proposed ages (and other ages we used) depend on age calibration used on the Fish Canyon Tuff standard, as has been reviewed by Hilgen and Kuiper (2009). This further supports the hypothesis that the age of EOB is not yet resolved.
Lacustrine records usually suffer from missing high-frequency astronomical cycles (obliquity and precession) and pollution from autogenic sedimentary cycles (Hajek and Straub, 2017). Therefore, the claimed 1 m scale precession cycles may be suspicious. I would like to see the argument against this comment.