Astronomical tunings of the Oligocene–Miocene transition from Pacific Ocean Site U1334 and implications for the carbon cycle

Astronomical tuning of sediment sequences requires both unambiguous cycle pattern recognition in climate proxy records and astronomical solutions, as well as independent information about the phase relationship between these two. Here we present two different astronomically tuned age models for the Oligocene–Miocene transition (OMT) from Integrated Ocean Drilling Program Site U1334 (equatorial Pacific Ocean) to assess the effect tuning has on astronomically calibrated ages and the geologic timescale. These alternative age models (roughly from ∼ 22 to ∼ 24 Ma) are based on different tunings between proxy records and eccentricity: the first age model is based on an aligning CaCO3 weight (wt%) to Earth’s orbital eccentricity, and the second age model is based on a direct age calibration of benthic foraminiferal stable carbon isotope ratios (δ13C) to eccentricity. To independently test which tuned age model and associated tuning assumptions are in best agreement with independent ages based on tectonic plate-pair spreading rates, we assign the tuned ages to magnetostratigraphic reversals identified in deep-marine magnetic anomaly profiles. Subsequently, we compute tectonic plate-pair spreading rates based on the tuned ages. The resultant alternative spreading-rate histories indicate that the CaCO3 tuned age model is most consistent with a conservative assumption of constant, or linearly changing, spreading rates. The CaCO3 tuned age model thus provides robust ages and durations for polarity chrons C6Bn.1n–C7n.1r, which are not based on astronomical tuning in the latest iteration of the geologic timescale. Furthermore, it provides independent evidence that the relatively large (several 10 000 years) time lags documented in the benthic foraminiferal isotope records relative to orbital eccentricity constitute a real feature of the Oligocene– Miocene climate system and carbon cycle. The age constraints from Site U1334 thus indicate that the delayed responses of the Oligocene–Miocene climate–cryosphere system and (marine) carbon cycle resulted from highly nonlinear feedbacks to astronomical forcing.


Introduction
Astronomically tuned age models are important in studies of Cenozoic climate change because they shed light on cause and effect relationships between insolation forcing and the linear and non-linear responses of Earth's climate system (e.g. Hilgen et al., 2012;Vandenberghe et al., 2012;Westerhold et al., 2017). As more Cenozoic paleoclimate records are generated that use astronomical tuning as the main highprecision dating tool, it is important to understand the assumptions and limitations inherent in this age calibration method, in particular with respect to assumptions related to phase relationships between tuning signal and target curves (i.e. climate proxy records and astronomical solutions, respectively). These phase assumptions have implications for (i) determining the absolute timing of events, (ii) the understanding of leads and lags in the climate system, and (iii) the exact astronomical frequencies that are present in climate proxy records after tuning.
Previously published astronomically tuned age models for high-resolution climate records that span the Oligocene-Miocene transition (OMT, ∼ 23 Ma) have used different tuning signal curves for sites from different paleoceanographic settings. In addition, different tuning target curves have been applied. For example, records from Ocean Drilling Program (ODP) Sites 926 and 929 from the Ceara Rise (equatorial Atlantic) were tuned using magnetic susceptibility and/or colour reflectance records (i.e. proxies for bulk sediment carbonate content) as a tuning signal curve and used obliquity as the main tuning target curve, sometimes with weaker precession and eccentricity components added (e.g. Shackleton et al., 1999Shackleton et al., , 2000Zachos et al., 2001;Pälike et al., 2006a). In contrast, sediments from ODP Site 1090 from the Agulhas Ridge (Atlantic sector of the Southern Ocean) and ODP Site 1218 from the equatorial Pacific Ocean were tuned using benthic foraminiferal stable oxygen (δ 18 O) and/or carbon (δ 13 C) isotope records as a tuning signal (e.g. Billups et al., 2004;Pälike et al., 2006b). These records used different combinations of eccentricity, obliquity, and/or precession as tuning targets (ETP curves).
More recently, Oligocene-Miocene records from ODP Site 1264 and middle Miocene records from Integrated Ocean Drilling Program (IODP) Site U1335 used the Earth's eccentricity solution as the sole tuning target. These studies used lithological data, such as elemental estimates based on X-ray fluorescence (XRF) core scanning records, as the sole tuning signal. The records from both these sites are characterized by a clear expression of eccentricity, either resulting from productivity-dominated cycles (at Site 1264; Liebrand et al., 2016) or dissolution-dominated cycles (at Site U1335; Kochhann et al., 2016). The general phase relationships between the ∼ 110 kyr cycles and 405 kyr cycles (in the case of Site U1335) in lithologic records and the stable eccentricity solution for this interval (Laskar et al., 2011a, b), i.e. whether maxima in signal curve correspond to minima or maxima in the target curve, were straightforward to derive Kochhann et al., 2016). These broadscale phase relationships were in agreement with those previously derived using benthic foraminiferal δ 18 O and δ 13 C records (e.g. Zachos et al., 2001;Pälike et al., 2006b).
The different options for astronomical age calibration of the Oligocene-Miocene time interval has resulted in large variations in the precise phase estimates after tuning between ∼ 110 kyr and 405 kyr cycles present in both the eccentricity solution and in lithologic and climatologic proxy records. In addition, the choice of tuning signal curve may result in different cyclostratigraphic interpretations and different ages and durations of geologic events. To obtain better constraints for the true phase relationships of the ∼ 110 and 405 kyr cycles between benthic foraminiferal stable isotope records and orbital eccentricity, and to better understand the implications that initial phase assumptions for astronomical age calibration have on absolute ages across the OMT, we need independent dates that are free from tuning phase assumptions. Previous studies have successfully used plate-pair spreading rates to date magnetochron reversals and used these ages as an independent age control (e.g. Hilgen et al., 1991a, b;Wilson, 1993;Lourens et al., 2004).
Here, we present two astronomically tuned age models for newly presented (estimates of) sediment CaCO 3 content and previously published high-resolution benthic foraminiferal δ 18 O and δ 13 C records across the OMT from IODP Site U1334 (eastern equatorial Pacific Ocean; Beddow et al., 2016). We select the sediment CaCO 3 content and benthic foraminiferal δ 13 C as tuning signals because these data are generally thought to represent two end-members in terms of tuning phase assumptions (Pälike et al., 2006a, b;Liebrand et al., 2016). We evaluate the implications of using these different tuning proxies for (i) absolute ages of magnetochron reversals and (ii) the leads and lags between the eccentricity tuning target and lithologic-paleoclimate tuning signals. We achieve this by computing the spreading-rate histories of a suite of tectonic plate pairs, after assigning the astronomically tuned ages to the magnetostratigraphic reversals in their anomaly profiles. The constraints given by the long-term evolutions of these alternative spreading-rate histories are sufficiently precise to discriminate between tuning options and phase assumptions.

Site description
Site U1334, located in the eastern equatorial Pacific (4794 m b.s.l.; 7 • 59.998 N, 131 • 58.408 W), was recovered during IODP Expedition 320 (Fig. 1). Upper Oligocene and lower Miocene sediments from Site U1334 were deposited at a paleodepth of ∼ 4200 m b.s.l. and consist of foraminiferand radiolaria-bearing nannofossil ooze and chalk (Pälike et al., 2010(Pälike et al., , 2012). An expanded Oligocene-Miocene section with a well-defined magnetostratigraphy was recovered (Pälike et al., 2010;Channell et al., 2013), and a continuous spliced record of Holes A, B, and C was placed on a core composite depth scale below the sea floor (CCSF-A; equivalent to metres composite depth; Figs. 2 and 3; Westerhold et al., 2012a). Samples were taken along the splice and all results presented here follow this depth model .

Coulometric CaCO 3 and magnetic susceptibility
Lithological records from Site U1334 that span the OMT show large variability in CaCO 3 content (Pälike et al., 2010). To obtain a high-resolution and continuous lithological proxy record, we estimate the CaCO 3 wt% of Figure 1. Locations of ODP and IODP drill sites discussed in this study. Location of IODP Site U1334 with reference to ODP Sites 1264, 1218, 926, 929, and 1090 the dry sediment (hereafter CaCO 3 content) by calibrating high-resolution shipboard magnetic susceptibility data (MS) to lower-resolution discrete shipboard coulometric CaCO 3 measurements for Site U1334 (Pälike et al., 2010). Minimum MS values correspond to maximum CaCO 3 values. The correlation between coulometric CaCO 3 measurements and MS was calculated using a linear regression line, with an R 2 value of 0.92 (Fig. 2), indicating that ∼ 90 % of the variability in the MS record is caused by changes in the bulk sediment CaCO 3 content. Middle Miocene CaCO 3 records from nearby Site U1335 show negatively skewed cycle shapes and have been interpreted as a dissolution-dominated signal (Herbert, 1994;Kochhann et al., 2016). In contrast, cycle shapes in the CaCO 3 content record for the Oligocene-Miocene of Site U1334 are less skewed, suggesting that here CaCO 3 content was predominantly controlled by a combination of productivity and dissolution.

Benthic foraminiferal stable isotope records and magnetostratigraphic age model
We use the benthic foraminiferal δ 18 O and δ 13 C records of Site U1334, which were measured on the Oridorsalis umbonatus and Cibicides mundulus benthic foraminifer species . To construct this mixed-species record, O. umbonatus values were corrected to C. mundulus values based on ordinary least squares linear regression that was based on an analysis of 180 pairs of inter-species isotope values to which a comparison was applied (for details, see Beddow et al., 2016). The benthic foraminiferal stable isotope datasets at Site U1334 were placed on a magnetostratigraphic age model calculated by fitting a third-order polynomial through 14 magnetostratigraphic age-depth tie points. Twelve of these chron boundaries fall within the study interval, are given in Table 1, and are shown in Figs. 3 and 4. This magnetostratigraphic age model yields an initial time period from ∼ 21.9 to 24.1 Ma for the study interval ( Fig. 4; Channell et al., 2013;Beddow et al., 2016).

Spectral analysis
We use the statistical software programme AnalySeries (Paillard et al., 1996) to conduct spectral analyses on the benthic foraminiferal δ 13 C and δ 18 O and the CaCO 3 datasets in the depth domain on the magnetostratigraphic age model ) and on both astronomically tuned age model options presented here. Prior to analysis, the CaCO 3 content and stable isotope data were resampled at 2 and 5 cm in the depth domain and at 2.5 and 3.0 kyr in the age domain, respectively, and trends longer than 6 m, or 600 kyr, were removed using a notch filter (Paillard et al., 1996). Blackman-Tukey spectral analysis was used to identify dominant periodicities present within the data, which subsequently were filtered using Gaussian filters. We applied cross-spectral analysis to identify coherency and phase relationships between the eccentricity and the CaCO 3 , δ 18 O, and δ 13 C chronologies. These calculations were performed at 95 % significance. Evolutive spectral analyses using a sliding fast Fourier transform (FFT) were computed using MAT-LAB.

Reversal ages based on plate-pair spreading rates
We use previously published magnetic anomaly profiles of tectonic plate-pair spreading rates (Wilson, 1993) to independently test the astronomical age models for Site U1334. This age comparison method is similar to that previously used to support astronomically tuned age models for the Miocene, Pliocene, and Pleistocene (Hilgen et al., 1991a, b;Krijgsman et al., 1999;Hüsing et al., 2007). We have selected plate pairs with high-quality anomaly profiles and relatively high spreading rates. These plate pairs are in order of decreasing spreading rate: Pacific-Nazca, Pacific-Juan de Fuca, Australia-Antarctic, and Pacific-Antarctic. Data for the Pacific-Nazca pair are limited to the northern part of the system, which is well surveyed from studies of the separation of the Cocos plate from the northern Nazca plate during chron C6Bn (Lonsdale, 2005;Barckhausen et al., 2008). Pacific-Juan de Fuca data are from immediately north of the Mendocino fracture zone. Reversal ages based on these spreading rates are also used in previous timescale calibrations (e.g. Cande and Kent, 1992) despite the fact that for the Oligocene-Miocene time interval only the Pacific plate record has survived and the Juan de Fuca plate was subducted. Wilson (1988) interpreted a sudden change in spreading-rate gradient for this pair from the south faster prior to C6Cn.2n(o) to the north faster after that reversal. The dataset for the Australia-Antarctic pair is similar to that presented by Cande and Stock (2004). It is expanded from that used by Lourens et al. (2004), who assigned reversal ages spanning from 18.524 to 23.030 Ma for the chron interval from C5Er (top) to C6Cn.2n (base) based on a linear interpolation of spreading rates of 69.9 mm yr −1 for this plate pair. Data for Pacific-Antarctic come primarily from more recent surveys near the Menard and Vacquier fracture zones (Croon et al., 2008).

Lithologic and paleoclimatic records
The synthetic wt% calcium carbonate record (CaCO 3 content wt%) ranges between ∼ 45 and 95 %, which is consistent with the coulometric CaCO 3 wt% measurements on discrete samples (Figs. 2 and 3). Variability is generally twice as large in the lower Miocene section of the record, between 88.95 and ∼ 102 m CCSF-A (core composite depth below the sea floor), varying by ∼ 40 % with several minima in the record dipping below 70 % (Fig. 3). There is little variability in CaCO 3 content across the OMT between ∼ 102 and ∼ 106 m CCSF-A. The benthic foraminiferal δ 18 O record captures a large, partially transient shift towards more positive values at the Oligocene-Miocene boundary, with maximum values of ∼ 2.4 ‰ occurring at 104.5 CCSF-A (Fig. 3). After the boundary, both δ 18 O and δ 13 C values show higher-amplitude variability and more permanent shifts towards higher values .

Spectral analysis in the depth domain
The power spectra of the CaCO 3 content record in the depth domain reveal strong spectral peaks at frequencies of 0.20 and 0.65 cycles m −1 (Fig. 3). These frequencies broadly correspond to those found in the benthic foraminiferal δ 18 O and δ 13 C depth series at 0.15 and 0.65 cycles m −1 . High-amplitude cycles with frequencies in the range between ∼ 0.20 and 0.80 cycles m −1 are present in all datasets with an approximate 1 : 4 ratio, suggesting a strong influence of eccentricity on the records (i.e. ∼ 110 : 405 kyr cycles). This interpretation of strong eccentricity is supported by the application of the initial magnetostratigraphic age model .

Initial age model
As a starting point for astronomical tuning we use an initial magnetostratigraphic age model Channel et al., 2013), which is based on the chron reversal ages of the 2012 geologic timescale (GTS2012; Vandenberghe et al., 2012;Hilgen et al., 2012; see Table 1, Fig. 4). On this initial age model, (time-evolutive) power spectra demonstrate that the CaCO 3 content and benthic foraminiferal δ 18 O and δ 13 C records are dominated by ∼ 110 and 405 kyr eccentricity- paced cycles, with short intervals of strong responses at higher frequencies (Fig. 5). To further assess the influence of eccentricity on the records from Site U1334, we filter the ∼ 110 and 405 kyr cycles of the CaCO 3 content and δ 13 C records (Figs. 6a and 7a). In total, we observe just over five 405 kyr cycles in both the filtered CaCO 3 content and δ 13 C records. There is a notable difference in the number of filtered ∼ 110 kyr cycles present between these two datasets. We observe 23 complete ∼ 110 kyr cycles in the CaCO 3 content record and 21 in the δ 13 C record. Visual assessment of the number of cycles is not always straightforward because not every ∼ 110 kyr cycle is expressed equally strong in all data records. In the eccentricity solution for the interval approximately between 21.9 and 24.1 Ma, we count five and a half 405 kyr cycles and 22 complete ∼ 110 kyr cycles. These numbers are largely in agreement with those obtained from visual assessment and Gaussian filtering.

Astronomical target curve
For our astronomical target curve, we select Earth's orbital eccentricity. Time series analyses on the CaCO 3 content and the benthic foraminiferal δ 18 O and δ 13 C records in the depth domain and on the initial age model indicate that eccentricity is the dominant cycle and that higher-frequency cycles are intermittently expressed (Fig. 5). Additional reasons to select eccentricity as the sole tuning target for the OMT of Site U1334 are the uncertain phase relationships of the data records to precession and the unknown evolution of tidal dissipation and dynamical ellipticity before 10 Ma (Zeeden et al., 2014). These parameters affect the long-term stability of both the precession and obliquity solutions (Lourens et al., 2004;Husing et al., 2007). We use the most recent nominal eccentricity solution (i.e. La2011_ecc3L; Laskar et al., 2011a, b;Westerhold et al., 2012b) as a tuning target, and for the OMT interval this solution is not significantly dif- ferent from the La2004 eccentricity solution , which was used to generate previous astronomically tuned high-resolution age models for this time interval (Pälike et al., 2006a, b).

Astronomical age calibration of the OMT from Site U1334
To test different ages and durations of the data from Site U1334 and the leads and lags of climate cycles with respect to eccentricity, we first consider the CaCO 3 content record and then the benthic foraminiferal δ 13 C record as tuning signals. Both tuning options are underpinned by assumptions of a consistent and linear in-phase relationship between the tuning signal and the eccentricity target. Previously tuned climate records for the OMT have shown that these two datasets represent end-members with respect to phase assumptions, with CaCO 3 content showing no lag or the smallest lag with respect to orbital eccentricity and with δ 18 O and δ 13 C showing increasingly larger lags to the ∼ 110 and 405 kyr eccentricity cycles Pälike et al., 2006a, b). Thus, by selecting the CaCO 3 content record and the benthic foraminiferal δ 13 C chronology, we span the full range of tuned ages that different phase assumptions between eccentricity and proxy data could possibly imply. We expect that the CaCO 3 tuned age model is in best agreement with independent ages based on spreading rates, and hence that benthic foraminiferal δ 13 C will show the largest lag with respect to eccentricity.
4.3.1 Astronomical tuning using the CaCO 3 content record We use the initial magnetostratigraphic age model as a starting point for a more detailed ∼ 110 kyr calibration of CaCO 3 content of the sediment to eccentricity. CaCO 3 maxima, mainly reflecting increased surface ocean productivity and/or decreased deep-ocean dissolution (e.g. Hodell et al., 2001), generally correspond to more positive δ 18 O values, which are indicative of cooler glacial periods. Hence, both bulk CaCO 3 content and benthic foraminiferal δ 18 O values are linked to eccentricity minima and are therefore anti-correlated with eccentricity (Zachos et al., 2001;Pälike et al., 2006a, b). The CaCO 3 content record is characterized by strong maxima, which we manually aligned to ∼ 110 kyr eccentricity minima by visually selecting tie points (Fig. 6c). In addition to these well-expressed ∼ 110 kyr cycles, we take the expression of the 405 kyr cycle into account to establish the tuned age model. on the CaCO 3 tuned age model. Linear sedimentation rates (LSRs) vary between 0.9 and 2.2 cm ky −1 (Fig. 6). On average this yields a sample resolution of 3.6 kyr for the benthic foraminiferal isotope records. Evolutive analyses (i.e. FFT using a sliding window) of the CaCO 3 content and benthic foraminiferal δ 18 O and δ 13 C records on the CaCO 3 tuned age model indicate that the 405 kyr cycle is relatively strongly expressed in all datasets (Fig. 5). However, this signal is weaker or absent across the OMT (∼ 23 Ma) in the evolutive spectrum of CaCO 3 content and post-OMT in benthic foraminiferal δ 18 O. The ∼ 110 kyr cycle is present in the data records on the CaCO 3 tuned age model between 23.4 and 22.2 Ma for CaCO 3 content, between 23.0 and 22.2 for benthic foraminiferal δ 18 O, and between 22.8 and 22.2 for benthic foraminiferal δ 13 C. The ∼ 110 kyr cycle is particularly pronounced in both the CaCO 3 and the benthic foraminiferal δ 18 O records, and we can identify power at both the 125 and the 95 kyr eccentricity cycles. We note that this could be a direct result from using eccentricity as a tuning target (see e.g. Shackleton et al., 1995;Huybers and Aharonson, 2010). For δ 13 C, the evolutive analysis and power spectra indicate that the ∼ 110 kyr cycle is more strongly expressed at the 125 kyr periodicity compared to the 95 kyr component. We find intermittent power present at a periodicity of ∼ 50 ky cycle −1 , which is either related to the obliquity cycle that is offset towards a slightly longer periodicity or to the first harmonic of the ∼ 110 kyr eccentricity cycle (King, 1996). The ∼ 50 kyr cy-cle is best expressed in the benthic foraminiferal δ 18 O record on the CaCO 3 tuned age model, in which we identify two main intervals with significant power at this periodicity, one between ∼ 23.5 and ∼ 23.8 Ma and the other between ∼ 22.4 and ∼ 22.6 Ma (Fig. 5).
Cross-spectral analyses between the CaCO 3 content, δ 18 O, and δ 13 C records on the CaCO 3 tuned age model and eccentricity indicate that all are significantly coherent at the 405, 125 and 95 kyr eccentricity cycles (Fig. 5). Phase estimates of benthic foraminiferal δ 18 O with respect to eccentricity indicate a lag of 21 ± 16 kyr at the 405 kyr period and 9 ± 3 kyr at the ∼ 110 kyr periodicity (95 % confidence on error bars). The δ 13 C record lags eccentricity by 29 ± 14 kyr at the 405 kyr cycle and by 9 ± 4 kyr at the ∼ 110 kyr cycle (Fig. 5). The coherence between CaCO 3 content and eccentricity is only just significant, and phase estimates are roughly in-phase with eccentricity: 6 ± 24 kyr at the 405 kyr cycle and −1 ± 2 kyr at the ∼ 110 kyr cycle. These phase estimates between CaCO 3 content and eccentricity are not surprising because CaCO 3 content was used to obtain astronomically tuned ages. These phase relationships between CaCO 3 and eccentricity thus confirm that the in-phase tuning assumption was applied successfully.

Astronomical tuning using the benthic foraminiferal δ 13 C record
An important consequence of the CaCO 3 tuned age model is that eccentricity-related variability within the benthic foraminiferal δ 13 C record is not in-phase with eccentricity ( Fig. 7b; Laurin et al., 2017). On both the initial magnetostratigraphic age model and on the CaCO 3 tuned age model, the phase lag, as visually identified in the filtered records, between the 405 kyr eccentricity cycle and the 405 kyr cycle in δ 13 C increases during the early Miocene (Figs. 6 and 7). The 405 kyr eccentricity pacing of δ 13 C is a consistent feature that characterizes the Cenozoic carbon cycle (Holbourn et al., 2004(Holbourn et al., , 2013Littler et al., 2014;Pälike et al., 2006a, b;Liebrand et al., 2016;Wade and Pälike, 2004), and to date no large changes in phase relationship have been documented. However, the increased phase lag in the response of the 405 kyr cycle in δ 13 C to eccentricity, as is suggested by the CaCO 3 tuned age model, could provide further support for a large-scale reorganization of the carbon cycle across the OMT as has previously been suggested based on a sudden increase in accumulation rates of benthic foraminifera and uranium-calcium values, suggesting increased organic carbon burial (Diester-Haas et al., 2011;Mawbey and Lear, 2013).
To test the validity of the large phase lag of the 405 kyr cycle in benthic foraminiferal δ 13 C to eccentricity and to test the potential increase in this lag, we generate another astronomically tuned age model. This time, we use the benthic foraminiferal δ 13 C record as the tuning signal and assume that the 405 kyr cycles and ∼ 110 kyr cycles in benthic www.clim-past.net/14/255/2018/ Clim. Past, 14, 255-270, 2018 Figure 5. Implication of age models on time series analysis. (a-c) Time-evolutive FFT analysis of CaCO 3 content on the initial magnetostratigraphic age model (i.e. a third-order polynomial), the CaCO 3 content tuned age model, and the δ 13 C tuned age model, respectively. Panels (d-f) are as in (a-c) but for benthic foraminiferal δ 18 O. Panels (g-i) are as in (a-c) but for benthic foraminiferal δ 13 C. For all records, periodicities larger than 600 kyr are removed using a notch filter. For panels (b) to (i): coherence with and phase relationships to eccentricity (La2011 solution) are depicted. All proxy data records were multiplied by −1 before computing the phase estimates.
foraminiferal δ 13 C are in-phase with eccentricity across the OMT (Fig. 7d). Approximately five 405 kyr cycles are identified in the benthic foraminiferal δ 13 C record, which facilitate initial visual alignment to the same cycle in the eccentricity solution. Subsequently, we correlated the maxima and minima in the benthic foraminiferal δ 13 C record, as identified in Gaussian filters centred around the ∼ 110 kyr cycle of this record on the initial magnetostratigraphic age model (Fig. 7a), to those identified in the filtered component of the eccentricity solution (Fig. 7d). On the benthic foraminiferal δ 13 C tuned age model, our data span the interval between 22.1 and 24.2 Ma (i.e. 2.1 Myr duration), resulting in an average time step of 3.4 kyr. LSRs generally range between 0.7 and 2.5 cm ky −1 , apart from an abrupt and short-lived increase across the OMT to ∼ 3.3 cm ky −1 . On the δ 13 C tuned age model, the CaCO 3 record remains in anti-phase with respect to ∼ 110 kyr eccentricity, but the benthic foraminiferal δ 13 C tuning results in an alternative alignment of CaCO 3 cycles to eccentricity, which yields a ∼ 110 kyr shorter duration of the record and causes the sudden increase in sedimentation rates across the OMT (Figs. 6 and 7). The evolutive analyses and power spectra are broadly consistent with the evolutive analyses from the CaCO 3 tuned age model, with dominant 405 kyr cyclicity in all three datasets, an increase in spectral power at ∼ 110 kyr eccentricity cycles after the OMT, and intermittent expression of higher-frequency astronomical cycles (Fig. 5). On the δ 13 C tuned age model, all datasets exhibit a relatively stronger response at the 95 kyr short eccentricity cycle than the 125 kyr short eccentricity cycle in contrast to the CaCO 3 tuned age model. In the late Oligocene, between ∼ 23.3 and 23.8 Ma, strong 40 kyr obliquity cycles are present in the benthic foraminiferal δ 18 O record on the δ 13 C tuned age model.
Cross-spectral analyses between the CaCO 3 content, δ 18 O, and δ 13 C records on the δ 13 C tuned age model and eccentricity indicate that all are significantly coherent at the 405, 125, and 95 kyr eccentricity cycles (Fig. 5). CaCO 3 content leads eccentricity by −24 ± 18 kyr at the 405 kyr cycle and by −7 ± 3 kyr at the ∼ 110 kyr cycle. On the δ 13 C tuned age model, phase estimates of δ 18 O with respect to eccentricity  (Laskar et al., 2011a, b). Tie points are represented by red dots and dashed lines. Gaussian filters were calculated in AnalySeries (Paillard et al., 1996) Figure 7. Site U1334 δ 13 C vs. age. The δ 13 C dataset and 405 kyr and ∼ 110 kyr Gaussian filters plotted on (a) the magnetostratigraphic age model, (b) the CaCO 3 tuned age model, and (c) the δ 13 C tuned age model. (d) Earth's orbital eccentricity solution is plotted in grey (Laskar et al., 2011a, b). Tie points are represented by red dots and dashed lines. Gaussian filters were calculated in AnalySeries (Paillard et al., 1996) with the following settings: 405 kyr -f: 2.5 bw: 0.8, ∼ 110 kyr -f: 10, bw: 3. (e) Sedimentation rates are calculated using the δ 13 C tuned age model.
show small leads of −4 ± 12 kyr at the 405 kyr cycle and of −1±4 kyr at the ∼ 110 kyr cycle. Benthic foraminiferal δ 13 C lags eccentricity by 19 ± 8 kyr at the 405 kyr cycle and by 3 ± 2 kyr at the ∼ 110 kyr eccentricity cycle, which is congruent with the in-phase tuning assumption between benthic foraminiferal δ 13 C and eccentricity that is used in this age model.

Age model comparison
The final eccentricity tuned age models for the OMT time interval differ for two reasons. Firstly, there are 21 complete ∼ 110 kyr cycles in the δ 13 C tuned age model and 22 in the CaCO 3 content record. The tuned age models are largely consistent with each other during the late Oligocene and OMT interval. The base of chron C6Cn.2n, which marks the Oligocene-Miocene boundary, occurs within 10 kyr on both age models. The two astronomically tuned age models diverge at ∼ 22.7 Ma, where the CaCO 3 content has an additional ∼ 110 kyr cycle on the initial magnetostratigraphic age model. A second factor contributing to the difference between the two astronomically tuned age models is the different phase relationships between the two proxy records and eccentricity (i.e. either CaCO 3 is in-phase eccentricity or benthic foraminiferal δ 13 C). These different phase assumptions that underpin the two tuned age models account for age differences up to 10 % at all periodicities in the two records (Table 2) in addition to the ∼ 110 kyr difference for the early Miocene interval of Site U1334 that results from the two different cyclostratigraphic interpretations. In turn, these interpretations are resultant from the initial phase assumptions. The longer lag time of δ 13 C with respect to eccentricity, in comparison with CaCO 3 , leads to older ages assigned to ∼ 110 kyr cycles in the δ 13 C age model. This is particularly notable between 22.7 and 24.2 Ma, when the difference between the age models is accounted for only by the difference in phase.

Spreading rates
To independently test whether the CaCO 3 tuned ages or the benthic foraminiferal δ 13 C tuned ages and their underlying phase assumption are most appropriate for tuning the deepmarine Oligocene-Miocene records from Site U1334, we assign the tuned magnetostratigraphic reversal ages from Site U1334 to those identified in an anomaly profile of tectonic plate pairs. We use the evolution through time of the spreading rates of these plate pairs as a control for our tuned age models (Wilson, 1993;Krijgsman et al., 1999). Rapid simultaneous fluctuations in the spreading rate of multiple plate pairs are highly unlikely and indicate errors in the tuned timescale. We propose using the astronomically tuned age model from Site U1334 that passes this test most successfully to provide ages for C6Bn.1n (o) to C7n.1r (o) and potentially revise those currently presented in the GTS2012. Reduced-distance plots for the labelled plate pairs implied by (a) the GTS2012, (b) the CaCO 3 tuned age model, and (c) the δ 13 C tuned age model. Reduced distance is the full spreading distance (D) minus the age (A) times the labelled spreading rate (R; see y axes). Distance scale is plotted inversely with spreading rate. This results in age errors that depart vertically from a straight line when spreading rates are constant. Inset scale bar shows the vertical offset resulting from a 100 kyr change in a reversal age. Dashed horizontal lines are viewing aids to evaluate the prediction that constant spreading at the reduction rate R will produce a horizontal line. Error bars are 95 % confidence. The CaCO 3 -based age model (b) gives the simplest spreading-rate history and represents the preferred tuning option. On the CaCO 3 tuned age model, the Australia-Antarctica, Pacific-Nazca, and Pacific-Antarctic plate pairs are all very close to a constant spreading rate (Fig. 8). The Juan de Fuca-Pacific plate pair indicates a sudden decrease in spreading rate (145 to 105 mm yr −1 ) at ∼ 23 Ma, consistent with expectations (see the above Sect. 2.5; Wilson, 1988). In contrast, the synchronous changes for the Australia-Antarctica, Pacific-Nazca, and Pacific-Antarctic plate pairs in the δ 13 C tuned age model, especially the faster spreading rates ∼ 22.5-23.0 Ma implied by older ages for C6Bn, make this tuning option less plausible. Differences between the CaCO 3 tuned age model for Site U1334 and GTS2012 are subtler. The longer duration of C6Cn.3n in the CaCO 3 tuned age model (106 vs. 62 kyr; Table 1) eliminates a brief and relatively small pulse of fast spreading implied by GTS2012, which is visible in Fig. 8a as positive slopes in age-distance during that chron. Over longer intervals, CaCO 3 tuned ages remove a slight but synchronous rate slowdown that is also implied by GTS2012 and which starts at ∼ 23.2 Ma.
The CaCO 3 tuned age model indicates a duration for C6Cn.2n of 67 kyr. This duration may be up to ∼ 40 kyr too short, as is suggested by the relatively short-lasting increase in spreading rates during this chron (see the positive slopes in Fig. 8b). The spreading-distance error bars indicate that this age discrepancy is marginally significant, with no overlap in reduced distance for the boundaries of this chron for three of four plate pairs. Despite this small uncertainty in the duration for chron C6Cn.2n on the CaCO 3 tuned age model, the base of this chron appears in good agreement with spreading rates and thus suggests a slightly older age for the Oligocene-Miocene boundary of approximately 23.06 Ma. Furthermore, the polarity chron ages from the CaCO 3 tuned ages are generally older by approximately 40 kyr on average than those presented in the GTS2012 (Table 1). In both the CaCO 3 content and δ 13 C record, the short interval around C6Cn.2n is difficult to align to the eccentricity solution (Figs. 5 and 6) because CaCO 3 content values are high with little variability, and benthic foraminiferal δ 13 C values correspond to the marked shift towards higher values at the Oligocene-Miocene carbon maximum (Hodell and Woodruff, 1994). The 83 kyr duration of C6Cn.2n from the δ 13 C tuned age model is better supported by spreading rates than the 67 kyr duration from the CaCO 3 tuned age model, and the 118 kyr duration in GTS2012 is even more consistent with constant spreading rates. If we extrapolate constant spreading rates across C6Cn.2n using the CaCO 3 tuned age for the base of 23.06 Ma, we obtain an age for the top of this normal polarity interval of ∼ 22.95 Ma and a duration of 110 kyr. An important implication of the CaCO 3 tuned ages is the delayed increase in spreading rates of the Juan de Fuca-Pacific plate pair. On the CaCO 3 tuned age model this occurred approximately 200 kyr later than those ages presented in the GTS2012 (i.e. during chron C6Cn.2n instead of C6Cn.3n; see Fig. 8).

Evaluation of tuning signals
Of the two astronomically tuned age models and GTS2012, the CaCO 3 tuned age model is most consistent with the assumption of the least amount of changes in plate-pair spreading rates, which makes it the preferred astronomically tuned age model option for Site U1334 (Fig. 8). This agreement between plate-pair spreading-rate history and the CaCO 3 tuned ages suggests that local and/or regional (i.e. lithological) tuning signals can produce more accurate age models in comparison with age models based on globally integrated isotope records. The latter data are known to produce significant lags relative to eccentricity as a result of highly non-linear feedback mechanisms (Laurin et al., 2017;Pälike et al., 2006b;Zeebe et al., 2017), a result that is confirmed by this study ( Table 2). The independent evidence that we provide for using a lithological (proxy) record for the astronomical age calibration of marine sediments yields further support for similar astronomical tuning methods. Examples are the middle Miocene (Kochhann et al., 2016) and Eocene-Oligocene (Westerhold et al., 2015) records from the equatorial Pacific Ocean and the Oligocene-Miocene records from the South Atlantic Ocean . We note, however, that these records show variable ratios of productivity to dissolution as the main source of variance in the data. Future additional testing of phase uncertainties could include statistical approaches, such as Monte Carlo simulations (Khider et al., 2017).

Implications for the carbon cycle
Benthic foraminiferal δ 13 C variations in the open ocean are typically interpreted to reflect the ratio between global organic and inorganic carbon burial (Shackleton, 1977;Broecker, 1982;Diester-Haas et al., 2013;Mawbey and Lear, 2013). Astronomical forcing of organic carbon burial is typically expected in the precessional band because organic carbon burial, notably in the marine realm, depends on clay fluxes and thus hydrology (Berner et al., 1983). However, the residence time of carbon (∼ 100 kyr) is so long (Broecker and Peng, 1982) that this energy is transferred into eccentricity bands (Pälike et al., 2006b;Ma et al., 2011;Laurin et al., 2017). Importantly, while the total marine carbon inventory is driven by ocean chemistry, the phase lag between eccentricity forcing and δ 13 C should primarily be a function of the residence time of carbon in the global exogenic carbon pool (Zeebe et al., 2017). Hypothetically, a change in total organic matter burial will only result in whole-ocean steady state when the δ 13 C of buried carbon equals that of the input (through rivers). Because the burial fluxes are small compared to the total carbon inventory, a pronounced time lag between eccentricity forcing and δ 13 C is expected (e.g. Zeebe et al., 2017). Interestingly, the CaCO 3 age model for Site U1334 suggests that the phase lag between the 405 kyr cycle in the δ 13 C record and the eccentricity forcing increases across the OMT (see position of minima and maxima of the 405 kyr filters of eccentricity and benthic foraminiferal δ 13 C in Fig. 7). In theory, an increase in the phase lag suggests an increase in the residence time of oceanic carbon, either through a rise in the total carbon inventory or a drop in the supply and burial of carbon (Zeebe et al., 2017). The lengthening of the phase lag of the 405 kyr cycle coincides with a large shift in the benthic foraminiferal δ 13 C record across the OMT to more positive values, evidencing a structural relative increase in the supply of 13 C-depleted carbon or a drop in the burial of 13 C-enriched carbon. Reliable reconstructions of CO 2 are rare across the OMT (www.p-co2.org) and the OMT does not seem associated with a large change in the depth of the Pacific calcite compensation depth (Pälike et al., 2012). Therefore, additional constraints on atmospheric CO 2 concentrations and burial fluxes are required to better understand the climatic and oceanographic mechanisms associated with the increased phase lag (Egger et al., 2018).

Conclusions
We explore the application of CaCO 3 content (estimated from magnetic susceptibility and shipboard coulometry) and benthic foraminiferal δ 13 C records as tuning signals for the OMT record at Site U1334 in the eastern equatorial Pacific. These two tunings highlight the importance of carefully considering the implications of tuning choices and assumptions when creating astronomical age models. Spreadingrate histories provide independent support for the CaCO 3 tuned age model. This suggests that lithological signals respond more directly (though still non-linearly) to eccentricity than the stable isotope signals, for which we find support for a delayed response to astronomical climate forcing. Tuning to CaCO 3 provides a valuable method to better understand the (lagged) response in benthic foraminiferal δ 18 O and δ 13 C, which are widely used and reproducible proxies for the global climate-cryosphere system and (marine) carbon cycle. One important implication of the CaCO 3 age model is that 405 kyr cycle in benthic foraminiferal δ 13 C shows a distinct phase lag with respect to orbital eccentricity. Lastly, the CaCO 3 age model for Site U1334 provides astronomically calibrated ages for C6Bn.1n to C7n.1r. The polarity chron ages from the CaCO 3 tuned ages are generally older by approximately 40 kyr on average than those presented in the GTS2012. We suggest that these updated early Miocene ages be incorporated in the next version of the geologic timescale.
Data availability. All data on the preferred CaCO 3 tuned age model can be downloaded from www.pangaea.de or by following this link: https://doi.pangaea.de/10.1594/PANGAEA.885365