The Late Devonian envelops one of Earth’s big five mass extinction events at the Frasnian–Famennian boundary (374 Ma). Environmental change across the extinction severely affected Devonian reef-builders, besides many other forms of marine life. Yet, cause-and-effect chains leading to the extinction remain poorly constrained as Late Devonian stratigraphy is poorly resolved, compared to younger cataclysmic intervals. In this study we present a global orbitally calibrated chronology across this momentous interval, applying cyclostratigraphic techniques. Our timescale stipulates that 600 kyr separate the lower and upper Kellwasser positive δ13C excursions. The latter excursion is paced by obliquity and is therein similar to Mesozoic intervals of environmental upheaval, like the Cretaceous Ocean-Anoxic-Event-2 (OAE-2). This obliquity signature implies coincidence with a minimum of the 2.4 Myr eccentricity cycle, during which obliquity prevails over precession, and highlights the decisive role of astronomically forced “Milankovitch” climate change in timing and pacing the Late Devonian mass extinction.
Frasnian–Famennian (F–F) boundary sections around the world are often characterized by two horizons of dark bituminous shale, the so-called lower and upper Kellwasser horizons (LKW and UKW)1,2. Both layers coincide with a positive δ13C excursion, as recognized in North America, Morocco, Europe, Russia, western Australia, and southern China1,3,4,5,6,7,8,9,10. The worldwide incidence of Kellwasser horizons indicates a major perturbation of the global carbon cycle, and is associated with one of the most prominent mass extinction events in Earth history, primarily affecting tropical marine benthos11. Stromatoporoid and coral reefs were ubiquitous during the Middle to Late Devonian, but never truly recovered after the Late Devonian mass extinction. Despite this major reshuffling of the Earth’s system, the timing and pacing of the environmental changes responsible for the mass extinction remain poorly constrained. Recently, however, cyclostratigraphic efforts yielded constraints on the numerical ages of stage boundaries within the Devonian System12,13,14,15. These studies provided a new chronometer for this part of the Paleozoic, based on the most stable astronomical cycle: the 405-kyr long eccentricity cycle. In this study, we take the application of Devonian astrochronology to sub-eccentricity resolution. Therefore, we considered the magnetic susceptibility and carbon isotope series of six globally distributed F–F sections (Fig. 1). Two of these sections, Kowala (Poland) and Section C (western Canada), were the subject of previous cyclostratigraphic studies15,16, yielding orbital chronologies based on 405-kyr long eccentricity cycles. We correlated the other four sections (from Belgium, China and the United States) into this astrochronologic framework, based on biostratigraphy, δ13C chemostratigraphy, and magnetic susceptibility proxy records. We then used a Monte-Carlo approach to further refine the original eccentricity-based astrochronology (“Methods”). The result is a common chronology for all six sections, i.e., a global astrochronology for the Late Devonian. This global chronology provides new insight into the rhythm of environmental change across the F–F transition, and reveals the obliquity signature of the UKW positive δ13C excursion. These results confirm the importance of astronomically forced climate change in pacing the biogeochemical interactions that led to the extinction event.
Six globally distributed Frasnian–Famennian sections
The six globally distributed F–F sections considered in this study are located in Poland (Kowala section), western Canada (Section C), Iowa (H-32 and CG-1 drill core), Belgium (Sinsin section), and South China (Fuhe section). The H-32, CG-1, and Sinsin proxy records were constructed in the framework of this study, whereas data from Section C17,18, Kowala16,19, and Fuhe3,20,21 have been previously published (for details see Fig. 1 caption). All six sections were deposited in a tropical setting, albeit in different parts of the Panthalassic, Rheic and Paleo-Tethys Oceans (Fig. 1). We selected sections that were deposited in basin-to-slope deep-water environments, so to maximize stratigraphic continuity. The CG-1 drill core is the exception to this rule, as it constitutes the shelf-margin time-equivalent section of deep-water section H-32.
The magnetic susceptibility series of Section C (western Canada) served as the basis for the Frasnian astrochronology published in a previous study by De Vleeschouwer et al.15. In that paper, 16 Frasnian long eccentricity cycles (Fr-LECs, each 405 kyr in duration) were counted. This chronology was later refined by Whalen et al.17, who revealed that half a 405-kyr long eccentricity cycle needed to be added to the chronology of Section C, after comparison with the contemporaneous Kowala section and by constructing a detailed δ13C record for the F–F interval (shown in Fig. 1). This revision reconciled the astrochronologic interpretations from Section C15 and the Kowala16, with a total of 16.5 Fr-LECs and with the LKW and UKW occurring in the 15th and 17th Fr-LEC, respectively. In this paper, we tie four additional sections (H-32, CG-1, Sinsin, and Fuhe) into the common astrochronologic framework of Section C and Kowala, so to attain a global astrochronology for the F–F mass extinction interval (Figs. 2–4). We establish the temporal relationships between the different sections by correlating distinct features in magnetic susceptibility (red ties in Fig. 5) and carbon isotope geochemistry (blue ties in Fig. 6), while respecting biostratigraphic constraints. The determination of stratigraphic relationships between globally distributed sections based on carbon isotope variations is well established22, yet interbasinal correlations based on magnetic susceptibility data are not undisputed. This is because the magnetic susceptibility of a rock sample depends on the concentration and type of magnetic minerals (often assumed to be a function of sea-level and climate), as well as the size and shape of the magnetic grains. Nevertheless, several Devonian examples exist of valid global correlations based on magnetic susceptibility, despite differences in palaeogeographic setting, facies, accumulation rate or depositional history3,23,24,25. These examples suggest the importance of a magnetic susceptibility forcing mechanism operating at the global scale. For example, Section C, H-32, Sinsin, and Fuhe exhibit a characteristic double minimum in magnetic susceptibility just prior to the F–F boundary (Fig. 1). This susceptibility signature corroborates the utility of magnetic susceptibility as a correlative tool in the framework of this Late Devonian study.
As mentioned earlier, the magnetic-susceptibility and carbon-isotope tie-points (Figs. 5 and 6) were drawn respecting biostratigraphic constraints. However, in two instances, correlating lines traverse different biostratigraphic zones. Specifically, we correlate the stratigraphic levels at 19 and 21.5 m at the CG-1 core with 320 and 330 m at Section C (Fig. 5). These levels occur in Frasnian Conodont Zone 11 in the CG-1 core, but occur in Frasnian Conodont Zone 12 in Section C. In this case, it is unclear whether this discrepancy is caused by diachronism between Iowa and western Canada, an inaccurate biostatigraphic zonation, or erroneous correlation. Yet, the excellent match between the susceptibility signals of these two records in this interval (Supplementary Fig. 1) strongly substantiates our preferred correlating lines (Fig. 5). The second instance consists of the correlation between the stratigraphic levels at 18 and 21.5 m in Fuhe (in the linguiformis Zone) with the stratigraphic levels at 355.5 and 359 m at Section C (in the rhenana Zone) (Figs. 5 and 6). Given the good chemostratigraphic control in this interval close to the LKW (Fig. 6), we consider it most likely that the rhenana–linguiformis boundary is identified too low within the Fuhe section. Once all correlating time-lines were established, we used those tie-points to transfer the astrochronology from Section C to the other sections, using the ages indicated in Figs. 5 and 6. The black ages on these figures represent the initial ages that we assigned to the correlating lines, based on the 405-kyr astrochronology of Section C. The green ages on these figures represent a refinement of the initial ages after our Monte-Carlo-based age modeling approach (see “Methods” and Supplementary Figs. 2–4 for more details).
The multitaper method (MTM) spectral plots of the MS records that were tied-in into the astrochronologic framework (Fig. 2) show multiple peaks that are associated with astronomical forcing parameters. The occurrence of elevated spectral power at the expected frequencies of 100-kyr eccentricity in the H-32 and CG-1 power spectra (Fig. 2), and obliquity in the H-32, CG-1, and Sinsin power spectra adds confidence to the global astrochronology. In order to subdue the risk for circular reasoning, we checked whether the astronomical imprint could also be observed when carrying out spectral analysis in the depth domain. Evolutive harmonic analysis (EHA) of the magnetic susceptibility depth-series of the H-32, CG-1, Fuhe, and Sinsin sections reveals that the different astronomical components can be traced in the depth domain (Supplementary Fig. 5). This implies that the astronomical imprint has not been introduced by the age modeling strategy adopted in this paper. The Fuhe section power spectrum is characterized by a significant spectral peak at 0.036 cycles/kyr (28 kyr period), which is slightly offset in comparison with the expected Devonian obliquity frequency of 0.031 cycles/kyr26 (32 kyr period), as observed at H-32, CG-1 and Sinsin. Yet, we associate this peak in the Fuhe spectrum to variations in the obliquity of the Earth’s rotational axis, implying that we observe obliquity-related peaks in all four spectra. This is remarkable given the (sub)tropical paleolatitudes of the studied sections, where the influence of obliquity on insolation is minor. A clear obliquity signal in (sub)tropical records is often interpreted as an indication of a climatic teleconnection between high and low latitudes14, for example through the remote influence of waxing and waning high-latitude ice-sheets. However, recent climate modeling results have demonstrated that tropical atmospheric circulation is highly susceptible to changes in the cross-equatorial insolation gradient27. This gradient is strongly influenced by obliquity and thus may explain a (sub)tropical obliquity imprint without invoking high-latitude ice sheets. In other words, the existence of continental ice sheets during the Frasnian remains an open question28.
The carbon isotope stratigraphy in Fig. 3 places the LKW halfway Fr-LEC 15, while the UKW corresponds to Fr-LEC 17 (which is the same cycle as Famennian long eccentricity cycle 1 (Fa-LEC 1)). The LKW is a relatively short-lasting event, with a total duration of about 200 kyr. The onset of the positive LKW δ13C excursion occurs ~800 kyr before the F–F boundary, while the end of the excursion falls 500–600 kyr prior to the F–F boundary. The peak of the LKW-positive δ13C excursion corresponds to the maximum of Fr-LEC 15. The UKW is significantly more protracted, compared to the LKW. The onset of the UKW δ13C excursion occurs in the lowermost part of Fr-LEC 17, about 150 kyr prior to the F–F boundary. The UKW excursion spans this entire 405-kyr cycle (Fr-LEC 17, Fa-LEC 1), with δ13C values stabilizing ~400 kyr after the F–F boundary (Fig. 3). The LKW and UKW thus both start close to a 405-kyr eccentricity cycle minimum, reaching their peak in the subsequent 405-kyr maximum. In terms of sea level, the LKW started during the transgressive systems trackt of transgressive–regressive (T–R) cycle IId-217, and the UKW corresponds to the latest Frasnian–earliest Famennian sea-level lowstand and transgression of T–R cycle IId-329,30,31,32. Maximum transgression is thus associated with maximum eccentricity during both Kellwasser events33. This is in accordance with numerical Late Devonian climate modeling, suggesting that high eccentricity configurations favored relatively warm and wet global climates34, and represents the same phase relationship between eccentricity and global climate as during the Cenozoic35. The timing of the Kellwasser events with respect to eccentricity bears a remarkable resemblance to the timing of Ocean Anoxic Event-2 (OAE-2) just prior to the Cenomanian–Turonian boundary. Indeed, Batenburg et al.36 place the base of the Livello Bonarelli (the expression of OAE-2 in the Umbria-Marche Basin, Italy) at the first short-eccentricity maximum after a 405-kyr minimum.
Having constructed an astronomically constrained relative timescale for the F–F interval, it is possible to evaluate the changing imprint of astronomical forcing across the UKW. Because of the similarity in timing of the UKW and OAE-2 described above, our assessment focuses on obliquity and follows the methodology introduced by Meyers et al.37 for OAE-2. The high-resolution δ13Ccarb series from Kowala and Fuhe are best suited for this analysis, given that they possess sufficient resolution (~10 kyr and ~6 kyr, respectively) to evaluate the imprint of obliquity. We perform EHA spectral analyses on the astronomically calibrated δ13Ccarb series, followed by integration of the spectrum over the obliquity band (0.015–0.04 cycles/kyr; Fig. 4). Maximum obliquity power occurs a few tens of thousands of years before the F–F boundary, both in the Kowala and in the Fuhe section. The marked increase in the strength of the obliquity signal at the time of global carbon cycle perturbation and organic carbon accumulation is thus an additional similarity between OAE-2 and the UKW. The strong obliquity signal during the earliest phase of the UKW could be interpreted as the influence of high-latitude climate processes on the paleoenvironmental setting of the studied (sub)tropical sections. However, this is rather unlikely given the greenhouse state of the climate system at the time of the F–F transition. Alternatively, a strong obliquity signal can be associated with a long-term minimum in eccentricity. We consider this interpretation to be more plausible, given that the obliquity imprint at Kowala reveals a notable increase, at the eccentricity minimum that separates Fr-LEC 15 and Fr-LEC 16, as well as at the eccentricity minimum separating Fr-LEC 16 and 17. The latter increase in obliquity power is associated with the onset of the UKW. Interestingly, several recent studies pointed to the link between long-term eccentricity forcing on the one hand and the Myr-scale behavior of the Mesozoic carbon cycle on the other hand36,38,39,40,41. These authors all associate positive excursions in δ13C with so-called “nodes” in eccentricity, i.e., minima of the 2.4 Myr or 9 Myr eccentricity cycle. During such a node, eccentricity is low for a prolonged period of time, such that the influence of precession on insolation is dampened and seasonal extremes in insolation are avoided. In other words, a strong obliquity signal is in agreement with an eccentricity node, being the only remaining astronomical parameter with a significant influence on insolation. In this scenario, the onset of the UKW δ13C excursion would not only correspond to the 405-kyr eccentricity minimum between Fr-LEC 16 and Fr-LEC 17, but also to a minimum of the long-term 2.4-Myr eccentricity cycle. During this period of low eccentricity, organic carbon on land could accumulate due to the avoidance of climates with extreme seasonality, causing marine δ13C to rise36,39,42 at the beat of obliquity. A few tens of thousands of years later, eccentricity increased rapidly and reaches its subsequent 405-kyr maximum (Fr-LEC 17, Fa-LEC 1). This sequence of astronomical configurations supposedly contributed to a rapid warming of global climate as well as to an intensification of the hydrological cycle34. Under such climatic conditions, sea level rise and increased weathering are instigated and likely contributed to the eutrophication of shallow seas43, and thus to the widespread deposition of the organic-rich UKW. Yet, astronomical climate forcing is not ultimately responsible for the Late Devonian mass extinction. During the Devonian, the global carbon cycle was in a vigorous state, with enhanced silicate weathering under warm and humid conditions, and increased carbon burial through a productivity-hypoxia-nutrient recycling feedback loop44,45,46,47. This state of vigorous carbon cycling made the Devonian quite vulnerable for ocean anoxia and mass extinction48. The ultimate cause for the Late Devonian mass extinction thus probably lies with a unique convergence of processes invigorating the global carbon cycle (e.g., evolution of land plants43, volcanism49,50, tectonic processes51,52,53), but the exact timing of the outbreak of the LKW and UKW seems to be linked to a particular succession of astronomical configurations.
In conclusion, the construction of a global astrochronology across the F–F boundary interval reveals the steering role of astronomical climate forcing during one of the most far-reaching biotic events in Earth’s history. Intriguing obliquity-signatures characterize the Late Devonian UKW event, as well as the Cretaceous OAE-2. These two greenhouse worlds are separated by ~200 million years. Nonetheless, astronomical “Milankovitch” forcing seems to have influenced global carbon cycle dynamics in a similar way during both periods. In both cases, long-term minima in eccentricity (“nodes”) coincide with major perturbations of the global carbon cycle and increased extinction rates, with devastating effects during the Late Devonian extinction event.
The Kowala section (50.79° N, 20.57° E) was deposited in the intrashelf Chêciny-Zbrza Basin. The F–F interval at Kowala consists of thin-bedded marls with intercalated limestone beds and cherty limestone strata with marly intercalations. The LKW and UKW horizons are marked by two increases in total organic carbon (TOC) content, but the two black shale horizons that typify most F–F sections in Central Europe are absent here19. The Kowala section holds a previously published astrochronology, which is based on the stacking pattern of the marl-limestone alternations16. Both Kellwasser-equivalent TOC maxima, as well as four younger black shale horizons in the Famennian part of the section, were each deposited during just a fraction of one 405-kyr cycle according to that chronology. This finding was later confirmed for the Hangenberg shale, through high-precision U–Pb dating54. For the F–F interval, high-resolution δ13Ccarb (N = 77) and low-resolution δ13Ccarb data (N = 34) are available from De Vleeschouwer et al.16 and low-resolution δ13Ccarb (N = 38) data are available from Joachimski et al.19. To our knowledge, no magnetic susceptibility series exists for the F–F interval of the Kowala section.
Section C (53.17° N, 118.18° W) is located along the southeast margin of the Ancient Wall platform in the western part of the Western Canada Sedimentary Basin55. The section records upper-slope and prograding outer-ramp facies. The base of Section C is late Frasnian in age and consists of clay- and locally silt-rich shales of the Mount Hawk Formation, which is characterized by high magnetic susceptibility values throughout the basin18,55. A sea-level deepening event in the very late Frasnian resulted in the progradation of ramp facies and low magnetic susceptibility values at Section C, reflecting the increased carbonate input. The early Famennian Sassenach Formation records an influx of siliciclastics into the basin and related higher magnetic susceptibility values. From Section C, 50-cm spaced magnetic susceptibility data (N = 365)18 and δ13Corg (N = 52)17 are available.
During the Late Devonian, the Fuhe section (24.99° N, 110.41° E) was located in a tectonically active basin, surrounded by carbonate platforms. Pelagic nodular limestones intercalated with calciturbidites and debris flow deposits dominate the F–F sequence. Chen and Tucker56 interpreted lithological cycles in the Fuhe section as the expression of precession cycles, stacked into meter-scale cycle-sets interpreted as 100-kyr eccentricity cycles. The UKW event is clearly marked by a +3‰ excursion in the high-resolution 10-cm spaced δ13Ccarb (N = 54) and δ13Corg (N = 52) records3. The LKW event occurs in the lower part of the section, in the upper rhenana conodont zone, and is characterized by a positive excursion in the low-resolution δ13Ccarb (N = 73) and δ13Corg (N = 54)20 (Fig. 1).
The Sinsin roadcut section (50.28° N, 5.24° E) consists of shales, marls, and (nodular) limestones, deposited on the continental shelf below fair-weather wave base57. In the framework of this study, we sampled the section at 5-cm resolution for magnetic susceptibility (N = 223) and at 10-cm resolution for δ13Ccarb (N = 116). The carbon isotope chemostratigraphy exhibits a gradual shift towards more positive δ13Ccarb values (Fig. 1). This +3‰ excursion concurs with the upper linguiformis conodont Zone58 and is therefore interpreted as the expression of the UKW. In the same interval as the positive δ13Ccarb excursion, TOC values peak up to 0.2 wt% in a 30-cm thick interval directly underlying the F–F boundary59. A previously published cyclostratigraphy does not exist for the Sinsin section. Kaiho et al.59 demonstrated the imprint of astronomical forcing in the Sinsin section through wavelet analysis, but did not delineate individual cycles.
The CG-1 core (42.93° N, 93.08° W) was deposited in a shelf margin environment and consists of fossiliferous shales and argillaceous limestones of the Lime Creek Formation. In the framework of this study, we sampled CG-1 at an average resolution of 11 cm for magnetic susceptibility (N = 329) and 26 cm for δ13Ccarb (N = 137). The H-32 core (40.47° N, 91.47° W) is the basinal, deep-water time-equivalent section of CG-1 and consists of the dark-colored Sweetland Creek shale. The overlying Grassy Creek shale contains seven layers of volcanic ash, none of which yielded datable zircons. We sampled H-32 at 3 or 4-cm intervals for magnetic susceptibility (N = 294) and at irregular intervals for δ13Ccarb (N = 165) and δ13Corg (N = 70). The carbon isotope chemostratigraphy for both sections exhibits distinct positive δ13C excursions (Fig. 1). The +3‰ excursion in the CG1 core begins within the upper part of Frasnian Zone 12. We thus interpret this excursion as the expression of the LKW. At H-32, a +2‰ δ13Corg excursion spans Zones 13b and 13c. We interpret this excursion as the UKW as the F–F boundary occurs at the base of the first ash bed just below 1000 cm. Between 800 and 900 cm, a smaller positive excursion is observed in both δ13Ccarb and δ13Corg, which we interpret as the LKW. The H-32 and Cerro Gordo Project Hole 1 (CG-1) drill cores have never been studied in terms of astronomical forcing before.
Magnetic susceptiblity measurements for the Fuhe and Sinsin sections were taken with a KLY-3S kappabridge at the University of Liège (Belgium). Samples from the CG-1 and H-32 cores were measured at the University of Wisconsin at Milwaukee (USA) with a MFK1 kappabridge. Both devices have a noise level <2 × 10−8 SI. Each magnetic susceptibility data point is the average of three measurements and has been corrected for sample mass. Samples typically have a mass larger than 10 g and were weighed with a precision of 0.01 g.
Carbon isotope stratigraphy
Bulk carbonate δ13C from the H-32, CG-1 and Sinsin sections and δ13Corg from H-32 were measured at the Vrije Universiteit Brussel (Belgium). δ13Ccarb was measured using a NuPerspective IRMS interfaced with a NuCarb automated carbonate device. We use the internal NCM standard calibrated against NBS19 (+2.09‰). The long-term standard deviation of the internal standard is 0.05‰ for δ13Ccarb. Powdered samples for δ13Corg were weighed (~10 mg) in silver capsules. The samples were decarbonated by adding 5% HCl in steps of 4 h and reaction at 50 °C, till no further reaction occurred. The δ13Corg was measured using a Thermo1112 flash elemental analyzer coupled via a Con-Flo III interface to a Thermo DeltaV isotope ratio mass spectrometer (IRMS). The international reference standard IAEA-CH-6 (−10.449‰) was used for calibration (1σ ≤ 0.2‰).
We took 118 samples for biostratigraphy throughout the CG-1 core. All samples are typical of the Frasnian Polygnathus biofacies. Samples from the lower 23 m of the Juniper Hill and lower Cerro Gordo members include Palmatolepis semichatovae and Pa. kireevae correlated with Frasnian Zone 1162,63. The first appearance of Polygnathus planarius is interpreted as marking the base of Zone 12 based on its known range in western Canada. The occurrence of Polygnathus samueli high in the Cerro Gordo Member, just below the onset of the LKW δ13C excursion, is high within Frasnian Zone 12. The joint occurrence of Ancyrognathus asymmetricus and Icriodus alternatus in the Owen Member is interpreted as Frasnian Zone 13a, as the latter first occurs very high in Zone 12 and ranges into Zones 13a and 13b. Stratigraphically, this level occurs above peak values of the LKW δ13C excursion.
We took 54 samples for biostratigraphy throughout Core H-32. Most of the Sweetland Creek Shale at H-32 correlates with Frasnian Subzones 13a to 13b. The overlying Grassy Creek shale, just below the F–F boundary, corresponds to Frasnian Subzones 13b–13c (i.e., the linguiformis interval). The conodont yields of H-32 samples are generally very small or barren, but nevertheless, clear zonal indicators allow for the construction of the biostratigraphic scheme presented in Fig. 1. The Zone 11 and Zone 12 interval in the Sweetland Creek Shale is condensed in less than 3 meters. Most of the Sweetland Creek Shale at H-32 represents an expanded record of the LKW through the very Early Famennian.
Age modeling and spectral analyses
Tie-points between H-32, CG-1, Sinsin, Fuhe, Kowala, and Section C are obtained by visually correlating distinct features in magnetic susceptibility (red ties in Fig. 5) and carbon isotope geochemistry (blue ties in Fig. 6). In a first step, we assign an age relative to the F–F boundary to each of these tie-points according to the 405-kyr astrochronologic framework of Section C (Figure 7 in De Vleeschouwer et al.15). These ages are listed in black in Figs. 5 and 6. In a second step, we apply a Monte Carlo procedure to distort time-differences between consecutive tie-points. The goal of this procedure is to slightly modify the tie-point ages, so to get a better expression of the astronomical frequencies in the power spectra of the F–F proxy-series. We run the Monte Carlo procedure 5000 times in our search for the best astronomical fit. The tie-point ages for the best-fitting Monte Carlo simulation are listed in green in Figs. 5 and 6. The fit of each Monte Carlo simulation is evaluated as follows: we compute the power spectra for all susceptibility time series and consider the spectral power in the 100-kyr eccentricity (0.008–0.013 cycles/kyr), obliquity (0.025–0.035 cycles/kyr) and precession (0.045–0.065 cycles/kyr) bands. A good astronomical fit exists when high spectral power occurs in each of these bands. We measure this fit by subtracting the maximum AR1 confidence level occurring within each band from 100%. Low percentages thus represent high spectral power within the considered frequency band. Additionally, we measure the misfit between the frequency of maximum AR1 confidence level, and the expected orbital frequency according to Berger et al.26 (at 375 Ma: 0.0105 per kyr for 100-kyr eccentricity, 0.031 per kyr for obliquity and 0.055 per kyr for precession). This frequency misfit is also expressed as a percentage. Finally, we measure the total astronomical fit of the Monte Carlo simulation in question by averaging the spectral power and misfit measures among all frequency bands and among all sections. Our age modeling strategy is illustrated in detail using three distorted eccentricity-tilt-precession (ETP) series in Supplementary Figs. 3–5.
All spectral analyses in this study were carried out using the MTM with three 2π -tapers64, as implemented in the R-package “astrochron”65. The confidence levels were calculated applying the conventional AR1 method for estimating the red noise spectrum66. The R-code used for age modeling and spectral analyses is available through GitHub (“Code availability”).
Software S1. R-script for the illustration of the age modeling strategy adopted in this study, using distorted eccentricity-tilt-precession (ETP) series is available at https://github.com/dadevlee/Late_Devonian. Software S2. R-script for age modeling of Late Devonian data is available at https://github.com/dadevlee/Late_Devonian. Software S3. R-script for spectral analyses and the generation of the data in Figs. 2, 3 and 4 is available at https://github.com/dadevlee/Late_Devonian
Magnetic susceptibility and carbon isotope series are available from https://github.com/dadevlee/Late_Devonian/tree/master/Data_depth_domain and https://doi.pangaea.de/10.1594/PANGAEA.882366
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This research was supported by PhD fellowships from the Research Foundation Flanders (FWO) to D.D.V. (1148713N and V421513N) and M.S. (FWOTM782). We thank the Académie royale de Belgique for financial support (Prix Annuel en Géologie 2014 awarded to D.D.V.). D.D.V. is a postdoctoral researcher in the ERC Consolidator Grant “EarthSequencing” awarded to Heiko Pälike. A.-C.D.S. acknowledges the Netherlands Organization for Scientific Research (NWO, grant WE.210012.1). D.C. and Z.G. were supported by the National Natural Science Foundation of China (Grants 41072079 and 41290260). P.C. thanks the FWO Hercules program and the VUB strategic research program. This paper is a contribution to IGCP-652 “Reading geologic time in Paleozoic sedimentary rock”.
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