Variations in the Earth’s orbit and spin vector are a primary control on insolation and climate; their recognition in the geological record has revolutionized our understanding of palaeoclimate dynamics1, and has catalysed improvements in the accuracy and precision of the geological timescale2. Yet the secular evolution of the planetary orbits beyond 50 million years ago remains highly uncertain, and the chaotic dynamical nature of the Solar System predicted by theoretical models has yet to be rigorously confirmed by well constrained (radioisotopically calibrated and anchored) geological data2,3,4. Here we present geological evidence for a chaotic resonance transition associated with interactions between the orbits of Mars and the Earth, using an integrated radioisotopic and astronomical timescale from the Cretaceous Western Interior Basin of what is now North America5. This analysis confirms the predicted chaotic dynamical behaviour of the Solar System, and provides a constraint for refining numerical solutions for insolation, which will enable a more precise and accurate geological timescale to be produced.
Subscribe to Journal
Get full journal access for 1 year
only $3.83 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
Hays, J. D., Imbrie, J. & Shackleton, N. J. Variations in the Earth’s orbit: pacemaker of the Ice Ages. Science 194, 1121–1132 (1976)
Hinnov, L. A. Cyclostratigraphy and its revolutionizing applications in the Earth and planetary sciences. Geol. Soc. Am. Bull. 125, 1703–1734 (2013)
Laskar, J. A numerical experiment on the chaotic behavior of the Solar System. Nature 338, 237–238 (1989)
Laskar, J. et al. A long-term numerical solution for the insolation quantities of the Earth. Astron. Astrophys. 428, 261–285 (2004)
Sageman, B. B. et al. Integrating 40Ar/39Ar, U-Pb, and astronomical clocks in the Cretaceous Niobrara Formation, Western Interior Basin, USA. Geol. Soc. Am. Bull. 126, 956–973 (2014)
Laskar, J. The chaotic motion of the Solar System: a numerical estimate of the size of the chaotic zones. Icarus 88, 266–291 (1990)
Laskar, J., Fienga, A., Gastineau, M. & Manche, H. La2010: a new orbital solution for the long-term motion of the Earth. Astron. Astrophys. 532, 89 (2011)
Laskar, J., Gastineau, M., Delisle, J.-B., Farres, A. & Fienga, A. Strong chaos induced by close encounters with Ceres and Vesta. Astron. Astrophys. 532, 4 (2011)
Fischer, A. G. in The Scientific Ideas of G.K. Gilbert (ed. Yochelson, E. I. ) Vol. 183, 93–104 (Spec. Pap. Geol. Soc. Am., 1980)
Locklair, R. E. & Sageman, B. B. Cyclostratigraphy of the Upper Cretaceous Niobrara Formation, Western Interior, U.S.A.: a Coniacian-Santonian orbital timescale. Earth Planet. Sci. Lett. 269, 540–553 (2008)
Wu, H. et al. Astrochronology of the Early Turonian-Early Campanian terrestrial succession in the Songliao Basin, northeastern China and its implications for long-period behavior of the Solar System. Palaeogeogr. Palaeoclimatol. Palaeoecol. 385, 55–70 (2013)
Thomson, D. J. Spectrum estimation and harmonic analysis. Proc. IEEE 70, 1055–1096 (1982)
Meyers, S. R., Sageman, B. B. & Arthur, M. A. Obliquity forcing of organic matter accumulation during Oceanic Anoxic Event 2. Paleoceanography 27, PA3212 (2012)
Taner, M. T., Koehler, F. & Sheriff, R. E. Complex trace analysis. Geophysics 44, 1041–1063 (1979)
Walaszczyk, I. & Cobban, W. A. Inoceramid faunas and biostratigraphy of the upper Turonian–lower Coniacian of the Western Interior of the United States. Palaeontol. Assoc. Lond. Spec. Pap. 64, 1–118 (2000)
Walaszczyk, I. & Cobban, W. A. Palaeontology and stratigraphy of the Middle-Upper Coniacian and Santonian inoceramids of the US Western Interior. Acta Geol. Polonica 56, 241–348 (2006)
Walaszczyk, I. & Cobban, W. A. Inoceramid fauna and biostratigraphy of the upper Middle Coniacian–lower Middle Santonian of the Pueblo Section (SE Colorado, US Western Interior). Cretac. Res. 28, 132–142 (2007)
Westerhold, T., Rohl, U. & Laskar, J. Time scale controversy: accurate orbital calibration of the early Paleogene. Geochem. Geophys. Geosyst. 13, Q06015 (2012)
Wu, H. et al. Time-calibrated Milankovitch cycles for the late Permian. Nat. Commun. 4, 2452 (2013)
Gilbert, G. K. Sedimentary measurement of geologic time. J. Geol. 3, 121–127 (1895)
Wagreich, M. “OAE 3”—regional Atlantic organic carbon burial during the Coniacean-Santonian. Clim. Past 8, 1447–1455 (2012)
Jenkyns, H. C. Geochemistry of oceanic anoxic events. Geochem. Geophys. Geosyst. 11, 1–30 (2010)
Herbert, T. D. A long marine history of carbon cycle modulation by orbital-climatic changes. Proc. Natl Acad. Sci. USA 94, 8362–8369 (1997)
Agterberg, F. G. Statistical procedures. In The Geologic Time Scale 2012 (eds Gradstein, F. M., Ogg, J.G., Schmitz, M. D. & Ogg, G. ) 269–274 (Elsevier, 2012)
Meyers, S. R. Astrochron: An R package for astrochronology. http://cran.r-project.org/package=astrochron (2014)
R Core Team R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computinghttp://www.R-project.org/ (2016)
Laskar, J., Joutel, F. & Boudin, F. Orbital, precessional and insolation quantities for the Earth from -20 Myr to +10 Myr. Astron. Astrophys. 270, 522–533 (1993)
Fienga, A. et al. INPOP08, a 4-D planetary ephemeris: from asteroid and time-scale computations to ESA Mars Express and Venus Express contributions. Astron. Astrophys. 507, 1675–1686 (2009)
Fienga, A., Manche, H., Laskar, J. & Gastineau, M. INPOP06: a new numerical planetary ephemeris. Astron. Astrophys. 477, 315–327 (2008)
Fienga, A. et al. The INPOP10a planetary ephemeris and its applications in fundamental physics. Celestial Mech. Dyn. Astron. 111, 363–385 (2011)
Meyers, S. R., Sageman, B. B. & Pagani, M. Resolving Milankovitch: consideration of signal and noise. Am. J. Sci. 308, 770–786 (2008)
Pälike, H. et al. The heartbeat of the Oligocene climate system. Science 314, 1894–1898 (2006)
Mitchell, R. N. et al. Oceanic anoxic cycles? Orbital prelude to the Bonarelli Level (OAE 2). Earth Planet. Sci. Lett. 267, 1–16 (2008)
Locklair, R., Sageman, B. & Lerman, A. Marine carbon burial flux and the carbon isotope record of Late Cretaceous (Coniacian-Santonian) Oceanic Anoxic Event III. Sedim. Geol. 235, 38–49 (2011)
Meyers, S. R. et al. Intercalibration of radioisotopic and astrochronologic time scales for the Cenomanian-Turonian boundary interval, Western Interior Basin, USA. Geology 40, 7–10 (2012)
Leckie, R. M., Bralower, T. J. & Cashman, R. Oceanic anoxic events and plankton evolution: Biotic response to tectonic forcing during the mid-Cretaceous. Paleoceanography 17, 13-1–13-29 (2002)
Sabatino, N. et al. High-resolution chemostratigraphy of the late Aptian-early Albian oceanic anoxic event (OAE 1b) from the Poggio le Guaine section (Umbria-Marche Basin, central Italy). Palaeogeogr. Palaeoclimatol. Palaeoecol. 426, 319–333 (2015)
This study was supported by NSF grants EAR-1151438 (S.R.M.) and EAR-0959108 (S.R.M. and B.B.S.). We thank R. Locklair for his cyclostratigraphic studies of the Libsack core, upon which this work builds. The Libsack core was donated to Northwestern University by EnCana, Inc., thanks to G. Gustason.
The authors declare no competing financial interests.
Reviewer Information Nature thanks H. Pälike, S. N. Raymond and the other anonymous reviewer(s) for their contribution to the peer review of this work.
Extended data figures and tables
Extended Data Figure 1 Palaeogeographic map for the Late Cretaceous (90 Myr ago; copyright 2015 Colorado Plateau Geosystems, used with permission).
The location of the Libsack core is indicated with a red star.
Extended Data Figure 2 Obliquity and short eccentricity band power for the theoretical astronomical solutions and the Libsack FMI record, including multiple anchoring options for the 405-kyr-tuned floating astrochronology, and the short eccentricity band power for La2011.
a, Timescale, biostratigraphy and the radioisotopically dated horizons for the Libsack core5,10. In total, five radioisotopic ages are used from the following biozones: D. bassleri, D. erdmanni, C. vermiformis, S. depressus and S. preventricosus. S. preventricosus is used as the nominal anchor in this study (see Methods). Each ash bed (except the nominal anchor) is associated with two ages: the top number is the age calculated based on the astrochronology (anchored to S. preventricosus), while the bottom number is the radioisotopic age for the bentonite layer, with its 2σ total uncertainty in parentheses. b, f, The astronomically tuned and anchored FMI data from the Libsack core. c–e, The obliquity band power extracted from the Libsack core, La2004 and La2010d, showing the youngest and oldest possible age models (Table 1) upon considering all sources of uncertainty (grey lines in d). g–j, The short eccentricity band power extracted from the Libsack core, La2004, La2010d, and La2011, showing the youngest and oldest possible age models (Table 1) upon considering all sources of uncertainty (grey lines in h). The approximately 1.2-Myr and 2.4-Myr cycles are labelled with dashed arcs.
Extended Data Figure 3 Obliquity and short eccentricity band power for the theoretical astronomical solutions and the Libsack FMI record, with FMI results normalized to total power <1/10,000 yr.
a, Timescale, biostratigraphy and the radioisotopically dated horizons for the Libsack core5,10. In total, five radioisotopic ages are used from the following bizones: D. bassleri, D. erdmanni, C. vermiformis, S. depressus and S. preventricosus. S. preventricosus is used as the nominal anchor in this study (see Methods). Each ash bed (except the anchor) is associated with two ages: the top one is the age calculated based on the astrochronology (anchored to S. preventricosus), while the bottom number is the radioisotopic age for the bentonite layer, with its 2σ total uncertainty in parentheses. b, g, The astronomically tuned and anchored FMI data from the Libsack core. c, d, f, The obliquity band power extracted from the Libsack core, La2004 and La2010d. e, The ratio of obliquity band power to total power in Libsack FMI data. h, i, k, The short eccentricity band power extracted from the Libsack core, La2004 and La2010d. j, The ratio of short eccentricity band power to total power in the Libsack FMI data. The approximately 1.2-Myr and 2.4-Myr cycles are labelled with dashed arcs. This analysis confirms the transition to an approximately 1.2-Myr cycle in short eccentricity power in the Coniacian. The normalized obliquity power result is more ambiguous, probably because it is normalized to a signal that it dominates. However, detection of the resonance transition requires assessment only of the eccentricity modulation, as previously proposed7.
Extended Data Figure 4 A comparison of amplitude modulations expressed in the Libsack FMI short eccentricity and long eccentricity signals.
a, Short eccentricity band power in the Libsack FMI record, determined by integration of spectral power between 0.007 and 0.012 cycles per kyr (142.9–83.3 kyr per cycle). b, The short eccentricity band power from a is normalized to total power ≤1/10,000 yr, to provide an alternative assessment that compensates for secular changes in the sensitivity of sedimentation to Milankovitch-forced climate change. c, The amplitude modulation (black line) of the Libsack 405-kyr FMI eccentricity cycle, as determined by Hilbert Transform of the bandpass-filtered long eccentricity signal (red line; from 0.002 cycles per kyr to 0.0035 cycles per kyr). The approximately 1.2-Myr and 2.4-Myr cycles are labelled with dashed arcs. This analysis confirms the chaotic transition from an approximately 2.4-Myr cycle to an approximately 1.2-Myr cycle in both short and long eccentricity modulation during the Coniacian. The phase relationship between long eccentricity and short eccentricity also exhibits the predicted anti-phased behaviour; for example, green boxes indicate locations when both short eccentricity assessments (a and b) show consistently low values. The timescale employed here uses the nominal radioisotopic anchor from the S. preventricosus ash bed.
Extended Data Figure 5 A comparison of amplitude modulations expressed in the La2004 short eccentricity and long eccentricity signals.
a, Short eccentricity band power in the La2004 solution, determined by integration of spectral power between 0.007 and 0.012 cycles per kyr (142.9–83.3 kyr per cycle). b, The amplitude modulation (black line) of the 405-kyr eccentricity cycle in the La2004 solution, determined by Hilbert Transform of the bandpass-filtered long eccentricity signal (red line; from 0.0015 cycles per kyr to 0.0035 cycles per kyr).
Extended Data Figure 6 Time-frequency analysis of the astronomically tuned and radioisotopically anchored FMI data from the Libsack core.
All analyses use three 2π prolate tapers, and a 500-kyr moving window. A linear trend was removed from each 500-kyr window before analysis. a, Evolutive Power Spectral Analysis (EPSA) results, and b, Evolutive Harmonic Analysis (EHA) results, normalized such that the maximum amplitude in each 500-kyr window is unity. Blue dashed boxes indicate the obliquity band used for integration of the power spectra, and black dashed boxes indicate the short eccentricity band. The timescale employed here uses the nominal radioisotopic anchor from the S. preventricosus ash bed.
Extended Data Figure 7 Time versus core-depth, based on astronomical tuning of the Libsack FMI data10.
The radioisotopically anchored astronomical timescale for the Niobrara Formation is constructed using the 405-kyr long eccentricity cycle observed in the Libsack FMI data10, and the nominal radioisotopic anchor from the S. preventricosus ash bed.
EXCEL file containing the Libsack FMI data. (XLSX 94 kb)
EXCEL file containing the radioisotopically anchored astronomical time scale for the Libsack FMI data. (XLSX 338 kb)
PDF file containing the computer script to reconstruct the analysis of the Libsack FMI data, and an analogous analysis of the Laskar et al. (2004) solution. The script uses the free statistical software R (https://cran.r-project.org) and the package 'Astrochron' (Meyers, 2014; https://CRAN.R-project.org/package=astrochron). (PDF 177 kb)
About this article
Cite this article
Ma, C., Meyers, S. & Sageman, B. Theory of chaotic orbital variations confirmed by Cretaceous geological evidence. Nature 542, 468–470 (2017). https://doi.org/10.1038/nature21402
A lower to middle Eocene astrochronology for the Mentelle Basin (Australia) and its implications for the geologic time scale
Earth and Planetary Science Letters (2020)
Cyclostratigraphy of Lower Triassic terrestrial successions in the Junggar Basin, northwestern China
Palaeogeography, Palaeoclimatology, Palaeoecology (2020)
Recognition of diagenetic contribution to the formation of limestone-marl alternations: A case study from Permian of South China
Marine and Petroleum Geology (2020)
Palaeogeography, Palaeoclimatology, Palaeoecology (2020)
An ∼34 m.y. astronomical time scale for the uppermost Mississippian through Pennsylvanian of the Carboniferous System of the Paleo-Tethyan realm