Theory of chaotic orbital variations confirmed by Cretaceous geological evidence

Journal name:
Nature
Volume:
542,
Pages:
468–470
Date published:
DOI:
doi:10.1038/nature21402
Received
Accepted
Published online

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.

At a glance

Figures

  1. Obliquity and short eccentricity band power for La2004, La2010d and the Libsack FMI record.
    Figure 1: Obliquity and short eccentricity band power for La2004, La2010d and the Libsack FMI record.

    a, Timescale and biostratigraphy (S.m. = Scaphites mariasensis, S.p. = Scaphites preventricosus, S.v. = Scaphites ventricosus, S.d. = Scaphites depressus, C.s. = Clioscaphites saxitonianus, C.v. = Clioscaphites vermiformis, C.c. = Clioscaphites choteauensis, D.e. = Desmoscaphites erdmanni, D.b. = Desmoscaphites bassleri, S.l. = Scaphites leei III, S.h. I = Scaphites hippocrepis I, S.h. II = Scaphites hippocrepis II) 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 selected as the nominal anchor in this study (see Methods). Each ash bed (except the anchor) is associated with two ages: the top number is the age calculated based on astrochronology (anchored to S. preventricosus), while the bottom number is the radioisotopic age for the bentonite layer, with its 2σ total uncertainty in parentheses (column X3 in Table 1). b, f, The astronomically tuned and anchored FMI data (in units of ohm metre) from the Libsack core. ce, The obliquity band power extracted from the Libsack core, La2004 and La2010d. gi, The short eccentricity band power extracted from the Libsack core, La2004 and La2010d. The approximately 1.2-Myr and 2.4-Myr cycles are labelled with dashed arcs. Tur., Turonian age.

  2. Palaeogeographic map for the Late Cretaceous (90 Myr ago; copyright 2015 Colorado Plateau Geosystems, used with permission).
    Extended Data Fig. 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.

  3. 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.
    Extended Data Fig. 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. ce, 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). gj, 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.

  4. 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.
    Extended Data Fig. 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.

  5. A comparison of amplitude modulations expressed in the Libsack FMI short eccentricity and long eccentricity signals.
    Extended Data Fig. 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.

  6. A comparison of amplitude modulations expressed in the La2004 short eccentricity and long eccentricity signals.
    Extended Data Fig. 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).

  7. Time-frequency analysis of the astronomically tuned and radioisotopically anchored FMI data from the Libsack core.
    Extended Data Fig. 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.

  8. Time versus core-depth, based on astronomical tuning of the Libsack FMI data.
    Extended Data Fig. 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.

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Author information

Affiliations

  1. Department of Geoscience, University of Wisconsin-Madison, Madison, Wisconsin, USA

    • Chao Ma &
    • Stephen R. Meyers
  2. Department of Earth and Planetary Sciences, Northwestern University, Evanston, Illinois, USA

    • Bradley B. Sageman

Contributions

S.R.M. conceived the project, designed the study, and developed the statistical software for the analysis. C.M. conducted the analysis with guidance from S.R.M. and B.B.S. All authors interpreted the results and wrote the manuscript.

Competing financial interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to:

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.

Author details

Extended data figures and tables

Extended Data Figures

  1. Extended Data Figure 1: Palaeogeographic map for the Late Cretaceous (90 Myr ago; copyright 2015 Colorado Plateau Geosystems, used with permission). (229 KB)

    The location of the Libsack core is indicated with a red star.

  2. 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. (366 KB)

    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. ce, 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). gj, 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.

  3. 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. (322 KB)

    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.

  4. Extended Data Figure 4: A comparison of amplitude modulations expressed in the Libsack FMI short eccentricity and long eccentricity signals. (332 KB)

    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.

  5. Extended Data Figure 5: A comparison of amplitude modulations expressed in the La2004 short eccentricity and long eccentricity signals. (295 KB)

    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).

  6. Extended Data Figure 6: Time-frequency analysis of the astronomically tuned and radioisotopically anchored FMI data from the Libsack core. (422 KB)

    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.

  7. Extended Data Figure 7: Time versus core-depth, based on astronomical tuning of the Libsack FMI data10. (77 KB)

    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.

Supplementary information

Excel files

  1. Supplementary Data 1 (94 KB)

    EXCEL file containing the Libsack FMI data.

  2. Supplementary Data 2 (338 KB)

    EXCEL file containing the radioisotopically anchored astronomical time scale for the Libsack FMI data.

PDF files

  1. Supplementary Data 3 (177 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).

Additional data