Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

The effect of energy feedbacks on continental strength


The classical strength profile of continents1,2 is derived from a quasi-static view of their rheological response to stress—one that does not consider dynamic interactions between brittle and ductile layers. Such interactions result in complexities of failure in the brittle–ductile transition and the need to couple energy to understand strain localization. Here we investigate continental deformation by solving the fully coupled energy, momentum and continuum equations. We show that this approach produces unexpected feedback processes, leading to a significantly weaker dynamic strength evolution. In our model, stress localization focused on the brittle–ductile transition leads to the spontaneous development of mid-crustal detachment faults immediately above the strongest crustal layer. We also find that an additional decoupling layer forms between the lower crust and mantle. Our results explain the development of decoupling layers that are observed to accommodate hundreds of kilometres of horizontal motions during continental deformation.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Strength profiles of the lithosphere.
Figure 2: Strain localization feedbacks in upper and lower crust.
Figure 3: Model results.


  1. Goetze, C. & Evans, B. Stress and temperature in the bending lithosphere as constrained by experimental rock mechanics. Geophys. J. R. Astron. Soc. 59, 463–478 (1979)

    ADS  Article  Google Scholar 

  2. Brace, F. W. & Kohlstedt, D. L. Limits on lithospheric stress imposed by laboratory experiments. J. Geophys. Res. 50, 6248–6252 (1980)

    ADS  Article  Google Scholar 

  3. Ranalli, G. & Murphy, D. C. Rheological stratification of the lithosphere. Tectonophysics 132, 281–295 (1987)

    ADS  Article  Google Scholar 

  4. Davis, G. H. & Coney, P. J. Geologic development of the Cordilleran metamorphic core complexes. Geology 7, 120–124 (1979)

    ADS  CAS  Article  Google Scholar 

  5. Miller, E. L., Gans, P. B. & Garing, J. The Snake Range décollement: an exhumed mid-Tertiary brittle-ductile transition. Tectonics 2, 239–263 (1983)

    ADS  Article  Google Scholar 

  6. Jolivet, L. et al. Midcrustal shear zones in postorogenic extension: example from the Tyrrhenian Sea. J. Geophys. Res. 103, 12123–12160 (1998)

    ADS  Article  Google Scholar 

  7. Wernicke, B. in The Cordilleran Orogen; Conterminous U.S. (eds Burchfiel, B. C., Lipman, P. W. & Zoback, M. L.) 553–581 (The Geology of North America, Geological Society of America, Boulder, Colorado, 1992)

    Google Scholar 

  8. Anderson, J. L. in Metamorphism and Crustal Evolution of the Western United States (ed. Ernst, W. G.) 502–525 (Prentice Hall, Engelwood Cliffs, New Jersey, 1987)

    Google Scholar 

  9. Buck, W. R. & Poliakov, A. N. B. Abyssal hills formed by stretching oceanic lithosphere. Nature 392, 272–275 (1998)

    ADS  CAS  Article  Google Scholar 

  10. Burov, E. B. & Diament, M. The effective elastic thickness (Te) of continental lithosphere: What does it really mean? J. Geophys. Res. 100, 3905–3927 (1995)

    ADS  Article  Google Scholar 

  11. Ellis, S. & Stöckhert, B. Elevated stresses and creep rates beneath the brittle–ductile transition caused by seismic faulting in the upper crust. J. Geophys. Res. 109, B05407 (2004) doi:10.1029/2003JB002744

    ADS  Article  Google Scholar 

  12. Shawki, T. G. An energy criterion for the onset of shear localization in thermal viscoplastic material, Part II: applications and implications. J. Appl. Mech. 61, 538–547 (1994)

    ADS  MathSciNet  Article  Google Scholar 

  13. Lister, G. S., Banga, G. & Feenstra, A. Metamorphic core complexes of the Cordilleran type in the Cyclades, Aegean Sea. Geology 12, 221–225 (1984)

    ADS  Article  Google Scholar 

  14. Ramsay, G. in Thrust and Nappe Tectonics (eds McClay, K. R. & Price, N. J.) 293–309 (Special Publication No. 9, Geological Society, Boulder, Colorado, 1981)

    Google Scholar 

  15. Cook, F. A. et al. LITHOPROBE crustal reflection structure of the southern Canadian Cordillera 1, foreland thrust and fold belt to Fraser River fault. Tectonics 11, 12–35 (1992)

    ADS  Article  Google Scholar 

  16. Wernicke, B. Low-angle normal faults in the Basin and Range province: Nappe tectonics in an extending orogen. Nature 291, 645–648 (1981)

    ADS  Article  Google Scholar 

  17. Gueydan, F., Leroy, Y., Jolivet, L. & Agard, P. Analysis of continental midcrustal strain localization induced by microfracturing and reaction-softening. J. Geophys. Res. 108, 2064 (2003) doi:10.1029/2001JB000611

    ADS  Article  Google Scholar 

  18. Butler, R. W. H. Thrust tectonics, deep structure and crustal subduction in the Alps and Himalayas. J. Geol. Soc. Lond. 143, 857–873 (1986)

    Article  Google Scholar 

  19. Laubscher, H. P. Detachment, Shear and Compression in the Central Alps 191–211 (Memoir 158, Geological Society of America, Boulder, Colorado, 1983)

    Google Scholar 

  20. Meissner, R. & Mooney, W. Weakness of the lower continental crust: a condition for delamination, uplift, and escape. Tectonophysics 296, 47–60 (1998)

    ADS  Article  Google Scholar 

  21. Rosenbaum, G., Regenauer-Lieb, K. & Weinberg, R. Continental extension: from core complexes to rigid block faulting. Geology 33, 609–612 (2005)

    ADS  Article  Google Scholar 

  22. Royden, L. H. et al. Surface deformation and lower crustal flow in eastern Tibet. Science 276, 788–790 (1997)

    CAS  Article  Google Scholar 

  23. Wobus, C., Heimsath, A., Whipple, K. & Hodges, K. Active out-of-sequence thrust faulting in the central Nepalese Himalaya. Nature 434, 1008–1011 (2005)

    ADS  CAS  Article  Google Scholar 

  24. Jackson, J. Strength of the continental lithosphere; time to abandon the jelly sandwich? GSA Today 12, 4–10 (2002)

    Article  Google Scholar 

  25. Regenauer-Lieb, K. & Yuen, D. Normal-mode excitation by Sumatran earthquake and short-timescale instabilities: Thermo-mechanics and rheology of the Earth's lithosphere. Eos 86 (18; Jt. Assem. Suppl.), abstr. U53A–02 (2005).

  26. Regenauer-Lieb, K. & Yuen, D. A. Positive feedback of interacting ductile faults from coupling of equation of state, rheology and thermal-mechanics. Phys. Earth Planet. Inter. 142, 113–135 (2004)

    ADS  Article  Google Scholar 

  27. ABAQUS/Standard Theory Manual Version 6.1 (Hibbit, Karlsson and Sorenson, Inc., Pawtucket, Rhode Island, 2000).

  28. Rice, J. R. in Theoretical and Applied Mechanics (ed. Koiter, W. T.) 207–220 (North-Holland, Amsterdam, 1977)

    Google Scholar 

  29. Rudnicki, J. W. & Rice, J. R. Conditions for localization of deformation in pressure-sensitive dilatant materials. J. Mech. Phys. Solids 23, 371–394 (1975)

    ADS  Article  Google Scholar 

  30. Needleman, A. & Tvergaard, V. Analyses of plastic flow deformation in metals. Appl. Mech. Rev. 45, 3–18 (1992)

    ADS  Article  Google Scholar 

Download references


We thank V. Lyakhovsky for comments on the manuscript. K.R.-L. acknowledges support from the Johannes Gutenberg-University Mainz and the Predictive Mineral Discovery Cooperative Research Centre.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Klaus Regenauer-Lieb.

Ethics declarations

Competing interests

Reprints and permissions information is available at The authors declare no competing financial interests.

Supplementary information

Supplementary Notes 1

This file contains Appendix 1, which is details of the Supplementary Equations. (DOC 166 kb)

Supplementary Notes 2

Appendix 2. Results of an extension model similar to Figure 3 but with surface heat flow of 60mW/m2. (PDF 543 kb)

Supplementary Notes 3

Appendix 3. Profiles at two time steps for the 70mW/m2 extension model (profile locations are indicated in Figure 3). (PDF 404 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Regenauer-Lieb, K., Weinberg, R. & Rosenbaum, G. The effect of energy feedbacks on continental strength. Nature 442, 67–70 (2006).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing