Skip to main content

First Steps Towards Modeling a Multi-Scale Earth System

  • Chapter
Advances in Geocomputing

Recent advances in computational geodynamics are applied to explore the link between Earth’s heat, its chemistry and its mechanical behavior. Computational thermal-mechanical solutions are now allowing us to understand Earth patterns by solving the basic physics of heat transfer. This approach is currently used to solve basic convection patterns of terrestrial planets. Applying the same methodology to smaller scales delivers promising similarities between observed and predicted structures which are often the site of mineral deposits. The new approach involves a fully coupled solution to the energy, momentum and continuity equations of the system at all scales, allowing the prediction of fractures, shear zones and other typical geological patterns out of a randomly perturbed initial state. The results of this approach are linking a global geodynamic mechanical framework over regional-scale mineral deposits down to the underlying micro-scale processes. Ongoing work includes the challenge of incorporating chemistry into the formulation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • ABAQUS/Standard 2000), 384pp., Hibbit, Karlsson and Sorenson Inc.

    Google Scholar 

  • Abraham, F. F., et al. (1998), Spanning the length scales in dynamic simulation, Computers in Physics, 12, 538–546.

    Article  Google Scholar 

  • Aifantis, E. C. (1987), The physics of plastic deformation, International Journal of Plasticity, 3, 211–247.

    Article  Google Scholar 

  • Albert, R. A., and R. J. Phillips (2002), Time-dependent effects in elastoviscoplastic models of loaded lithosphere, Geophysical Journal International, 151, 612–621.

    Article  Google Scholar 

  • Axen, G. J., and J. Selverstone (1994), Stress state and fluid-pressure level along the whipple detachment fault, California, Geology, 22, 835–838.

    Article  Google Scholar 

  • Ben-Zion, Y., and C. G. Sammis (2003), Characterization of fault zones, Pure and Applied Geophysics, 160, 677.

    Article  Google Scholar 

  • Benallal, A., and D. Bigoni (2004), Effects of temperature and thermo-mechanical couplings on material instabilities and strain localization of inelastic materials, Journal of the Mechanics and Physics of Solids, 52, 725.

    Article  Google Scholar 

  • Brace, F. W., and D. L. Kohlstedt (1980), Limits on lithospheric stress imposed by laboratory experiments, Journal of Geophysical Research, 50, 6248–6252.

    Article  Google Scholar 

  • Braeck, S., and Y. Y. Podladchikov (2007), Spontaneous thermal runaway as an ultimate failure mechanism of materials, Physical Review Letters, 98.

    Google Scholar 

  • Bulatov, V., et al. (1998), Connecting atomistic and mesoscale simulations of crystal plasticity, Nature, 391, 669–672.

    Article  Google Scholar 

  • Bunge, H. P., M. A. Richards, and J. R. Baumgardner (1997), A sensitivity study of three-dimensional spherical mantle convection at 108 Rayleigh number: effects of depth-dependent viscosity, heating mode, and endothermic phase change, Journal of Geophysical Research, 102, 11991–12007.

    Article  Google Scholar 

  • Byerlee, J. D. (1978), Friction of rocks, Pure and Applied Geophysics, 116, 615–626.

    Article  Google Scholar 

  • Caristan, Y. (1982), The transition from high temperature creep to fracture in Maryland Diabase, Journal of Geophysical Research, 87, 6781–6790.

    Article  Google Scholar 

  • Christiansen, P. P., and D. D. Pollard (1997), Nucleation, growth and structural development of mylonitic shear zones in granitic rock, Journal of Structural Geology, 19, 1159–1172.

    Article  Google Scholar 

  • Chrysochoos, A., et al. (1989), Plastic and dissipated work and stored energy, Nuclear Engineering and Design, 114, 323–333.

    Article  Google Scholar 

  • Dieterich, J. H. (1979), Modeling of rock friction .1. Experimental results and constitutive equations, Journal of Geophysical Research, 84, 2161–2168.

    Article  Google Scholar 

  • Enquist, E., and Z. Huang (2003), Heterogeneous multiscale method: a general methodology for multiscale modeling, Physical Reviews B, 67, 092101: 092101–092104.

    Article  Google Scholar 

  • Fleck, N. A., and J. W. Hutchinson (2001), A reformulation of strain gradient plasticity, Journal of the Mechanics and Physics of Solids, 49, 2245–2271.

    Article  Google Scholar 

  • Fleitout, L., and C. Froidevaux (1980), Thermal and mechanical evolution of shear zones, Journal of Structural Geology, 2, 159–164.

    Article  Google Scholar 

  • Gao, H., et al. (1999), Modeling plasticity at the micrometer scale, Naturwissenschaften, 86, 507–515.

    Article  Google Scholar 

  • Gruntfest, I. J. (1963), Thermal feedback in liquid flow – plane shear at constant stress, Transactions of the Society of Rheology, 7, 195–207.

    Article  Google Scholar 

  • Hall, C. E., et al. (2003), Catastrophic initiation of subduction following forced convergence across fracture zones, Earth and Planetary Science Letters, 212, 15–30.

    Article  Google Scholar 

  • Handy, M. R., et al. (2001), Rheology and geodynamic modelling: the next step forward, International Journal of Earth Sciences, 90, 149–156.

    Article  Google Scholar 

  • Hobbs, B. E., et al. (1986), Earthquakes in the ductile regime, Pure and Applied Geophysics, 124, 310–336.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Kaus, B., and Y. Podladchikov (2006), Initiation of localized shear zones in viscoelastoplastic rock, Journal of Geophysical Research, 111, B04412, doi:04410.01029/02005JB003652.

    Article  Google Scholar 

  • Kohlstedt, D. L., et al. (1995), Strength of the lithosphere: constraints imposed by laboratory measurements, Journal of Geophysical Research, 100, 17587–17602.

    Article  Google Scholar 

  • Kusznir, N. J. (1991), The distribution of stress with depth in the lithosphere: thermo-rheological and geodynamic constraints, Philosophical Transaction of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences, 337, 95–110.

    Article  Google Scholar 

  • Kusznir, N. J., and R. G. Park (1984a), Intraplate lithosphere deformation and the strength of the lithosphere, Geophysical Journal of the Royal Astronomical Society, 79, 513–538.

    Google Scholar 

  • Kusznir, N. J., and R. G. Park (1984b), The strength of intraplate lithosphere, Physics of the Earth and Planetary Interiors, 36, 224–235.

    Google Scholar 

  • Lemonds, J., and A. Needleman (1986), Finite element analyses of shear localization in rate and temperature dependent solids, Mechanics of Materials, 5, 339–361.

    Article  Google Scholar 

  • Li, J., et al. (2002), Atomistic mechanisms governing elastic limit and incipient plasticity in crystals, Nature, 418, 307–310.

    Article  Google Scholar 

  • Lu, C., and I. Jackson (1998), Seismic-frequency laboratory measurements of shear mode viscoelasticity in crustal rocks II: thermally stressed quartzite and granite, Pure and Applied Geophysics, 153, 441.

    Article  Google Scholar 

  • Lyakhovsky, V., et al. (1997), Distributed damage, faulting, and friction, Journal of Geophysical Research-Solid Earth, 102, 27635–27649.

    Article  Google Scholar 

  • Martyushev, L. M., and V. D. Seleznev (2006), Maximum entropy production principle in physics, chemistry and biology, Physics Reports-Review Section of Physics Letters, 426, 1–45.

    Google Scholar 

  • McKenzie, D. P. (1977), The initiation of trenches: a finite amplitude instability, in Island Arcs Deep Sea Trenches and Back-Arc Basins, edited by M. Talwani and W. C. Pitman, pp. 57–61, Maurice Ewing Ser. Vol. 1.

    Google Scholar 

  • Nagel, T. J., and W. R. Buck (2007), Control of rheological stratification on rifting geometry: a symmetric model resolving the upper plate paradox, International Journal of Earth Sciences, 96, 1047–1057.

    Article  Google Scholar 

  • Ogawa, M. (1987), Shear instability in a viscoelastic material as the cause of deep focus earthquakes, Journal of Geophysical Research, 92, 13801–13810.

    Article  Google Scholar 

  • Ord, A., and B. E. Hobbs (1989), The strength of the continental crust, detatchment zones and the development of plastic instabilities, Tectonophysics, 158, 269–289.

    Article  Google Scholar 

  • Pinto da Cunha, A. (1993), Scale Effect in Rock Masses 93, A.A. Balkema, Rotterdam.

    Google Scholar 

  • Prager, W. (1959), An Introduction to Plasticity, Addison Wesley, Reading, Massachusetts.

    Google Scholar 

  • Regenauer-Lieb, K., and D. Yuen (1998), Rapid conversion of elastic energy into shear heating during incipient necking of the lithosphere, Geophysical Research Letters, 25, 2737–2740.

    Article  Google Scholar 

  • Regenauer-Lieb, K., and D. A. Yuen (2003), Modeling shear zones in geological and planetary sciences: solid- and fluid- thermal- mechanical approaches, Earth Science Reviews, 63, 295–349.

    Article  Google Scholar 

  • Regenauer-Lieb, K., and D. A. Yuen (2004), Positive feedback of interacting ductile faults from coupling of equation of state, rheology and thermalmechanics, Physics of Earth and Planetary Interiors, 142, 113–135.

    Article  Google Scholar 

  • Regenauer-Lieb, K., and D. Yuen (2006), Quartz rheology and short time-scale crustal instabilities, Pure and Applied Geophysics, 163, 1915–1932.

    Article  Google Scholar 

  • Regenauer-Lieb, K., et al. (2001), The initiation of subduction: criticality by addition of water? Science, 294, 578–580.

    Article  Google Scholar 

  • Regenauer-Lieb, K., et al. (2004), On the thermodynamics of listric faults, Earth Planets and Space, 56, 1111–1120.

    Google Scholar 

  • Regenauer-Lieb, K., et al. (2006a), From point defects to plate tectonic faults, Philosophical Magazine, 86, 3371–3392.

    Google Scholar 

  • Regenauer-Lieb, K., et al. (2006b), The effect of energy feedbacks on continental strength, Nature, 442, 67–70.

    Google Scholar 

  • Rice, J. R. (1977), The localization of plastic deformation, in Theoretical and Applied Mechanics, edited by W. T. Koiter, pp. 207–220, North-Holland, Amsterdam.

    Google Scholar 

  • Shawki, T. G. (1994), An energy criterion for the onset of shear localization in thermal viscoplastic material, Part II: Applications and implications, Journal of Applied Mechanics, 61, 538–547.

    Article  Google Scholar 

  • Shawki, T. G., and R. J. Clifton (1989), Shear band formation in thermal viscoplastic materials, Mechanics of Materials, 8, 13–43.

    Article  Google Scholar 

  • Shimada, M. (1993), Lithosphere strength inferred from fracture strength of rocks at high confining pressures and temperatures, Tectonophysics, 217, 55–64.

    Article  Google Scholar 

  • Siret, D., et al. (2008), PreMDB, a thermodynamically consistent material database as a key to geodynamic modelling, Geotechnica Acta, DOI 10.1007/s11440-008-0065-0.

    Google Scholar 

  • Tullis, T. E., et al. (1991), Flow laws for polyphase aggregates from end member flow laws, Journal of Geophysical Research, 96, 8081–8096.

    Article  Google Scholar 

  • Wang, Y. (2001), Heat flow pattern and lateral variations of lithosphere strength in China mainland: constraints on active deformation, Physics of the Earth and Planetary Interiors, 126, 121–146.

    Article  Google Scholar 

  • Weinberg, R., et al. (2007), Mantle detachment faults and the break-up of cold continental lithosphere, Geology, 35, 1035–1038.

    Article  Google Scholar 

  • Yuen, D. A., et al. (1978), Shear deformation zones along major transform faults and subducting slabs, Geophysical Journal of the Royal Astronomical Society, 54, 93–119.

    Google Scholar 

  • Ziegler, H. (1983), An Introduction to Thermomechanics, North Holland, Amsterdam.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Regenauer-Lieb, K. et al. (2009). First Steps Towards Modeling a Multi-Scale Earth System. In: Advances in Geocomputing. Lecture Notes in Earth Sciences, vol 119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85879-9_1

Download citation

Publish with us

Policies and ethics