Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Brittle Tectonics: A Nonlinear Dynamic System

Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27737-5_44-2

Definition of the Subject

Brittle deformation is the primary mode of deformation of the Earth’s crust. At the long timescale it is manifested by faulting and on the short timescale by earthquakes. It is one of the best-known examples of a system exhibiting self-organized criticality. A full understanding of this system is essential to the evaluation of earthquake hazard.

Introduction

The upper part of the Earth’s crust is brittle and under a state of all-round compression. It responds to deformation by faulting: the formation and propagation of shear cracks. The crack walls support normal stresses, and hence fault propagation must overcome not only the rupture resistance of the fault tips but friction between its interior interfaces. This friction is usually velocity weakening, such that any slippage results in stick–slip instability. The resulting dynamically running crack-like shear instability radiates elastic waves, producing the shaking known as an earthquake. Thus brittle...

Keywords

Large Earthquake Stress Drop Slip Rate Small Earthquake Cellular Automaton Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access

Bibliography

Primary Literature

  1. Ackermann RV, Schlische RW, Withjack MO (2001) The geometric and statistical evolution of normal fault systems: an experimental study of the effects of mechanical layer thickness on scaling laws. J Struct Geol 23:1803–1819CrossRefADSGoogle Scholar
  2. Bak P, Tang C (1989) Earthquakes as a self-organized critical phenomenon. J Geophys Res 94:15635–15637CrossRefADSGoogle Scholar
  3. Bak P, Tang C, Weisenfeld K (1987) Self-organized criticality: An explanation of 1/f noise. Phys Rev Lett 59:381–384CrossRefADSGoogle Scholar
  4. Beeler NM, Hickman SH, Wong TF (2001) Earthquake stress drop and laboratory-inferred interseismic strength recovery. J Geophys Res-Solid Earth 106:30701–30713CrossRefGoogle Scholar
  5. Brown SR, Scholz CH, Rundle JB (1991) A simplified spring-block model of earthquakes. Geophys Res Lett 18:215–218CrossRefADSGoogle Scholar
  6. Burridge R, Knopoff L (1967) Model and theoretical seismicity. Bull Seism Soc Am 57:341–362Google Scholar
  7. Carlson JM, Langer JS (1989) Properties of earthquakes generated by fault dynamics. Phys Rev Lett 62:2632–2635CrossRefADSGoogle Scholar
  8. Christensen K, Olami Z (1992) Variation of the Gutenberg-Richter B values and nontrivial temporal correlations in a spring-block model for earthquakes. J Geophys Res-Solid Earth 97:8729–8735CrossRefGoogle Scholar
  9. Cowie PA, Scholz CH, Edwards M, Malinverno A (1993) Fault strain and seismic coupling on midocean ridges. J Geophys Res-Solid Earth 98:17911–17920CrossRefGoogle Scholar
  10. Cowie PA, Sornette D, Vanneste C (1995) Multifractal scaling properties of a growing fault population. Geophys J Int 122:457–469CrossRefADSGoogle Scholar
  11. Davison F, Scholz C (1985) Frequency-moment distribution of earthquakes in the Aleutian Arc: a test of the characteristic earthquake model. Bull Seismol Soc Am 75:1349–1362Google Scholar
  12. Davy P, Sornette A, Sornette D (1990) Some consequences of a proposed fractal nature of continental faulting. Nature 348:56–58CrossRefADSGoogle Scholar
  13. Dawers NH, Anders MH, Scholz CH (1993) Growth of normal faults – displacement-length scaling. Geology 21:1107–1110CrossRefADSGoogle Scholar
  14. Gupta A, Scholz CH (2000) Brittle strain regime transition in the afar depression: implications for fault growth and seafloor spreading. Geology 28:1087–1090CrossRefADSGoogle Scholar
  15. Hanks TC (1977) Earthquake stress drops, ambient tectonic stresses and stresses that drive plate motions. Pure Appl Geophys 115:441–458CrossRefADSGoogle Scholar
  16. Jensen HJ (1998) Self-organized criticality: emergent complex behavior in physical and biological systems. Cambridge University Press, CambridgeCrossRefMATHGoogle Scholar
  17. Olami Z, Feder HJS, Christensen K (1992) Self-organized criticality in a continuous, nonconservative cellular automaton modeling earthquakes. Phys Rev Lett 68:1244–1247CrossRefADSGoogle Scholar
  18. Pacheco JF, Sykes LR (1992) Seismic moment catalog of large shallow earthquakes, 1900 to 1989. Bull Seismol Soc Am 82:1306–1349Google Scholar
  19. Pacheco JF, Scholz CH, Sykes LR (1992) Changes in frequency-size relationship from small to large earthquakes. Nature 355:71–73CrossRefADSGoogle Scholar
  20. Schlische RW, Young SS, Ackermann RV, Gupta A (1996) Geometry and scaling relations of a population of very small rift-related normal faults. Geology 24:683–686CrossRefADSGoogle Scholar
  21. Scholz CH (1968) The frequency-magnitude relation of microfracturing in rock and its relation to earthquakes. Bull Seismol Soc Am 58:399–415Google Scholar
  22. Scholz CH (1994) A reappraisal of large earthquake scaling. Bull Seismol Soc Am 84:215–218Google Scholar
  23. Scholz CH (1997a) Earthquake and fault populations and the calculation of brittle strain. Geowissenschaften 3–4:124–130Google Scholar
  24. Scholz CH (1997b) Size distributions for large and small earthquakes. Bull Seismol Soc Am 87:1074–1077Google Scholar
  25. Scholz CH (1998a) Earthquakes and friction laws. Nature 391:37–42CrossRefADSGoogle Scholar
  26. Scholz CH (1998b) A further note on earthquake size distributions. Bull Seismol Soc Am 88:1325–1326Google Scholar
  27. Scholz CH (2002) The mechanics of earthquakes and faulting, 2nd edn. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  28. Scholz CH, Lawler TM (2004) Slip tapers at the tips of faults and earthquake ruptures. Geophys Res Lett 31, L21609. doi:10.1029/2004GL021030CrossRefADSGoogle Scholar
  29. Scholz CH, Dawers NH, Yu JZ, Anders MH (1993) Fault growth and fault scaling laws – preliminary-results. J Geophys Res-Solid Earth 98:21951–21961CrossRefGoogle Scholar
  30. Shaw BE, Scholz CH (2001) Slip-length scaling in large earthquakes: observations and theory and implications for earthquake physics. Geophys Res Lett 28:2995–2998CrossRefADSGoogle Scholar
  31. Shaw BE, Wesnouski SG (2008) Slip-length scaling in large earthquakes: the role of deep penetrating slip below the seismogenic layer. Bull Seismol Soc Am 98:1633–1641CrossRefGoogle Scholar
  32. Sornette D, Virieux J (1992) Linking short-timescale deformation to long-timescale tectonics. Nature 357:401–403CrossRefADSGoogle Scholar
  33. Spyropoulos C, Griffith WJ, Scholz CH, Shaw BE (1999) Experimental evidence for different strain regimes of crack populations in a clay model. Geophys Res Lett 26:1081–1084CrossRefADSGoogle Scholar
  34. Spyropoulos C, Scholz CH, Shaw BE (2002) Transition regimes for growing crack populations. Phys Rev E 65:056105. doi:10.1103/PhysRevE.65.056105CrossRefADSGoogle Scholar
  35. Stein RS (1999) The role of stress transfer in earthquake occurrence. Nature 402:605–609CrossRefADSGoogle Scholar
  36. Townend J, Zoback MD (2000) How faulting keeps the crust strong. Geology 28:399–402CrossRefADSGoogle Scholar
  37. Tse S, Rice J (1986) Crustal earthquake instability in relation to the depth variation of frictional slip properties. J Geophys Res 91:9452–9472CrossRefADSGoogle Scholar
  38. Turcotte DL (1999) Seismicity and self-organized criticality. Phys Earth Planet Inter 111:275–293CrossRefADSGoogle Scholar

Books and Reviews

  1. Sornette D (2003) Critical phenomena in natural systems: Chaos, fractals, self-organization, and disorder. Springer, BerlinGoogle Scholar
  2. Turcotte DL (1997) Fractals and chaos in geology and geophysics. Cambridge University Press, Cambridge/New YorkCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Lamont-Doherty Earth ObservatoryColumbia UniversityNew YorkUSA