Skip to main content
SpringerLink
Log in

Seismicity, Critical States of: From Models to Practical Seismic Hazard Estimates Space

  • Reference work entry
Encyclopedia of Complexity and Systems Science

Definition of the Subject

The most fundamental question in earthquake science is whether earthquake prediction is possible. Related issues include the following: Can a prediction of earthquakes solely based on the emergence of seismicity patterns be reliable? In other words, is there a single or several “magic” parameters, which become anomalous prior to a large earthquake? Are pure observational methods without specific physical understanding, like the pattern recognition approach of Keilis–Borok and co-workers [41], sufficient? Taking into account that earthquakes are monitored continuously only for about 100 years and the best available data sets (“earthquake catalogs”) cover only a few decades, it seems questionable to forecast earthquakes solely on the basis of observed seismicity patterns . This is because large earthquakes have recurrence periods of decades to centuries; consequently, data sets for most regions include less than ten large events making a reliable...

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 3,499.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 549.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Abbreviations

Bayesian analysis:

A model estimation technique that accounts for incomplete knowledge. Bayes' theorem is a mathematical formulation of how an a priori estimate of the probability of an event can be updated, if a new information becomes available.

Critical earthquake concept:

The occurrence of large earthquakes may be described in terms of statistical physics and thermodynamics. In this view, an earthquake can be interpreted as a critical phase transition in a system with many degrees of freedom. The preparatory process is characterized by acceleration of the seismic moment release and growth of the spatial correlation length as in the percolation model. This interpretation of earthquake occurrence is referred to as the critical earthquake process.

Earthquake forecast/prediction:

The forecast or prediction of an earthquake is a statement about time, hypocenter location, magnitude, and probability of occurrence of an individual future event within reasonable error ranges.

Fault model :

A fault model calculates the evolution of slip, stress, and related quantities on a fault segment or a fault region. The range of fault models varies from conceptual models of cellular automaton or slider-block type to detailed models for particular faults.

Probability:

A quantitative measure of the likelihood for an outcome of a random process. In the case of repeating a random experiment a large number of times (e.?g. flipping a coin), the probability is the relative frequency of a possible outcome (e.?g. head). A different view of probability is used in the ? Bayesian analysis.

Seismic hazard :

The probability that a given magnitude (or peak ground acceleration) is exceeded in a seismic source zone within a pre-defined time interval, e.?g. 50 years, is denoted as the seismic hazard.

Self-organized criticality:

Self-organized criticality (SOC) as introduced by Bak [2] is the ability of a system to organize itself in the vicinity of a critical point independently of values of physical parameters of the system and initial conditions. Self-organized critical systems are characterized by various power law distributions. Examples include models of sandpiles and forest-fires.

Bibliography

  1. Aki K, Richards PG (2002) Quantitative seismology. University ScienceBooks, Sansalito

    Google Scholar 

  2. Bak P (1996) How Nature Works. The science of self-organisedcriticality. Springer, New York

    Google Scholar 

  3. Bak P, Tang C (1989) Earthquakes as a phenomenon of self-organisedcriticality. J Geophys Res 94:15635–156637

    ADS  Google Scholar 

  4. Båth M (1965) Lateral inhomogeneities in the upper mantle. Tectonophysics2:483–514

    Google Scholar 

  5. Ben-Zion Y (1996) Stress, slip, and earthquakes in models of complexsingle-fault systems incorporating brittle and creep deformations. J Geophys Res 101:5677–5706

    ADS  Google Scholar 

  6. Ben-Zion Y (2001) Dynamic rupture in recent models of earthquake faults. J MechPhys Solids 49:2209–2244

    ADS  Google Scholar 

  7. Ben-Zion Y (2003) Appendix 2, Key Formulas in Earthquake Seismology. In: LeeWHK, Kanamori H, Jennings PC, Kisslinger C (eds) International Handbook of Earthquake and Engineering Seismology, Part B. Academic Press, San Diego, pp 1857–1875

    Google Scholar 

  8. Ben-Zion Y, Lyakhovsky V (2002) Accelerated seismic release and related aspectsof seismicity patterns on earthquake faults. Pure Appl Geophys 159:2385–2412

    ADS  Google Scholar 

  9. Ben-Zion Y, Lyakhovsky V (2006) Analysis of aftershocks in a lithosphericmodel with seismogenic zone governed by damage rheology. J Geophys Int 165:197–210; doi:10.1111/j.1365-246X2006.02878.x

    ADS  Google Scholar 

  10. Ben-Zion Y, Rice JR (1993) Earthquake failure sequences along a cellularfault zone in a three-dimensional elastic solid containing asperity and nonasperity regions. J Geophys Res98:14109–14131

    ADS  Google Scholar 

  11. Ben-Zion Y, Dahmen K, Lyakhovsky V, Ertas D, Agnon A (1999) Self-drivenmode switching of earthquake activity on a fault system. Earth Plan Sci Lett 172:11–21

    ADS  Google Scholar 

  12. Ben-Zion Y, Eneva M, Liu Y (2003) Large Earthquake Cycles and IntermittentCriticality On Heterogeneous Faults Due To Evolving Stress and Seismicity. J Geophys Res 108:2307; doi:10.1029/2002JB002121

    Google Scholar 

  13. Bernardo JM, Smith AFM (1994) Bayesian Theory. Wiley,Chichester

    Google Scholar 

  14. Binney JJ, Dowrick NJ, Fisher AJ, Newman MEJ (1993) The theory of criticalphenomena. Oxford University Press, Oxford

    Google Scholar 

  15. Bowman DD, Oullion G, Sammis CG, Sornette A, Sornette D (1998) Anobservational test of the critical earthquake concept. J Geophys Res 103:24359–24372

    ADS  Google Scholar 

  16. Brace WF (1960) An extension of the Griffith theory of fracture to rocks. J Geophys Res 65:3477–3480

    ADS  Google Scholar 

  17. Bufe CG, Varnes DJ (1993) Predicitive modeling of the seismic cycle of thegreater San Francisco Bay region. J Geophys Res 98:9871–9883

    ADS  Google Scholar 

  18. Burridge R, Knopoff L (1967) Model and theoretical seismicity. Bull Seim SocAm 57:341–371

    Google Scholar 

  19. Byerlee JD (1978) Friction of rocks. Pure Appl Geophys116:615–616

    ADS  Google Scholar 

  20. Chinnery M (1963) The stress changes that accompany strike-slipfaulting. Bull Seim Soc Am 53:921–932

    Google Scholar 

  21. Corral Á (2004) Long-term clustering, scaling, and universality in thetemporal occurrence of earthquakes. Phys Rev Lett 92:108501; doi:10.1103/PhysRevLett.92.108501

  22. Dahmen K, Ertas D, Ben-Zion Y (1998) Gutenberg–Richter andcharacteristic earthquake behavior in simple mean-field models of heterogeneous faults. Phys Rev E 58:1494–1501

    ADS  Google Scholar 

  23. Daley DJ, Vere-Jones D (1988) An Introduction to the Theory of PointProcesses, Springer Series: Probability and its Applications. Springer, Heidelberg

    Google Scholar 

  24. Dieterich JH (1994) A constitutive law for earthquake production and itsapplication to earthquake clustering. J Geophys Res 99:2601–2618

    ADS  Google Scholar 

  25. Dor O, Rockwell TK, Ben-Zion Y (2006) Geologic observations of damageasymmetry in the structure of the San Jacinto, San Andreas and Punchbowl faults in southern California: A possible indicator for preferred rupturepropagation direction. Pure Appl Geophys 163:301–349; doi:10.1007/s00024-005-0023-9

    ADS  Google Scholar 

  26. Ellsworth WL, Matthews MV, Nadeau RM, Nishenko SP, Reasenberg PA, Simpson RW(1999) A physically based earthquake recurrence model for estimation of long-term earthquake probabilities. US Geol Surv Open-File Rept,pp 99–522

    Google Scholar 

  27. Fisher DS, Dahmen K, Ramanathan S, Ben-Zion Y (1997) Statistics of earthquakesin simple models of heterogeneous faults. Phys Rev Lett 78:4885–4888

    ADS  Google Scholar 

  28. Geller RJ, Jackson DD, Kagan YY, Mulargia F (1997) Earthquakes cannot bepredicted. Science 275:1616–1617

    Google Scholar 

  29. Gumbel EJ (1960) Multivariate Extremal Distributions. Bull Inst Int Stat37:471–475

    MathSciNet  Google Scholar 

  30. Gutenberg B, Richter CF (1956) Earthquake magnitude, intensity, energy andacceleration. Bull Seismol Soc Am 46:105–145

    Google Scholar 

  31. Hainzl S, Zöller G (2001) The role of disorder and stress concentration innonconservative fault systems. Phys A 294:67–84

    Google Scholar 

  32. Hainzl S, Zöller G, Kurths J (1999) Similar power laws for fore- andaftershock sequences in a spring-block model for earthquakes. J Geophys Res 104:7243–7253

    Google Scholar 

  33. Hainzl S, Zöller G, Kurths J (2000) Self-organization ofspatio-temporal earthquake clusters. Nonlin Proc Geophys 7:21–29

    Google Scholar 

  34. Hainzl S, Zöller G, Kurths J, Zschau J (2000) Seismic quiescence as anindicator for large earthquakes in a system of self-organized criticality. Geophys Res Lett 27:597–600

    Google Scholar 

  35. Hainzl S, Zöller G, Scherbaum F (2003) Earthquake clusters resulting fromdelayed rupture propagation in finit fault segments. J Geophys Res 108:2013; doi:10.1029/2001JB000610

  36. Hillers G, Mai PM, Ben-Zion Y, Ampuero JP (2007) Statistical Properties ofSeismicity Along Fault Zones at Different Evolutionary Stages. J Geophys Int 169:515–533; doi:10.1111/j.1365-246X2006.03275.x

    ADS  Google Scholar 

  37. Huang J, Turcotte DL (1990) Are earthquakes an example of deterministic chaos?Geophys Res Lett 17:223–226

    ADS  Google Scholar 

  38. Jaumé SC, Sykes LR (1999) Evolving towards a critical point: A review ofaccelerating seismic moment/energy release prior to large and great earthquakes. Pure Appl Geophys 155:279–306

    Google Scholar 

  39. Jones LM, Molnar P (1979) Some characteristics of foreshocks and theirpossible relation to earthquake prediction and premonitory slip on faults. J Geophys Res 84:3596–3608

    ADS  Google Scholar 

  40. Kagan YY, Knopoff L (1978) Statistical study of the occurrence of shallowearthquakes. J Geophys R Astron Soc 55:67–86

    Google Scholar 

  41. Keilis-Borok VI, Soloviev AA (2003) Nonlinear Dynamics of theLithosphere and Earthquake Prediction, Springer Series in Synergetics. Springer, Heidelberg

    Google Scholar 

  42. Lomnitz-Adler J (1999) Automaton models of seismic fracture: constraintsimposed by the magnitude-frequency relation. J Geophys Res 98:17745–17756

    Google Scholar 

  43. Main IG, O'Brian G, Henderson JR (2000) Statistical physics of earthquakes:Comparison of distribution exponents for source area and potential energy and the dynamic emergence of log-periodic quanta. J Geophys Res105:6105–6126

    ADS  Google Scholar 

  44. Matthews MV, Ellsworth WL, Reasenberg PA (2002) A Brownian model forrecurrent earthquakes. Bull Seism Soc Am 92:2233–2250

    Google Scholar 

  45. Narteau C, Shebalin P, Hainzl S, Zöller G, Holschneider M (2003) Emergence ofa band-limited power law in the aftershock decay rate of a slider-block model. Geophys Res Lett 30:1568; doi:10.1029/2003GL017110

  46. Nur A, Booker JR (1972) Aftershocks caused by pore fluid flow? Science175:885–887

    ADS  Google Scholar 

  47. Okada Y (1992) Internal deformation due to shear and tensile faults ina half space. Bull Seism Soc Am 82:1018–1040

    Google Scholar 

  48. Olami Z, Feder HS, Christensen K (1992) Self-organized criticality ina continuous, nonconservative cellular automaton modeling earthquakes. Phys Rev Lett 68:1244–1247

    ADS  Google Scholar 

  49. Omori F (1894) On the aftershocks of earthquakes. J Coll Sci Imp Univ Tokyo7:111–200

    Google Scholar 

  50. Patel JK, Kapadia CH, Owen DB (1976) Handbook of statisticaldistributions. Marcel Dekker, New York

    Google Scholar 

  51. Reasenberg P (1985) Second-order moment of central Californiaseismicity. J Geophys Res 90:5479–5495

    ADS  Google Scholar 

  52. Reid HF (1910) The Mechanics of the Earthquake, The California Earthquake ofApril 18, 1906. Report of the State Investigation Commission, vol 2. Carnegie Institution of Washington, Washington

    Google Scholar 

  53. Rundle JB, Klein W, Turcotte DL, Malamud BD (2000) Precursory seismicactivation and critical point phenomena. Pure Appl Geophys 157:2165–2182

    ADS  Google Scholar 

  54. Saleur H, Sammis CG, Sornette D (1996) Discrete scale invariance, complexfractal dimensions, and log-periodic fluctuations in seismicity. J Geophys Res 101:17661–17677

    ADS  Google Scholar 

  55. Savage JC, Svarc JL, Prescott WH (1999) Geodetic estimates of fault slip ratesin the San Francisco Bay area. J Geophys Res 104:4995–5002

    ADS  Google Scholar 

  56. Scholz CH (1998) Earthquakes and friction laws. Nature391:37–42

    ADS  Google Scholar 

  57. Shcherbakov R, Turcotte DL (2004) A damage mechanics model foraftershocks. Pure Appl Geophys 161:2379; doi:10.1007/s00024-004-2570-x

  58. Shin TC, Teng TL (2001) An overview of the 1999, Chichi, Taiwan,earthquake. Bull Seismol Soc Am 91:895–913

    Google Scholar 

  59. Sornette D (2004) Self-organization and Disorder: Concepts &Tools, Springer Series in Synergetics. Springer, Heidelberg

    Google Scholar 

  60. Sornette D, Sammis CG (1995) Complex critical exponents from renormalizationgroup theory of earthquakes: Implication for earthquake predicitions. J Phys 1(5):607–619

    Google Scholar 

  61. Sornette D, Sornette A (1999) Renormalization of earthquakeaftershocks. Geophys Res Lett 6:1981–1984

    ADS  Google Scholar 

  62. Field EH et al. (2007) Special Issue: Regional Earthquake Likelihood Models. Seismol ResLett 78:1

    Google Scholar 

  63. Steacy SJ, McCloskey J, Bean CJ, Ren JW (1996) Heterogeneity ina self-organized critical earthquake model. Geophys Res Lett 23:383–386

    ADS  Google Scholar 

  64. Turcotte DL (1997) Fractals and chaos in geology and geophysics. CambridgeUniversity Press, New York

    Google Scholar 

  65. Turcotte DL, Newman WI, Shcherbakov R (2003) Micro and macroscopic models ofrock fracture. J Geophys Int 152:718–728

    ADS  Google Scholar 

  66. Utsu T (2002) Statistical features of seismicity. In: Int Assoc Seismol& Phys Earth's Interior (ed) International handbook of earthquake and engineering seismology, vol 81A. Academic Press, San Diego, pp 719–732

    Google Scholar 

  67. Utsu T, Ogata Y, Matsu'ura RS (1995) The centenary of the Omori formula fora decay law of aftershock activity. J Phys Earth 43:1–33

    Google Scholar 

  68. Wesnousky SG (1994) The Gutenberg–Richter or characteristic earthquakedistribution, which is it? Bull Seismol Soc Am 90:525–530; 84:1940–1959

    Google Scholar 

  69. Wiemer S, Baer M (2000) Mapping and removing quarry blast events from seismiccatalogs: Examples from Alaska, the Western United States, and Japan. Bull Seismol Soc Am 90:525–530

    Google Scholar 

  70. Working Group on California Earthquake Probabilities (2003) Earthquakeprobabilities in the San Francisco Bay region. US Geol Survey Open File Report 03–214, US Geological Survey

    Google Scholar 

  71. Wyss M (1997) Cannot earthquakes be predicted? Science278:487

    ADS  Google Scholar 

  72. Wyss M, Habermann RE (1988) Precursory seismic quiescence. Pure Appl Geophys126:319–332

    ADS  Google Scholar 

  73. Zaliapin I, Liu Z, Zöller G, Keilis-Borok V, Turcotte DL (2002) Onincrease of earthquake correlation length prior to large earthquakes in California. Comp Seismol 33:141–161

    Google Scholar 

  74. Zöller G, Ben-Zion Y, Holschneider M, Hainzl S (2007) Estimating recurrencetimes and seismic hazard of large earthquakes on an individual fault. J Geophys Int 170:1300–1310; doi:10.1111/j.1365-246X200703480.x

  75. Zöller G, Hainzl S (2001) Detecting premonitory seismicity patterns based oncritical point dynamics. Nat Hazards Earth Syst Sci 1:93–98

    Google Scholar 

  76. Zöller G, Hainzl S (2002) A systematic spatiotemporal test of thecritical point hypothesis for large earthquakes. Geophys Res Lett 29:1558; doi:10.1029/2002GL014856

  77. Zöller G, Hainzl S, Kurths J (2001) Observation of growing correlation lengthas an indicator for critical point behavior prior to large earthquakes. J Geophys Res 106:2167–2175

    Google Scholar 

  78. Zöller G, Hainzl S, Kurths J, Zschau J (2002) A systematic test onprecursory seismic quiescence in Armenia. Nat Hazards 26:245–263

    Google Scholar 

  79. Zöller G, Holschneider M, Ben-Zion Y (2004) Quasi-static andquasi-dynamic modeling of earthquake failure at intermediate scales. Pure Appl Geophys 161:2103–2118; doi:10.1007/s00024-004-2551-0

  80. Zöller G, Holschneider M, Ben-Zion Y (2005) The role of heterogeneities asa tuning parameter of earthquake dynamics. Pure Appl Geophys 162:1027; doi:10.1007/s00024-004-2660-9

  81. Zöller G, Hainzl S, Holschneider M, Ben-Zion Y (2005) Aftershocks resultingfrom creeping sections in a heterogeneous fault. Geophys Res Lett 32:L03308; doi:10.1029/2004GL021871

  82. Zöller G, Hainzl S, Ben-Zion Y, Holschneider M (2006) Earthquake activityrelated to seismic cycles in a model for a heterogeneous strike-slip fault. Tectonophys 423:137–145; doi:10.1016/j.tecto.2006.03.007

Download references

Acknowledgments

We thank Jürgen Kurths, James R. Rice, Frank Scherbaum, Karin Dahmen, Donald L. Turcotte, and many others for useful discussions. GZ and MH acknowledge support from the collaborative research center “Complex Nonlinear Processes” (SFB 555) of the German Research Society (DFG). SH acknowledges support from the DFG-project SCHE280/14 and the EU-project SAFER. YBZ acknowledges support from the National Science Foundation, the United States Geological Survey, and the Southern California Earthquake Center. GZ and YBZ thank the Kavli Institute for Theoretical Physics, UC Santa Barbara, for hospitality during a 2005 program on Friction, Fracture and Earthquake Physics, and partial support based on NSF grant PHY99–0794. We thank James R. Holliday, Vladimir Keilis-Borok and Willie Lee for providing comments on the paper.

Author information

Authors and Affiliations

  1. Institute of Mathematics and Centre for Dynamics of Complex Systems, University of Potsdam, Potsdam, Germany

    Gert Zöller & Matthias Holschneider

  2. GFZ German Research Centre for Geosciences, Potsdam, Germany

    Sebastian Hainzl

  3. Department of Earth Sciences, University of Southern California, Los Angeles, USA

    Yehuda Ben-Zion

Authors
  1. Gert Zöller
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sebastian Hainzl
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yehuda Ben-Zion
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Matthias Holschneider
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag

About this entry

Cite this entry

Zöller, G., Hainzl, S., Ben-Zion, Y., Holschneider, M. (2009). Seismicity, Critical States of: From Models to Practical Seismic Hazard Estimates Space. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_466

Download citation

Publish with us

Policies and ethics

Search

Navigation