A diagram illustrating the interseismic, preseismic, and postseismic periods for a subduction zone earthquake cycle. The over-riding plate bends to accumulate stress during the interseismic period and rebounds back to its previous position to release stress.

The earthquake cycle refers to the phenomenon that earthquakes repeatedly occur on the same fault as the result of continual stress accumulation and periodic stress release.[1][2] Earthquake cycles can occur on a variety of faults including subduction zones and continental faults.[3][4] Depending on the size of the earthquake, an earthquake cycle can last decades, centuries, or longer.[1][5] The Parkfield portion of the San Andreas fault is a well-known example where similarly located M6.0 earthquakes have been instrumentally recorded every 30–40 years.[6]

Theory

After Harry F. Reid proposed the elastic-rebound theory in 1910 based on the surface rupture record from the 1906 San Francisco earthquake, and accumulated geodetic data demonstrated continual stress loading from the plate motion, a theory of the "cyclic" earthquake re-occurrence began to form in the late twentieth century.[1]

Stress accumulation and elastic rebound

Earthquake-cycle theory combines the stress-accumulation hypothesis and elastic-rebound theory.[1] A complete earthquake cycle can be divided into interseismic, preseismic, coseismic and postseismic periods.[1] During the interseismic period, stress accumulates on a locked fault due to plate motion.[2] In the preseismic period, this stress is approaching the rupture limit, and some earthquake precursors may occur.[1] When this stress finally exceeds the rupture limit, the fault will start to move and both sides rebound to their previous positions, releasing their accumulated stress via an earthquake. During the postseismic period, the relaxation of the other parts of the fault caused by redistributed stresses may cause afterslip.[1] Because Earth's plate movement constantly stresses faults, this cycle will likely repeat.[2]

A diagram of the spring-slider model. A block on a rough surface is connected to a spring that is pulled at a constant velocity u.

Spring-slider model

The simple spring-slider coupling model helps explain the recurrence of earthquake cycles.[1] The premise is that a stationary block in contact with a rough surface is dragged by a spring that is pulled at a constant velocity. This process causes stress to continuously accumulate on the spring. Once the drag force exceeds the static friction limit f(0), the block will slide along the ground surface.[1][2] Assuming that the kinematic friction is smaller than the static friction,[7] the block's initial movement is unstable, which is equivalent to a fault rupture. Once the block comes to rest at a new location, stress begins to accumulate again. Coupled systems of spring-slider models have successfully reproduced the Gutenberg–Richter law.[7]

Rupture variety

Although simple models of earthquake recurrence are fully predictable, many real-world factors can significantly alter cycle length, including uneven stress accumulation, time-varying crustal strengths, and fluid migration.[2][8] Under different conditions, stress can be released via rapid ruptures, aseismic slow slips, or earthquake swarms. Understanding the irregularity of these different slip types is crucial to comprehending earthquakes cycles.[8][9][10]

Observations

So far, complete earthquake cycles have barely been recorded, and geodetic and geology data become key sources for the analysis of different stages in an earthquake cycle.[1]

Geodetic measurement

Geodetic measurements are important tools to verify the interseismic stage stress accumulation and postseismic stage stress redistribution in earthquake cycles. For example, the GPS data collected in the past few decades has shown steady strain accumulations for the San Andreas fault system[11] and continuous surface uplift of the Nankai subduction zone's overriding plate caused by the stress accumulation.[1] Analysis of the slip rate on the southern San Andreas fault system with the interferometric radar (InSAR) technology also suggests that this fault may be approaching the end of its interseismic stage.[12] A significant amount of aseismic slow slip and creep during the interseismic period has also been discovered on both subduction zones and continental faults through GPS and InSAR measurements.[8]

The Wallace Creek offset across the San Andreas Fault. The present channel offset represents a recent fault rupture. There are multiple abandoned channels on the left of the current channel representing multiple ancient fault ruptures.

Geologic evidence

Geological surveys are another method used to uncover ancient earthquake reoccurrences. The multiple offsets of the stream channels across the San Andreas fault at Wallace creek on Carrizo Plain is the classic evidence of fault rupture recurrence.[1][4] Once an earthquake happened, the stream across the fault was cut off, leaving the offset channel abandoned, and a new channel forms. A set of abandoned channels has been discovered and is believed to be the remains of multiple ancient earthquake cycles.[1] The sediment record is another key clue to finding ancient earthquakes. Examples are the coastal-uplift records of Muroto point near the Nankai subduction zone, caused by repeated megathrust earthquakes over many centuries; coastal uplift and tsunami records near the Hikurangi subduction margin, caused by 10 potential subduction earthquakes in the past 7000 years;[3] and sediment accumulation recorded by 24 successive earthquakes on the strike-slip Alpine fault in the past 8000 years.[13] Three repeated continental earthquakes in the Mongolia within the past 50,000 years have also been discovered from sediment-layer offset and growth records.[14]

Dynamic fault modeling

More complicated than the spring-slider model, dynamic modeling of fault ruptures based on the constitutive framework (such as the rate-and-state friction law and elastic equations) is widely used in earthquake-cycle analysis.[10] Dynamic fault modeling allows us to examine the role of different fault parameters in rupture-cycle behavior[10] and reproduces many seismic observations.[8]

Rate-and-state friction law

The rate-and-state friction law is widely applied in dynamic fault models[8][10][15] and critically influences a fault's possible slip features.[10][16] The rate-and-state friction law assumes that the friction coefficient is a function of both the sliding velocity (the rate) and the system conditions (the state).[16][17][18][19] In the rate-and-state friction law, the friction coefficient increases when the slip velocity abruptly increases and then gradually decreases to reach a new steady value.[16] The rate-and-state friction relation is influenced by a set of factors including thermal activation, the real area of contact (at the atomic scale), and molecular bonding effects.[16][19][20]

Recent developments

Dynamic fault modeling helps explain the mechanisms driving earthquake cycles. Based on the rate-and-state friction law, the transfer from slow-slip events to rapid rupture earthquakes related to geometric and elastic parameters of the fault zone has been discovered.[10] A computationally faster quasi-dynamic model that simplifies stress transfers allows new models taking plastic effects into consideration.[15] However, comparison of quasi-dynamic models with fully dynamic models of the same systems shows that the modeling approach has significant impacts on the proposed earthquake-cycle slip features.[21]

Earthquake prediction applications

Although many scientists still view earthquake predictions as challenging or impossible,[22] earthquake-cycle theories and modeling have long been consulted to produce hazard forecast values. For example, empirical models have been applied to forecast the likelihood of large earthquakes hitting the San Francisco Bay area in the near future.[23] In addition, scientists have established a fully dynamic model for the Parkfield portion of the San Andreas Fault. This model successfully reproduces complete earthquake cycles that match the last half century's seismic records and shows promise for future earthquake predictions.[5]

References

  1. 1 2 3 4 5 6 7 8 9 10 11 12 13 Scholz, Christopher H., ed. (2002). "The seismic cycle". The Mechanics of Earthquakes and Faulting (2 ed.). Cambridge: Cambridge University Press. pp. 244–299. ISBN 978-0-511-81851-6. Retrieved 2022-02-15.
  2. 1 2 3 4 5 Kanamori, Hiroo; Brodsky, Emily E (2004-07-13). "The physics of earthquakes". Reports on Progress in Physics. 67 (8): 1429–1496. Bibcode:2004RPPh...67.1429K. doi:10.1088/0034-4885/67/8/r03. ISSN 0034-4885. S2CID 250877470.
  3. 1 2 Clark, Kate; Howarth, Jamie; Litchfield, Nicola; Cochran, Ursula; Turnbull, Jocelyn; Dowling, Lisa; Howell, Andrew; Berryman, Kelvin; Wolfe, Franklin (2019-06-01). "Geological evidence for past large earthquakes and tsunamis along the Hikurangi subduction margin, New Zealand". Marine Geology. 412: 139–172. Bibcode:2019MGeol.412..139C. doi:10.1016/j.margeo.2019.03.004. ISSN 0025-3227. S2CID 135147628.
  4. 1 2 Sieh, Kerry E.; Jahns, Richard H. (1984-08-01). "Holocene activity of the San Andreas fault at Wallace Creek, California". GSA Bulletin. 95 (8): 883–896. Bibcode:1984GSAB...95..883S. doi:10.1130/0016-7606(1984)95<883:HAOTSA>2.0.CO;2. ISSN 0016-7606.
  5. 1 2 Barbot, Sylvain; Lapusta, Nadia; Avouac, Jean-Philippe (2012-05-11). "Under the Hood of the Earthquake Machine: Toward Predictive Modeling of the Seismic Cycle". Science. 336 (6082): 707–710. Bibcode:2012Sci...336..707B. doi:10.1126/science.1218796. PMID 22582259. S2CID 21183948.
  6. ↑ Murray, Jessica; Langbein, John (2006-09-01). "Slip on the San Andreas Fault at Parkfield, California, over Two Earthquake Cycles, and the Implications for Seismic Hazard". Bulletin of the Seismological Society of America. 96 (4B): S283–S303. Bibcode:2006BuSSA..96S.283M. doi:10.1785/0120050820. ISSN 0037-1106.
  7. 1 2 Burridge, R.; Knopoff, L. (1967-06-01). "Model and theoretical seismicity". Bulletin of the Seismological Society of America. 57 (3): 341–371. Bibcode:1967BuSSA..57..341B. doi:10.1785/BSSA0570030341. ISSN 0037-1106.
  8. 1 2 3 4 5 Avouac, Jean-Philippe (2015-05-30). "From Geodetic Imaging of Seismic and Aseismic Fault Slip to Dynamic Modeling of the Seismic Cycle". Annual Review of Earth and Planetary Sciences. 43 (1): 233–271. Bibcode:2015AREPS..43..233A. doi:10.1146/annurev-earth-060614-105302. ISSN 0084-6597.
  9. ↑ Lohman, R. B.; McGuire, J. J. (2007). "Earthquake swarms driven by aseismic creep in the Salton Trough, California". Journal of Geophysical Research: Solid Earth. 112 (B4). Bibcode:2007JGRB..112.4405L. doi:10.1029/2006JB004596. hdl:1912/3621. ISSN 2156-2202.
  10. 1 2 3 4 5 6 Barbot, Sylvain (2019-10-05). "Slow-slip, slow earthquakes, period-two cycles, full and partial ruptures, and deterministic chaos in a single asperity fault". Tectonophysics. 768: 228171. Bibcode:2019Tectp.76828171B. doi:10.1016/j.tecto.2019.228171. ISSN 0040-1951. S2CID 202197354.
  11. ↑ Smith, Bridget; Sandwell, David (June 2003). "Coulomb stress accumulation along the San Andreas Fault system". Journal of Geophysical Research: Solid Earth. 108 (B6): 2296. Bibcode:2003JGRB..108.2296S. doi:10.1029/2002jb002136. ISSN 0148-0227.
  12. ↑ Fialko, Yuri (22 June 2006). "Interseismic strain accumulation and the earthquake potential on the southern San Andreas fault system". Nature. 441 (7096): 968–971. Bibcode:2006Natur.441..968F. doi:10.1038/nature04797. ISSN 1476-4687. PMID 16791192. S2CID 4432269.
  13. ↑ Berryman, Kelvin R.; Cochran, Ursula A.; Clark, Kate J.; Biasi, Glenn P.; Langridge, Robert M.; Villamor, Pilar (2012-06-29). "Major Earthquakes Occur Regularly on an Isolated Plate Boundary Fault". Science. 336 (6089): 1690–1693. Bibcode:2012Sci...336.1690B. doi:10.1126/science.1218959. ISSN 0036-8075. PMID 22745426. S2CID 206539939.
  14. ↑ Bollinger, Laurent; Klinger, Yann; Forman, Steven L.; Chimed, Odonbaatar; Bayasgalan, Amgalan; Munkhuu, Ulziibat; Davaasuren, Ganzorig; Dolgorsuren, Tulga; Enkhee, Bayarsaikhan; Sodnomsambuu, Demberel (2021-09-08). "25,000 Years long seismic cycle in a slow deforming continental region of Mongolia". Scientific Reports. 11 (1): 17855. Bibcode:2021NatSR..1117855B. doi:10.1038/s41598-021-97167-w. ISSN 2045-2322. PMC 8426405. PMID 34497291.
  15. 1 2 Erickson, Brittany A.; Dunham, Eric M.; Khosravifar, Arash (2017-12-01). "A finite difference method for off-fault plasticity throughout the earthquake cycle". Journal of the Mechanics and Physics of Solids. 109: 50–77. Bibcode:2017JMPSo.109...50E. doi:10.1016/j.jmps.2017.08.002. ISSN 0022-5096.
  16. 1 2 3 4 Segall, Paul (2010-01-04). Earthquake and Volcano Deformation. Princeton University Press. doi:10.1515/9781400833856. ISBN 978-1-4008-3385-6.
  17. ↑ Ruina, Andy (1983-12-10). "Slip instability and state variable friction laws". Journal of Geophysical Research: Solid Earth. 88 (B12): 10359–10370. Bibcode:1983JGR....8810359R. doi:10.1029/jb088ib12p10359. ISSN 0148-0227.
  18. ↑ Dieterich, James H. (1979). "Modeling of rock friction: 1. Experimental results and constitutive equations". Journal of Geophysical Research. 84 (B5): 2161. Bibcode:1979JGR....84.2161D. doi:10.1029/jb084ib05p02161. ISSN 0148-0227.
  19. 1 2 Barbot, Sylvain (2022). "A Rate-, State-, and Temperature-Dependent Friction Law With Competing Healing Mechanisms". Journal of Geophysical Research: Solid Earth. 127 (11). doi:10.1029/2022JB025106. S2CID 253608123.
  20. ↑ Ronsin, Olivier; Coeyrehourcq, Karine Labastie (2001-06-08). "State, rate and temperature–dependent sliding friction of elastomers". Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences. 457 (2010): 1277–1294. arXiv:cond-mat/0005531. Bibcode:2001RSPSA.457.1277R. doi:10.1098/rspa.2000.0718. S2CID 15920211.
  21. ↑ Thomas, Marion Y.; Lapusta, Nadia; Noda, Hiroyuki; Avouac, Jean-Philippe (2014). "Quasi-dynamic versus fully dynamic simulations of earthquakes and aseismic slip with and without enhanced coseismic weakening". Journal of Geophysical Research: Solid Earth. 119 (3): 1986–2004. Bibcode:2014JGRB..119.1986T. doi:10.1002/2013JB010615. ISSN 2169-9356.
  22. ↑ Geller, Robert J. (1997-12-01). "Earthquake prediction: a critical review". Geophysical Journal International. 131 (3): 425–450. Bibcode:1997GeoJI.131..425G. doi:10.1111/j.1365-246X.1997.tb06588.x. ISSN 0956-540X.
  23. ↑ Bufe, Charles G.; Varnes, David J. (1993). "Predictive modeling of the seismic cycle of the Greater San Francisco Bay Region". Journal of Geophysical Research: Solid Earth. 98 (B6): 9871–9883. Bibcode:1993JGR....98.9871B. doi:10.1029/93JB00357. ISSN 2156-2202.
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