Skip to main content
SpringerLink
Log in

Record-Breaking Intervals: Detecting Trends in the Incidence of Self-Similar Earthquake Sequences

  • Published:
Pure and Applied Geophysics Aims and scope Submit manuscript

Abstract

We introduce a method of resolving temporal incidence trends in earthquake sequences. We have developed a catalog partitioning method based on canonical earthquake scaling relationships, and have further developed a metric based on record-breaking interval (RBI) statistics to resolve increasing and decreasing seismicity in time series of earthquakes. We calculated the RBI metric over fixed-length sequences of earthquake intervals and showed that the length of those sequences is related to the magnitude of the earthquake to which the method is sensitive—longer sequences resolve large earthquakes, shorter sequences resolve small-magnitude events. This sequence length effectively constitutes a local temporal catalog constraint, and we show that spatial constraints can be defined from rupture length scaling. We have applied the method to several high-profile earthquakes and have shown that it consistently resolves aftershock sequences after a period of accelerating seismicity before the targeted mainshock. The method also suggests a minimum detectable (forecastable) mainshock magnitude on the basis of the catalog’s minimum completeness magnitude \(m_{\rm c}\).

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  • Ammon, C. J., Lay, T., Kanamori, H., and Cleveland, M.: A rupture model of the 2011 off the Pacific coast of Tohoku Earthquake, Earth Planets Space, 63, 693–696, doi:10.5047/eps.2011.05.015, 2011.

  • ANSS: Advanced National Seismic System (ANSS) Catalog Search, http://www.ncedc.org/anss/catalog-search.html, 2013.

  • Båth, M.: Lateral inhomogeneities in the upper mantle, Tectonophysics, 2, 483–514, 1965.

  • Benestad, R. E.: Record-values, nonstationarity tests and extreme value distributions, Global Planet. Change, 44, 11–26, doi:10.1016/j.gloplacha.2004.06.002, 2004.

  • Benestad, R. E.: A simple test for changes in statistical distributions, Eos, 89, 389–390, doi:10.1029/2008EO410002, 2008.

  • Bouchon, M., Karabulut, H., Aktar, M., Özalaybey, S., Schmittbuhl, J., and Bouin, M.-P.: Extended Nucleation of the 1999 Mw 7.6 Izmit Earthquake, Science , 331, 877–880, doi:10.1126/science.1197341, 2011.

  • Bowman, D. D., Ouillon, G., Sornette, A., and Sornette, D.: An observational test of the critical earthquake concept, Journal of Geophysical Research-Solid Earth, 103, 24359–24372, 1998.

  • Bufe, C. G. and Varnes, D. J.: Predictive modeling of the seismic cycle of the greater San Francisco Bay-region, Journal of Geophysical Research-Solid Earth, 98, 9871–9833, 1993.

  • Bufe, C. G., Nishenko, S., and Varnes, D. J.: Seismicity trends and potential for large earthquakes in the Alaska-Aleutian region, PAGEOPH, 142, 83–99, 1994.

  • Dieterich, J. H.: Preseismic fault slip and earthquake prediction, J. Geophys. Res., 83, 3940–3948, 1978.

  • Felzer, K. and Brodsky, E.: Decay of aftershock density with distance indicates triggering by dynamic stress, Nature, 441, 735–738, doi:10.1038/nature04799, 2006.

  • Fraser-Smith, A. C., Bernardi, A., McGill, P. R., Ladd, M. E., Helliwell, R. A., and Villard, Jr., O. G.: Low-frequency magnetic field measurements near the epicenter of the Ms 7.1 Loma Prieta Earthquake, Geophysical Research Letters, 17, 1465–1468, doi:10.1029/GL017i009p01465, 1990.

  • Gabrielov, A., Dmitrieva, O., Keilis-Borok, V., Kossobokov, V., Kouznetsov, I., Levshina, T., Mirzoev, K., Molchan, G., Negmatullaev, S., Pisarenko, V., Prozoroff, A., Renehard, W., Rotwain, I., Shebalin, P., Shnirman, M., and Schreider, S.: Algorithms of long-term earthquakes’ prediction, in: CRESIS, p. 61, Lima, Peru, 1986.

  • Glick, N.: Breaking records and breaking boards, Am. Math Monthly, 85, 2–26, 1978.

  • Gran, J. D., Rundle, J. B., and Turcotte, D. L.: A possible mechanism for aftershocks: time-dependent stress relaxation in a slider-block model, Geophys. J. Int., 191, 459–466, doi:10.1111/j.1365-246X.2012.05628.x, 2012.

  • Guarino, A., Garcimartin, A., and Ciliberto, S.: An experimental test of the critical behaviour of fracture precursors, Eur. Phys. J. B., 6, 13–24, 1998.

  • Gutenberg, B., and Richter, C. F.: Seismicity of the Earth and Associated Phenomenon, Princeton Univ. Press, 2nd edn., 1954.

  • Hardebeck, J. L., Felzer, K. R., and Michael, A. J.: Improved tests reveal that the accelerating moment release hypothesis is statistically insignificant, J. Geophys. Res., 113, doi:10.1029/2007JB005410, 2008.

  • Helmstetter, A.: Is Earthquake Triggering Driven by Small EArthquakes?, Physical Review Letters, 91, 058 501–1:4, doi:10.1103/PhysRevLett.91.058501, 2003.

  • Holliday, J. R., Turcotte, D. L., and Rundle, J. B.: Self-similar branching of aftershock sequences, Physica A, 387, 933–943, 2008.

  • Jolliffe, I. T. and Stephenson, D. B.: Forecast Verification, a Practitioner’s Guide in Atmospheric Science, Wiley, 2003.

  • Kagan, Y.: Aftershock Zone Scaling, Bull. Seismol. Soc. Am., 92, 641–655, doi:10.1785/0120010172, 2002.

  • King, C.-Y.: Gas geochemistry applied to earthquake prediction: An overview, Journal of Geophysical Research: Solid Earth, 91, 12269–12281, doi:10.1029/JB091iB12p12269, http://onlinelibrary.wiley.com/doi/10.1029/JB091iB12p12269/full, 2012.

  • Li, Y.-G., Vidale, J. E., Day, S. M., Oglesby, D. D., and Cochran, E.: Postseismic Fault Healing on the Rupture Zone of the 1999 M 7.1 Hector Mine, California, Earthquake, Bulletin of the Seismological Society of America, 93, 854–869, doi:10.1785/0120020131, 2003.

  • Marone, C., Vidale, J. E., and Ellsworth, W. L.: Fault healing inferred from time dependent variations in source properties of repeating earthquakes, Geophysical Research Letters, 22, 3095–3098, doi:10.1029/95GL03076, 1995.

  • Michalske, T. A. and Frieman, S. W.: A Molecular Mechanism for Stress Corrosion in Vitreous Silica, Journal of the American Ceramic Society, 66, 284–288, doi:10.1111/j.1151-2916.1983.tb15715.x, 1983.

  • Niu, F., Silver, P. G., Daley, T. M., Cheng, X., and Majer, E. L.: Preseismic velocity changes observed from active source monitoring at the Parkfield SAFOD drill site, Nature, 454, 204–208, doi:10.1038/nature07111, 2008.

  • Ogata, Y.: Statistical models for earthquake occurrences and residual analysis for point processes, J. Am. Stat. Assoc., 83, 9–27, 1988.

  • Omori, F.: On the aftershocks of earthquakes, Journal of the College of Science, Imperial University of Tokyo, 7, 111–200, 1894.

  • Pacheco, J. F., Scholz, C. H., and Sykes, L. R.: Changes in frequency-size relationship from small to large earthquakes, Nature, 355, 71–73, 1992.

  • Pegler, G. and Das, S.: Analysis of the relationship between seismic moment and fault length for large crustal strike-slip earthquakes between 1977–92, Geophys. Res. Lett., 23, 905–908, 1996.

  • Redner, S. and Petersen, M. R.: Role of global warming on the statistics of record-breaking temperatures, Phys. Rev. E, 74, doi:10.1103/PhysRevE.74.061114, 2006.

  • Rundle, J. B.: Derivation of the Complete Gutenberg–Richter Magnitude-Frequency Relation Using the Principle of Scale Invariance, J. Geophys. Res., 94, 12,337–12,342, 1989.

  • Rundle, P. B., Rundle, J. B., Tiampo, K. F., Donnelan, A., and Turcotte, D. L.: Virtual California: Fault model, frictional parameters, applications. Pure and Applied Geophysics, 163, 1819–1846, 2006.

  • Rundle, J. B., Holliday, J. R., Yoder, M. R., Sachs, M. K., Donnellan, A., Turcotte, D. L., Tiampo, K. F., Klein, W., and Kellogg, L. H.: Earthquake Precursors: Activation or Quiescence, Geophys. J. Int., 187, 225–236, 2011.

  • Saleur, H., Sammis, C. G., and Sornette, D.: Renormalization group theory of earthquakes, Proc. Geoph., 3, 102–109, 1996.

  • Sammis, C., Sornette, D., and Saleur, H.: Reduction and Predictability of Natural Disasters, vol. XXV, chap. Complexity and earthquake forecasting, SFI Studies in the Sciences of Complexity, pp. 143–156, Addison-Wesley, 1996.

  • Scholz, C. H.: The Mechanics of Earthquakes and Faulting, Cambridge University Press, 2012.

  • Schubnel, A., Thompson, B. D., Fortin, J., Guguen, Y., and Young, R. P.: Fluid-induced rupture experiment on Fontainebleau sandstone: Premonitory activity, rupture propagation, and aftershocks, Geophys. Res. Lett., 34, 2007.

  • Shcherbakov, R. and Turcotte, D. L.: A modified form of Båth’s law, Bull. Seis. Soc. Am, 94, 1968–1975, doi:10.1785/012003162, 2004.

  • Shcherbakov, R., Yakovlev, G., Turcotte, D. L., and Rundle, J. B.: Model for the distribution of aftershock interoccurrence times, Phys. Rev. Let., 95, doi:10.1103/PhysRevLett.95.218501, 2005.

  • Shcherbakov, R., Turcotte, D. L., and Rundle, J. B.: Scaling properties of the Parkfield aftershock sequence, Bull. Seis. Soc. Am., 96, S376–S384, doi:10.1785/0120050815, 2006.

  • Sornette, D. and Sammis, C.: Complex critical exponents from renormalization group theory of earthquakes : Implications for earthquake predictions, J. Phys. I., 5, 607–619, 1995.

  • Sykes, L. and Jaume, S.: Seismic activity on neighboring faults as a long-term precursor to large earthquakes in the San Francisco Bay Area, Nature, 348, 595–599, 1990.

  • Tahir, M., Grasso, J.-R., and Amorese, D.: The largest aftershock: How strong, how far away, how delayed?, Geophysical Research Letters, 39, L04 301, doi:10.1029/2011GL050604, 2012.

  • Tata, M.: On outstanding values in a sequence of random variables, Z. Wahrsch. verw. Geb., 12, 9–20, doi:10.1007/BF00538520, 1969.

  • USGS: USGS Tohoku (2011) earthquake data, http://earthquake.usgs.gov/earthquakes/recenteqsww/Quakes/usc0001xgp.php, 2011.

  • USGS: The Parkfield, California, Earthquake Experiment, http://earthquake.usgs.gov/research/parkfield/index.php, (last modified 2012), 2012.

  • USGS: USGS Significant Earthquake and News Headlines Archive, http://earthquake.usgs.gov/earthquakes/eqinthenews/, accessed April 2013.

  • USGS: USGS 2004 Parkfield earthquake data, http://earthquake.usgs.gov/research/parkfield/2004.php, accessed 23 April 2013, 2013.

  • USGS: USGS Historic Earthquakes: Coalinga 1983k m=6.4, http://earthquake.usgs.gov/earthquakes/states/events/1983_05_02.php, (last viewed 2014), 2014.

  • USGS-CSEP: Collaboratory for the Study of Earthquake Predictability, http://www.cseptesting.org/, accessed April 2013, 2013.

  • Utsu, T.: A method for determining the value of b in a formula log n = a - bM showing the magnitude-frequency relation for earthquakes, Geophys. Bull. Hokkaido Univ., 13, 99–103, 1965.

  • Utsu, T.: Estimation of parameters for recurrence models of earthquakes, Earthquake Res. Insti. Univ. Tokyo, 59, 53–66, 1984.

  • Van Aalsburg, J., Turcotte, D. L., Newman, W. I., and Rundle, J. B.: Record-breaking earthquakes, Bull. Seimol. Soc. Am., 100, 1800–1805, doi:10.1785/0120090015, 2010.

  • Wall, J. and Jenkins, C.: Practical Statistics for Astronomers, Cambridge Observing Handbooks for Research Astronomers, 2003.

  • Yikilmaz, M. B., Turcotte, D. L., Yakovlev, G., Rundle, J. B., and Kellogg, L. H.: Virtual California earthquake simulations: simple models and their application to an observed sequence of earthquakes, Geophysical Journal International, 180, 734–742, doi:10.1111/j.1365-246X.2009.04435.x, 2010.

  • Yikilmaz, M. B., Heien, E. M., Turcotte, D. L., Rundle, J. B., and Kellogg, L. H.: A fault and seismicity based composite simulation in northern California, Nonlin. Proc. Geophys., 18, 955–966, doi:10.5194/npg-18-955-2011, 2011.

  • Yoder, M. R.: Record-breaking earthquake precursors, Ph.D. thesis, University of California Davis, 2011.

  • Yoder, M. R.: Earthquakes: Risk Factors, Seismic Effects, and Economic Consequences, chap. Chapter 9, 1/F and the Earthquake Problem: Earthquake Forecasting and a Framework for Predictability – Past, Present and Future, pp. 195–227, Nova Science Publishers Inc, New York, 2014.

  • Yoder, M. R., Turcotte, D. L., and Rundle, J. B.: Record-breaking earthquake intervals in a global catalog and an aftershock sequence, Nonlin. Processes Geophys., 17, 169–176, 2010.

  • Yoder, M. R., Van Aalsburg, J., Turcotte, D. L., Abaimov, S., and Rundle, J. B.: Statistical Variability and Tokunaga Branching of Aftershock Sequences Utilizing BASS Model Simulations, Pure and Applied Geophysics, pp. 1–17, doi:10.1007/s00024-011-0411-2, 2011.

  • Yoder, M. R., Holliday, J. R., Turcotte, D. L., and Rundle, J. B.: A geometrical frequency-magnitude scaling transition: Measuring \(b=1.5\) for large earthquakes, Tectonophys., 532–535, 157–174, doi:10.1016/j.tecto.2012.01.034, 2012a.

  • Yoder, M. R., Turcotte, D. L., and Rundle, J. B.: Extreme Events and Natural Hazards: The Complexity Perspective, Geophys. Monogr. Ser., vol. 196, chap. Earthquakes: Complexity and extreme events, pp. 17–26, AGU, Washington D.C., doi:10.1029/2011GM001071, 2012b.

  • Yoder, M. R., Rundle, J., and Glasscoe, M.: Near-field ETAS constraints and applications to seismic hazard assessment, Pure Ap. Geophys., (In press), doi:10.1007/s00024-014-0785-z, 2014a.

  • Yoder, M. R., Turcotte, D. L., and Rundle, J. B.: Scaling constraints to detect pre-seismic acceleration: A record-breaking framework for earthquake predictability, Tectonophys., (under revision), 2014b.

  • Zalohar, J.: Explaining the physical origin of the Båth’s law, Journal of Structural Geology, 60, 30–45, (published online 2013, published in print 2014), 2014.

  • Zang, A., Wanger, F. C., Stanchits, S., Dresen, G., Andersen, R., and Haidekker, M. A.: Source analysis of acoustic emissions in Aue granite cores under symmetric and asymmetric compressive loads, Phys. Rev. E, 135, 1113–1130, doi:10.1046/j.1365-246X.1998.00706.x, 1998.

Download references

Acknowledgments

This work is supported by JPL Subcontract 1291967 and NASA Grant NNX08AF69G. I (MRY) would also like to thank my very good friend Alger for his support and friendship during the course of this research.

Author information

Authors and Affiliations

  1. Department of Physics, University of California Davis, Davis, CA, 95616, USA

    Mark R. Yoder & John B. Rundle

  2. Department of Earth and Planetary Sciences, University of California Davis, Davis, CA, 95616, USA

    John B. Rundle

  3. Santa Fe Institute, Santa Fe, NM, 87501, USA

    John B. Rundle

Authors
  1. Mark R. Yoder
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. John B. Rundle
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mark R. Yoder.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (pdf 2839 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yoder, M.R., Rundle, J.B. Record-Breaking Intervals: Detecting Trends in the Incidence of Self-Similar Earthquake Sequences. Pure Appl. Geophys. 172, 2215–2235 (2015). https://doi.org/10.1007/s00024-014-0887-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00024-014-0887-7

Keywords

Search

Navigation