The Pattern of Earthquake Magnitude Clustering Based on Interevent Distance and Time
DOI:
https://doi.org/10.26443/seismica.v3i2.1094Keywords:
Earthquake Statistics, Magnitude Clustering, Seismology, rupture physicsAbstract
The clustering of earthquake magnitudes is poorly understood compared to spatial and temporal clustering. Better understanding of correlations between earthquake magnitudes could provide insight into the mechanisms of earthquake rupture and fault interactions, and improve earthquake forecasting models. In this study we present a novel method of examining how seismic magnitude clustering occurs beyond the next event in the catalog and evolves with time and space between earthquake events. We first evaluate the clustering signature over time and space using double-difference located catalogs from Southern and Northern California. The strength of magnitude clustering appears to decay linearly with distance between events and logarithmically with time. The signature persists for longer distances (more than 50km) and times (several days) than previously thought, indicating that magnitude clustering is not driven solely by repeated rupture of an identical fault patch or Omori aftershock processes. The decay patterns occur in all magnitude ranges of the catalog and are demonstrated across multiple methodologies of study. These patterns are also shown to be present in laboratory rock fracture catalogs but absent in ETAS synthetic catalogs. Incorporating magnitude clustering decay patterns into earthquake forecasting models such as ETAS could improve their accuracy.
References
Barés, J., Dubois, A., Hattali, L., Dalmas, D., & Bonamy, D. (2018). Aftershock sequences and seismic-like organization of acoustic events produced by a single propagating crack. Nature Communications, 9(1). https://doi.org/10.1038/s41467-018-03559-4 DOI: https://doi.org/10.1038/s41467-018-03559-4
Box, G. E. P., Jenkins, G. M., Reinsel, G. C., & Ljung, G. M. (2015). Time series analysis: Forecasting and control. Wiley.
Brodsky, E. E. (2011). The spatial density of foreshocks: THE SPATIAL DENSITY OF FORESHOCKS. Geophysical Research Letters, 38(10). https://doi.org/10.1029/2011gl047253 DOI: https://doi.org/10.1029/2011GL047253
Cao, A., & Gao, S. S. (2002). Temporal variation of seismic b‐values beneath northeastern Japan island arc. Geophysical Research Letters, 29(9). https://doi.org/10.1029/2001gl013775 DOI: https://doi.org/10.1029/2001GL013775
Corral, Á. (2006). Dependence of earthquake recurrence times and independence of magnitudes on seismicity history. Tectonophysics, 424(3–4), 177–193. https://doi.org/10.1016/j.tecto.2006.03.035 DOI: https://doi.org/10.1016/j.tecto.2006.03.035
Davidsen, J., & Green, A. (2011). Are Earthquake Magnitudes Clustered? Physical Review Letters, 106(10). https://doi.org/10.1103/physrevlett.106.108502 DOI: https://doi.org/10.1103/PhysRevLett.106.108502
Goebel, T. H. W., Becker, T. W., Schorlemmer, D., Stanchits, S., Sammis, C., Rybacki, E., & Dresen, G. (2012). Identifying fault heterogeneity through mapping spatial anomalies in acoustic emission statistics. Journal of Geophysical Research: Solid Earth, 117(B3). https://doi.org/10.1029/2011jb008763 DOI: https://doi.org/10.1029/2011JB008763
Gutenberg, B., & Richter, C. F. (1944). Frequency of earthquakes in California*. Bulletin of the Seismological Society of America, 34(4), 185–188. https://doi.org/10.1785/bssa0340040185 DOI: https://doi.org/10.1785/BSSA0340040185
Hainzl, S. (2016). Rate‐Dependent Incompleteness of Earthquake Catalogs. Seismological Research Letters, 87(2A), 337–344. https://doi.org/10.1785/0220150211 DOI: https://doi.org/10.1785/0220150211
Hainzl, S. (2021). ETAS-Approach Accounting for Short-Term Incompleteness of Earthquake Catalogs. Bulletin of the Seismological Society of America, 112(1), 494–507. https://doi.org/10.1785/0120210146 DOI: https://doi.org/10.1785/0120210146
Hampton, J., Gutierrez, M., & Matzar, L. (2019). Microcrack Damage Observations near Coalesced Fractures Using Acoustic Emission. Rock Mechanics and Rock Engineering, 52(10), 3597–3608. https://doi.org/10.1007/s00603-019-01818-4 DOI: https://doi.org/10.1007/s00603-019-01818-4
Hardebeck, J. L., Llenos, A. L., Michael, A. J., Page, M. T., & van der Elst, N. (2018). Updated California Aftershock Parameters. Seismological Research Letters, 90(1), 262–270. https://doi.org/10.1785/0220180240 DOI: https://doi.org/10.1785/0220180240
Hauksson, E., Yang, W., & Shearer, P. M. (2012). Waveform Relocated Earthquake Catalog for Southern California (1981 to June 2011). Bulletin of the Seismological Society of America, 102(5), 2239–2244. https://doi.org/10.1785/0120120010 DOI: https://doi.org/10.1785/0120120010
Helmstetter, A. (2006). Comparison of Short-Term and Time-Independent Earthquake Forecast Models for Southern California. Bulletin of the Seismological Society of America, 96(1), 90–106. https://doi.org/10.1785/0120050067 DOI: https://doi.org/10.1785/0120050067
Kagan, Y. Y. (2004). Short-Term Properties of Earthquake Catalogs and Models of Earthquake Source. Bulletin of the Seismological Society of America, 94(4), 1207–1228. https://doi.org/10.1785/012003098 DOI: https://doi.org/10.1785/012003098
Klinger, Y. (2010). Relation between continental strike‐slip earthquake segmentation and thickness of the crust. Journal of Geophysical Research: Solid Earth, 115(B7). https://doi.org/10.1029/2009jb006550 DOI: https://doi.org/10.1029/2009JB006550
Lei, X. (2003). How do asperities fracture? An experimental study of unbroken asperities. Earth and Planetary Science Letters, 213(3–4), 347–359. https://doi.org/10.1016/s0012-821x(03)00328-5 DOI: https://doi.org/10.1016/S0012-821X(03)00328-5
Lin, Q., Wan, B., Wang, S., Li, S., & Fakhimi, A. (2019). Visual detection of a cohesionless crack in rock under three-point bending. Engineering Fracture Mechanics, 211, 17–31. https://doi.org/10.1016/j.engfracmech.2019.02.009 DOI: https://doi.org/10.1016/j.engfracmech.2019.02.009
Lin, Q., Wan, B., Wang, Y., Lu, Y., & Labuz, J. F. (2019). Unifying acoustic emission and digital imaging observations of quasi-brittle fracture. Theoretical and Applied Fracture Mechanics, 103, 102301. https://doi.org/10.1016/j.tafmec.2019.102301 DOI: https://doi.org/10.1016/j.tafmec.2019.102301
Lin, Q., Yuan, H., Biolzi, L., & Labuz, J. F. (2014). Opening and mixed mode fracture processes in a quasi-brittle material via digital imaging. Engineering Fracture Mechanics, 131, 176–193. https://doi.org/10.1016/j.engfracmech.2014.07.028 DOI: https://doi.org/10.1016/j.engfracmech.2014.07.028
Lippiello, E., de Arcangelis, L., & Godano, C. (2008). Influence of Time and Space Correlations on Earthquake Magnitude. Physical Review Letters, 100(3). https://doi.org/10.1103/physrevlett.100.038501 DOI: https://doi.org/10.1103/PhysRevLett.100.038501
Lippiello, E., Godano, C., & de Arcangelis, L. (2012). The earthquake magnitude is influenced by previous seismicity. Geophysical Research Letters, 39(5). https://doi.org/10.1029/2012gl051083 DOI: https://doi.org/10.1029/2012GL051083
Lippiello, Eugenio. (2018). Spatiotemporal Clustering of Seismic Occurrence and Its Implementation in Forecasting Models. In Complexity of Seismic Time Series (pp. 61–93). Elsevier. https://doi.org/10.1016/b978-0-12-813138-1.00003-1 DOI: https://doi.org/10.1016/B978-0-12-813138-1.00003-1
Lockner, D. A., Byerlee, J. D., Kuksenko, V., Ponomarev, A., & Sidorin, A. (1991). Quasi-static fault growth and shear fracture energy in granite. Nature, 350(6313), 39–42. https://doi.org/10.1038/350039a0 DOI: https://doi.org/10.1038/350039a0
McLaskey, G. C., & Lockner, D. A. (2018). Shear failure of a granite pin traversing a sawcut fault. International Journal of Rock Mechanics and Mining Sciences, 110, 97–110. https://doi.org/10.1016/j.ijrmms.2018.07.001 DOI: https://doi.org/10.1016/j.ijrmms.2018.07.001
Mignan, A., & Woessner, J. (2012). Estimating the magnitude of completeness for earthquake catalogs. Community Online Resource for Statistical Seismicity Analysis. https://doi.org/10.5078/CORSSA-00180805
Mizrahi, L., Nandan, S., & Wiemer, S. (2021). Embracing Data Incompleteness for Better Earthquake Forecasting. Journal of Geophysical Research: Solid Earth, 126(12). https://doi.org/10.1029/2021jb022379 DOI: https://doi.org/10.1029/2021JB022379
Moradpour, J., Hainzl, S., & Davidsen, J. (2014). Nontrivial decay of aftershock density with distance in Southern California. Journal of Geophysical Research: Solid Earth, 119(7), 5518–5535. https://doi.org/10.1002/2014jb010940 DOI: https://doi.org/10.1002/2014JB010940
Nandan, S., Ouillon, G., & Sornette, D. (2019). Magnitude of Earthquakes Controls the Size Distribution of Their Triggered Events. Journal of Geophysical Research: Solid Earth, 124(3), 2762–2780. https://doi.org/10.1029/2018jb017118 DOI: https://doi.org/10.1029/2018JB017118
Nandan, S., Ouillon, G., Wiemer, S., & Sornette, D. (2017). Objective estimation of spatially variable parameters of epidemic type aftershock sequence model: Application to California. Journal of Geophysical Research: Solid Earth, 122(7), 5118–5143. https://doi.org/10.1002/2016jb013266 DOI: https://doi.org/10.1002/2016JB013266
Ogata, Y., & Zhuang, J. (2006). Space–time ETAS models and an improved extension. Tectonophysics, 413(1–2), 13–23. https://doi.org/10.1016/j.tecto.2005.10.016 DOI: https://doi.org/10.1016/j.tecto.2005.10.016
Pan, X.-H., Xiong, Q.-Q., & Wu, Z.-J. (2018). New Method for Obtaining the Homogeneity Index m of Weibull Distribution Using Peak and Crack-Damage Strains. International Journal of Geomechanics, 18(6). https://doi.org/10.1061/(asce)gm.1943-5622.0001146 DOI: https://doi.org/10.1061/(ASCE)GM.1943-5622.0001146
Peng, Z., Vidale, J. E., Ishii, M., & Helmstetter, A. (2007). Seismicity rate immediately before and after main shock rupture from high‐frequency waveforms in Japan. Journal of Geophysical Research: Solid Earth, 112(B3). https://doi.org/10.1029/2006jb004386 DOI: https://doi.org/10.1029/2006JB004386
Richards-Dinger, K., Stein, R. S., & Toda, S. (2010). Decay of aftershock density with distance does not indicate triggering by dynamic stress. Nature, 467(7315), 583–586. https://doi.org/10.1038/nature09402 DOI: https://doi.org/10.1038/nature09402
Schorlemmer, D., & Woessner, J. (2008). Probability of Detecting an Earthquake. Bulletin of the Seismological Society of America, 98(5), 2103–2117. https://doi.org/10.1785/0120070105 DOI: https://doi.org/10.1785/0120070105
van der Elst, N. J. (2021). B‐Positive: A Robust Estimator of Aftershock Magnitude Distribution in Transiently Incomplete Catalogs. Journal of Geophysical Research: Solid Earth, 126(2). https://doi.org/10.1029/2020jb021027 DOI: https://doi.org/10.1029/2020JB021027
Veen, A., & Schoenberg, F. P. (2008). Estimation of Space–Time Branching Process Models in Seismology Using an EM–Type Algorithm. Journal of the American Statistical Association, 103(482), 614–624. https://doi.org/10.1198/016214508000000148 DOI: https://doi.org/10.1198/016214508000000148
Waldhauser, F. (2009). Near-Real-Time Double-Difference Event Location Using Long-Term Seismic Archives, with Application to Northern California. Bulletin of the Seismological Society of America, 99(5), 2736–2748. https://doi.org/10.1785/0120080294 DOI: https://doi.org/10.1785/0120080294
Waldhauser, Felix, & Schaff, D. (2007). Regional and teleseismic double‐difference earthquake relocation using waveform cross‐correlation and global bulletin data. Journal of Geophysical Research: Solid Earth, 112(B12). https://doi.org/10.1029/2007jb004938 DOI: https://doi.org/10.1029/2007JB004938
Wiemer, S. (2000). Minimum Magnitude of Completeness in Earthquake Catalogs: Examples from Alaska, the Western United States, and Japan. Bulletin of the Seismological Society of America, 90(4), 859–869. https://doi.org/10.1785/0119990114 DOI: https://doi.org/10.1785/0119990114
Woessner, J. (2005). Assessing the Quality of Earthquake Catalogues: Estimating the Magnitude of Completeness and Its Uncertainty. Bulletin of the Seismological Society of America, 95(2), 684–698. https://doi.org/10.1785/0120040007 DOI: https://doi.org/10.1785/0120040007
Xiong, Q., Brudzinski, M. R., Gossett, D., Lin, Q., & Hampton, J. C. (2023). Seismic magnitude clustering is prevalent in field and laboratory catalogs. Nature Communications, 14(1). https://doi.org/10.1038/s41467-023-37782-5 DOI: https://doi.org/10.1038/s41467-023-37782-5
Xiong, Qiquan, & Hampton, J. C. (2020). Non‐Local Triggering in Rock Fracture. Journal of Geophysical Research: Solid Earth, 125(11). https://doi.org/10.1029/2020jb020403 DOI: https://doi.org/10.1029/2020JB020403
Xiong, Qiquan, & Hampton, J. C. (2021). A Laboratory Observation on the Acoustic Emission Point Cloud Caused by Hydraulic Fracturing, and the Post-pressure Breakdown Hydraulic Fracturing Re-activation due to Nearby Fault. Rock Mechanics and Rock Engineering, 54(12), 5973–5992. https://doi.org/10.1007/s00603-021-02585-x DOI: https://doi.org/10.1007/s00603-021-02585-x
Xiong, Qiquan, Lin, Q., Gao, Y., & Hampton, J. C. (2022). Fundamental physics distinguishes the initial stage acoustic emission (AE) behavior between compressive and fracture toughness tests in rock. Engineering Fracture Mechanics, 275, 108829. https://doi.org/10.1016/j.engfracmech.2022.108829 DOI: https://doi.org/10.1016/j.engfracmech.2022.108829
Xiong, Qiquan, Lin, Q., & Hampton, J. C. (2021). Temporal evolution of a shear-type rock fracture process zone (FPZ) along continuous, sequential and spontaneously well-separated laboratory instabilities—from intact rock to thick gouged fault. Geophysical Journal International, 226(1), 351–367. https://doi.org/10.1093/gji/ggab041 DOI: https://doi.org/10.1093/gji/ggab041
Zambrano Moreno, A. F., & Davidsen, J. (2020). Magnitude correlations in a self-similar aftershock rates model of seismicity. Nonlinear Processes in Geophysics, 27(1), 1–9. https://doi.org/10.5194/npg-27-1-2020 DOI: https://doi.org/10.5194/npg-27-1-2020
Additional Files
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Derreck Gossett, Michael R. Brudzinski, Qiquan Xiong, Jesse C. Hampton
This work is licensed under a Creative Commons Attribution 4.0 International License.