Abstract
The earthquake size distribution follows, in most instances, a power law1,2, with the slope of this power law, the ‘b value’, commonly used to describe the relative occurrence of large and small events (a high b value indicates a larger proportion of small earthquakes, and vice versa). Statistically significant variations of b values have been measured in laboratory experiments, mines and various tectonic regimes such as subducting slabs, near magma chambers, along fault zones and in aftershock zones3. However, it has remained uncertain whether these differences are due to differing stress regimes, as it was questionable that samples in small volumes (such as in laboratory specimens, mines and the shallow Earth's crust) are representative of earthquakes in general. Given the lack of physical understanding of these differences, the observation that b values approach the constant 1 if large volumes are sampled4 was interpreted to indicate that b = 1 is a universal constant for earthquakes in general5. Here we show that the b value varies systematically for different styles of faulting. We find that normal faulting events have the highest b values, thrust events the lowest and strike-slip events intermediate values. Given that thrust faults tend to be under higher stress than normal faults we infer that the b value acts as a stress meter that depends inversely on differential stress.
Access options
Subscribe to Journal
Get full journal access for 1 year
220,50 €
only 4,32 € per issue
All prices include VAT for France.
Rent or Buy article
Get time limited or full article access on ReadCube.
from$8.99
All prices are NET prices.
References
- 1.
Ishimoto, M. & Iida, K. Observations of earthquakes registered with the microseismograph constructed recently. Bull. Earthquake Res. Inst. Tokyo Univ. 17, 443–478 (1939)
- 2.
Gutenberg, B. & Richter, C. F. Frequency of earthquakes in California. Bull. Seismol. Soc. Am. 34, 185–188 (1944)
- 3.
Wiemer, S. & Wyss, M. Mapping spatial variability of the frequency–magnitude distribution of earthquakes. Adv. Geophys. 45, 259–302 (2002)
- 4.
Frohlich, C. & Davis, S. D. Teleseismic b values; or, much ado about 1.0. J. Geophys. Res. 98, 631–644 (1993)
- 5.
Kagan, Y. Y. Universality of the seismic moment–frequency relation. Pure Appl. Geophys. 155, 537–574 (1999)
- 6.
Bender, B. Maximum likelihood estimation of b values for magnitude grouped data. Bull. Seismol. Soc. Am. 73, 831–851 (1983)
- 7.
Shi, Y. & Bolt, B. A. The standard error of the magnitude–frequency b-value. Bull. Seismol. Soc. Am. 72, 1677–1687 (1982)
- 8.
Utsu, T. Report of the Joint Research Institute for Statistical Mathematics Vol. 34, 139–157 (Institute for Statistical Mathematics, Tokyo, 1992)
- 9.
Hauksson, E. Crustal structure and seismicity distribution adjacent to the Pacific and North America plate boundary in southern California. J. Geophys. Res. 105, 13875–13903 (2000)
- 10.
Mogi, K. Magnitude–frequency relations for elastic shocks accompanying fractures of various materials and some related problems in earthquakes. Bull. Earthquake Res. Inst. Univ. Tokyo 40, 831–853 (1962)
- 11.
Scholz, C. H. The frequency–magnitude relation of microfracturing in rock and its relation to earthquakes. Bull. Seismol. Soc. Am. 58, 399–415 (1968)
- 12.
Wyss, M. Towards a physical understanding of the earthquake frequency distribution. Geophys. J. R. Astron. Soc. 31, 341–359 (1973)
- 13.
Mori, J. & Abercrombie, R. E. Depth dependence of earthquake frequency–magnitude distributions in California: Implications for rupture initiation. J. Geophys. Res. 102, 15081–15090 (1997)
- 14.
Gerstenberger, M., Wiemer, S. & Giardini, D. A systematic test of the hypothesis that the b value varies with depth in California. Geophys. Res. Lett. 28, 57–60 (2001)
- 15.
Wyss, M. & Matsumura, S. Most likely locations of large earthquakes in the Kanto and Tokai areas, Japan, based on the local recurrence times. Physics of the Earth and Planetary Interiors 131, 173–184 (2002)
- 16.
Kagan, Y. Y. Seismic moment distribution revisited: I. Statistical results. Geophys. J. Int. 148, 520–541 (2002)
- 17.
Amitrano, D. Brittle–ductile transition and associated seismicity: Experimental and numerical studies and relationship with the b value. J. Geophys. Res., B2044 (2003) (doi:10.1029/2001JB000680)
- 18.
Urbancic, T. I., Trifu, C. I., Long, J. M. & Young, R. P. Space-time correlations of b-values with stress release. Pure Appl. Geophys. 139, 449–462 (1992)
- 19.
Wiemer, S., McNutt, S. R. & Wyss, M. Temporal and three-dimensional spatial analysis of the frequency-magnitude distribution near Long Valley caldera. California. Geophys. J. Int. 134, 409–421 (1998)
- 20.
Hauksson, E. Earthquakes, faulting, and stress in the Los Angeles basin. J. Geophys. Res. 95, 15365–15394 (1990)
- 21.
Amelung, F. & King, G. The difference between earthquake scaling laws for creeping and non-creeping faults. Geophys. Res. Lett. 24, 507–510 (1997)
- 22.
Wiemer, S. & Wyss, M. Mapping the frequency–magnitude distribution in asperities: An improved technique to calculate recurrence times? J. Geophys. Res. 102, 15115–15128 (1997)
- 23.
Schorlemmer, D., Wiemer, S. & Wyss, M. Earthquake statistics at Parkfield: 1. Stationarity of b-values. J. Geophys. Res. 109, B12307 (2004) (doi:10.1029/2004JB003234)
- 24.
Schorlemmer, D. & Wiemer, S. Microseismicity data forecast rupture area. Nature 434, 1086 (2005)
- 25.
Huang, J. & Turcotte, D. L. Fractal distributions of stress and strength and variations of b-value. Earth Planet. Sci. Lett. 91, 223–230 (1988)
- 26.
Smith, W. D. The b-values as an earthquake precursor. Nature 289, 136–139 (1981)
- 27.
Lei, X. et al. Detailed analysis of acoustic emission activity during catastrophic fracture of faults in rock. J. Struct. Geol. 26, 247–258 (2004)
- 28.
Oglesby, D. D., Archuleta, R. J. & Nielsen, S. B. Dynamics of dip-slip faulting: Explorations in two dimensions. J. Geophys. Res. 105, 13643–13653 (2000)
Acknowledgements
We thank E. Hauksson, D. Giardini, M. Mai, M. Gerstenberger, D. Jackson, J. Woessner and G. Hillers for discussions. We thank the Northern California Seismic Network, US Geological Survey, Menlo Park, and the Berkeley Seismological Laboratory, University of California, Berkeley, for the catalogue including phase data, and the National Research Institute for Earth Science and Disaster Prevention for mechanism solutions of the Kanto-Tokai area.
Author information
Affiliations
Swiss Seismological Service, ETH Zürich, ETH Hönggerberg, Schafmattstr. 30, 8093 Zürich, Switzerland
- Danijel Schorlemmer
- & Stefan Wiemer
World Agency of Planetary Monitoring and Earthquake Risk Reduction, Route de Jargonnant 2, 1207 Genève, Switzerland
- Max Wyss
Authors
Search for Danijel Schorlemmer in:
Search for Stefan Wiemer in:
Search for Max Wyss in:
Competing interests
Reprints and permissions information is available at npg.nature.com/reprintsandpermissions. The authors declare no competing financial interests.
Corresponding author
Correspondence to Danijel Schorlemmer.
Rights and permissions
To obtain permission to re-use content from this article visit RightsLink.
About this article
Further reading
-
1.
Characteristics of foreshock activity inferred from the JMA earthquake catalog
Earth, Planets and Space (2018)
-
2.
Mapping of seismic parameters of the Iberian Peninsula by means of a geographic information system
Central European Journal of Operations Research (2018)
-
3.
Constraining the Seismic Potentiality Analysis for Andaman Arc System, NE Indian Ocean
Journal of the Geological Society of India (2018)
-
4.
Probabilistic seismic hazard assessment for South-Eastern France
Bulletin of Earthquake Engineering (2018)
-
5.
Seismic Parameters of Mining-Induced Aftershock Sequences for Re-entry Protocol Development
Pure and Applied Geophysics (2018)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.