Abstract
To adaptively forecast forthcoming large aftershocks of the 2008 Mw7.9 Wenchuan, China, earthquake, we construct a new hazard model to describe the occurrence rate of aftershocks in a study region along the Longmenshan fault. The model is denoted by SRJ since it is a combination of the Reasenberg–Jones (RJ) model and a spatial hazard model that is obtained by taking a reference of previous earthquakes in the study region. We employ the maximum likelihood (ML) method to estimate the SRJ model based on aftershocks that occurred within 1 or 2 days after the Wenchuan earthquake. The probabilities of M ≥ 5.0 aftershocks at each of the grids in the study region during next few days are then computed according to the estimated SRJ model, and hence the corresponding relative aftershock hazard (RAH) map is constructed. Finally, according to a variety of criteria for evaluating the hazard maps on depicting possible rupture area of forthcoming large aftershocks, the SRJ-based RAH map is demonstrated to be more efficient than the RAH maps constructed based on the RJ model incorporated with the gridding method using a fixed radius or varying radii.
Similar content being viewed by others
References
Aki, K. (1965). Maximum likelihood estimate of b in the formula logN = a-bM and its confidence limits. Bulletin of Earthquake Research Institute Tokyo University,43, 237–239.
Bamber, D. C. (1975). The area above the ordinal dominance graph and the area below the receiver operating characteristic graph. Journal of Mathematical Psychology,12(4), 387–415. https://doi.org/10.1016/0022-2496(75)90001-2.
Chen, Y. I., Huang, C. S., & Liu, J. Y. (2015). Statistical analysis of earthquakes after the 1999 Mw 7.7 Chi-Chi, Taiwan, earthquake based on a modified Reasenberg–Jones model. Journal of Asia Earth Science,114(2), 299–304. https://doi.org/10.1016/j.jseaes.2015.02.018.
Gerstenberger, M., Jones, L. M., & Wiemer, S. (2007). Short-term aftershock probabilities: case studies in California. Seismological Research Letters,78(1), 66–77. https://doi.org/10.1785/gssrl.78.1.66.
Gerstenberger, M., Wiemer, S., Jones, L. M., & Reasenber, P. A. (2005). Real-time forecasts of tomorrow’s earthquakes in California. Nature,435(7074), 328–331. https://doi.org/10.1038/nature03622.
Gutenberg, R., & Richter, C. F. (1944). Frequency of earthquakes in California. Bulletin of the Seismological Society of America,34(4), 185–188.
Kass, R. E., & Raftery, A. E. (1995). Bayes factors. Journal of the American Statistical Association,90(430), 773–795.
Kisslinger, C., & Jones, L. M. (1991). Properties of aftershocks in southern California. Journal of Geophysical Research,96(b7), 11947–11958.
Li, Z. X., Chen, Z. L., Zhao, C. P., Shao, Z. G., Hua, W., Wang, Q., et al. (2009). Uneven aftershock distribution of Wenchuan Ms8.0 earthquake and possible mechanism. Geodesy and Geodynamics,2(2), 7–12. https://doi.org/10.3724/SP.J.1246.2011.0007.
Lusted, L. B. (1960). Logical analysis in roentgen diagnosis. Radiology,74, 178–193.
Mann, H. B., & Whitney, D. R. (1947). On a test of whwther one of 2 random variables is stochastically larger than the other. Annals of Mathematical Statistics,18(1), 50–60.
Morris, J. A., & Gardner, M. J. (1988). Calculating confidence intervals for relative risks (odds ratios) and standardized ratios and rates. British Medical Journal,296(6632), 1313–1316. https://doi.org/10.1136/bmj.296.6632.1313.
Ogata, Y. (1983). Estimation of the parameters in the modified Omori formula for aftershock sequences by the maximum likelihood procedure. Journal of Physics of the Earth,31(2), 115–124. https://doi.org/10.4294/jpe1952.31.115.
Omori, F. (1894). On the aftershocks of earthquake. Journal of the College of Science, Imperial University of Tokyo,7, 111–200.
Reasenberg, P. A., & Jones, L. M. (1989). Earthquake hazard after a mainshock in California. Science,243(4895), 1173–1176. https://doi.org/10.1126/science.243.4895.1173.
Reasenberg, P. A., & Jones, L. M. (1994). Earthquake aftetshocks: Update. Science,265(5176), 1251–1252.
Shapiro, S. S., & Wilk, M. B. (1965). An analysis of variance test for normality (complete samples). Biometrika,52(3), 591–611. https://doi.org/10.1093/biomet/52.3-4.591.
Shi, Y., Liu, J., & Zhang, G. (2001). An evaluation of Chinese annual earthquake predictions. Journal of Applied Probability,38(a), 222–231. https://doi.org/10.1239/jap/1085496604.
Smith, W. D. (1981). The b-value as an earthquake precursor. Nature,289(5794), 136–139. https://doi.org/10.1038/289136a0.
Smyth, C., Mori, J., & Jiang, C. (2010). Model ensembles for prediction of Wenchuan aftershock activity. Bulletin of Seismological Society of America,100(5B), 2532–2538. https://doi.org/10.1785/0120090300.
Swets, J. (1988). Measuring the accuracy of diagnostic systems. Science,240(4857), 1285–1293. https://doi.org/10.1126/science.3287615.
Utsu, T. (1961). A statistical study on the occurrence of aftershocks. Geophysical Magazine,30(4), 521–605.
Utsu, T., Ogata, Y., & Matsuura, R. S. (1995). The centenary of the Omori formula for a decay law of aftershock activity. Journal of Physics of the Earth,43(1), 1–33. https://doi.org/10.2469/cfm.v24.n4.5.
Wieme, S. (2000). Introducing probabilistic aftershock hazard mapping. Geophysical Research Letters,27(20), 3405–3408. https://doi.org/10.1785/0119990114.
Wiemer, S., & Katsumata, K. (1999). Spatial variability of seismicity parameters in aftershock zones. Journal of Geophysical Research,104(b6), 13135–13151. https://doi.org/10.1029/1999JB900032.
Wiemer, S., & Wyss, M. (1997). Mapping the frequency-magnitude distribution in asperities; an improved technique to calculate recurrence times? Journal of Geophysical Research,102(b7), 15115–15128. https://doi.org/10.1029/97JB00726.
Wiemer, S., & Wyss, M. (2000). Minimum magnitude of completeness in earthquake catalogs: Example from Alaska, the western US and Japan. Bulletin of the Seismological Society of America,90(4), 859–869. https://doi.org/10.1785/0120020035.
Youden, W. J. (1950). Index for rating diagnostic tests. Cancer,3(1), 32–35. https://doi.org/10.1002/1097-0142.
Zhang, Y., Feng, W. P., Xu, L. S., Zhou, C. H., & Chen, Y. T. (2008). Spatio-temporal rupture process of the 2008 great Wenchuan earthquake. Science in China Series DL Earth Sciences,52(2), 145–154. https://doi.org/10.1007/s11430-008-0148-7.
Acknowledgements
This research is supported by the Ministry of Sciences and Technology of Taiwan under the grant MOST 107-2119-M-008-018.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Chen, YI., Liu, JY. & Lai, HW. Assessment of Space–Time Hazard of Large Aftershocks of the 2008 Mw7.9 Wenchuan Earthquake. Pure Appl. Geophys. 177, 27–36 (2020). https://doi.org/10.1007/s00024-019-02193-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00024-019-02193-5