Abstract
The main purpose of this study is to propose an innovative methodology to forecast the cumulative probability of future larger earthquakes for any given magnitude. It is based on applying an innovative approach to explicitly incorporate the logarithmic mean annual seismicity rate and its standard deviation, replacing the conventional Gutenberg–Richter (G–R) relation, which is only expressed by the arithmetic mean. The new representation of the G–R relation can provide the median annual seismicity rate and upper and lower bounds of recurrence time period for future larger earthquakes in different regions of Taiwan. Subsequently, the logarithmic mean is found to have a more well-behaved lognormal distribution. The selected crustal earthquake data for 3.0 ≤ Mw ≤ 5.0 are used to obtain alternative Gutenberg–Richter relations for different regions. The results are as follows: \(\log_{10} N = 5.74 - 1.07M_{\text{w}} \pm ( - 0.18 + 0.12M_{\text{w}} )\) in and Taiwan; \(\log_{10} N = 5.08 - 1.07M_{\text{w}} \pm (0.23 + 0.05M_{\text{w}} )\) for northeastern Taiwan offshore; \(\log_{10} N = 5.48 - 0.95M_{\text{w}} \pm ( - 0.32 + 0.14M{}_{\text{w}})\) for eastern Taiwan offshore; \(\log_{10} N = 4.57 - 0.84M_{\text{w}} \pm (0.07 + 0.07M_{\text{w}} )\) for southeastern Taiwan offshore. These results can be used for preventing and mitigating seismic hazards.
Similar content being viewed by others
References
Aki, K. (1965). Maximum likelihood estimate of b in the formula log N = a − bM and its confidence limits. Bulletin of Earthquake Research Institute, University of Tokyo, 43, 237–239.
Bayrak, Y., & Bayrak, E. (2012). Regional variations and correlations of Gutenberg–Richter parameters and fractal dimension for the different seismogenic zones in Western Anatolia. Journal of Asian Earth Sciences, 58, 98–107.
Chang, W. Y., Chen, K. P., & Tsai, Y. B. (2016). An updated and refined catalog of earthquakes in Taiwan (1900–2014) with homogenized M w magnitudes. Earth, Planets and Space, 68(45), 1–9. https://doi.org/10.1186/s40623-016-0414-4.
Chen, K. P., & Tsai, Y. B. (2008). A catalog of Taiwan earthquakes (1900–2006) with homogenized M w magnitudes. Bulletin of the Seismological Society of America, 98, 483–489. https://doi.org/10.1785/0120070136.
Cheng, S. N. & Yeh, Y. T. (1999) Photo Album of ten disastrous earthquakes in Taiwan. Report Central Weather Bureau and Inst. Earth Sci., Acad. Sin., ROC, 255 pp (in Chinese).
Gutenberg, B., & Richter, C. F. (1941). Seismicity of the earth. Geological Society of America, Special Papers, 34, 1–131.
Gutenberg, B., & Richter, C. F. (1944). Frequency of earthquakes in California. Bulletin of the Seismological Society of America, 34, 185–188.
Hsu, M. T. (1971). Seismicity of Taiwan and some related problem. Bulletin of the International Institute of Seismology and Earthquake Engineering, 8, 41–160.
Kijko, A. (1985). A modified form of the Gutenberg–Richter magnitude-frequency relation: Maximum likelihood estimation of its parameters. Bulletin of the Seismological Society of America, 75, 319–322.
Ma, K. F., Lee, C. T., Tsai, Y. B., Shin, T. C., & Mori, J. (1999). The Chi-Chi, Taiwan earthquake: Large sueface displacements on an inland thrust fault. Eos, Transactions American Geophysical Union, 80, 605–611.
Ogata, Y., & Zhuang, J. (2006). Space-time ETAS models and an improved extension. Tectonophysics, 413, 13–23.
Shin, T. C., & Teng, T. L. (2001). An overview of the Chi–Chi, Taiwan earthquake. Bulletin of the Seismological Society of America, 91, 895–913.
Tsai, Y. B. (1985). A study of disastrous earthquakes in Taiwan, 1683–1985. Bulletin of Institution of the Earth Science, 5, 1–44.
Wang, J. H., & Kuo, H. C. (1995). A catalogue of Ms > 7 Taiwan earthquakes (1900–1994). Journal of the Geological Society of China, 38, 95–106.
Wessel, P., & Smith, W. H. F. (1998). New improved version of generic mapping tools released. Eos, Transactions American Geophysical Union, 79, 579.
Wyss, M. (1973). Towards a physical understanding of the earthquake frequency distribution. Geophysical Journal of the Royal Astronomical Society, 31, 341–359.
Acknowledgements
The paper is dedicated to my respected advisor Professor Yi-Ben Tsai. This study is supported by the Ministry of Science and Technology (MOST). We would like to thank Anthony Abram (http://www.uni-edit.net) for editing and proofreading this manuscript.
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.
Rights and permissions
About this article
Cite this article
Chen, KP., Chang, WY. & Yen, HY. Forecasting Methodology Based on Alternative Presentation of the Gutenberg–Richter Relation. Pure Appl. Geophys. 176, 3411–3423 (2019). https://doi.org/10.1007/s00024-019-02146-y
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00024-019-02146-y