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A Dimensional Analysis Method for Improved Load–Unload Response Ratio

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Abstract

The load–unload response ratio (LURR) method is proposed to measure the damage extent of source media and the criticality of earthquake. Before the occurrence of a large earthquake, anomalous increase in the time series of LURR within the certain temporal and spatial windows has often been observed. In this paper, a dimensional analysis technique is devised to evaluate quantitatively the magnitude and time of the ensuing large earthquake within the anomalous areas derived from the LURR method. Based on the π-theorem, two dimensionless quantities associated with the earthquake time and magnitude are derived from five parameters (i.e. the seismic energy (E S), the average seismic energy (E W), the maximum value of LURR’s seismogenic integral (I PP), the thickness of seismogenic zone (h), the time interval from I PP to earthquake (T 2), and the shear strain rate (\(\dot{\gamma }\))). The statistical relationships between the earthquakes and the two dimensionless quantities are derived by testing the seismic data of the 50 events of M4.5 ~ 8.1 occurred in China since 1976. In earthquake prediction, the LURR method is used to detect the areas with anomalous high LURR values, and then our dimensional analysis technique is applied to assess the optimal critical region, magnitude, and time of the ensuing event, when its seismogenic integral is peaked (I PP). As study examples, we applied this approach to study four large events, namely the 2012 M S5.3 Hami, 2015 M S5.8 Alashan, 2015 M S8.1 Nepal earthquakes, and the 2013 Songyuan earthquake swam. Results show that the predicted location, time, and magnitude correlate well with the actual events. This provides evidence that the dimensional analysis technique may be a useful tool to augment current predictive power of the traditional LURR approach.

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References

  • Aki, K. (1965). Maximum likelihood estimate of b in the formula logN = a-bm and its confidence limits. Bulletin of the Earthquake Research Institute, Tokoyo university, 43, 237–239.

    Google Scholar 

  • Bai, Y. L., Xia, M. F., Ke, F. J., & Li, H. L. (2002). Closed trans-scale statistical microdamage mechanics. Acta Mechanica Sinica, 18, 1–17.

    Article  Google Scholar 

  • Bowman, D. D., Ouillen, G., Sammis, C. G., Sornette, A., & Sornette, D. (1998). An observational test of the critical earthquake concept. Journal of Geophysical Research, 103, 24359–24372.

    Article  Google Scholar 

  • Buckingham, E. (1914). On physically similar systems: Illustrations of the use of dimensional analysis. Physical Review, 4, 345–376.

    Article  Google Scholar 

  • Gu, G. H., Shen, X. H., Wang, M., Zheng, G. M., Fang, Y., & lI, P. (2001). General characteristics of the recent horizontalcrustal movement in Chinesemainland. Acta Seismological Sinica, 23, 362–369.

    Google Scholar 

  • Gutenberg, B., & Richter, C. F. (1944). Frequency of earthquakes in California. Bulletin of the Seismological Society of America, 34, 185–188.

    Google Scholar 

  • Jaume, S. C., & Sykes, L. R. (1999). Evolving towards a critical point: a review of accelerating seismic moment/energy release prior to large and great earthquakes. Pure and Applied Geophysics, 155, 279–306.

    Article  Google Scholar 

  • Jiang, Z. S., Ma, Z. J., Zhang, X., Wang, Q., & Wang, S. X. (2003). Horizontal strain field and tectonic deformation of china mainland revealed by preliminary GPS result. Chinses J Geophysics, 46, 352–358.

    Google Scholar 

  • Kachanov, L. M. (1986). Introduction to continuum damage mechanics. Dordrecht: MartinusNijhoff Publishers.

    Book  Google Scholar 

  • Kasahara, K. (1981). Earthquake mechanics. Cambridgo: Cambridge University Press.

    Google Scholar 

  • Lemaitre, J. (1992). A course on damage mechanics. Berlin/Heidelberg: Springer-Verlag.

    Book  Google Scholar 

  • Li, H. L., Bai, Y. L., Xia, M. F., Ke, F. J., & Yin, X. C. (2000). Damage localization as a possible precursor of earthquake rupture. Pure and Applied Geophysics, 157, 1929–1943.

    Article  Google Scholar 

  • Li, Y. X., Li, Z., & Zhang, J. H. (2004). Horizontal strain field in the Chinese mainland and its surrounding areas. Chinese Journal of Geophysics, 47, 222–231. (in Chinese with English abstract).

    Google Scholar 

  • Liu Y (2014) Study of several issues concerning Load-Unload Response Ratio in Earthquake Prediction. PhD Thesis of the Graduate School of the Chinese, Academy of Sciences (in Chinese with English abstract).

  • Liu, Y., Yin, X. C., Yuan, S., & Zhang, L. P. (2012). Exploration study of dimensional analysis applying to earthquake prediction. Chinese Journal of Geophysics, 55, 3043–3050. (in Chinese with English abstract).

    Google Scholar 

  • Melchior, P. (1983). The tides of the planet Earth. Oxford: Pergamon Press.

    Google Scholar 

  • Reches, Z., & Lockner, D. A. (1994). Nucleation and growth of faults in brittle rocks. Journal of Geophysical Research, 99, 18159–18173.

    Article  Google Scholar 

  • Rundle, J. B., Tiampo, K. F., Klein, W., & Martins, J. S. S. (2002). Self-organization in leaky threshold systems: The influence of near-mean field dynamics and its implications for earthquakes, neurobiology, and forecasting. Proceedings of the National academy of Sciences of the United States of America, 99, 2514–2521.

    Article  Google Scholar 

  • Scholz, C. H., Sykes, L. R., & Aggrawal, Y. P. (1972). Earthquake prediction: A physical basis. Science, 181, 803–810.

    Article  Google Scholar 

  • Sedov, L. I. (1959). Similarity and dimensional methods in mechanics[M]. London: Academic Press.

    Google Scholar 

  • Shen, Z. K., Wang, M., Gan, W. J., & Zhang, Z. S. (2003). Contemporary tectonic strain rate field of chinese continent and its geodynamic implications. Earth Science Frontiers, 10(suppl), 93–100.

    Google Scholar 

  • Song, Z. P., Yin, X. C., Wang, Y. C., Xu, P., & Xue, Y. (2000). The tempo-spatial evolution characteristics of the load/unload response ratio befor strong earthquakes in California of America and its predicting implication. Acta Seismological Sinica, 22(6), 588–595. (in Chinese with English abstract).

    Google Scholar 

  • Tan, Q. M. (2011). Dimensional analysis: with case studies in mechanics[M]. New York: Springer Science & Business Media.

    Book  Google Scholar 

  • Wang, Y. C., Yin, C., Mora, P., Yin, X. C., & Peng, K. Y. (2004). Spatio -temporal scanning and statistical test of the accelerating moment release (AMR) model using Australian earthquake data. Pure and Applied Geophysics, 161, 2281–2293.

    Google Scholar 

  • Yang, S. M., Li, J., & Wang, Q. (2008). The deformation pattern and fault rate in the Tianshan Mountains inferred from GPS observations. Science in China, Series D: Earth Sciences, 51(8), 1064–1080.

    Article  Google Scholar 

  • Yin, X. C. (1987). A new approach to earthquake prediction. Earthquake Research in China, 3, 1–7. (in Chinese with English abstract).

    Google Scholar 

  • Yin, X. C. (1993). A new approach to earthquake prediction. Russia’s “Nature”, 1, 21–27. (in Russian).

    Google Scholar 

  • Yin, X. C., Chen, X. Z., Song, Z. P., & Yin, C. (1995). A new approach to earthquake prediction: the load/unload response ratio (lurr) theory. Pure and Applied Geophysics, 145, 701–715.

    Article  Google Scholar 

  • Yin, X. C., & Liu, Y. (2014). Load-Unload response ratio-an interplay between earthquake prediction and mechanics. Advances in Mechanics, 43, 555–580. (in Chinese with English abstract).

    Google Scholar 

  • Yin, X. C., Liu, Y., Peter, M., Yuan, S., & Zhang, L. P. (2013). New progress in LURR-integrating with the dimensional method. Pure and Applied Geophysics, 170, 229–236.

    Article  Google Scholar 

  • Yin, X. C., Liu, Y., & Zhang, L. P. (2012). Load-unload response ratio and its new progress[M]. In Y. G. Li (Ed.), Imaging, modeling and assimilation in seismology (pp. 219–244). Boston: High Education Press and Walter De Gruyter GmbH & Co. KG.

    Google Scholar 

  • Yin, X. C., Mora, P., Peng, K. Y., Wang, Y. C., & Weatherly, D. (2002). Load-unload Response Ratio and Accelerating Moment/Energy Release, Critical Region Scaling and Earthquake Prediction. Pure and Applied Geophysics, 159, 2511–2524.

    Article  Google Scholar 

  • Yin, X. C., Zhang, L. P., Zhang, H. H., Yin, C., Wang, Y. C., Zhang, Y. X., et al. (2006). LURR’s twenty years and its perspective. Pure and Applied Geophysics, 163, 2317–2341.

    Article  Google Scholar 

  • Yin, X. C., Zhang, L. P., & Zhang, Y. X. (2008). LURR anomoly with great tempo-spatial scale before large earthquake-Prediction of the upcoming great earthquake in the Chinese mainland. The researches on prediction of the strong earthquake tendency for Chinese mainland in 2009 (pp. 144–150). Beijing: Seismological Press.

    Google Scholar 

  • Yu, H. Z., Cheng, J., & Wan, Y. G. (2015). The sensitivity of loa/unload response ratio and critical region selection before large earthquakes. Pure and Applied Geophysics, 172, 2203–2214.

    Article  Google Scholar 

  • Yu, H. Z., Cheng, J., Zhang, X. T., Zhang, L. P., Liu, J., & Zhang, Y. X. (2013). Multi-methods combined analysis of the future earthquake potential. Pure and Applied Geophysics, 170, 173–183.

    Article  Google Scholar 

  • Yu, H. Z., Cheng, J., Zhu, Q. Y., & Wan, Y. G. (2011). Critical sensitivity of load/unload response ratio and stress accumulation before large earthquakes: Example of the 2008 M W7.9 Wenchuan Earthquake. Natural Hazards, 58(1), 251–267.

    Article  Google Scholar 

  • Yu, H. Z., Shen, Z. K., Wan, Y. G., & Zhu, Q. Y. (2006). Increasing critical sensitivity of the Load/Unload Response Ratio before large earthquakes with identified stress accumulation pattern. Tectonophysics, 428, 87–94.

    Article  Google Scholar 

  • Yu, H. Z., Zhou, F. R., Cheng, J., Zhang, X. T., & Zhang, Y. X. (2016). Development of a combination approach for seismic hazard evaluation. Pure and Applied Geophysics, 173, 221–233.

    Article  Google Scholar 

  • Yu, H. Z., & Zhu, Q. Y. (2010). A probabilistic approach for earthquake potential evaluation based on the Load/Unload Response Ratio method. Concurr Comp-Pract E, 22, 1520–1533.

    Article  Google Scholar 

  • Zhang, H. H. (2006). Prediction of catastrophic failure in heterogeneous brittle media-study and practice of Load/Unload Response Ratio (LURR). PhD Thesis of The Graduate School of the Chinese Academy of Sciences (in Chinese with English abstract).

  • Zhang, S. F., Wu, Z. L., & Jiang, C. S. (2016). The central china north–south seismic belt: seismicity, ergodicity, and five-year pi forecast in testing. Pure and Applied Geophysics, 173, 245–254.

    Article  Google Scholar 

  • Zhang, L. P., Yu, H. Z., & Yin, X. C. (2013). Failure potential evaluation in engineering experiments using Load/Unload Response Ratio Method. Pure and Applied Geophysics, 170, 237–245.

    Article  Google Scholar 

  • Zhang, L. P., & Zhuang, J. C. (2011). An improved version of the load/unload response ratio method for forecasting strong aftershocks. Tectonophysics, 509, 191–197.

    Article  Google Scholar 

  • Zohuri, B. (2015). Dimensional analysis and self-similarity methods for engineers and scientists[M]. New York: Springer.

    Book  Google Scholar 

  • Zubovich, A. V., Wang, X. Q., Scherba, Y. G., et al. (2010). GPS velocity field for the Tien Shan and surrounding regions. Tectonics. https://doi.org/10.1029/2010TC002772.

    Google Scholar 

Download references

Acknowledgements

The catalog data are taken from the China Earthquake Networks Center (CENC). The shear strain data are provided by Professor Zai-sen Jiang, Zheng-kang Shen and Guo-hua Gu. Parts of the calculations in the paper are conducted in Supercomputing Center of Computer Network information Center, Chinese Academy of Sciences (CAS). Professor Huai-zhong Yu gives constructive advices. This research is supported by the Institute of Earthquake Forecasting CAE (2015IES0102). We are grateful here.

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  1. Institute of Earthquake Forecasting, China Earthquake Administration, No. 63, Fuxing Road, Haidian District, Beijing, 100036, China

    Yue Liu & Xiang-chu Yin

  2. State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100019, China

    Xiang-chu Yin

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  1. Yue Liu
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Correspondence to Yue Liu.

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Liu, Y., Yin, Xc. A Dimensional Analysis Method for Improved Load–Unload Response Ratio. Pure Appl. Geophys. 175, 633–645 (2018). https://doi.org/10.1007/s00024-017-1716-6

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