# Earthquake probability based on multidisciplinary observations with correlations

- 139 Downloads
- 3 Citations

## Abstract

A number of researchers have formulated earthquake probabilities based on precursory anomalies of multidisciplinary observations in which the underlying assumption is that the occurrence of one precursory anomaly is independent from those of other kinds of anomalies. Observations were classified into two groups, those events followed by an earthquake and those that were not, and the ratio of observed precursors in both groups was taken into consideration. In the present report, recent advances in statistical seismology are considered within the framework of these earthquake probabilities, and the formulations are extended to cases in which precursory anomalies are observed as continuous measurements. The effects originating from mutual correlations between two precursory anomalies are also considered. It is assumed that observed values of each discipline follow a normal distribution, either as a group of observations followed by an earthquake (conditional density distribution) or as a group of observations not followed by an earthquake (background density distribution). Special attention is given to the case in which two kinds of observations are correlated in the conditional density distribution but not in the background density distribution. The results obtained are compared with cases in which the observations are independent of each other in both distributions. The geometrical mean of the probability gain is greater in the correlated case than in the independent case and becomes infinitely large when the absolute value of the correlation coefficient approaches one. This finding enables a wider application of earthquake probability than has been previously possible based on multidisciplinary observations.

### Key words

Earthquake probability multidisciplinary observation correlation information gain Kullback-Leibler information quantity### References

- Aki, K., A probabilistic synthesis of precursory phenomena, in
*Earthquake Prediction*, edited by D. W. Simpson and P. G. Richards, pp. 566–574, AGU, 1981.Google Scholar - Daley, D. J. and D. Vere-Jones,
*An introduction to the Theory of Point Processes, vol. 1, Elementary Theory and Methods*, Second edition, 469 pp., Springer, New York, 2003.Google Scholar - Evison, F. F. and D. Rhoades, The precursory earthquake swarm in New Zealand: hypothesis tests II,
*N. Z. J. Geol. Geophys.*,**40**, 537–547, 1997.CrossRefGoogle Scholar - Evison, F. F. and D. Rhoades, The precursory earthquake swarm in Japan: hypothesis test,
*Earth Planets Space*,**51**, 1267–1277, 1999.CrossRefGoogle Scholar - Geller, R. J., Earthquake predicton: a critical review,
*Geophys. J. Int.*,**131**, 425–450, 1997.CrossRefGoogle Scholar - Grandori, G., E. Guagenti, and F. Perotti, Alarm systems based on a pair of short-term earthquake precursors,
*Bull. Seismol. Soc. Am.*,**78**, 1538–1549, 1988.Google Scholar - Hamada, K., A probability model for earthquake prediction,
*Earthq. Prediction Res.*,**2**, 227–234, 1983.Google Scholar - Hayakawa, M., O. A. Molchanov, T. Ondoh, and E. Kawai, Anomalies in the sub-ionospheric VLF signals for the 1995 Hyogo-ken Nanbu earthquake,
*J. Phys. Earth*,**44**, 413–418, 1996.CrossRefGoogle Scholar - Imoto, M., Application of the stress release model to the Nankai earthquake sequence, southwest Japan,
*Tectonophysics*,**338**, 287–295, 2001.CrossRefGoogle Scholar - Imoto, M., A testable model of earthquake probability based on changes in mean event size,
*J. Geophys. Res.*,**108**, ESE 7.1–12 No. B2, 2082, doi:10.1029/2002JB001774, 2003.Google Scholar - Imoto, M., Probability gains expected for renewal process models,
*Earth Planets Space*,**56**, 563–571, 2004.CrossRefGoogle Scholar - Imoto, M. and N. Yamamoto, Verification test of the mean event size model for moderate earthquakes in the Kanto region, central Japan,
*Tectonophysics*,**417**, 131–140, 2006.CrossRefGoogle Scholar - Jones, L., Foreshocks and time-dependent earthquake hazard assessment in southern California,
*Bull. Seismol. Soc. Am.*,**75**, 1669–1679, 1985.Google Scholar - Katao, H., N. Maeda, Y. Hiramatsu, Y. Iio, and S. Nakao, Detailed mapping of focal mechanisms in/around the 1995 Hyogo-ken Nanbu earthquake rupture zone,
*J. Phys. Earth*,**45**, 105–119, 1997.CrossRefGoogle Scholar - Mogi, K., Magnitude-frequency relations for elastic shocks accompanying fractures of various materials and some related problems in earthquakes,
*Bull. Earthq. Res. Inst.*,**40**, 831–853, 1962.Google Scholar - Mori, J. and R. E. Abercrombie, Depth dependence of earthquake frequency-magnitude distribution in California: Implications for rupture initiation,
*J. Geophys. Res.*,**102**, 15081–15090, 1997.CrossRefGoogle Scholar - Reasenberg, P. and M. Matthews, Precursory seismic quiescence: A preliminary assessment of the hypothesis,
*Pageoph*,**126**, 373–406, 1988.CrossRefGoogle Scholar - Sakamoto, Y., M. Ishiguro, and G. Kitagawa,
*Akaike Information Criterion Statistics*, D. Reidel, Dordrecht, 290 pp., 1983.Google Scholar - Scholz, C. H., The frequency-magnitude relation of microfracturing in rock and its relation to earthquake,
*Bull. Seismol. Soc. Am.*,**58**, 399–415, 1968.Google Scholar - Schorlemmer, D., S. Wiemer, and M. Wyss, Earthquake statistics at Parkfield: 1. Stationarity of b values,
*J. Geophys. Res.*,**109**, B12307, doi:10.1029/2004JB003234, 2003.CrossRefGoogle Scholar - Schorlemmer, D., S. Wiemer, and M. Wyss, Variations in earthquakesize distribution across different stress regimes,
*Nature*,**437**, 539–542, doi:10.1038/nature04094, 2005.CrossRefGoogle Scholar - Tsunogai, U. and H. Wakita, Anomalous changes in groundwater chemistry—Possible precursors of the 1995 Hyogo-ken Nanbu earthquake,
*Japan, J. Phys. Earth*,**44**, 381–390, 1996.CrossRefGoogle Scholar - Utsu, T., Probalities in earthquake prediction,
*Zisin II*,**30**, 179–185, 1977 (in Japanese).Google Scholar - Utsu, T., Probabilities in earthquake prediction (the second paper),
*Bull. Earthq. Res. Inst.*,**57**, 499–524, 1982 (in Japanese).Google Scholar - Vere-Jones, D., Probabilities and information gain for earthquake forecasting,
*Comput. Seismol.*,**30**, 248–263, 1998.Google Scholar - Wiemer, S. and M. Wyss, Mapping the frequency-magnitude distribution in asperities: an improved technique to calculate recurrence times?,
*J. Geophys. Res.*,**102**, 15,115–15,128, 1997.CrossRefGoogle Scholar - Wyss, M., Towards a physical understanding of the earthquake frequencymagnitude distribution,
*Geophys. J. R. Astron. Soc.*,**31**, 341–359, 1973.CrossRefGoogle Scholar - Wyss, M. and D. C. Booth, The IASPEI procedure for the evaluation of earthquake precursors,
*Geophys. J. Int.*,**131**, 423–424, 1997.CrossRefGoogle Scholar - Wyss, M. and S. Matsumura, Mosl likely locations of large earthquakes in the Kanto and Tokai areas, Japan, based on the local recurrence times,
*Phys. Earth Planet. Interiors*,**131**, 173–184, 2002.CrossRefGoogle Scholar - Yamada, T. and K. Oike, Electromagnetic radiation phenomena before and after the 1995 Hyogo-ken Nanbu earthquake,
*J. Phys. Earth*,**44**, 405–412, 1996.CrossRefGoogle Scholar - Zuñiga, F. R. and M. Wyss, Most- and least-likely locations of large to great earthquakes along the pacific coast of Mexico estimated from local recurrence times based on
*b*-values,*Bull. Seismol. Soc. Am.*,**91**(6), 1717–1728, 2001.CrossRefGoogle Scholar