Taylor's power law (TPL) describes the scaling relationship between the temporal or spatial variance and mean of population densities by a simple power law. TPL has been widely testified across space and time in biomedical sciences, botany, ecology, economics, epidemiology, and other fields. In this paper, TPL is analytically reconfirmed by testifying the variance as a function of the mean of the released energy of earthquakes with different magnitudes on varying timescales during the Wenchuan earthquake sequence. Estimates of the exponent of TPL are approximately 2, showing that there is mutual attraction among the events in the sequence. On the other hand, the spatio-temporal distribution of the Wenchuan aftershocks tends to be nonrandom but approximately definite and deterministic, which highly indicates a stable spatio-temporally dependent energy release caused by regional stress adjustment and redistribution during the fault revolution after the mainshock. The effect of different divisions on estimation of the intercept of TPL straight line has been checked, while the exponent is kept to be 2. The result shows that the intercept acts as a logarithm function of the time division. It implies that the mean'variance relationship of the energy release from the earthquakes can be predicted, although we cannot accurately know the occurrence time and locations of imminent events.
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Acknowledgements. We thank Joel E. Cohen for providing valuable help during the preparation of this work. We are also thankful to the editor and three reviewers for their productive comments. The work has been funded from the NSFC (National Natural Science Foundation of China) under grant no. 41774084 and National Key R&D Program of China under grant no. 2018YFC1503506. Peijian Shi was supported by the Priority Academic Program Development of Jiangsu Higher Education institutions.
© Author(s) 2019.