Analysis of the return period and correlation between the reservoir-induced seismic frequency and the water level based on a copula: A case study of the Three Gorges reservoir in China

Studies have considered the many factors involved in the mechanism of reservoir seismicity. Focusing on the correlation between reservoir-induced seismicity and the water level, this study proposes to utilize copula theory to build a correlation model to analyze their relationships and perform the risk analysis. The sequences of reservoir induced seismicity events from 2003 to 2011 in the Three Gorges reservoir in China are used as a case study to test this new methodology. Next, we construct four correlation models based on the Gumbel, Clayton, Frank copula and M-copula functions and employ four methods to test the goodness of fit: Q-Q plots, the Kolmogorov-Smirnov (K-S) test, the minimum distance (MD) test and the Akaike Information Criterion (AIC) test. Through a comparison of the four models, the M-copula model fits the sample better than the other three models. Based on the M-copula model, we find that, for the case of a sudden drawdown of the water level, the possibility of seismic frequency decreasing obviously increases, whereas for the case of a sudden rising of the water level, the possibility of seismic frequency increasing obviously increases, with the former being greater than the latter. The seismic frequency is mainly distributed in the low-frequency region (Y ⩽ 20) for the low water level and in the middle-frequency region (20 < Y ≤ 80) for both the medium and high water levels; the seismic frequency in the high-frequency region (Y > 80) is the least likely. For the conditional return period, it can be seen that the period of the high-frequency seismicity is much longer than those of the normal and medium frequency seismicity, and the high water level shortens the periods.