Alternative representation of the Gutenberg–Richter relation in terms of the logarithmic mean annual seismicity rate and its standard deviation

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• 作者：Wen-Yen Chang ; Kuei-Pao Chen ; Yi-Ben Tsai
• 关键词：Arithmetic mean ; Arithmetic standard deviation ; Logarithmic mean ; Logarithmic standard deviation
• 刊名：Natural Hazards
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：85
• 期：3
• 页码：1297-1322
• 全文大小：
• 刊物类别：Earth and Environmental Science
• 刊物主题：Natural Hazards; Hydrogeology; Geophysics/Geodesy; Geotechnical Engineering & Applied Earth Sciences; Civil Engineering; Environmental Management;
• 出版者：Springer Netherlands
• ISSN：1573-0840
• 卷排序：85

文摘

Gutenberg and Richter developed an empirical relation, \(\log_{10} N(M) = a - bM\), to quantify the seismicity rate of various magnitudes in a given region and time period. They found the equation fit observed data well both globally and for particular regions. In conventional G–R relation, N(M) represents an arithmetic mean. As a result, the arithmetic standard deviation cannot be explicitly incorporated in the log-linear G–R relation. Moreover, this representation is susceptible to influence of spuriously large numbers of aftershocks of major earthquake sequences. To overcome these shortcomings, we propose an alternative representation of the G–R relation in terms of the logarithmic mean annual seismicity rate and its standard deviation. We select the crustal earthquake data from 1973 to 2011, as listed in the National Earthquake Information Center (NEIC) global catalog and the Central Weather Bureau (CWB) Taiwan regional catalog, to illustrate our methodology. We first show that by using the logarithmic annual seismicity rates we can significantly suppress the influences of spuriously large numbers of aftershocks following major earthquake sequences contained in the Taiwan regional catalog. More significantly, both the logarithmic mean annual seismicity rate and its standard deviation can be explicitly represented in the Gutenberg–Richter relation as follows:$${\text{For}}\,{\text{global}}\,{\text{crustal}}\,{\text{seismicity}}{:}\;\log_{10} N = 8.14 - 1.03M \pm (0.04M - 0.13);$$$${\text{For}}\,{\text{Taiwan}}\;{\text{crustal}}\,{\text{seismicity}}{:}\;\log_{10} N = 5.62 - 0.90M \pm (0.02M + 0.17)$$where log₁₀N represents the logarithmic annual seismicity rate. Above analytical equations are very well constrained by observed global seismicity data with \(5.0 \le M \le 7.0\) and by Taiwan seismicity data with \(3.0 \le M \le 5.0\). Both equations can be extrapolated with confidence to simultaneously estimate not only the median annual seismicity rates but also their uncertainties for large earthquakes for the first time since inception of the G–R relation. These equations can be used to improve the conventional probabilistic seismic hazard assessment by including the dispersion of the annual seismicity rate. Finally, the corresponding numerical median annual seismicity rate with its upper and lower bounds obtained from above equations for \(5.0 \le M \le 9.0\) is listed in Table 1.Table 1Observed and estimated median annual seismicity rate and return period with their dispersions for Taiwan and global crustal earthquakes