Forecasting Methodology Based on Alternative Presentation of the Gutenberg–Richter Relation

Abstract

The main purpose of this study is to propose an innovative methodology to forecast the cumulative probability of future larger earthquakes for any given magnitude. It is based on applying an innovative approach to explicitly incorporate the logarithmic mean annual seismicity rate and its standard deviation, replacing the conventional Gutenberg–Richter (G–R) relation, which is only expressed by the arithmetic mean. The new representation of the G–R relation can provide the median annual seismicity rate and upper and lower bounds of recurrence time period for future larger earthquakes in different regions of Taiwan. Subsequently, the logarithmic mean is found to have a more well-behaved lognormal distribution. The selected crustal earthquake data for 3.0 ≤ M_w ≤ 5.0 are used to obtain alternative Gutenberg–Richter relations for different regions. The results are as follows: $\log_{10} N = 5.74 - 1.07M_{\text{w}} \pm ( - 0.18 + 0.12M_{\text{w}} )$ in and Taiwan; $\log_{10} N = 5.08 - 1.07M_{\text{w}} \pm (0.23 + 0.05M_{\text{w}} )$ for northeastern Taiwan offshore; $\log_{10} N = 5.48 - 0.95M_{\text{w}} \pm ( - 0.32 + 0.14M{}_{\text{w}})$ for eastern Taiwan offshore; $\log_{10} N = 4.57 - 0.84M_{\text{w}} \pm (0.07 + 0.07M_{\text{w}} )$ for southeastern Taiwan offshore. These results can be used for preventing and mitigating seismic hazards.