Estimation of Parameters for a Recurrence Model of Small Earthquakes in Taiwan

Taiwan, which is located on the border between the Philippine Sea tectonic plate and the Eurasian tectonic plate, has a very high level of seismic activity. For this reason, sufficient data is available for a detailed investigation of earthquake frequency-magnitude recurrence relations. The standard recurrence model is the well-known Gutenberg-Richter model (G-R model, log N=a - b M, where N: number of earthquakes, M: magnitude, a: intercept, b: slope). In this study we adopt a new recurrence model for small earthquakes in Taiwan and compare this model with the predictions of the G-R model. We used the catalog of the Taiwan Central Weather Bureau and chose earthquakes from the period 1973 to 2001 with local magnitudes of 3.0<=ML<4.0. A regression analysis of these data shows that the so-called Gamma model has the best fit to the observed cumulative probability-interval time curve for these small earthquakes. The Gamma model is described by two parameters: c and r, where c is the scaling parameter and r is the shape parameter. In this application, the parameter c represents the number of earthquakes while the shape parameter, r, describes the temporal pattern of the earthquakes. If r < 1, the earthquakes are clustered in time. Considering the seismicity of all of Taiwan, the c value of the Gamma model is very similar to the value of the G-R model. The r value is less than 1, indicating some clustering. Considering only central Taiwan, the r value is quite low due to the temporal clustering of aftershocks of the Chi-Chi earthquake. We have also compared the two recurrence models specifically for the aftershock zone of the 1999 M=7.6 Chi-Chi earthquake. We have estimated the c and r values of the Gamma model and the a and b values of the G-R model in three year time windows from 1973 to 1999. We find that the c, a and b values all show a pattern of low-high-low with a period of nine years, whereas the r value increases in the last nine years prior to the Chi-Chi earthquake. By the value and definition of these parameters, we find that the aftershock zone of the Chi-Chi earthquake was seismically quiet in the nine years prior to the Chi-Chi earthquake. The parameters c, r, a and b show systematic variations.