Statistical model for standard seismicity and detection of anomalies by residual analysis

Abstract

A statistical point-process model is derived to describe the standard activity of earthquake occurrences by assuming that general seismicity is given by the superposition of aftershock sequences. The parameters are estimated by the maximum likelihood method. Using the estimated model the "residual point process" of the data is defined and used to find the anomalies which are included in the data set but not captured in the considered model for the standard seismicity. For instance, seismic quiescences can be measured quantitatively by using the residual process. Some examples are provided to illustrate such analyses. Furthermore, a time series of the magnitudes on the residual point process is considered, to investigate its dependence either on the time or on the history of the seismicity. By assuming the exponential distribution at each time and modelling of the b-value, we can examine such dependences and estimate them. Two practical examples are shown.