Semi-Periodic Sequences and Extraneous Events in Earthquake Forecasting: I. Theory and Method,Parkfield Application

We present a new method to identify semi-periodic sequences in the occurrence times of large earthquakes, which allows for the presence of multiple semi-periodic sequences and/or events not belonging to any identifiable sequence in the time series. The method, based on the analytic Fourier transform, yields estimates of the departure from periodicity of an observed sequence, and of the probability that the sequence is not due to chance. These estimates are used to make and to evaluate forecasts of future events belonging to each sequence. Numerous tests with synthetic catalogs show that the method is surprisingly capable of correctly identifying sequences, unidentifiable by eye, in complicated time series. Correct identification of a given sequence depends on the number of events it contains, on the sequence’s departure from periodicity, and, in some cases, on the choice of starting and ending times of the analyzed time window; as well as on the total number of events in the time series. Some particular data combinations may result in spectra where significant periods are obscured by large amplitudes artifacts of the transform, but artifacts can be usually recognized because they lack harmonics; thus, in most of these cases, true semi-periodic sequences may not be identified, but no false identifications will be made. A first example of an application of the method to real seismicity data is the analysis of the Parkfield event series. The analysis correctly aftcasts the September 2004 earthquake. Further applications to real data from Japan and Venezuela are shown in a companion paper.