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In order to analyze observed seismicity in central Japan and Venezuela, we applied a new method to identify semi-periodic sequences in the occurrence times of large earthquakes, which allows for the presence of multiple periodic sequences and/or events not belonging to any sequence in the time series. We also explored a scheme for diminishing the effects of a sharp cutoff magnitude threshold in selecting the events to analyze. A main four-event sequence with probability P = 0.991 of not having occurred by chance was identified for earthquakes with M ≥ 8.0 in central Japan. Venezuela is divided, from West to East, into four regions; for each of these, the magnitude ranges and identified sequences are as follows. Region 1: M ≥ 6.0, a six-event sequence with P = 0.923, and a four-event sequence with P = 0.706. Region 2: M ≥ 5.6, a five-event sequence with P = 0.942. Region 3: M ≥ 5.6, a four-event sequence with P = 0.882. Region 4: M ≥ 6.0, a five-event sequence with P = 0.891. Forecasts are made and evaluated for all identified sequences having four or more events and probabilities ≥0.5. The last event of all these sequences was satisfactorily aftcast by previous events. Whether the identified sequences do, in fact, correspond to physical processes resulting in semi-periodic seismicity is, of course, an open question; but the forecasts, properly used, may be useful as a factor in seismic hazard estimation. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]