New features of Caccamo's “Delta/Sigma” method for earthquake replica forecasting

In 2006 D. Caccamo developed the method for the prediction of the major earthquake replicas, called Delta/Sigma. This method is based on the study of anomalies in the main-aftershock sequences (Caccamo et al., 2006b) and it is derived from some problems encountered in the statistical analysis of temporal series of seismic data (Caccamo et al., 2002). The first version of Delta/Sigma algorithm was implemented in Matlab environment by C. Laganà and F. M. Barbieri (Caccamo et al., 2006a). The method was tested on several aftershock sequences by V. Pirrone (Caccamo et al., 2013), (Caccamo, et al., 2017). Recently, new results have been studied in collaboration with L. Puccio, L. Restuccia, R. Lotronto, expert in computer science, and the graduating student in mathematics A. Calderone. This research stems from the need to test the method Delta/Sigma on recent earthquakes, making predictions in “real time” (Caccamo, et al., 2017). The earthquakes, examined in this contribution, present features very different from those that characterize the earthquake in Chile, February 27, 2010 and Japan, March 03, 2011. In the scientific literature, the two mentioned earthquakes represent the foundations, representing the starting point of the research field, concerning the forecasting of strong earthquake replicas. By virtue of their typology, they have allowed to highlight the feasibility of forecasting of strong replicas of crusty earthquakes of the main-aftershock type. Recent papers have shown that these forecasts can also be made in “real time”, and not only retrospectively, with a high percentage of forecasting (Caccamo et al., 2017). However, to do this it is essential to have in real time all the data necessary to make the forecasts. Unfortunately, database queries do not yet provide the information with the timeliness we need. Nevertheless, the studies of this research continue, because we can make forecasts in the ten days following the considered event, in the sense that for some earthquakes the delays of databases in publishing information are less than 10 days (usually for some earthquakes, the information is provided after 3 - 4 days from the studied event). It is clear that deficiency of this information has effects on the goodness of the forecasts. In spite of this, after September 2017, we began to analyze very recent earthquakes, to test the possibility of making “real time” forecasts. Using the USGS (United States Geological Survey) database, we managed the situation to make “real time” forecasts on several days of the sequence of the earthquakes. Here, we report some obtained results for the earthquake in Mexico, September 08, 2017; h 04 m 49 sec 19; Lat 15.0222, Long -93.8993; Depth 47.39 km; M 8.2.