The M8S algorithm was designed in course application of the modified version of the M8 algorithm aimed at prediction of earthquakes of moderate size in Italy (Romashkova et al., 2001, Kossobokov et al., 2001). The M8S algorithm provides determination of stabilized areas of alarms by analysing multiple application of the M8 algorithm in circles of investigation centred at nodes of a fine grid that span seismically active territory.
The essence of M8S can be summarised as follows:
Consider seismic territory covered by data from a given catalogue and exclude the band of about 0.5R1.0R near its boundary. R is the radius of circles of investigation, CI’s, used in M8.

Scan the territory with smaller circles of radius r distributed over a fine grid. Find all local seismically active places, keeping only the grid points where the average annual rate of seismic activity, within the small circle, is above a given threshold a. The lowactivity grid points are excluded from further analysis.

Exclude the grid points, where the data are insufficient for application of M8 algorithm in CI’s centred at them. Remove single or pairs of isolated grid points.

Apply M8 algorithm using CI’s, centred at each of the remaining grid points.

Disregard the M8 alarms as randomly attributed if they do not satisfy the following clustering condition: overwhelming majority, i.e. n%, of the CI’s, centred at the neighbouring grid points that remain in the analysis, are in state of alarm.
The union of alarms confirmed by alarms in neighbouring circles forms the alarm area of the M8S algorithm.
If the data permits, the M8S algorithm may deliver a hierarchy of predictions related to a number of magnitude ranges M_{0}+, M_{0} ≤ M < M_{0} + ΔM. Originally, the two different magnitude ranges defined by M_{0} = 6.5 and 6.0 were considered in Italy. Then the M8S predictions were extended to even smaller earthquakes, down to magnitude 5.5 (Romashkova et al., 2002).
The following values of parameters are prefixed in the M8S application in Italy: The grid spacing s equals to the linear dimension of the target earthquakes; the radius of small circles r=28 km; the activity cutoff a=0.3 main shocks of magnitude 3 or above per year; n%=75% of the neighbouring grid points remaining in the analysis from a 3×3grid square; Δ M=0.5.
At the moment the M8S algorithm is set up for the first experimental testing in Italy (Peresan et al., 2005). We continue our investigation of its properties in application to other territories, e.g. to California and Nevada or to the great earthquakes worldwide.