**The Algorithm M8** was designed by retroactive analysis of the
seismicity preceding the greatest (M8+) earthquakes worldwide, hence its name. It is based
on a simple physical scheme of prediction, which can be briefly described as follows:

**Prediction is aimed at earthquakes of magnitude M0 and above**. We consider different values of M0 with a step 0.5. Overlapping circles with the diameter D(M0) scan the seismic territory. Within each circle the sequence of earthquakes is considered with aftershocks removed {ti, mi, hi, bi(*e*)}, i = 1, 2 ... Here ti is the origin time, ti <= t i + 1; mi is the magnitude, hi**is**focal depth, and bi(*e*)**is**the number of aftershocks during the first*e*days. The sequence is normalized by the lower magnitude cutoff Mmin(Ñ), Ñ being the standard value of the average annual number of earthquakes in the sequence. The magnitude scale we use should reflect the size of the earthquake sources. Accordingly,*MS*usually is taken for larger magnitudes while*mb*is used for smaller ones. For many catalogs, using the maximal reported magnitude could set this up, (we do so in the case of the NEIC GHDB).**Several running averages are computed for this sequence**in the sliding time windows (t -*s,*t) and magnitude range M0>=Mi >=Mmin(Ñ). They depict different measures of intensity**in**earthquake flow, its deviation from the long-term trend**,**and clustering of earthquakes. These averages include:

N(t)**,**the number of main**;**

L(t)**,**the deviation of N(t) from the long-term trend, L(t) = N(t) - Ncum(t-*s*)x(t-t0)/(t-s-t0), Ncum(t) being the cumulative number of main shocks with M >= Mmin(Ñ) from the beginning of the sequence t0 to t**;**

Z(t)**,**linear concentration of the main shocks estimated as the ratio of the average diameter of the source, l,**;**and B(t) = max{bi}**,**the maximal number of aftershocks (a measure of earthquake clustering).*p*, M0 -*q*).

Each of the functions N, L, Z is calculated for Ñ = 20 and Ñ = 10. As a result, the earthquake sequence is given a robust averaged description by seven functions: N, L, Z (twice each)**,**and B.**"Very large" values are identified for each function**using the condition that they exceed*Q*percentiles (i.e., they are higher than*Q*% of the encountered values).**An alarm or a TIP, “time of increased probability”, is declared**for five years, when at least six out of seven functions, including B, become "very large" within a narrow time window (t -*u*, t). To stabilize prediction**,**this condition is required for two consecutive moments, t and t+0.5 years.

The following standard values of parameters indicated above are
prefixed in the algorithm M8: D(M0)={exp(M0- 5.6)+1}0 in degrees of meridian (this is 384
km, 560 km, 854 km and 1333 km for M0 = 6.5, 7.0, 7.5** **and 8 respectively),* s*
= 6 years, *s*' = 1 year, *g* = .5, *p* = 2, *q* = .2, *u* = 3
years,** **and* Q* = 75% for B and 90% for the other **six** functions. The
running averages are defined in a robust way, so that a reasonable variation of parameters
does not affect the predictions.