Global M8MSc IntermediateTerm Predictions
The list of the regions where predictions are being made together with the magnitude range of the earthquakes we aim to predict.
In the experiment we aim at prediction of magnitude 8 and above earthquakes in 262 circles of investigation, CI’s, each of 667km radius. Their locations, i.e. coordinates of their centers, are listed in Table CI’s 8.0. The CI’s are set along seismic belts with a nearuniform step and cover all the areas on the Earth where the M8 algorithm could run in its original version that requires annual rate of activity of 16 or more mainshocks.
We will also consider predictions of magnitude 7.5 and above earthquakes in 180 CI’s, each of 427km radius. Their locations, i.e. coordinates of their centers, are listed in Table CI’s 7.5. As in case of magnitude 8, the CI’s are set along seismic belts and cover all the areas on the Earth where the original version of M8 algorithm could run to predict magnitude 7.5+ earthquakes.
Note: This is an extension of the Test of M8 in Circum Pacific (Healy et al., 1992): all the parameters of the algorithms including the locations of CI’s remain the same as they were set in 1990. The Mw magnitudes not reported in the NEIC Hypocenters Data Base before 1993 are not considered. The Test of M8 extended to the AlpineHymalayan seismic belt. Furthermore, we now aim at prediction of both M7.5+ and M8.0+ earthquakes and include additional analysis of each alarm by the MSc algorithm.
Maps of these regions.
The locations of the 262 CI’s of 667km radii and those of the 180 CI’s of 427km radii.
The schedule of the updating of predictions.
We will update the global catalog and evaluate predictions each halfyear as it was done in (Healy et al., 1992). We presume a continuation of independent preprocessing of the catalog by James Dewey of USGS/NEIC (Golden, CO), John Healy of USGS (Menlo Park), and Vladimir Kossobokov of IEPT (Moscow). In the update, the global catalog is extended with the Weekly Preliminary Determinations of Epicenters, PDEW, and the PDEW of the previous update are substituted with the final PDEMonthly, now published with a delay of about one year. To exclude about two month delay in compilation of the data set and, correspondingly, in our predictions, we now use the NEIC Quick Earthquake Determinations (QED) available on January 1 and July 1 and issue predictions at the beginning of January and July.
The 11 April 2012, M8.6 and M8.2 earthquakes off the West coast of Northern Sumatra
The 2011 off the Pacific coast of Tohoku Earthquake
The February 27, 2010, Mw8.8 Chile Earthquake
The December 26, 2004, Mw9.0 Indian Ocean Earthquake
1985  1999  
2000  2014  
2015 to the present 
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(С), С 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(С). They depict different measures of intensity in earthquake flow, its deviation from the longterm trend, and clustering of earthquakes. These averages include: N(t), the number of main shocks; L(t), the deviation of N(t) from the longterm trend, L(t) = N(t)  Ncum(ts)x(tt0)/(tst0), Ncum(t) being the cumulative number of main shocks with M >= Mmin(С) 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, to the average distance, r, between them; and B(t) = max{bi}, the maximal number of aftershocks (a measure of earthquake clustering). The earthquake sequence {i} is considered in the time window (t  s', t) and in the magnitude range (M0  p, M0  q). Each of the functions N, L, Z is calculated for С = 20 and С = 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.
The stabilised M8 (M8S) algorithm
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.
Lecture I  Lecture II  Lecture III  Lecture IV  Lecture V 
 Lecture I. Catalogs of Earthquakes: Record of seismicity on global, regional, and local scales
 Lecture II. Functions on earthquake flow
 Lecture III. Earthquake prediction algorithm M8
 Lecture IV. Reduction of earthquake prediction uncertainty: Algorithm MSc (Mendocino Scenario)
 Lecture V. Application of M8 and MSc algorithms since 1985