≈100L: the Parkfield earthquakes with a magnitude of ≈6 are preceded by a rise of activity in as far as the Great Basin or the Gulf of California. Such an area may include different types of faults. Many examples for different regions worldwide can be found (10–13). Other evidence and possible mechanisms of long-range correlations are discussed in the last section.
(ii) Premonitory Phenomena. Before a strong earthquake, the earthquake flow in a medium magnitude range becomes more intense and irregular; earthquakes become more clustered in space and time and the range of their correlation probably increases (12, 13). These symptoms may be interpreted as an increased response of the lithosphere to excitation (possibly provided by consecutive earthquakes themselves); such a response is symptomatic of a critical state in many other nonlinear systems. Some of these symptoms are formally defined in the next section.
(iii) Similarity. In robust definition, the normalized premonitory phenomena are identical in the magnitude range of at least M≥4.5 and for a wide variety of neotectonic environments (12–14), which include subduction zones, transform faults, intraplate faults in the platforms, induced seismicity near artificial lakes, and rock bursts in mines. This similarity is limited and on its background the regional variations of premonitory phenomena begin to emerge.
(iv) The Non-Earth-Specific Nature of Some Premonitory Phenomena. Many premonitory seismicity patterns are found in the models of exceedingly simple design. Some of such models, consisting of lattices of interacting point elements, are totally free of Earth-specific (or even solid-body-specific) mechanisms (15–17); other models retain only the simplest mechanism-friction (18–21). A stochastic model suggested in ref. 22 goes a long way toward explaining swarms, quiescence, foreshocks, and mainshocks as a coordinated sequence.
The algorithms reviewed here are based on a common general scheme of data analysis and on premonitory seismicity patterns with similar scaling and normalization. We outline these common features first.
Scheme of Data Analysis. The scheme of data analysis (Fig. 1) can be summarized as follows:
Strong earthquakes are identified by the condition M≥ M0. M0 is the given threshold chosen in such a way that the average time interval between strong earthquakes is suffi
ciently large in the area considered. The intervals (M0, M0+ 0.5) may be analyzed separately.
Prediction is aimed at determination of a time of increased probability (TIP) that is the time interval within which a strong earthquake has to be expected.
A seismic region under investigation is overlaid by areas whose size depends on M0. In each area, the sequence of earthquakes is analyzed. We determine its robust averaged traits, which are useful for prediction (the most commonly considered traits are indicated in Fig. 1). These traits are depicted by functions of time t defined in the sliding time windows with a common end t. We search for the functions whose values have different distributions inside and outside the TIPs. One or several of such functions could be used for prediction; a combination of precursors may be useful for prediction even if some of them show unsatisfactory performance when used separately. A variety of premonitory seismicity patterns was found in such a way.
Obviously this scheme is open for inclusion of other traits and other data, not necessarily seismological ones.
Major Common Characteristics. Major common characteristics of premonitory patterns considered here include the following:
Robustness. We have to look for the patterns common in a wide variety of regions and magnitude ranges as well as within sufficiently long time periods; otherwise the test of prediction algorithms would be practically impossible. Accordingly, premonitory patterns are given robust definitions in which the diversity of circumstances is averaged away while some predictive power is retained.
Time scale. The earthquake flow is averaged over time intervals a few years long and duration of alarms is about the same. These intervals do not depend on M0, while according to the Gutenberg-Richter relation the earthquakes with smaller magnitudes occur more frequently; the average time between the earthquakes of magnitude M is proportional to 10BM.* This is not a contradiction, since the Gutenberg-Richter law refers to a given region, the same for all magnitudes, while premonitory patterns are defined for an area with a linear dimension proportional to 10aM0. The average time between the earthquakes in such an area would be proportional to 10(B−av)M0 where v is the fractal dimension of the cloud of the epicenters. The existing estimations of parameters B (≈1), a (0.5−1), and v (1.2−2) do not contradict the hypothesis that the expression in brackets is close to 0 as if the earthquakes with different magnitudes have about the same recurrence time in their own cells. Still, for some premonitory patterns the time scale may depend on M0 (23).
Normalization. Normalization of an earthquake flow is necessary to ensure that a prediction algorithm can be applied with the same set of adjustable parameters in the regions with different seismicity. In the studies reviewed here, an earthquake flow is normalized by the minimal magnitude cutoff Mmin? defined by one of the two conditions: Mmin=(M0−a) or Ñ(Mmin)=b, Ñ being the average annual number of earthquakes with magnitude M≥Mmin; parameters a and b are common for all areas. If the second condition is applied, the intensity of the earthquake flow considered is the same in different areas, while Mmin may be different.
I now describe the prediction algorithms; the first one is defined in greater detail, for illustration.
Algorithm M8 (13) was designed by retrospective analysis of seismicity preceding the greatest (M≥8) earthquakes world-