Charles Richter, the famed American seismologist and inventor of the
earthquake magnitude measurement
which bears his name, once
said
that earthquake prediction, "provides a happy hunting ground for cranks and publicity seeking fakers". Richter, who spent most of his life looking for ways to predict earthquakes, to little or no avail, lamented the "rush to any suggestion of earthquake prediction like hogs toward a full trough," by journalists and the general public. Richter, however, didn't have the advantage that today's scientists have - because Richter's work came before scientists began to recognise chaos in natural processes.
It turns out that many of the patterns which are to be found in analyzing seismic activity leading up to an earthquake are *self-similar*. Self-similarity is an important notion which comes out of the study of chaos and nonlinear equations, and it's really much easier to visualize, than to define. Very informally though, when speaking in terms of simple surfaces or curves, self-similarity exists when any portion of the surface or curve (picture) can be magnified (or scaled/zoomed), resulting in a new curve or surface which is identical to the original. When this independence of scale is observed, the surface or curve is called a *fractal*. Some of the more interesting examples of so-called "deterministic" fractals include the
Mandelbrot set,
and the
Sierpinski Gasket, which some readers may already be familiar with.

In the study of seismic *premonitory* patterns which predict earthquakes, Kellis-Borok claims that self-similarity can also be observed - the groups of small and medium-sized tremors which precede a large earthquake tend to "look alike", for any given magnitude of the earthquake to be predicted. Formally, according to Kellis-Borok, "earthquakes follow a general hierarchical process that proceeds via a sequence of inverse cascades to produce self-similar scaling."^{1} This type of self-similarity, which usually results from a natural process, gives us so-called "random" fractals which are said to be "statistically self-similar". Instead of being exactly mappable onto itself for some scaling, a random fractal looks similar to itself at all degrees of magnification. Using this result, along with several well-known patterns, Keilis-Borok claims that it's possible to predict earthquakes more reliably, and on a more timely basis, than ever before.

The study of seismic event patterns is nothing new, though. There are hundreds of published scientific works which investigate every conceivable aspect of major earthquakes and the events which lead up to them. Many of these works propose so-called "functionals", which are defined on a sequence of shocks within a given area and magnitude range. These functionals eventually capture a specific *pattern* of seismic activity over a given area, a pattern which the author then may claim is premonitory to a larger event.

There are two primary problems with all of the functionals (and their associated patterns) which have been proposed to date, either they aren't timely enough - they precede large earthquakes by a period of years instead of months or weeks; or they aren't reliable enough - they precede large earthquakes by relatively short time periods, but they also give "false alarms". Therefore, to come up with a short-term predictor of large earthquakes, Keilis-Borok had to step back and see the bigger picture, so to speak, much as we do when we "zoom out" on a small bit of the Mandelbrot set. To accomplish this, he used a technique called *renormalization*, a rather complex data-reduction process, but which essentially means that he applied a scaling factor to existing functionals via manipulating their adjustable parameters so that their tendency to correctly predict large earthquakes was maximized.

In plain English, Keilis-Borok let the tail wag the dog - and in more ways than just renormalization of the data - but that's not necessarily a bad thing, as you'll see next.

Keilis-Borok's team utilizes three distinct, and previously known patterns when issuing a prediction. Two of these patterns, named **ROC** and **Accord**, were apparently discovered and proposed by Keilis-Borok himself during the last two decades. The ROC pattern analyzes the (relatively) simultaneous occurrence of medium sized shocks at relatively "large" distances from each other which form "chains", while the Accord pattern looks for uniformly distributed shocks within a "grid" of land tracts imposed upon some large land area. The third pattern, simply called **U**, analyzes the relative increase in frequency of these same shocks anywhere within the area under study. Each of these patterns, when taken individually, demonstrates one or more of the problems discussed previously when used to predict earthquakes. Accord and ROC can predict earthquakes months in advance, but they yield numerous false alarms. Pattern U is a more reliable predictor, but increased frequency of shocks within a given large area can begin years in advance of a major earthquake, and all three are subject to bias introduced by residual shocks (aftershocks) from previous earthquakes within the same boundary. When utilized together however, Keilis-Borok's team claims that these three patterns can provide a much more reliable short-term prediction.

To establish this claim, Keilis-Borok post-analyzed a
large area
of southern California, in a
scientific paper
published late in 2002^{2}. Five large (> 6.4 magnitude) earthquakes which had occured four to five years apart during the last 20 years in the given area were considered. In each case, the individual patterns, ROC, Accord, and U, were somewhat reliable as predictors, but also subject to false alarms, or long waiting periods. Taken together though, they reliably predicted all of the earthquakes in the study to within a period of months. This was a significant result - enough to get them published, in any case - which has not been accomplished with any other functional/pattern. The study concluded by emphasizing that the new technique reliably predicted earthquakes independent of scale, magnitude, and time, implying that the technique is truly able to capture the chaotic, but self-similar nature of the earthquake process.

The combined technique which was developed out of that study is now referred to by Keilis-Borok as
"tail wagging the dog"^{3}, and since then it's been used to predict two actual major earthquakes - a magnitude 8.1 quake near Hokkaido, Japan, in September of 2003 and a magnitude 6.5 shock that struck Paso Robles, California in December 2003^{4}. In both cases, earthquakes of similar magnitudes had not occurred in the respective areas for years preceding the predicted event.

The technique developed in the original study had to be adapted for real-life predictions of course, to see the "tail" first, and then analyze the bigger picture - thus "wagging the dog". To that end, the Kellis-Borok team first looks for the ROC pattern, a "long chain" of earthquakes occurring within a relatively short time frame, and relatively widely dispersed - specifically, there must be at least 6 quakes of magnitude 2.9 or greater along a chain of at least 110 miles (175km) . The ROC pattern is the natural place to begin looking, as it does not require a bounding area be introduced beforehand. When such a chain is found, the bounding area is then set, and the other two patterns, Accord and U, are searched for. If they're found within the area defined by the original chain, then a warning is issued for the subsequent 9 months.

That's pretty much how it works, this "holy grail" of seismology - now the question is, how reliable is it? By most accounts, Keilis-Borok is two for two, but one seismologist, Susan Hough from USGS in Pasadena, who is mentioned in only one of the various articles written about Keilis-Borok to date,
claims
that there have actually been three predictions issued by the Keilis-Borok team, and that one of them was incorrect. This claim seems to be countered by the January
press release,
which states that, "The team's current predictions have not missed any earthquake, and have had its two most recent ones come to pass.", and this reporter was unable to verify her claim. In any case, it's safe to say that if the Keilis-Borok team is correct in their current prediction, they'll likely garner more than a few new followers and believers in their "tail wags the dog" technique.

For now, although the scientific community is "split" about the findings, a "wait and see" approach is prevalent. For one thing, the area targeted by the current prediction is very large - indeed, the probability for an earthquake of magnitude 6.4 or greater occurring randomly in the area is at least 10%, according to the CEPEC report mentioned earlier. And while CEPEC is cautiously optimistic about Keilis-Borok's work, they also feel that the "results do not at this time warrant any special public policy actions in California". Keilis-Borok remains undaunted by the skepticism however, saying, "Application of nonlinear dynamics and chaos theory is often counter-intuitive, so acceptance by some research teams will take time. Other teams, however, accepted it easily."

Indeed. The more we learn about chaos and nonlinear dynamics, the more we understand that they are inherent in most, if not all, natural processes - and any attempt at predicting the outcome of such processes reliably must take chaos into account. At the same time we should pay heed to Richter's admonishment, and not "rush like hogs to a full trough" towards Keilis-Borok's prediction - and furthermore, how many of us *really* want the prediction to be true? It seems just slightly morbid to hope for an earthquake...

In any case we must ask, if Keilis-Borok's prediction actually is borne out, how useful is it, really, to be able to predict earthquakes months, instead of years in advance? Clearly, a months-long warning is too short to change building codes, and much too long to order evacuations. Nevertheless, if Keilis-Borok is right, it will be a significant victory for science and understanding the world we live in, and will certainly help to persuade preventive efforts, and planning in the future, if nothing else. That fact alone could save millions of lives.

**References:**

- Earthquake Prediction: Basics, Achievements, Perspectives - Keilis-Borok
- Premonitory patterns of seismicity months before a large earthquake: Five case histories in Southern California - Keilis-Borok, et al. - 2002
- Earthquakes can be predicted
months in advance, report UCLA scientists who predicted San Simeon earthquake - Press Release, UCLA, Jan. 6, 2004
- Documented prediction of San Simeon Earthquake 6 months in advance: Premonitory change of seismicity, tectonic setting, physical mechanism - SEISMOLOGICAL SOCIETY OF AMERICA Abstract, 2004
- The Fractal Microscope - a java-based set of tools for playing with fractals.