The Mathematics of Earthquake Prediction

Earthquake prediction is much like taking on the stock market; you can see patterns, you have an idea what is going on, but can you make a prediction? Also, timing is important: to say that an earthquake will happen in a certain town "sometime in the next 17.5 years" is of limited value.

Earthquake Prediction and the Power Law

Earthquakes behave very much like other seemingly random phenomena such as wind bursts, solar flares, and storms. Mathematically, these episodic events can be modeled using the "power law". For stocks, you might notice a consistent pattern where 1% price-swings happen 8 times more often than 2% price swings, which also occurs 8 times more often than a 4% change. Once in a while, there is a major 'stock-quake' with a huge price change.

Earthquakes generally follow a power law, as well. They are rated in terms of magnitude, which works on a logarithmic scale. An M3 earthquake has about 30 times more energy than an M2. Also, M2 earthquakes occur 10 times more often than M3's, which are 10 times more frequent than M4's, etc.

Most elements of nature, on some level, follow power laws. The ever-expanding sections of a sea shell spiral, or the pattern of indentations in a leaf, can all be aligned to power law calculations. Because the power law is so ubiquitous, one can generally find patterns in any natural event.

False Connections

In the history of earthquake prediction, people have tried to associate earthquakes with other natural events, hoping to find a pattern that can be used to predict future quakes. People have 'associated' the onset of an earthquake with such things as animal behavior, the weather, motion in the level of water wells, etc. Unfortunately, these efforts have met with limited success - usually marked by the unexpected arrival of the next earthquake.

Useful Earthquake Predictions

To be truly useful, earthquake prediction has to be precise in magnitude, time and place. Useless earthquake predictions tend to be overly general, 'predicting' such things as a small earthquake in California 'any day now'.

As scientists study earthquakes they will become more precise in their estimates of seismic hazard, using such advanced tools as real-time GPS. In time, these new tools may evolve into a reliable system of earthquake prediction.