Self-organized criticality and earthquakes
In 1987 the team of Bak, Tang, and Weisenfeld presented a paper on "Self-organized Criticality" which hoped to provide a very simplified model to explain the complexity that is found in nature. Prior to this, many models describing complex systems had been developed however there was no general theory of complexity built on a strong mathematical foundation. The theory with which the team attempted in their paper explains the "self-organized critical state" (SOC) by comparing it to that of a steep sand pile which emits avalanches of all sizes as more sand is added to the system. This state is characterized by the fact that the system has self-organized itself to a point where it is on the border between predictability and unpredictability to the so called "edge of chaos." For the specific case of earthquakes, it can be postulated that the crust of the earth is a highly self-organized system which features earthquakes that are unpredictably strong, where the intensity and frequency of the quakes follow a power law distribution. Power law distributions are a key aspect of SOC.
The Sandpile Paradigm
Sandpile Applet[1]
The 'edge of chaos' and power law distributions
The gutenberg-richter law
The crust of the Earth is in a self-organized critical state
Sources
Self-Organized Criticality: Emergent Complex Behavior in Physical and Biological Systems. Cambridge Lecture Notes in Physics Part 10.
How Nature Works: The Science of Self-Organized Criticality. Per Bak.
Modeling Extinction. M.E.J. Newman, R.G. Palmer. Santa Fe Institute Studies in the Sciences of Complexity.