Some mathematical musings about extreme events for geotechnical risk, without (much of) the math

ABSTRACT: Extreme events seem to occur with surprising regularity, at frequencies greatly exceeding those expected from a typical analysis of probabilities that assume well-behaved statistical characteristics. Many natural phenomena, including those involving geologic materials, have heavy tails that decay much slower than a normal distribution, often as a power law, with fractal geometric character and associated non-intuitive behavior, particularly for the rare events that represent the tails of the probability distributions. This paper exploits an example from an unrelated field – finance – to illustrate key behaviours of power law phenomena before returning to those of geologic materials, with discussion of important implications to geohazard risk assessment.