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Geologic picture without a scale

Almost all geology is fractal and scale-invariant. That means you should always put in a scale when taking pictures of rock formations. For example, in this picture, you can’t tell if it is 6 m or 6 km across. It’s actually an ASTER satellite image of a mountain range.

Scale-invariance is also the main rule for faults and earthquakes. However, an apparent exception confuses this picture: the Characteristic Earthquake, which is a repeating, large earthquake that appears more frequently than local seismic monitoring would suggest [1] . Characteristic earthquakes are usually defined from paleoseismology observations [2] .

As you would realize, this has important implications for seismic hazard calculations (and earthquake insurance rates!). It is basically saying that you can have a section of a fault that has very little observed seismicity, but is a high hazard because the paleoseismic studies show a regular pattern of large earthquakes.

On the surface, this is a contradiction of the fundamental principle of scale invariance. Consider a pile of sand, where you are constantly dribbling on new grains (try this at home!). You get an amazing pattern of frequent little slides, and less frequent larger slides. The process is completely scale-invariant.

Piling on sand grains

As shown in the figure, we have an ideal analogy of the earthquake process (fault mechanics). All earth materials, from tiny sand grains, to the crushed rock in giant faults, basically behave the same. In this example, the grains are coloured according to their stability (stable grains are going to stay in one spot, and unstable grains are ready to move). If these colours could just randomly turn off and on like Christmas lights, then we would not have the standard distribution of small to large failures – only individual grains would move.

The fundamental friction and fault friction properties allow stress shedding, and cause more and more grains in proximity to become the same colour. When this happens, there is a large failure, and the grains reset to a more scattered pattern; in effect, a large earthquake.

To allow the concept of characteristic earthquakes, there has to be some modification to this picture. That could mean there is no scale invariance (plate tectonics?), or, most likely, as suggested in recent papers, that there is a problem with sample size. In other words, a particular fault may appear to have characteristic earthquakes, but the stress-shedding region, as a whole, behaves in a normal manner. It is like just looking at the surface of the sand pile, and not the whole system.