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One of the most accepted frameworks for the relationship between the magnitude and frequency of an earthquake is that of the critical phenomena. In this framework, the magnitude of events must be distributed following a power law.

However the Gutenberg-Richter law clearly shows a deviation at low magnitudes from the power law called a roll-off. How can the roll-off deviation of the GR prediction be explained?

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The roll off deviation appears to mostly be due to difficulties with accurate measurements at low magnitudes. In order to preserve the GR law you'd need to exhaustively record all earthquake measurements below the roll off magnitude and this is largely infeasible.

A good example to look at (figure 3.1) is the difference between the Sumatra 2004 and Kobe 1995 earthquakes. The Kobe event was recorded with extreme accuracy (p669) using the Japanese strong-motion network and so displays no roll-off.

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