A geometric frequency–magnitude scaling transition: Measuring b = 1.5 for large earthquakes

We identify two distinct scaling regimes in the frequency–magnitude distribution of global earthquakes. Specifically, we measure the scaling exponent b = 1.0 for “small” earthquakes with 5.5 < m < 7.6 and b = 1.5 for “large” earthquakes with 7.6 < m < 9.0. This transition at mt = 7.6, can be explained by geometric constraints on the rupture. In conjunction with supporting literature, this corroborates theories in favor of fully self-similar and magnitude independent earthquake physics. We also show that the scaling behavior and abrupt transition between the scaling regimes imply that earthquake ruptures have compact shapes and smooth rupture-fronts.

► Measure the GR slope of large, m > 7.6, earthquakes b = 1.5.
► Show that this scaling transition is consistent with self-similarity.
► Discuss the fractal dimension and shape of earthquake ruptures.
► Show that the frequency–magnitude scaling implies integer dimensions D = 2, D = 1.
► We discuss the implications for hazard assessment and earthquake simulators.