The Correspondence of Earthquakes and Faults

Abstract

A compilation of many data sets indicates that the exponents α for the cumulative length distribution N(L) = CL^−α, of small faults of L < T, the brittle thickness, and for large faults of L > T, are both approximately 2. The same result was found by Zou and Fialko (2024, https://doi.org/10.1029/2024ea003824), but that was fortuitous: their finding being contingent on two compensating errors. If α is 2 for both distributions, it indicates that the exponent B of the cumulative moment distribution N(M_g) = cMg^−B is −2/3 for small faults and −1 for large faults, the same values as found for small and large earthquakes. The moment release rates obtained from both earthquake and fault data have also been found to correspond. This demonstrates that in continental regions the long-assumed correspondence between earthquakes and faults is inclusive. All tectonic earthquakes must occur on faults and faults must slip predominately in earthquakes. The relative contribution of small earthquakes/faults to strain is minor for a single large fault over the recurrence time of the fault-rupturing earthquake because that case is governed by the characteristic earthquake model. In contrast, over a larger region containing many moderate sized faults, for which the Gutenberg–Richter distribution holds, the relative contribution of small earthquakes/faults to strain may be significant. These different behaviors characterize mature smooth versus immature segmented fault systems.