Beyond b-value: The True Nature of Deviations in Earthquake Size Distributions

It is well-accepted that the earthquake magnitude-frequency relationship over large areas is well-described by the Gutenberg-Richter (G-R) relationship which is characterized by a constant, b, that is usually close to 1.0. At smaller scales many have found a G-R relationship with b ≠ 1 . 0 . The idea that b values vary is puzzling because summing G-R relationships with different exponents does not produce a G-R relationship for the data overall. To visualize the magnitude-frequency relationship more precisely we plot magnitude, M, vs. the ratio, r, between how many ≥ M earthquakes are observed to how many would be expected for a given b-value. Variations from the assumed G-R relationship show up as deviations from r = 1 , allowing for clear visualization. We find that most distributions appearing to have b ≠ 1.0 actually follow b = 1 . 0 for part of the magnitude range, deviating at the higher end often because of finite fault or stress effects that can be reproduced with a percolation model, or at the lower end because of magnitude errors. We expect the finite-fault effects to be long-term. In particular there are very different magnitude distributions in the California catalog before and after magnitude calculation changes were made in 2008 (and propagated back to 2005). The older part of the Southern California catalog shows strong irregularities for M < 3 because smaller magnitudes were systematically overestimated at that time, while the latter part shows a less severe irregularity in more sparsely instrumented parts of the region that may extend up to M = 5 . We also observe that magnitude distributions change temporally in aftershock zones, but again we are not truly seeing a change in b-value but rather that there are systematic variations in the number of larger earthquakes while the smaller earthquakes remain consistent with G-R with b = 1 . 0 .