Harmonic Fluctuation of the Slope of the Frequency–Magnitude Distribution (b‐Value) as a Function of the Angle of Rake

Abstract

Previous works suggested that the slope (b-value) of the frequency–magnitude distribution of earthquakes might significantly vary as a function of the style of faulting. In this work, we resume such hypothesis using improved datasets and procedures and by testing a simple harmonic functional form of the b-value as a function of the angle of rake λ. Using the Global Centroid Moment Tensor (CMT) catalog updated to the middle of 2016, we reliably compute the b-value over 12 nonoverlapping rake windows with width γ 30° showing a clear oscillating behavior with highs for normal and lows for reverse mechanisms. We also test the existence of a spatial link between variations of the style of faulting and of the b-value by determining the rake and the b-value separately from the Global CMT catalog and from a magnitude homogenized version of the bulletin of the International Seismological Centre, respectively, based on a spatial tessellation of the Earth’s surface. For both approaches, we verify, using two statistical methods, that the b-values computed from earthquakes with different tectonic styles are actually different from each other for many combinations of rakes and particularly for all combinations of almost pure tectonic styles. We find that the fitted harmonic function has zero phase and unit frequency, thus indicating that b-value modulation is about proportional to −sin λ. Because the latter corresponds to the dot product between the unit versors of the coseismic displacement and of the gravity force component along the fault plane, b-value modulation appears to be about proportional to the work done by the gravity force during the fault slip.