The estimation of the ‐value of the Gutenberg–Richter law is of great importance in different seismological applications. However, its estimate is strongly dependent upon selecting a proper temporal and spatial scale, due to the multiscale nature of the seismicity. For this reason, we propose a novel approach (MUltiscale Spatial and Temporal estimation of the ‐value [MUST‐B]), which allows consistent estimation of the ‐value, avoiding subjective “a priori” choices, by considering simultaneously different temporal or spatial scales. A reliable appraisal of the ‐value is obtained by applying a robust median over the estimates computed over all the considered scales.
We validate the method using a synthetic dataset, showing its superior performances, compared to traditional approaches, in detecting sharp changes in the ‐value as well as inconsistently mapping it for highly heterogeneous catalogs.
We apply MUST‐B to study the temporal and spatial variations of the ‐value during the complex 2016–2017 seismic sequence in central Italy, revealing various interesting patterns. In particular, we observe a marked drop of the ‐value after the Accumoli (24 August 2016 M 6.0) mainshock. The drop is also observed when realizing a tridimensional mapping of the ‐values, showing the drop occurs mainly in the proximity of major earthquake hypocenters. In accordance with previous studies, we interpret these variations as the effect of the release of crustal fluids following the major earthquakes.
We maintain that MUST‐B can also be applied to other contexts, such as volcanic and induced seismicity, because of its capacity of dealing consistently with highly heterogeneous seismicity patterns.