Multiscale Temporal and Spatial Estimation of the b-Value

Abstract

The estimation of the b-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 B-value [MUST-B]), which allows consistent estimation of the b-value, avoiding subjective “a priori” choices, by considering simultaneously different temporal or spatial scales. A reliable appraisal of the b-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 b-value as well as inconsistently mapping it for highly heterogeneous catalogs. We apply MUST-B to study the temporal and spatial variations of the b-value during the complex 2016–2017 seismic sequence in central Italy, revealing various interesting patterns. In particular, we observe a marked drop of the b-value after the Accumoli (24 August 2016 M 6.0) mainshock. The drop is also observed when realizing a tridimensional mapping of the b-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.

Gutenberg–Richter B-Value Time Series Forecasting: A Weighted Likelihood Approach

“…To further validate our methodology, we also compared the weighted likelihood approach with the novel MUST-B estimator introduced by García-Hernández et al [25]. This estimator avoids subjective biases in the choice of the window size by taking the median values of different b-values estimated using rolling windows of different lengths.…”

“…This estimator avoids subjective biases in the choice of the window size by taking the median values of different b-values estimated using rolling windows of different lengths. This method was successfully applied to the 2016-2017 central Italy seismic sequence; in our exercise, we retained the parameters' values described in García-Hernández et al [25]. Bayes Factor values suggest that our methodology performed better than MUST-B, for both the TABOO (ln(BF) = 3.1), and the CMT (ln(BF) = 6.1) catalogues, respectively.…”

b-value of what? Complex behavior of the magnitude distribution during and within the 2016–2017 central Italy sequence

“…found a 𝑏-value variation during the course of the sequence, in particular (i) a drop after the Amatrice event (especially in the area to the north where the Norcia mainshock occurred afterward), interpreted as a still impending large earthquake, and (ii) a 𝑏-value increase « after the Norcia mainshock, interpreted as a substantially reduced chance for a further large event similar to the tectonic background rate. García-Hernăndez et al [2021] also observed a "marked drop of the 𝑏-value" after the Amatrice event (resolved spatially and in depth) and a recovery of the 𝑏-value to the background level after the Norcia mainshock; they exclude that these variations are caused by an increased 𝑀 c after the main events. However, those studies did not (i) use a high-resolution catalog, (ii) account for the complexity of the sequence including its depth-dependent structure, and (iii) resolve what happened in the days before the largest event (Norcia).…”

A comprehensive suite of earthquake catalogues for the 2016-2017 Central Italy seismic sequence

“…These catalogues can help test hypothesis such as the predictive value of a spatiotemporal variations in terms of b-value (e.g., Gulia and Wiemer 19 ; García-Hernández et al . 20 ; Herrmann et al . 21 ).…”