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.

We performed a comprehensive statistical analysis over six functional expressions of frequency–magnitude distributions (FMDs). We tested the goodness of fit on the basis of the Kolmogorov–Smirnov criterion, and performed a model selection using the Akaike information criterion over 15,000 subcatalogs spanning different sizes and covering different areas of the world. Results showed that the FMD proposed by Ogata and Katsura (1993) usually performs better than the others even if, in general, it would be appropriate to check the goodness of fit and do a model selection using statistical tools.

Tenerife (Canary Islands, Spain) is an active oceanic volcanic island where low to moderate seismicity provides one of the few direct windows into the present stress state, hydrothermal, and volcanic activity. The island contains four main volcanic systems that interact in complex ways, and its seismic behaviour is also influenced by regional tectonic stresses, including the fault zone between Tenerife and Gran Canaria. Since 2016, small but persistent changes in the rate and spatial pattern of local earthquakes have been observed. These changes raise the question of how Gutenberg–Richter parameters and related metrics respond to an evolving volcanic–tectonic setting. In this study, we use a catalogue-based, multi-parameter approach to investigate the factors controlling variations in the Gutenberg–Richter a and b values in Tenerife. The analysis is complemented by simple fractal measures that describe how earthquake hypocentres cluster in time and space. We track the spatial and temporal evolution of these parameters using moving windows at different scales, paying particular attention to magnitude completeness, as seismicity is strongly concentrated in a few areas of the island. We explicitly separate background seismicity from well-defined swarm episodes. Swarms are analysed both independently and as part of the whole catalogue, allowing us to quantify the extent to which they influence overall estimates of a, b, and the fractal dimension. By comparing the resulting parameter patterns with the main volcanic systems, rift zones, and structural lineaments, we explore how variations in b-value and clustering reflect differences in stress conditions and structural complexity. Special attention is given to areas and time periods in which, based on independent geochemical data, the hydrothermal system is known to have played an important role, as fluid circulation can enhances microseismicity in Tenerife This work aims to provide observational constraints on the interpretation of Gutenberg–Richter parameters and fractal metrics in an ocean-island setting. We show how this simple but information-rich framework can help distinguish volcanic, tectonic, and hydrothermal contributions to seismicity in Tenerife, and can serve as a basis for future models that link b-value variability to underlying physical processes in interacting volcanic systems.

The analysis of multiparametric geophysical and geochemical datasets presents significant challenges due to the diverse nature of measurements and their potential interactions. The development of advanced statistical and data mining techniques has enabled researchers to identify and characterise complex patterns within such datasets. This work builds upon a previous study that applied Independent Vector Analysis (IVA) to analyse multiparametric measurements collected at Teide volcano crater (Tenerife, Canary Islands) between 2020 and 2024. Our main goal is to extend the initial findings by identifying endogenous and exogenous factors influencing the observed patterns and characterising their temporal behaviour.The dataset includes spontaneous potential, CO2 and H2S fluxes, and thermal gradient measurements taken within the crater of Teide volcano on 38 fixed points. The application of IVA, which is an extension of Independent Component Analysis (ICA), allows for a multivariate approach that leverages vectorial data instead of scalar quantities. This method has proven effective for disentangling spatio-temporal interactions and isolating independent processes that govern the observed geophysical and geochemical variations.Based on previous preliminary results, this study incorporates new data collected during 2023 and 2024, allowing a better definition of the spatio-temporal patterns. Using the IVA, we identify and quantify evolving endogenous patterns potentially related to magmatic processes. Simultaneously, we assess the influence of exogenous factors such as seasonal temperature fluctuations and hydrological changes.Our results highlight the robustness of IVA in separating and characterising independent processes contributing to spatio-temporal multivariate datasets, such as the specific case of the Teide volcano. The results reveal a strong correlation between spontaneous potential anomalies and localised gas emissions, validating this methodology in volcanic environments. Moreover, this extended study underscores the importance of integrating temporal dynamics into multivariate analyses to improve the understanding of volcanic systems.This work demonstrates the potential of IVA as a powerful tool for analysing repeated geophysical and geochemical surveys. It offers significant advantages for monitoring active volcanic systems. Future applications could include adding more datasets, such as remote sensing and/or other geophysical or geochemical parameters, to understand volcanic processes comprehensively.