Volcano-hydrothermal systems are governed by complex interactions between fluid transport, and geochemical and mechanical processes. Evidence of this close interplay has been testified by distinct spatial and temporal correlations in geochemical and geophysical observations at Vulcano Island (Italy). To understand the interaction between fluid circulation and the geochemical and geophysical manifestations, we perform a parametric study to explore different scenarios by implementing a hydro-geophysical model based on the equations for heat and mass transfer in a porous medium and thermo-poroelastic theory. Numerical simulations allow us to define the controlling role of permeability distribution on the different modeled parameters as well as on the geophysical observables. Changes in the permeability within the highly fractured crater area could be responsible for the fluctuations in gas emission and temperature recorded during the crisis periods, which are accompanied by shallow volcano-seismicity in the absence of significant deformation and gravity variations. Despite the general medium permeability of the volcanic edifice, the presence of more highly permeable pathways, which allow the gas to rapidly escape, as testified by the presence of a well-developed fumarolic field, prevents the pressure buildup at shallow depths. Graphic abstract

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When approximating elliptic problems by using specialized approximation techniques, we obtain large structured matrices whose analysis provides information on the stability of the method. Here we provide spectral and norm estimates for matrix sequences arising from the approximation of the Laplacian via ad hoc finite differences. The analysis involves several tools from matrix theory and in particular from the setting of Toeplitz operators and Generalized Locally Toeplitz matrix sequences. Several numerical experiments are conducted, which confirm the correctness of the theoretical findings.