The ups and downs of volcanic unrest: Insights from integrated geodesy and numerical modelling

Part of the Advances in Volcanology book seriesThis is the final version of the chapter. Available from the publisher via the DOI in this record.Volcanic eruptions are often preceded by small changes in the shape of the volcano. Such volcanic deformation may be measured using precise surveying techniques and analysed to better understand volcanic processes. Complicating the matter is the fact that deformation events (e.g., inflation or deflation) may result from magmatic, non-magmatic or mixed/hybrid sources. Using spatial and temporal patterns in volcanic deformation data and mathematical models it is possible to infer the location and strength of the subsurface driving mechanism. This can provide essential information to inform hazard assessment, risk mitigation and eruption forecasting. However, most generic models over-simplify their representation of the crustal conditions in which the deformation source resides. We present work from a selection of studies that employ advanced numerical models to interpret deformation and gravity data. These incorporate crustal heterogeneity, topography, viscoelastic rheology and the influence of temperature, to constrain unrest source parameters at Uturuncu (Bolivia), Cotopaxi (Ecuador), Soufrière Hills (Montserrat), and Teide (Tenerife) volcanoes. Such model complexities are justified by geophysical, geological, and petrological constraints. Results highlight how more realistic crustal mechanical conditions alter the way stress and strain are partitioned in the subsurface. This impacts inferred source locations and magmatic pressures, and demonstrates how generic models may produce misleading interpretations due to their simplified assumptions. Further model results are used to infer quantitative and qualitative estimates of magma supply rate and mechanism, respectively. The simultaneous inclusion of gravity data alongside deformation measurements may additionally allow the magmatic or non-magmatic nature of the source to be characterised. Together, these results highlight how models with more realistic, and geophysically consistent, components can improve our understanding of the mechanical processes affecting volcanic unrest and geodetic eruption precursors, to aid eruption forecasting, hazard assessment and risk mitigation.s Work presented herein has received funding by the European Commission (FP7; Theme: ENV.2011.1.3.3-1; Grant 282759: VUELCO)

Solitary waves in the Nonlinear Dirac Equation

In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three spatial dimensions and the equations they satisfy. We present the associated explicit solutions in one dimension and numerically obtain their analogues in higher dimensions. The stability is subsequently discussed from a theoretical perspective and then complemented with numerical computations. Finally, the dynamics of the solutions is explored and compared to its non-relativistic analogue, which is the nonlinear Schr{\"o}dinger equation. A few special topics are also explored, including the discrete variant of the nonlinear Dirac equation and its solitary wave properties, as well as the PT-symmetric variant of the model

Unexpected large eruptions from buoyant magma bodies within viscoelastic crust

Large volume effusive eruptions with relatively minor observed precursory signals are at odds with widely used models to interpret volcano deformation. Here we propose a new modelling framework that resolves this discrepancy by accounting for magma buoyancy, viscoelastic crustal properties, and sustained magma channels. At low magma accumulation rates, the stability of deep magma bodies is governed by the magma-host rock density contrast and the magma body thickness. During eruptions, inelastic processes including magma mush erosion and thermal effects, can form a sustained channel that supports magma flow, driven by the pressure difference between the magma body and surface vents. At failure onset, it may be difficult to forecast the final eruption volume; pressure in a magma body may drop well below the lithostatic load, create under-pressure and initiate a caldera collapse, despite only modest precursors

Preconditioned Conjugate Gradient Method for Solution of Large Finite Element Problems on CPU and GPU

In this article the preconditioned conjugate gradient (PCG) method, realized on GPU and intended to solution of large finite element problems of structural mechanics, is considered. The mathematical formulation of problem results in solution of linear equation sets with sparse symmetrical positive definite matrices. The authors use incomplete Cholesky factorization by value approach, based on technique of sparse matrices, for creation of efficient preconditioning, which ensures a stable convergence for weakly conditioned problems mentioned above. The research focuses on realization of PCG solver on GPU with using of CUBLAS and CUSPARSE libraries. Taking into account a restricted amount of GPU core memory, the efficiency and reliability of GPU PCG solver are checked and these factors are compared with data obtained with using of CPU version of this solver, working on large amount of RAM. The real-life large problems, taken from SCAD Soft collection, are considered for such a comparison