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The behaviour of low-viscosity, pressure-driven compressible pore fluid flows in viscously deformable porous media is studied here with specific application to gas flow in lava domes. The combined flow of gas and lava is shown to be governed by a two-equation set of nonlinear mixed hyperbolic–parabolic type partial differential equations describing the evolution of gas pore pressure and lava porosity. Steady state solution of this system is achieved when the gas pore pressure is magmastatic and the porosity profile accommodates the magmastatic pressure condition by increased compaction of the medium with depth. A one-dimensional (vertical) numerical linear stability analysis (LSA) is presented here. As a consequence of the pore-fluid compressibility and the presence of gravitation compaction, the gradients present in the steady-state solution cause variable coefficients in the linearized equations which generate instability in the LSA despite the diffusion-like and dissipative terms in the original system. The onset of this instability is shown to be strongly controlled by the thickness of the flow and the maximum porosity, itself a function of the mass flow rate of gas. Numerical solutions of the fully nonlinear system are also presented and exhibit nonlinear wave propagation features such as shock formation. As applied to gas flow within lava domes, the details of this dynamics help explain observations of cyclic lava dome extrusion and explosion episodes. Because the instability is stronger in thicker flows, the continued extrusion and thickening of a lava dome constitutes an increasing likelihood of instability onset, pressure wave growth and ultimately explosion. 

Abstract. We detail a new prediction-oriented procedure aimed at volcanic hazardassessment based on geophysical mass flow models constrained withheterogeneous and poorly defined data. Our method relies on an itemizedapplication of the empirical falsification principle over an arbitrarily wideenvelope of possible input conditions. We thus provide a first step towards aobjective and partially automated experimental design construction. Inparticular, instead of fully calibrating model inputs on past observations,we create and explore more general requirements of consistency, and then weseparately use each piece of empirical data to remove those input values thatare not compatible with it. Hence, partial solutions are defined to the inverseproblem. This has several advantages compared to a traditionally posedinverse problem: (i) the potentially nonempty inverse images of partialsolutions of multiple possible forward models characterize the solutions tothe inverse problem; (ii) the partial solutions can provide hazard estimatesunder weaker constraints, potentially including extreme cases that areimportant for hazard analysis; (iii) if multiple models are applicable,specific performance scores against each piece of empirical information canbe calculated. We apply our procedure to the case study of the Atenquiquevolcaniclastic debris flow, which occurred on the flanks of Nevado de Colimavolcano (Mexico), 1955. We adopt and compare three depth-averaged modelscurrently implemented in the TITAN2D solver, available from https://vhub.org(Version 4.0.0 – last access: 23 June 2016). The associated inverse problemis not well-posed if approached in a traditional way. We show that our procedurecan extract valuable information for hazard assessment, allowing the explorationof the impact of synthetic flows that are similar to those that occurred in thepast but different in plausible ways. The implementation of multiple models isthus a crucial aspect of our approach, as they can allow the covering of otherplausible flows. We also observe that model selection is inherently linked tothe inversion problem.