[1] This contribution presents a semiempirical model describing the effective relative viscosity of crystalbearing magmas as function of crystal fraction and strain rate. The model was applied to an extensive data set of magmatic suspensions and partially molten rocks providing a range of values for the fitting parameters that control the behavior of the relative viscosity curves as a function of the crystal fraction in an intermediate range of crystallinity (30-80 vol % crystals). The analysis of the results and of the materials used in the experiments allows for evaluating the physical meaning of the parameters of the proposed model. We show that the model, by varying the parameters within the ranges obtained during the fitting procedure, is able to describe satisfactory the effective relative viscosity as a function of crystal fraction and strain rate for suspensions having different geometrical characteristics of the suspended solid fraction.Components: 6984 words, 4 figures, 1 table.Keywords: melts; concentrated suspensions; viscosity; strain rate. Caricchi, and N. Bagdassarov (2009), A model for the rheology of particle-bearing suspensions and partially molten rocks, Geochem. Geophys. Geosyst., 10, Q03010,

[1] The relationship between permeability and porosity is reviewed and investigated. The classical Kozeny-Carman approach and a fractal pore-space geometry assumption are used to derive a new permeability-porosity equation. The equation contains only two fitting parameters: a Kozeny coefficient and a fractal exponent. The strongest features of the model are related to its simplicity and its capability to describe measured permeability values of different non-granular porous media better than other models.Citation: Costa, A. (2006), Permeability-porosity relationship: A reexamination of the Kozeny-Carman equation based on a fractal pore-space geometry assumption, Geophys. Res. Lett., 33, L02318,

[1] We develop a model to describe ash aggregates in a volcanic plume. The model is based on a solution of the classical Smoluchowski equation, obtained by introducing a similarity variable and a fractal relationship for the number of primary particles in an aggregate. The considered collision frequency function accounts for different mechanisms of aggregation, such as Brownian motion, ambient fluid shear, and differential sedimentation. Although model formulation is general, here only sticking efficiency related to the presence of water is considered. However, the different binding effect of liquid water and ice is discerned. The proposed approach represents a first compromise between the full description of the aggregation process and the need to decrease the computational time necessary for solving the full Smoluchowski equation. We also perform a parametric study on the main model parameters and estimate coagulation kernels and timescales of the aggregation process under simplified conditions of interest in volcanology. Further analyses and applications to real eruptions are presented in the companion paper by Folch et al.

[1] We present a reliable methodology to estimate the energy associated with the subaerial diffuse degassing of volcanic-hydrothermal fluids. The fumaroles of 15 diffuse degassing structures (DDSs) located in eight volcanic systems in the world were sampled and analyzed. Furthermore, each area was measured for soil temperature gradients and for soil CO 2 fluxes. The results show that each hydrothermal or volcanic system is characterized by a typical source fluid which feeds both the fumaroles and diffuse degassing through the soil. Experimental data and the results of physical numerical modeling of the process demonstrate that the heat released by condensation of steam at depth is almost totally transferred by conduction in the uppermost part of the soil. A linear relationship is observed between the log of the steam/gas ratio measured in the fumaroles and the log of the ratio between soil thermal gradient and soil-gas flux. The main parameter controlling this relation is the thermal conductivity of the soil (K c ). For each area, we computed the values of K c which range from 0.4 to 2.3 W m À1°CÀ1 . Using the CO 2 soil fluxes as a tracer of the deep fluids, we estimated that the total heat released by steam condensation in the systems considered varies from 1 to 100 MW.

Volume determination of tephra deposits is necessary to the characterization of active volcanoes, with obvious implications for environmental and climatic impact, estimation of magma-production rate, long-term hazard assessments and forecasting of future eruptions. Several methods have been proposed that mainly include the integrations of various deposit-thinning relationships and the inversion of field observations using computational models. Regardless of their strong dependence on tephra-deposit exposure, empirical integrations of deposit-thinning trends still represent the most widely adopted strategy due to their practical and fast application. The choice of best-fitting trends (e.g., exponential and power-law thinning on semi-log plots) has been subject of lively debate because they are all characterized by various advantages and disadvantages. We propose a new empirical method that is based on the Weibull distribution and shows a better agreement with observed data reconciling the debate on the use of the exponential versus power-law methods. Nonetheless, we also show that all empirical methods used to derive erupted volume based on integration of deposit thinning strongly depend on the available data and are affected by various degrees of uncertainties. Application of various empirical and analytical methods can help to assess the associated uncertainties

[1] The rheological properties of suspensions containing high solid fractions are investigated. Attention is focused on viscosity of silicate and magmatic melt systems. A general empirical equation which describes the relative viscosity of suspensions as a function of suspended solid fraction is proposed. In the limit of very dilute solid concentrations it reduces to the Einstein equation. The proposed relationship is satisfactorily applied to reproduce available experimental data relative to silicate melts. Moreover, the extrapolation of the model to very high concentrations is compared with experimental observations on partially-melted granite.

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Applying probabilistic methods to infrequent but devastating natural events is intrinsically challenging. For tsunami analyses, a suite of geophysical assessments should be in principle evaluated because of the different causes generating tsunamis (earthquakes, landslides, volcanic activity, meteorological events, and asteroid impacts) with varying mean recurrence rates. Probabilistic Tsunami Hazard Analyses (PTHAs) are conducted in different areas of the world at global, regional, and local scales with the aim of understanding tsunami hazard to inform tsunami risk reduction activities. PTHAs enhance knowledge of the potential tsunamigenic threat by estimating the probability of exceeding specific levels of tsunami intensity metrics (e.g., run‐up or maximum inundation heights) within a certain period of time (exposure time) at given locations (target sites); these estimates can be summarized in hazard maps or hazard curves. This discussion presents a broad overview of PTHA, including (i) sources and mechanisms of tsunami generation, emphasizing the variety and complexity of the tsunami sources and their generation mechanisms, (ii) developments in modeling the propagation and impact of tsunami waves, and (iii) statistical procedures for tsunami hazard estimates that include the associated epistemic and aleatoric uncertainties. Key elements in understanding the potential tsunami hazard are discussed, in light of the rapid development of PTHA methods during the last decade and the globally distributed applications, including the importance of considering multiple sources, their relative intensities, probabilities of occurrence, and uncertainties in an integrated and consistent probabilistic framework.