Mathematical and Numerical Models of Lava Dome Dynamics

Dome-building eruptions may vary from unthreatening effusion to highly unpredictable and hazardous activity including collapse of domes and associated pyroclastic flow hazards. We analyse the influence of the thermal cooling and the crystal content growth on the lava dome morphology at Volcán de Colima in Mexico during a long dome-building episode lasting from early 2007 to fall 2009 without explosive dome destruction. For this, we develop several mathematical models of lava dome dynamics including the kinetics of crystal content growth, temperature-dependence of melt viscosity, latent heat, and nonlinear heat exchange between the lava and the air. Camera images of the lava dome growth together with recorded volumes of the erupted lava have been used to constrain our numerical models and hence to fit the observation data of the dome growth at Volcán de Colima by nudging model forecasts to observations. We shall present the mathematical models and results of the ongoing modelling

Numerical thermo-mechanical modelling of lava dome growth during the 2007-2009 dome-building eruption at Volcán de Colima

Lava domes form during effusive eruptions due to an extrusion of highly viscous magmas from volcanic vents. We present here a study of the lava dome growth at Volcán de Colima, Mexico during 2007-2009 using numerical modelling. The mathematical model treats the lava dome extrusion dynamics as a thermo-mechanical problem. The equations of motion, continuity, and heat transfer are solved with the relevant boundary and initial conditions in the assumption that the viscosity depends on the volume fraction of crystals and temperature. Numerical experiments have been performed to analyse the internal structure of the lava dome (i.e., the distributions of the temperature, crystal content, viscosity, and velocity) depending on various heat sources and thermal boundary conditions. It was demonstrated earlier that the lava dome dynamics at Volcán de Colima during short (for a couple of months) dome-building episodes can be modelled by an isothermal lava extrusion with the viscosity depending on the volume fraction of crystals. We show here that cooling plays a significant role during long (up to several years) dome-building episodes. A carapace develops as a response to a convective cooling at the lava dome interface with the air. The carapace becomes thicker if the radiative heat loss at the interface is also considered. The thick carapace influences the lava dome dynamics constraining its lateral advancement. The latent heat of crystallization leads to higher temperatures inside the lava dome and to a relative flattening of the dome. The developed thermo-mechanical model of lava dome dynamics at Volcán de Colima can be used elsewhere to analyze effusive eruptions, dome carapace evolution and its failure potentially leading to pyroclastic flow hazards

Visualization of lithosphere subduction: application to the mantle evolution beneath the Japanese Islands

In this article we illustrate how visualization of scientific data helps in interpreting results of three-dimensional numerical modeling. We visualize the evolution of the descending lithosphere (lithosphere subduction) beneath the Japanese Islands assimilating geophysical, geodetic, and geological data. Using three-dimensional visualization tools we illustrate here that the hot mantle upwelling beneath the descending Pacific plate penetrated through the plate into the mantle wedge

Quantitative reconstruction of thermal and dynamic characteristics of lava flow from surface thermal measurements

International audienceWe study a model of lava flow to determine its thermal and dynamic characteristics from thermal measurements of the lava at its surface. Mathematically this problem is reduced to solving an inverse boundary problem. Namely, using known conditions at one part of the model boundary we determine the missing condition at the remaining part of the boundary. We develop a numerical approach to the mathematical problem in the case of steady-state flow. Assuming that the temperature and the heat flow are prescribed at the upper surface of the model domain, we determine the flow characteristics in the entire model domain using a variational (adjoint) method. We have performed computations of model examples and showed that in the case of smooth input data the lava temperature and the flow velocity can be reconstructed with a high accuracy. As expected, a noise imposed on the smooth input data results in a less accurate solution, but still acceptable below some noise level. Also we analyse the influence of optimization methods on the solution convergence rate. The proposed method for reconstruction of physical parameters of lava flows can also be applied to other problems in geophysical fluid flows

Three-dimensional forward and backward numerical modeling of mantle plume evolution: Effects of thermal diffusion

International audienceWe investigate the effects of thermal diffusion on the evolution of mantle plumes by means of three-dimensional numerical modeling forward and backward in time. Mantle plumes are fed by a hot, low-viscous material from the thermal boundary layer. The material of the plumes is mainly advected toward the Earth's surface with some effects of thermal diffusion. However, the feeding can become weaker with time, and then thermal diffusion can take over and control the evolution of the plumes. Numerical experiments forward in time show that a week feeding of mantle plumes by the hot material from the boundary layer results in the diffusive disappearance of plume tails first and plume heads later. This is the most likely explanation for the seismically detected low-velocity mantle structures (mantle plumes) with prominent heads and almost invisible tails at midmantle depths. We develop restoration models (backward in time) to recover strong features of mantle plumes in the geological past after they have dissipated due to thermal diffusion and analyze effects of thermal diffusion and temperature-dependent viscosity on the reconstruction of the mantle plumes. We investigate the impact of thermal diffusion on the performance of our restoration (variational data assimilation) algorithm. For a given range of Rayleigh number Ra and two values of the viscosity ratio r (between the upper and lower boundaries of the model domain) we show that (1) the residuals between the temperature predicted by the forward model and that reconstructed by the backward modeling become larger and (2) the restoration process becomes poorer as Ra decreases and r increases. We assimilate temperature obtained from high-resolution seismic tomography data for the southeastern Carpathians and show that present diffused mantle structures can be restored to their prominent state in the Miocene times. We discuss the problems of smoothness of model input and output data, errors associated with the modeling, and some other challenges in the data assimilation for thermoconvective flow in the mantle