S. Tait

September 2005 Manda Hararo‐Dabbahu rifting event, Afar (Ethiopia): Constraints provided by geodetic data

faults. The volume of the 2005 dike (1.5–2.0 km 3 ) is not balanced by sufficient volume loss at Dabbahu and Gabho volcanoes (0.42 and 0.12 km 3 , respectively). Taking into account the deflation of a suspected deep midsegment magma chamber simultaneously to dike intrusion produces a smoother opening distribution along the southern segment. Above the dike, faults slipped by an average 3 m, yielding an estimated geodetic moment of 3.5 � 10 19 Nm, one order of magnitude larger than the cumulative seismic moment released during the earthquake swarm. Between Dabbahu and Ado’Ale volcanic complexes, significant opening occurred on the western side of the dike. The anomalous location of the dike at this latitude, offset to the east of the axial depression, may explain this phenomenon. A two-stage intrusion scenario is proposed, whereby rifting in the northern Manda Hararo Rift was triggered by magma upwelling in the Dabbahu area, at the northern extremity of the magmatic segment. Although vigorous dike injection occurred during the September 2005 event, the tectonic stress deficit since the previous rifting episode was not fully released, leading to further intrusions in 2006–2009.

The dimensions of magmatic inclusions as a constraint on the physical mechanism of mixing

Abstract Silicic lavas often bear inclusions of more mafic lava. Several physical processes have been proposed by which these magmas may become mixed. Measurements of the sizes of mafic inclusions in lavas of two calc–alkaline volcanoes are used here to obtain a characteristic length scale for this type of mixing and provide a means to discriminate between different mixing processes. We quantitatively assess the proposal that, in a stratified reservoir, dynamic interactions of rising gas bubbles with the interface between a lower layer of mafic magma and an upper layer of silicic magma lead to the formation of vesiculated blobs of the lower magma in the upper one. This is due to gravitational instability of a foam layer growing at the interface between the two magmas. Our theoretical calculations of this instability predict both the correct order of magnitude for the characteristic size of inclusions and the way in which inclusion size varies with the physical properties of the magmas. This fluid dynamic framework is used to map out different possible flow regimes and place constraints on the fraction of gas in these systems.

Eruption versus intrusion? : arrest of propagation of constant volume, buoyant, liquid-filled cracks in an elastic, brittle host.

Received 9 January 2009; revised 31 March 2009; accepted 3 April 2009; published 5 June 2009. [1] When a volume of magma is released from a source at depth, one key question is whether or not this will culminate in an eruption or in the emplacement of a shallow intrusion. We address some of the physics behind this question by describing and interpreting laboratory experiments on the propagation of cracks filled with fixed volumes of buoyant liquid in a brittle, elastic host. Experiments were isothermal, and the liquid was incompressible. The cracks propagated vertically because of liquid buoyancy but were then found to come to a halt at a configuration of static mechanical equilibrium, a result that is inconsistent with the prediction of the theory of linear elastic fracture mechanics in two dimensions. We interpret this result as due to a three-dimensional effect. At the curved crack front, horizontal cracking is necessary in order for vertical propagation to take place. As the crack elongates and thins, the former becomes progressively harder and, in the end, impossible to fracture. We present a scaling law for the final length and breadth of cracks as a function of a governing dimensionless parameter, constructed from the liquid volume, the buoyancy, and host fracture toughness. An important implication of this result is that a minimum volume of magma is required for a volcanic eruption to occur for a given depth of magma reservoir.

An experimental study of the surface thermal signature of hot subaerial isoviscous gravity currents: Implications for thermal monitoring of lava flows and domes

Received 22 July 2011; revised 23 November 2011; accepted 23 November 2011; published 7 February 2012. [1] Management of eruptions requires a knowledge of lava effusion rates, for which a safe thermal proxy is often used. However, this thermal proxy does not take into account the flow dynamics and is basically time-independent. In order to establish a more robust framework that can link eruption rates and surface thermal signals of lavas measured remotely, we investigate the spreading of a hot, isoviscous, axisymmetric subaerial gravity current injected at constant rate from a point source onto a horizontal substrate. We performed laboratory experiments and found that the surface thermal structure became steady after an initial transient. We develop a theoretical model for a spreading fluid cooled by radiation and convection at its surface that also predicts a steady thermal regime. We show that, despite the model’s simplicity relative to lava flows, it yields the correct order of magnitude for the effusion rate required to produce the radiant flux measured on natural lava flows. For typical thermal lava properties and an effusion rate between 0.1 and 10 m 3 s � 1 , the model predicts a steady radiated heat flux ranging from 10 8 to 10 10 W. The assessed effusion rate varies quasi-linearly with the steady heat flux, with much weaker dependence on the flow viscosity. This relationship is valid only after a transient time which scales as the diffusive time, ranging from a few days for small basaltic flows to several years for lava domes. The thermal proxy appears thus less reliable to follow sharp variations of the effusion rate during an eruption.

Effect of solidification on a propagating dike.

[1]xa0Magma migration through the brittle crust from depth occurs by the propagation of hydraulic fractures or dikes. Volcanic eruptions occur at the last stage if and when a propagating dike reaches the surface. Dike propagation involves complex physics because of several processes that are simultaneously occurring such as viscous flow of magma, rock fracture, elastic deformation of the host rock, and potentially large changes of the physical properties of the magma (crystallization, degassing, solidification, etc.). Currently the most practical way in the field or in terms of field measurements to follow the migration of magma before it reaches the surface is the analysis of the seismicity generated; nevertheless, a physical model that quantitatively relates the flux of magma in the dike to the seismicity is lacking. We present here laboratory experiments involving propagation of a fluid-filled crack such that the fluid solidifies upon contact with the cold elastic host. We show that this can lead to a way of estimating the flux of the injection as a function of the surface creation rate. The latter is shown to be a more reliable gauge of magma flux than the upward propagating velocity. In the geologic application of a propagating dike, the rate of creation of surface area may be related to the rate of release of seismic energy. Although this latter relation needs further work to be quantitatively reliable, our new model nevertheless indicates how a new general framework can be constructed.

The rise and fall of turbulent fountains: a new model for improved quantitative predictions

Turbulent fountains are of major interest for many natural phenomena and industrial applications, and can be considered as one of the canonical examples of turbulent flows. They have been the object of extensive experimental and theoretical studies that yielded scaling laws describing the behaviour of the fountains as a function of source conditions (namely their Reynolds and Froude numbers). However, although such scaling laws provide a clear understanding of the basic dynamics of the turbulent fountains, they usually rely on more or less ad hoc dimensionless proportionality constants that are scarcely tested against theoretical predictions. In this paper, we use a systematic comparison between the initial and steady-state heights of a turbulent fountain predicted by classical top-hat models and those obtained in experiments. This shows scaling agreement between predictions and observations, but systematic discrepancies regarding the proportionality constant. For the initial rise of turbulent fountains, we show that quantitative agreement between top-hat models and experiments can be achieved by taking into account two factors: (i) the reduction of entrainment by negative buoyancy (as quantified by the Froude number), and (ii) the fact that turbulence is not fully developed at the source at intermediate Reynolds number. For the steady-state rise of turbulent fountains, a new model (‘confined top-hat) is developed to take into account the coupling between the up-flow and the down-flow in the steady-state fountain. The model introduces three parameters, calculated from integrals of experimental profiles, that highlight the dynamics of turbulent entrainment between the up-flow and the down-flow, as well as the change of buoyancy flux with height in the up-flow. The confined top-hat model for turbulent fountains achieves good agreement between theoretical predictions and experimental results. In particular, it predicts a systematic increase of the ratio between the initial and steady-state heights of turbulent fountains as a function of their source Froude number, an observation that was not handled properly in previous models.

A fluid dynamics perspective on the interpretation of the surface thermal signal of lava flows

Abstract Effusion rate is a crucial parameter for the prediction of lava-flow advance and should be assessed in near real-time in order to better manage a volcanic crisis. Thermal remote sensing offers the most promising avenue to attain this goal. We present here a ‘dynamic’ thermal proxy based on laboratory experiments and on the physical framework of viscous gravity currents, which can be used to estimate the effusion rate from thermal remote sensing during an eruption. This proxy reproduces the first-order relationship between effusion rate measured in the field and associated powers radiated by basaltic lava flows. Laboratory experiments involving fluids with complex rheology and subject to solidification give additional insights into the dynamics of lava flows. The introduction of a time evolution of the supply rates during the experiments gives rise to a transient adjustment of the surface thermal signal that further compromises the simple proportionality between the thermal flux and the effusion rate. Based on the experimental results, we conclude that a thermal proxy can only yield a minimum and time-averaged estimate of the effusion rate.

Modeling Volcanic Processes: The dynamics of dike propagation

Overview The aim of this chapter is to provide an overview of physical models of the dynamics of propagation of magmatic dikes. Experimental studies of fissure propagation provide an important way of validating hypotheses made in theoretical models, and hence provide a vital link between theory and field observations. Geological field observations of dikes can provide detailed information about rock and magma properties and post-emplacement dike geometry, but do not permit assessment of propagation rates. Conversely, geophysical studies can record dike emplacement as it takes place, allowing estimates of speed or demonstrating intermittency of propagation, but giving little information about dike geometry. We highlight some examples of field observations of dike dynamics that provide useful constraints for models. We discuss the main assumptions and key results of theoretical models that treat dike emplacement into both homogeneous and heterogeneous media. These models predict both the geometry of a propagating dike and the emplacement dynamics (e.g., speed), although they require assumptions about the source conditions, such as magma supply rates. There are open questions arising from shortcomings of current theory, which can be addressed using laboratory experiments that permit detailed investigation of real-time geometric and dynamic information. Notable among recent studies are attempts to quantify factors that may lead to arrest of a dike before it reaches the surface, the potential for solidification to influence the dynamic regime of propagation, and the influence of three-dimensional fracturing effects on propagation.