Density and viscosity gradients in zoned magma chambers, and their influence withdrawal dynamics

The liquid being sampled from a draining reservoir of density-stratified fluid, such as an erupting zoned magma chamber, is derived from a relatively thin withdrawal layer adjacent to the level of the chamber outlet. This is a consequence of the buoyancy force associated with the density gradient inhibiting vertical motion so that the opportunity for widely separated density levels (compositions) to be tapped and mingled syneruptively is suppressed.Density gradients in zoned chambers of 0.02 – 10 kgm⁻³/m are suggested by data from caldera-forming eruptions. Viscosity gradients can be specified for a given density gradient using calculated relationships between viscosity and density. Published compositional and geothermometric data are used to show that zoned high-silica rhyolites decrease in viscosity upward because of the roofward concentration of dissolved volatiles. Other zoned calc-alkaline magmas increase in viscosity upward because of decreasing temperature and concentration of network modifying cations.A method is developed of calculating the scale of the withdrawal layer thickness, δ, for given kinematic viscosity, eruption rate, and density and viscosity gradients. The method is systematized by the identification of specific flow regimes describing the action of either viscous or inertial forces in balancing the buoyancy force. Thin withdrawal layers are favoured by small eruption rates, small viscosity, and by large density gradients. For particularly steep density gradients, however, the consequently large viscosity gradient plays a role in determining the withdrawal layer thickness. Withdrawal layer thicknesses of the order of 100 m are calculated for typical pyroclastic eruptions of zoned acid magma, and are mostly independent of the viscosity gradient.The vertical scale at which a zoned chamber is instantaneously being tapped during an eruption is equal to the scale of the withdrawal layer thickness. Thus, an eruption that causes collapse of a caldera block through a height that is less than that of the withdrawal layer scale will produce magmas from deeper levels than that to which the chamber roof sinks. In this case the eruption is said to oversample the chamber with respect to the amount of caldera collapse and will produce an essentially constant range of compositions throughout. Alternatively, if the caldera collapse distance is much greater than δ then the selective withdrawal process leads to successive levels of the chamber being “skimmed off” (on a scale δ). This allows the compositional stratigraphy of the chamber to be inverted by the eruptive process, with little opportunity for syneruptive mixing between diverse magma compositions. The geological record shows that most calderas associated with zoned magmas collapsed through vertical distances in excess of 100 m (the characteristic estimate for δ) and, in agreement with our modelling of selective withdrawal, show smooth correlations between composition, or temperature, and the order of eruption.