Some numerical experiments on the withdrawal of magma from crustal reservoirs

Abstract

Compositional heterogeneity in the form of continuous or discontinuous chemical and thermal gradients in lava and/or pyroclastic flows is very common. An understanding of the dynamics of magma withdrawal is essential to palinspastic reconstruction of intensive variable gradients in magma reservoirs. Important parameters governing the extent of subterranean magma mixing triggered by an eruption include the vertical structure of density and viscosity within the chamber, the discharge, the size and shape of the chamber, and whether eruption takes place along a sublinear fissure, a ring fracture, or a central vent. A numerical model has been set up to study isoviscous magma withdrawal from a central vent conduit as a function of the Reynolds number, the reservoir to conduit width ratio, reservoir aspect ratio (width/depth), and differing kinematic boundary conditions. Both open (magma recharge) and closed (caldera collapse) system behavior are considered. Finite difference solutions to the vorticity transport and Poisson equations enable determination of vorticity, stream function, and velocity fields as a function of time. The most petrologically significant output is the stream function (particle trajectories) and evacuation isochron diagrams. An evacuation isochron represents the locus of points within the chamber such that magma parcels along a given isochron arrive at the bottom of the volcanic conduit concurrently. Open systems evolve toward a time invariant state (fully developed flow). Spin‐up times depend on chamber aspect ratio (Br/Dr), reservoir/conduit width ratio (Br/Bc), and Reynolds number (Re). Br, Dr, and Bc represent chamber half‐width, depth, and conduit half‐width, respectively. Spin‐up times are relatively small (1/10 to 1/5) fractions of typical eruption durations. The shape and orientation of evacuation isochrons (EI) depend on Re (increasing Re decreases withdrawal depth) and geometric factors (increasing Br/Bc at constant Re and Br/Dr or decreasing Br/Br at constant Br/Bc and Re increases withdrawal depth). A significant amount of roofward magma can remain untapped in a chamber even for long duration eruptions. Systems driven by caldera collapse also involve juxtaposition of roofward and deep‐seated magma during the course of an eruption. Relative to the magma recharge (open system) situation, EI's are laterally elongated. The extent of vertical mixing is thus smaller although still significant in this case. Maximum withdrawal depths vary monotonically in both cases. There is excellent qualitative agreement between predictions based on the numerical experiments and Fe‐Ti oxide temperatures for a thermally zoned ash flow deposit south of Mono Lake in eastern California (Bishop Tuff).