Simulations of magma withdrawal from compositionally zoned bodies

Abstract

Heterogeneities in the form of continuous (less common) or discontinuous (more common) mineralogical, geochemical and thermal gradients within volcanic deposits are ubiquitous in the geologic record. Examples cover a wide spectrum of eruptive volumes (10−2 km3 to > 103 km3), compositions (felsic to mafic), mass discharges (103 to 109 kg/s) and eruptive styles (Plinian air falls, pyroclastic flows, lava flows). An understanding of the dynamics of the magma withdrawal process is essential for accurate reconstruction of pre‐emptive chemical and thermal fields within crustal magma bodies. A model based on numerical solution of the governing conservation equations has been devised in order to investigate the dynamics and systematics of central vent and ring fracture eruptions from flat‐roofed and sloped‐roof magma bodies strongly zoned in density and viscosity. Scale analysis of the conservation equations together with about 150 numerical experiments enables development of quantitative correlations for the mass discharge, , and the duration of mixed magma eruption, Δt, with the effective driving pressure, σ. Natural eruptions span the entire range of dynamic regimes from viscous through inertial. For central vent eruptions in the viscous regime, is proportional to σ/(dη) where d is the conduit length and η is the viscosity. In the transitional and inertial regimes, the intensity varies as (σ/ρ)3/5 and (σ/ρ)½, respectively, where ρ is the density. Similarly, Δt depends on (σ/d)−5, σ−3/5 and σ−½ in the viscous, transitional, and inertial regimes, respectively. For systems with layered viscosity structure, Δt is nearly independent of the viscosity ratio. Pressures (above hydrostatic∥ needed to drive eruptions are proportional to , 5/3, and 2 in the three dynamic regimes. Typical eruptions in the viscous and transitional regimes require pressure anomalies of order 102)103 Pa whereas high intensity (inertial) eruptions demand anomalies of order 106 Pa. Because the lower values are less than or equal to maximum tidally induced stresses, Earth tides appear capable of exciting eruptions. Several scenarios for producing variable discharge during a single eruptive phase were also studied. These include arbitrary changes in the basal pressure and eruptions controlled by density and viscosity gradients. It is demonstrated quantitatively that compositional gaps and episodes of mixed‐magma eruption can originate due to the withdrawal process itself and are not necessarily related to pre‐eruptive gradients within the magma body.