Constraints on magma source conditions from hydraulic fracture models and seismic observations of dyke tip deceleration

Timothy Davis , Juliet Biggs

Seismicity shows that magmatic dykes decelerate as they propagate laterally. Hydraulic fracture theory shows this deceleration relates to the coupling between the source and the dyke. Here, we use hydraulic fracture models to derive scaling laws for the length, width, and shape of dykes driven by three source boundary conditions: constant flux, constant pressure, and a finite volume release. These span end-member source behaviours: a stiff source supplying steady flux regardless of dyke pressure, a compliant reservoir in pressure equilibrium whose supply decays with time, and an instantaneous release representing rapid exhaustion of the supply. Denoting dyke length and height as L and H respectively, we obtain analytical solutions for two end-member geometries: an early, vertically tall fracture (L less than H) that transitions to a laterally long, vertically short one (L greater than H) as the dyke propagates. While L/H is much less than 1 the constant-pressure condition yields exponential growth in length, but once L is greater than H constant flux gives L ∝ t^(4/5), constant source pressure gives L ∝ t^(1/2), and a finite volume release gives L ∝ t^(1/5). Comparing these predictions to six lateral dyking episodes with L less than 25 km, we find the seismicity fronts consistently follow L ∝ t^(1/2), indicating that dykes are driven by a near-constant source pressure. A well-constrained source condition is a prerequisite for any model that probes the dynamics of dyke intrusions, including the mechanisms of arrest and start-stop behaviour. Thus, hydraulic fracture models offer a framework for forecasting the temporal evolution of dyke propagation.