An experimental approach to dike propagation : the effects of stress, solidification and internal flow

This thesis addresses dike propagation from various vantage points, in order to construct a holistic conceptual model of how they behave in nature. Each chapter explorers a different aspect of propagation using analogue experiments, in which gelatin models the solid medium. Dikes are important to study, in that they are fundamental to magma migration. Most basaltic eruptions (e.g. the large 2018 eruption at Kilauea, Hawai’i and the 2014 eruption of Bardarbunga, Iceland) are fed by dikes. Recharge events, which supplies fresh magma from depth to shallow magma reservoirs and are associated to eruptions (e.g. the 1991 eruption of Pinatubo, Philippines), are commonly considered to be fed by propagating dikes. To start, I investigated the surface deformation due to buoyantly propagating, oil-filled dikes, in order to quantify the uncertainties associated to the Okada model, which models the surface deformation as functions of the geometry and position. To do so, I performed Bayesian inversions on deformation data from laboratory experiments, to estimate the dike geometry. I then compared these estimates with visual measurements, to quantify which parameters (e.g. length, depth) well-resemble reality. I found that the Okada model produces good, first-order approximations for most parameters, but crucially, the dike depth is not well-constrained, especially for shallow dikes. The mismatch is primarily due to the shape simplification of the Okada model, which assumes the dike to have a rectangular shape, whereas real dikes are elliptical. Next, I discuss how dike propagation is affected by the stress distribution in the surrounding medium, with a focus on the stresses around magmatic reservoirs. I made experiments modeling a reservoir, using a simple balloon embedded in gelatin, and injected buoyant, oil-filled dikes from below, allowing them to reorient due to the stress field. I found that a compressional stress field around an inflated, over-pressurized reservoir encourages dikes to propagate toward the reservoir, since the orientation of principal stresses cause dikes to propagate radial to, and therefore toward, the reservoir. By contrast, an extensional stress field around a deflated, under-pressurized reservoir encourages dikes to avoid the reservoir, since the principal stresses cause dikes to propagate tangentially around the reservoir. The magnitude of stress influences how close a dike can approach a reservoir before it begins to change orientation and, at the natural scale, this corresponds to a maximum of a few tens of kilometers radius. In Chapter 3, I explore magma migration from a thermal perspective, in order to understand the pathway geometry that develops over a long-term scale. I performed a series of experiments, repeatedly injecting a volume of warm, liquid gelatin into cold, solid gelatin and observed what types of structures developed with time. Liquid gelatin is a convenient material to use as it is transparent, has a temperature-dependent viscosity and seems to have a shear-independent viscosity; in short we can visually measure its thickness and it behaves like a gas-poor magma. When the time interval between injections was short, the initial dike rapidly channelized into a sub-cylindrical conduit, elliptical in cross-section. This structure remained ‘open’, allowing persistent liquid flux to pass from the source to the surface. In contrast, a long time interval between injections allowed dikes to completely solidify, prompting subsequent liquid injections to form new dikes. Over the course of an experiment, such behavior resulted in the intrusion of a dike swarm, in which each injection made a discrete dike. I found that the injection flux controlled the thermal stability of an injection, in which a critical flux rate is necessary for a dike to propagate to the surface before solidifying. Dikes with a lower flux exhibit unstable, piecewise propagation, in which the leading tip of the dike solidifies and forces propagation to resume at the base, near the point of injection. Finally, I investigated the internal liquid flow of a propagating, and subsequently erupting, dike. In this case, I injected either vegetable oil (buoyant, intermediate-viscosity Newtonian liquid), water (weakly-buoyant, low-viscosity Newtonian liquid), or liquid gelatin (buoyant, temperature-dependent viscosity), in order to model the internal flow depending on the buoyancy and viscous forces, as well as cooling in the dike. We seeded the liquids with particles that were tracked using Particle Image Velocimetry and Particle Tracking Velocimetry, to serve as a proxy for the internal flow field evolution. When the liquid is initially injected, the dike’s internal flow takes on a vertically circulating pattern, with a central upward jet and return flow along the lateral fringes. As the dike grows, the circulation pattern weakens and transitions to simple, ascending flow. This change of behavior corresponds to the buoyancy of the liquid, which builds in magnitude as the dike elongates and favors upward motion. The form of propagation relates to these flow patterns, in which the dike initially propagates radially, in the form of a penny-shaped crack. When buoyancy forces become dominant, the propagation becomes vertical, with little horizontal growth. This thesis provides a broad view on the factors controlling dike propagation and evolution, from analysis on the driving forces of propagation to the effect of the stresses in the medium to the thermal viability and vulnerability to solidification. Since magmatic dikes propagate in response to such various processes, this approach offers valuable and fundamental insights into their nature.Doctor of Philosoph