Gelatin is a commonly used material for analog experiments in geophysics, investigating fluid-filled fracture propagation (e.g., magmatic dikes), as well as fault slip. Quantification of its physical properties, such as the Young's modulus, is important for scaling experimental results to nature. Traditional methods to do so are either time consuming or destructive and cannot be performed in situ. We present an optical measurement technique, using shear waves. Polarizing filters enable visualization of the deviatoric stresses in a block of gelatin, so shear wave propagation can be observed. We demonstrate how the wave velocity can be measured and related to the Young's modulus, show how the results are comparable to another methodology and discuss processing techniques that maximize the measurement precision. This methodology is useful for experimentalist, as it is simple to implement into a laboratory setting, can make precise, time-efficient estimates of the material strength and additionally is non-destructive and can be performed in situ.

We investigate the conditions under which magma prefers to migrate through the crust via a dike or a conduit geometry. We performed a series of analogue experiments, repeatedly injecting warm, liquid gelatin, into a cold, solid gelatin medium and allowing the structure to evolve with time. We varied the liquid flux and the time interval between discrete injections of gelatin. The time interval controls the geometry of the migration, in that long intervals allow the intrusions to solidify, favoring the propagation of new dikes. Short time intervals allow the magma to channelize into a conduit. These times are characterized by the Fourier number (Fo), a ratio of time and thermal diffusion to dike thickness, so that long times scales have Fo > 102 and short time scales have Fo < 100. Between these time scales, a transitional behavior exists, in which new dikes nest inside of previous dikes. The flux controls the distance a dike can propagate before solidifying, in that high fluxes favor continual propagation, whereas low fluxes favor dike arrest due to solidification. For vertically propagating dikes, this indicates whether or not a dike can erupt. A transitional behavior exist, in which dikes may erupt at the surface in an unstable, on‐and‐off fashion. We supplemented the experimental findings with a 2‐D numerical model of thermal conduction to characterize the temperature gradient in the crust as a function of intrusion recurrence frequency. For very infrequent intrusions (Fo > 104 to 105) all thermal energy is lost, while more frequent intrusions allow heat to build up nearby.

We investigate the effect of magmatic reservoir pressure on the propagation of dikes that approach from below, using analogue experiments. We injected oil into gelatin and observed how dike propagation responded to the stress field around a pressurized, spherical reservoir, filled with water. The reservoir was modeled using two different setups: one simply using an inflatable rubber balloon and the other by constructing a liquid-filled cavity. We find that the dike's response is dependent on the sign of the reservoir pressure (i.e., inflated/overpressurized and deflated/underpressurized) as well as on the dike's initial orientation (i.e., if its strike is radially, circumferentially, or obliquely oriented to the reservoir). Dikes that are initially strike radial respond, respectively, by propagating toward or away from overpressurized or underpressurized reservoirs, taking advantage of the reservoir's hoop stresses. Otherwise-oriented dikes respond by changing orientation, twisting and curling into a form dictated by the principal stresses in the medium. For overpressurized reservoirs, they are coaxed to propagate radially to, and therefore approach, the reservoir. For underpressurized reservoirs, they generally reorient to propagate tangentially, which causes them to avoid the reservoir. The magnitude of reservoir pressure controls at which distance dikes can be affected, and, at natural scales, we estimate that this occurs within a radius of a few tens of kilometers. This diminishes with time, due to viscous stress relaxation of the crust, which will occur on a timescale of hundreds of years.Plain Language Summary Magma commonly moves up toward the surface by creating cracks in the crust. It flows inside of the cracks and propagates by applying pressure that drives the flow and damages surrounding rocks. Nature always finds the easiest path for the crack, so if it takes less pressure to push apart the ground vertically or horizontally, the crack will grow accordingly. As it makes its way to the surface, it may encounter local stress variations that change its propagating direction. This applies near magma storage regions, below volcanoes. If such a region is highly pressurized or deflated, then nearby cracks will "feel" the change in their surrounding conditions and react by aligning in a direction of favorable stress. This makes it look like they are growing toward or circling around the storage region, respectively. We studied this behavior using scaled model experiments in laboratory conditions. We use different types of materials to represent nature, such as gelatin as rock and oil as magma. We were able to show how these cracks change shape for different reservoir pressures. We found that after a large eruption, subsequent eruptions are more likely to occur farther from the summit of a volcano.

This study uses analogue experiments to understand the role of bubbles in inducing conduit convection, for persistently degassing lava lake systems. To do so, air was fluxed through an initially stagnant column of liquid and the resulting return flow was measured. The dynamics suggested by the experimental results is compared to that of quiescent, persistently active volcanoes, with a focus on eight volcanoes that exhibit summit lava lakes. We find that magma flux is a function of combined gas flux, conduit size and magma rheology. Experiments with high gas fluxes through low viscosity liquid took on turbulent characteristics, which correspond to high degree of return flow, whereas lower gas fluxes through high viscosity liquids yielded slug flow, which corresponded to less return flow. We model the magma flux due to bubble ascent and find that gas-driven liquid flow can yield faster flow rates than other mechanisms at work in volcanic conduits. This can explain the discrepancy between previous estimates of magma flow in conduits and relatively fast, lava lake surface velocity observations. We show how bubble-driven convective flow can work alongside density-driven convection and discuss the depths in the conduit where each are likely to dominate the system.

We present analog experiments on dike propagation, followed by a numerical model of horizontal and vertical growth, which is partially analytical and partially based on empirical observations. Experimental results show that the growth rates are similar until buoyancy becomes significant and, afterward, vertical growth dominates. The numerical model is defined for different conditions in a homogeneous medium: (a) constant flux, fracture‐limited propagation; (b) constant flux, viscous‐limited propagation; and (c) variable flux dependent on the driving pressure and dike dimensions. These conditions distinguish between cases when the influx depends on the deeper source of magma (e.g., a conduit, independent of the dike geometry) and when it depends on the dike, so the influx can change as it grows. In all cases, the ratio of vertical to horizontal propagation is proportional to the ratio of buoyancy pressure to source pressure, in which buoyancy drives vertical propagation. We test the numerical model on dikes observed at Piton de la Fournaise, in which the dimensions were estimated using geodetic and seismic data. The results show that the final dimensions can be reproduced using magma‐crust density differences of 50–300 kg/m3, viscosities of 30–300 Pa·s, influxes of 50–750 m3/s and shear moduli of ∼10 GPa. The modeled magma and host rock parameters agree with previous studies of the volcano, while the flux is higher than what is typically observed during eruption. This implies a variable injection condition, in which the flux peaks during propagation and diminishes by the onset of eruption.

Analog experiments indicate that dike propagation in the vertical and horizontal directions depends on the buoyancy and source pressure • We define a numerical model in which growth depends on influx and different pressure ratios, which evolve with time • The model reproduces the geometries and velocities for nine dikes in nature, using plausible values for magma and host rock rheology

We conducted analogue experiments to examine flux‐driven and buoyancy‐driven magma ascent, which included a series of isothermal experiments and thermal, solidification‐prone experiments. We measured the internal flow using 2D particle image velocimetry, which indicates that buoyancy has a strong control on the flow pattern of isothermal dikes. Dikes that are not buoyant (likely driven by source pressure) take on a circulating pattern, while buoyant dikes assume an ascending flow pattern. Solidification modifies the flow field so that flow is confined to the dike's upper head region. The lower tail becomes mostly solidified, with a narrow conduit connecting the source to the head. We interpret that this conduit acts as a high velocity point source to the head, promoting a circulating flow pattern, even as the dike becomes buoyant. We then perform particle tracking velocimetry on several particles to illustrate the complexity of their paths. In a circulating flow pattern, particles rise to the top of the dike, descend near the lateral edge, and then are drawn back into the upward flow. In an ascending pattern, particles ascend slightly faster than the propagation velocity, and therefore are pushed to the side as they approach the upper tip. In erupting dikes, particles simply flow to the vent. In the context of crystal growth in magmatic dikes, these results suggest that crystal growth patterns (e.g., normal or oscillatory zoning) can reflect the magma flow pattern, and potentially the driving forces.

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. General methodologyThroughout this thesis, I rely heavily on analogue modeling, which entails performing small, laboratory-scale experiments to understand what happens at the much-larger, natural, volcanic scale. In each experiment, I prepare a block of gelatin, which represents Earth's crust, and inject a fluid of some kind to represent the migrating magma. Since gelatin is brittle and elastic (like the Earth's crust on the spatial-and temporal-scale of a propagating dike), the injected fluid fractures the gelatin to create a small dike. This solid medium, by its very nature, produces planar dike geometries, similar to those found around volcanoes. In each chapter, I discuss in more detail the particulars of each specific If we choose to study a dike with a constant influx, we can non-dimensionalize the flux in different ways. A typical method is to consider the influx into the tail, so that magma flux, Q, and viscosity, μ, correspond to a thicker tail, whereas buoyancy draws magma upwards and corresponds to a thinner tail. The scale tail thickness, H∞, is quantified by H∞ = (Qμ/Δρg) 1/3 (Roper & Lister, 2007). The scale influx Q∞ is then quantified by Q∞ = Q/H∞. Note that in this methodology, Q is a 2D flux, meaning the flux per unit length (Roper & Lister, 2007;. When the parameter is large, it indicates that the dike is relatively thick. Another way to non-dimensionalize the flux is thermally, via a balance between heating a cooling. The influx provides heat to the dike at a rate determined by the influx, Q (now regular 3D flux) and dike thickness, H, while the cooling via conduction of heat into the surrounding crust depends on the surface area and the thermal diffusivity, α. If the dike has an approximate surface area of its vertical length, L, by its horizontal breadth, B, the dimensionless flux, Φ, is quantified by Φ = QH/(αLB) . When the value is large, it indicates that the flow is high and heat flows upward through the dike; when small, the heat is lost into the crust. Via the material selection and dimensionless numbers, we can control how the liquid and solid interact, as well as the relative size, shape and dynamics of a dike, so that they match nature. Chapter 1: Application of the Okada model to propagating dikes in analogue experiments: Comparing inversion estimates to lab measurements 15 Chapter 1: Application of the Okada model to propagating dikes in analogue experiments: Comparing inversion estimates to lab measurements