IAP-24-067

Diffusion Clocks: Decoding Magma Ascent Speed Beneath Volcanoes

Motivation. Understanding the dynamics of magma ascent during eruption is a crucial step towards improving hazard assessment and eruption forecasting. There is good evidence that the explosive energy of eruptions is linked to the speed with which magma ascends through the subvolcanic plumbing system. Hence, understanding what controls magma ascent rates in different volcanoes is the key to understanding and predicting their eruption style.

A new and promising avenue for decoding magma ascent rates of past eruptions is the study of element diffusion profiles recorded in crystals, melt inclusions, or melt embayments, as well as in volcanic glass around growing crystals or bubbles, sampled from erupted ash and lava. This project will develop and apply a framework for robust interpretation and ultimately prediction of these data through numerical modelling of diffusion profiles evolving during magma ascent.

The successful PhD candidate will be trained in advanced numerical methods at the cutting edge of magma physics and chemistry. A flexible conduit flow model will be developed to investigate different magma ascent scenarios, based on which an ensemble of diffusion profiles will be computed. The conduit-flow model will capture the behaviour of variably crystalline and vesiculated magma as it convects in and ascends through a range of subvolcanic reservoir and conduit geometries. Passive tracers seeded throughout the model domain will record pressure-temperature-composition histories along trajectories of melt, crystals, and bubbles, from which diffusion clocks can be modelled assuming statistically distributed instances of formation and closure of crystals, inclusions, or embayments.

Research Questions.
• Can diffusion clocks reliably record magma ascent rates?
• Can measured diffusion profiles be used to reconstruct complex flow trajectories due to repeated convective cycling before final ascent?
• What type and amount of data must be collected to reliably determine conditions and rates of magma ascent for a given eruption?
• Can diffusion clock analysis and modelling help explain the cause of sudden high-intensity paroxysm in volcanoes otherwise marked by persistent, low- intensity activity?

Research Team. The student will be supervised by internationally recognised experts in magma physics and chemistry. The project will be hosted at the University of Glasgow under the lead supervision of Dr. Tobias Keller, an expert in modelling magma transport from source to surface. The project will also be embedded in the research groups of Prof. Ed Llewellin, a volcanologist and expert in the physics of volcanic eruptions, and Prof. Madeleine Humphreys, a geochemist and expert in the analysis of volatiles in magmatic systems. Together, the team of supervisors combine leading expertise in their field with an engaging, diverse, and team-oriented research environment. Both the Universities of Glasgow and Durham are internationally recognised institutes with a long tradition of research and teaching excellence.

Background. Volcanoes are highly complex systems where solids (crystals), liquids (melt), and gases (bubbles) interact to give rise to strongly non-linear flow phenomena. Since many volcanoes exist in close proximity to major population centres, assessing hazards and forecasting the intensity and duration of future eruptions is of great importance. Among many factors that might reasonably contribute to eruption intensity, it is now thought that magma ascent is the key predictor [1,2]. However, magma flow rate is a complex and still poorly understood function of plumbing system geometry, physical and chemical magma properties, and other system parameters. What is clear is that the exsolution of volatile vapour bubbles, which often coincides with crystallisation, both provides the main driving force for magma ascent but also changes the magma’s resistance to flow [3]. Non-linear feedback loops are at play as faster ascent promotes more rapid bubble exsolution and also increased expansion of existing bubbles, which create volume, increase pressure, and hence further boost ascent speed.

A fundamental challenge in understanding volcanoes is that the pertinent processes are challenging to access by direct observations. Many indirect methods of observation are restricted in spatial and temporal resolution or are subject to inferences and auxiliary assumptions. The most promising diagnostics available at or near real-time are gas flux and composition emitted from the conduit, and seismic activity and ground deformation of the edifice. What is missing are process-based models of how these signals are produced by different magma flow regimes in the subsurface [4]. To help establish this link, we propose to reconstruct the magma dynamics preceding eruptive episodes by modelling diffusion clocks set by different flow scenarios and comparing them to samples taken from the eruptive products of the same eruptions.

Diffusion clocks are compositional profiles measured by high-resolution microanalytical methods across phenocrysts, melt inclusions, melt embayments, and volcanic glass around growing crystals and bubbles [5-7]. If conditions on one end of the profile (e.g., rim of crystal or bubble) change on a time scale similar to the diffusivity of an element through the material (e.g., interior of crystal, glass surrounding bubble), it may be possible to reconstruct the rate of said change in conditions once the diffusion is arrested by quenching upon eruption.

The interpretation of what process rates the diffusion clocks record, however, remains open to debate. To date, attempts at interpretation have been limited to modelling 1D-diffusion profiles assuming simple step changes or linear shifts in pressure, temperature, and therefore composition. What this project will contribute are process-based models of magma convection and ascent in volcanic plumbing systems, which will predict more complex, non-linear evolution trajectories and the diffusion profiles produced as a consequence – these in turn can be directly compared back to those sampled from active volcanoes.

This project will focus on the development of cutting-edge magma flow and diffusion clock models, which will be applied to case studies leveraging both existing data and new sampling and analyses of recent lavas. The student will focus on a class of volcanoes characterised by persistently active conduits from which more heat and gas are emitted than is explained by the minor amounts of erupted lava. From time to time these gentle giants wake to produce great paroxysms during which eruptive intensity increases by at least an order of magnitude and massive emissions of ash and lava flow threaten surrounding communities.

Within this category fall the relatively well-studied examples of Stromboli and Mt. Etna, Italy, Hawaii, USA, and Mt. Erebus, Antarctica. Their long-term background activity is well explained by persistent convection of magma in a conduit where degassing, bubbly magma rises up while outgassed, denser magma sinks back down [8]. What leads to the sudden switch to increased ascent speed triggering a paroxysm remains unresolved. Possible candidates are conduit flow instabilities arising from the complex nature of multi-phase flows, or the supply of a batch of fresh, hot, and volatile-rich magma to the shallow plumbing system.

To help resolve this puzzle, the student will develop cutting-edge multi-phase flow models of magma ascent driven by bubble exsolution and hindered by crystallisation. The finite-difference models will be prototyped in Matlab and later implemented in Julia for efficient parallel computing. Model formulation will be based on recent theory [9] and modelling [8,10] of Dr. Tobias Keller (lead supervisor). The model will simulate the flow of variably crystalline and vesiculated magma through different reservoir and conduit geometries. The flow model will be coupled to a thermo-chemical evolution model tracking temperature, major element, trace, and volatile composition. The model will allow for the segregation of crystals and bubbles from the magma. Most components of this models have been tested in previous work and will be assembled into a dedicated code by the student.

Given a magma flow model, diffusion clocks can be extracted by seeding the flow with statistically distributed passive tracers recording pressure (P), temperature (T), and composition (X) along flow trajectories of melt, crystals, and bubbles. Given these trajectories through P,T,X-space, diffusion profiles can be generated and statistically analysed in post-processing. The result will be populations of diffusion profiles, for example of H2O through clinopyroxene and olivine, which can now be compared to existing data and new analyses obtained by the student and collaborators at Durham.

To apply this new method to a natural case study, the student will visit a relevant field site (e.g., Hawai’i, USA, or Mt. Etna, Sicily) and sample lavas from recent eruptions that are well constrained by surface observations. The student will be trained to use the Secondary Ion Mass Spectrometer (SIMS) instrument at the University of Edinburgh to analyse diffusion profiles of H2O through clinopyroxene and olivine. Using their custom-built model, the student will then be able to interpret the analytical results to find how diffusion clocks can constrain the subsurface magma dynamics and ascent rates leading up to high-intensity eruptions.

Year 1

In Yr1, the student will receive basic training in scientific programming and volcanological field work and sampling. The first objective of Yr1 is to implement the mechanical part of the multi-phase flow solver for magma ascent with crystal and bubble segregation along with a routine to statistically sample flow trajectories by seeding passive tracers into the flow model. The second objective is to visit and take samples from a first case study site (most likely Mt. Etna, Sicily, if possible exploiting synergies with ongoing field studies at Durham).

Year 2

In Yr2, the student will focus on refining their model development skills and receive basic training in the laboratory techniques required to analyse diffusion profiles in crystals. The first objective of Yr2 is to add a thermo-chemical evolution module to the mechanical flow model produced in Yr1, which will allow diffusion profiles to be calculated corresponding to P,T,X-trajectories recorded by flow tracers. The second objective is to receive basic training in using a SIMS instrument to analyse diffusion profiles in samples taken during Yr1. During Yr2, the student will write a first study reporting on the development of a conduit flow model with thermo-chemical evolution and dynamic volatile exsolution.

Year 3

In Yr3, the student will perform further field, analytical, and modelling work to investigate a second field site (or return to the first field site with refined focus). The first objective is to perform statistical analyses on diffusion profiles obtained in a range of flow model scenarios to investigate how well flow conditions and ascent rates can be reconstructed from data and what biases or non- uniquenesses may have to be considered. The second objective is to continue sampling and analysing lavas to better characterise the chosen case studies. During Yr3, the student will write their second study reporting on the reconstruction of magma ascent speeds from modelled populations of diffusion clocks.

Year 3.5

In Yr3.5 (note, the project funding covers 3.5 years), the student will finalise their analytical and modelling work from Yr3 to conclude a third study focusing on the chosen case study, and combining new analyses, flow modelling, statistical analyses, and interpretation.

The successful candidate will benefit from expert training and collaborations in a broad range of geoscience disciplines, including computational modelling, field volcanology, and microanalytical techniques. In addition, the student will have the opportunity to develop highly desirable and marketable skills such as computer programming, scientific writing, and public speaking.

Computational modelling. The student will receive state-of-the art training in scientific programming and model composition. The student will work closely with TK at Glasgow, a leading expert in developing theory and numerical models for multi-phase reactive transport problems in igneous processes. The student will also interact with other collaborators in Glasgow, Oxford, and Imperial, including world experts in developing codes for deformation and transport in complex multi-phase materials. TK is a member of the Glasgow Computational Engineering Centre, offering a collaborative and team-oriented environment for code development. The student will attend dedicated training workshops in scientific programming both at Glasgow and other institutes.

Field volcanology. The student will be trained in advanced field skills including observation, documentation and interpretation of complex volcanic outcrops that vary over a large range of spatial scales. This field experience will allow the student to contextualise the numerical work, and represent a significant skill development opportunity alongside the principal numerical work that is the core of this project.

Microanalytical techniques. The student will be introduced to advanced microanalytical laboratory techniques used to obtain major, trace, and volatile element diffusion profiles in volcanic glass and crystals using a SIMS instrument. This microanalytical experience will provide the student with an in-depth understanding of how the data is obtained which this modelling project aims to interpret and predict.