IAP-25-021

Diffusion Clocks: Decoding Magma Ascent Speed Beneath Volcanoes

Motivation. Understanding magma ascent dynamics is crucial for improving volcanic hazard assessment and eruption forecasting. Evidence shows that the explosive energy of eruptions is linked to the rate at which magma ascends through the subvolcanic plumbing system. Hence, identifying the factors controlling ascent rates is key to predicting eruption style.

A promising new approach for constraining magma ascent rates in past eruptions lies in analysing element diffusion profiles in crystals, melt inclusions, embayments, and volcanic glass around crystals or bubbles. These samples, collected from erupted ash and lava, record the time-dependent evolution of magmatic conditions. This project will develop and apply a numerical modelling framework to interpret and predict such diffusion profiles as they evolve during magma ascent.

The PhD candidate will receive training in advanced numerical methods at the frontier of magma physics and chemistry. A flexible conduit-flow model will be developed to simulate a range of ascent scenarios. From these simulations, ensembles of diffusion profiles will be computed. The model will capture the behaviour of variably crystalline and vesiculated magma as it convects within and ascends through diverse subvolcanic plumbing system geometries. Passive tracers will record pressure–temperature–composition histories along trajectories of melt, crystals, and bubbles, enabling diffusion clocks to be modelled under statistically distributed formation and closure times of crystals, inclusions, and embayments.

Research Questions
• Can diffusion clocks reliably record magma ascent rates?
• Can measured diffusion profiles be used to reconstruct complex flow trajectories involving repeated convective cycling before final ascent?
• What type and amount of data are required to reliably determine ascent conditions and rates for a given eruption?
• Can diffusion clock modelling help explain the causes of sudden, high-intensity paroxysms in otherwise persistently low-intensity volcanoes?

Research Team. The project will be hosted at the University of Glasgow under the supervision of Dr Tobias Keller, an expert in modelling magma transport from source to surface. Co-supervisors are Prof Ed Llewellin (Durham University), a volcanologist specialising in the physics of magma flow and eruption dynamics, and Prof Madeleine Humphreys (Durham University), a geochemist specialising in volatile analysis in magmatic systems. Together, the supervisors provide complementary expertise in magma physics, chemistry, and field volcanology, within a collaborative and dynamic research environment. The Universities of Glasgow and Durham are internationally recognised for research and teaching excellence in Earth sciences.

Background. Volcanoes are complex systems where solids (crystals), liquids (melt), and gases (bubbles) interact to produce highly non-linear flow behaviour. Because many volcanoes are near population centres, forecasting eruption intensity and duration is of critical importance. Among the many contributing factors, magma ascent rate is now recognised as a primary predictor of eruption intensity [1,2]. However, ascent rate depends on a complex interplay of plumbing geometry, magma rheology, composition, and volatile content. Volatile exsolution, which often accompanies crystallisation, both drives ascent and increases magma viscosity [3]. This creates a non-linear feedback: faster ascent accelerates bubble exsolution and expansion, which in turn increases pressure and further enhances ascent speed but also increases viscosity and hence resistance to flow.

Direct observation of these processes is extremely difficult. Indirect methods such as gas flux and composition, seismicity, and ground deformation offer valuable insights but are limited in resolution and often require strong assumptions. What remains missing are process-based models linking such observable signals to underlying magma flow regimes [4]. To address this gap, the project will reconstruct the magma dynamics preceding eruptions by modelling diffusion clocks produced under different conduit flow scenarios and comparing them to samples from eruptive products.

Diffusion clocks are compositional profiles measured with high-resolution microanalytical methods across phenocrysts, melt inclusions, embayments, and volcanic glass [5–7]. When boundary conditions (e.g., at a crystal rim or bubble wall) change on a timescale comparable to element diffusivity, diffusion profiles record the rate of those changes until arrested by quenching upon eruption.

The interpretation of what physical rates these clocks record remains debated. Existing approaches typically model 1D diffusion with simplified boundary changes. This project will go further by simulating physically consistent magma convection and ascent, generating complex, non-linear evolution trajectories and corresponding diffusion profiles that can be directly compared with natural samples from active volcanoes.

This project will develop state-of-the-art models of magma flow and diffusion clocks, applied to case studies combining existing datasets with new sampling and analyses of recent lavas. The focus will be on volcanoes with persistently active conduits that emit far more heat and gas than can be explained by their modest lava output. These “gentle giants” occasionally produce powerful paroxysms—brief episodes of eruptive intensity increasing by over an order of magnitude, releasing large volumes of ash and lava that endanger nearby populations.

Representative examples include Stromboli and Mt Etna (Italy), Hawaii (USA), and Mt Erebus (Antarctica). Their long-term background activity is attributed to persistent conduit convection, where volatile-rich, bubbly magma ascends while degassed, denser magma sinks [8]. The mechanism behind sudden transitions to high-intensity paroxysms remains unresolved. Possible causes include intrinsic instabilities of multi-phase conduit flow or injections of fresh, hot, volatile-rich magma into the shallow plumbing system.

To address this, the student will develop advanced multi-phase flow models of magma ascent and convection driven by volatile exsolution and inhibited by crystallisation. Finite-difference models will first be prototyped in MATLAB and later implemented in Julia for efficient parallel computation, using modern backend-agnostic packages such as chmy.jl, allowing execution on both CPU and GPU architectures without altering source code. Model formulation will build on recent theoretical and numerical advances by Keller et al. [8–10]. The framework will simulate the flow of variably crystalline and vesiculated magma through diverse reservoir and conduit geometries, coupled to a thermo-chemical evolution model tracking temperature, major and trace elements, and volatile species. The formulation will also permit the segregation of bubbles and crystals from the melt. Core components of this approach have been tested in previous work and will be integrated by the student into a dedicated simulation code.

Once the magma flow model is established, diffusion clocks will be generated by seeding the simulated domain with statistically distributed passive tracers that record pressure (P), temperature (T), and composition (X) along the trajectories of melt, crystals, and bubbles. These P–T–X histories will be used to calculate diffusion profiles in post-processing and to produce statistical ensembles of profiles, for example, H₂O diffusion in clinopyroxene and olivine, which can be compared with existing datasets and new analyses performed by the student and collaborators at Durham.

For the natural case study, the student will conduct fieldwork at a relevant site such as Mt Etna, sampling lavas from recent, well-monitored eruptions. They will receive training in Secondary Ion Mass Spectrometry (SIMS) at the University of Edinburgh to measure H₂O diffusion profiles in plagioclase, clinopyroxene, olivine, and/or glass. These measurements, interpreted using the custom numerical model, will allow the student to determine how diffusion clocks constrain subsurface magma dynamics and ascent rates preceding high-intensity eruptions.

Year 1

The student will begin with training in scientific programming and volcanological fieldwork and sampling.

• Objective 1: Implement the mechanical component of a multi-phase flow solver for magma ascent and convection, including segregation, and develop routines to sample flow trajectories using passive tracers.
• Objective 2: Conduct an initial field campaign, likely at Mt Etna (Sicily), in coordination with ongoing studies at Durham, to collect samples for later analysis.

Year 2

Focus will shift to refining model development and acquiring laboratory skills for diffusion-profile analysis.

• Objective 1: Extend the flow solver with a thermo-chemical evolution module including crystal and bubble growth, enabling calculation of diffusion profiles along P–T–X trajectories from flow tracer data.
• Objective 2: Receive training in Secondary Ion Mass Spectrometry (SIMS) to analyse diffusion profiles in samples collected in Year 1.
• Output: Produce a first study describing the development of the conduit flow model, including thermo-chemical evolution and dynamic volatile exsolution.

Year 3

The student will integrate field, analytical, and modelling work to explore a second case study (or revisit the first with refined focus).

• Objective 1: Perform statistical analyses of modelled diffusion profiles across flow scenarios to evaluate how reliably flow conditions and ascent rates can be reconstructed, and to assess possible biases or non-uniqueness.
• Objective 2: Continue targeted field sampling and analysis as appropriate to enhance characterisation of the case-study volcano(es).
• Output: Prepare a second study on reconstructing magma ascent speeds from modelled populations of diffusion clocks.

Year 3.5

The final six months (within the 3.5-year funding period) will focus on synthesis and completion.

• Objective: Finalise analytical and modelling work to produce a third study integrating new data, flow modelling, statistical analysis, and interpretation for the selected case study.
• Output: Prepare a third study which synthesises the knowledge gained from the PhD in a high-impact, case study-focussed format.

The successful candidate will receive expert training across computational modelling, field volcanology, and microanalytical techniques, supported by a network of leading researchers. In addition, they will develop widely transferable skills in computer programming, scientific writing, and public communication.

Computational Modelling. The student will receive state-of-the-art training in scientific programming and numerical model development. Working closely with Dr Tobias Keller (University of Glasgow), an expert in multi-phase reactive transport in igneous systems, the student will learn to design and implement advanced simulation codes. They will collaborate with researchers at Glasgow, Oxford, and Imperial College London, including participants in the ExaGEO doctoral training initiative (exageo.org), which develops GPU-accelerated computational tools for Earth and environmental sciences. As part of the Glasgow Computational Engineering Centre, the student will benefit from a collaborative and technically rich environment for code development and will attend specialised workshops in scientific computing at Glasgow and partner institutions.

Field Volcanology. Training will include advanced field methods for observing, documenting, and interpreting volcanic deposits across multiple spatial scales. This experience will help the student connect field observations with model-based interpretations, providing essential geological context and complementing the project’s computational focus.

Microanalytical Techniques. The student will be introduced to advanced laboratory methods for measuring major, trace, and volatile element diffusion profiles in volcanic glass and crystals using Secondary Ion Mass Spectrometry (SIMS). This experience will provide first-hand understanding of how diffusion-clock data are produced—critical for interpreting and validating model predictions.