Mitigating the risks associated with volcanoes requires a detailed understanding of the transport and eruption of magma through cracks and conduits in Earth's crust. Seismic waves excited by magma flow and its coupling to the elastic wall rocks can be used to place valuable constraints on parts of the volcanic system that are otherwise inaccessible. The complexity of observed seismic signals and the difficulty of modeling the coupled fluid-solid system present a formidable challenge. The objective of this collaborative proposal is to develop numerical models describing the high-speed flow of compressible, viscous fluids through narrow channels in elastic bodies, together with the propagation of seismic waves through the solid. The fluid and solid response is fully coupled: elastic deformation changes the cross-sectional area of the conduit through which fluid flows, and changes in fluid pressure push the conduit walls in and out, exciting seismic waves.

Specifically, the project group will develop a provably stable and accurate numerical method for time-dependent quasi-one-dimensional fluid flow through conduits in a solid body, together with the elastodynamic response of that solid. The model will include changes in compressibility, sound speed, viscosity, and drag from gas exsolution. The code will be used first to explore the role of conduit wall deformation on steady state eruption dynamics. The group will then assess the stability of steady state eruption solutions. Preliminary analyses indicate that for sufficiently rapid flows, the fluid-solid system is unstable to long wavelength perturbations that appear as conduit wall oscillations of growing amplitude. One first focus will be on seismic waves from basaltic fissure eruptions within the currently implemented two-dimensional plane-strain framework. The group will then extend the model to the axisymmetric geometry appropriate for cylindrical conduits, and study seismic waves from explosive eruptions. Finally, they will calculate far-field body and surface waves and link the time dependence of equivalent single force and moment tensor representations to detailed source processes.

This project is supported by the Geophysics and Petrology & Geochemistry Programs.

Project Report

Seismicity often heralds and accompanies volcanic eruptions. The overall goal of this project was to relate seismic waves, which can be recorded with instruments on Earth's surface, to magma flow beneath the volcano. We developed several theoretical models describing magma flowing through cracks and conduits in the Earth. One part of the project focused on a specific form of seismicity known as harmonic tremor that was observed prior to several explosions in the 2009 eruption of Redoubt Volcano, Alaska. We developed a model of rapidly repeating earthquakes occurring beneath the vent that explained many features of the observed seismicity. In our model, the earthquakes are stick-slip events, possibly on the walls of the conduit, that are being driven by upward movement and pressurization of magma prior to each explosion. The model places constraints on how magma ascends toward the surface in these eruptions. A second focus of the project was on estimating the geometry of fluid-filled cracks; such cracks are a common feature of many natural and engineered systems. Like an organ pipe, fluid-filled cracks will resonate at specific frequencies. We found that properties of these resonances, as measured, for example, from spectral peaks in seismic data, can uniquely constrain fracture length and aperture. We applied the method to infer the geometry of magma-filled cracks (dikes and sills) beneath volcanoes. This is of interest because dikes and sills are some of the primary geologic features associated with magma transport in the brittle crust. The method can also be applied to other systems. We constrained the geometry of water layers beneath glaciers and ice sheets, as well as the geometry of engineered hydraulic fractures in a natural gas reservoir. A third focus of the project was on sound wave propagation in magma, a mixture of liquid melt and gas bubbles. We developed a theoretical description of sound waves that accounted for gravitational restoring forces and time-dependent exsolution of gas. These sound waves are expected to be observable in low viscosity magmas. This description can ultimately be integrated into a detailed model of the magma plumbing system involved conduits with dikes and sills branching off of them. When subject to some external or internal disturbance, certain components of the system will oscillate (these can be either sound waves in the conduits or crack waves in the dikes and sills, or any combination thereof). These oscillations can be observed in seismic data or, if there is an open vent, perhaps also in infrasound. The project involved training for several graduate students, postdocs, and an undergraduate student in Earth science, physics, math, and scientific computing.

National Science Foundation (NSF)
Division of Earth Sciences (EAR)
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Raffaella Montelli
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University of California-San Diego Scripps Inst of Oceanography
La Jolla
United States
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