Very long period (VLP, 2–100 s) seismic signals at basaltic volcanoes like Kilauea, Hawai‘i, and Mount Erebus, Antarctica are likely from resonant oscillations of magma within the shallow plumbing system. The system consists of conduits connected to cracks (dikes and sills) or reservoirs of other shapes. A quantitative understanding of wave propagation and resonance in a coupled conduit‐crack system is required to interpret observations. In this work, we idealize the system as an axisymmetric conduit coupled to a tabular crack, accounting for fluid inertia, compressibility, and viscosity, buoyancy, and crack wall elasticity. We perform time domain simulations and eigenmode analyses of the governing equations, linearized about a rest state. The fundamental mode or conduit‐reservoir mode reflects the balance of conduit magma inertia with buoyancy (and, for small cracks, crack wall elasticity). Magma oscillates in an effectively incompressible manner within the conduit, deflating and inflating the crack, which couples to the surrounding solid to produce observable surface displacements. For sufficiently low viscosity magmas, viscous effects are confined to boundary layers. Shorter period modes are primarily reverberating crack waves with negligible coupling to the conduit. Finally, we introduce an approximate reduced model for the conduit‐reservoir mode, which can also handle more general reservoir geometries (e.g., spherical chambers). The reduced model connects the observable VLP period and quality factor to two uniquely constrained parameters: the inviscid oscillation period
Fluid resonance in elastic-walled englacial transport networks
Abstract Englacial water transport is an integral part of the glacial hydrologic system, yet the geometry of englacial structures remains largely unknown. In this study, we explore the excitation of fluid resonance by small amplitude waves as a probe of englacial geometry. We model a hydraulic network consisting of one or more tabular cracks that intersect a cylindrical conduit, subject to oscillatory wave motion initiated at the water surface. Resulting resonant frequencies and quality factors are diagnostic of fluid properties and geometry of the englacial system. For a single crack–conduit system, the fundamental mode involves gravity-driven fluid sloshing between the conduit and the crack, at frequencies between 0.02 and 10 Hz for typical glacial parameters. Higher frequency modes include dispersive Krauklis waves generated within the crack and tube waves in the conduit. But we find that crack lengths are often well constrained by fundamental mode frequency and damping rate alone for settings that include alpine glaciers and ice sheets. Branching crack geometry and dip, ice thickness and source excitation function help define limits of crack detectability for this mode. In general, we suggest that identification of eigenmodes associated with wave motion in time series data may provide a pathway toward inferring englacial hydrologic structures.
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- Award ID(s):
- 2036980
- NSF-PAR ID:
- 10322704
- Date Published:
- Journal Name:
- Journal of Glaciology
- Volume:
- 67
- Issue:
- 266
- ISSN:
- 0022-1430
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract T 0and the viscous diffusion timeτ v i s across the conduit radius. Our models can be extended to study the seismic response of more complex magmatic systems. -
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jog.2021.48
