Magma Oscillations in a Conduit‐Reservoir System, Application to Very Long Period (VLP) Seismicity at Basaltic Volcanoes: 1. Theory

Abstract

AbstractVery 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 T0 and the viscous diffusion time τvis across the conduit radius. Our models can be extended to study the seismic response of more complex magmatic systems.