Volcanic eruptions are often accompanied by spatiotemporal migration of
ground deformation, a consequence of pressure changes within magma reser-
voirs and pathways. We model the propagation of pressure variations by
eruptive magma withdrawal during the early episodes of the ongoing Pu'u
̄ o-Kupaianaha eruption of K ̄ılauea Volcano, Hawai'i. Tilt measurements
' O' ̄
̄ o was typically ac-
show that the onset of fountaining episodes at Pu'u ' O' ̄
companied by abrupt deflation and followed by a sudden onset of gradual
re-inflation, once the eruptive episode ended. Tilt at K ̄ılauea's summit un-
derwent similar patterns of deflation and inflation, albeit with time delays
of several hours during most episodes. The observed delay times for dif-
ferent episodes vary between 3 and 12 hours. These can be reproduced by
modelling the space-time evolution of pressure variations within an elastic-
walled dike that connects K ̄ılauea's summit to its east rift zone. As pressure
changes travel through the dike, the interplay between elastic response of
the dike wall and viscous resistance of the fluid determines the delay time.
̄ o causes a decrease in pressure and
Magma withdrawal beneath Pu'u ' O' ̄
deflation. The resultant increase in magma flow rate causes deflation of the
Halema'uma'u magma reservoir at the summit, although delayed in time
because of the finite propagation velocity of both the pressure changes and
the surge in magma flow rate within the dike. The time delay depends on
dike dimensions, elasticity of the wall rock, magma viscosity, as well as mag-
nitude and duration of the pressure variations themselves. The dike width is
the most important parameter in determining delay times: pressure changes
propagate noticeably faster (slower) in a slightly wider (narrower) dike, as
a consequence of smaller (larger) viscous dissipation. It is unlikely that the
east rift zone magmatic pathway is of uniform dimensions: variation of its width could represent spatially localized changes, possibly due to removal
of a constriction or partial collapse of wall-rock during repose periods. A
transport efficiency for the dike system can be defined, providing a measure
of the ease of flow for magma along the east rift zone and its variations
in time, and thus an insight on the evolution of the magmatic system of
K ̄ılauea Volcano.

1. dikes
2. magma dynamics