A dynamic balance between magma supply and eruption rate at Kilauea volcano, Hawaii

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Abstract
The dynamic balance between magma supply and vent output at Kilauea volcano is used to estimate both the volume of magma stored within Kilauea volcano and its magma supply rate. Throughout most of 1991 a linear decline in volume flux from the Kupaianaha vent on Kilauea's east rift zone was associated with a parabolic variation in the elevation of Kilauea's summit as vent output initially exceeded then lagged behind the magma supply to the volcano. The correspondence between summit elevation and tilt established with over 30 years of data provided daily estimates of summit elevation in terms of summit tilt. The minimum in the parabolic variation in summit tilt and elevation (or zero elevation change) occurs when the magma supply to the reservoir from below the volcano equals the magma output from the reservoir to the surface, so that the magma supply rate is given by vent flux on that day. The measurements of vent flux and tilt establish that the magma supply rate to Kilauea volcano on June 19, 1991, was 217,000±10,000 m3/d (or 0.079±0.004 km3/yr). This is close to the average eruptive rate of 0.08 km3/yr between 1958 and 1984. In addition, the predictable response of summit elevation and tilt to each east rift zone eruption near Puu Oo since 1983 shows that summit deformation is also a measure of magma reservoir pressure. Given this, the correlation between the elevation of the Puu Oo lava lake (4 km uprift of Kupaianaha and 18 km from the summit) and summit tilt provides an estimate for magma pressure changes corresponding to summit tilt changes. The ratio of the change in volume to the change in reservoir pressure (dV/dP) during vent activity may be determined by dividing the ratio of volume erupted to change in summit tilt (dV/dtilt) by the ratio of pressure change to change in summit tilt (dP/dtilt). This measure of dV/dP, when combined with laboratory measurements of the bulk modulus of tholeitic melt, provides an estimate of 240±50 km3 for the volume of Kilauea's magma reservoir. This estimate is much larger than traditional estimates but consistent with seismic tomographic imaging and geophysical modeling of Kilauea's magma system.
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