Variable inflation rate of a magmatic deformation source beneath Aira caldera after the 1914 eruption of Sakurajima volcano: Inferences from a linear Maxwell viscoelastic model constrained by geodetic data

Abstract

Temporal variation of ground surface displacement rates at volcanoes may represent changes to the volumetric magma supply rate over time. If crustal rock responds elastically to a magmatic deformation source, the volume change of the source has a simple one-to-one relation to the surface deformation. For viscoelastic crustal rock, however, the correlation is not always straightforward, particularly at volcanoes where crustal viscosity is lowered by a high geothermal gradient. For a continuous inflation of the deformation source, the viscoelastic surface displacement depends on the balance between the uplift due to magma supply and subsidence due to viscoelastic relaxation. In this study, using a 3D finite element model composed of an elastic layer underlain by a linear Maxwell viscoelastic layer with a spatially uniform viscosity, we estimate the temporal variation of volumetric magma supply rate into the upper crust beneath Aira caldera in southern Kyushu, Japan, after the 1914 eruption of Sakurajima volcano. It is found that the geodetic data, including levelling and GNSS displacement fields, require a sill-like magmatic deformation source at a depth of 11 km to inflate at the following rates for six different periods: (I) ~6.9–9.4 × 106 m3/yr in 1914–1934, (II) ~9.1–16.7 × 106 m3/yr in 1934–1960, (III) ~1.6–3.8 × 106 m3/yr in 1960–1968, (IV) ~8.1–11.0 × 106 m3/yr in 1968–1976, (V) ~ −1.0–2.2 × 106 m3/yr in 1976–1997, and (VI) ~5.8–9.4 × 106 m3/yr in 1997–2007. The constrained viscosity (ηc) of the viscoelastic crust ranges from ~5 × 1018 Pa s to ~1020 Pa s or more. The lowest and highest values produce the best fit to the data in the earliest period and in period V showing surface subsidence, respectively, but for the other periods any viscosity is acceptable unless it is lower than ~1018 Pa s. The lowest viscosity providing the best fit in the earliest period indicates that viscoelastic displacement in response to the 1914 eruption plays an important role in the surface deformation field. The observed surface subsidence in period V can be explained either by inflation or deflation of the deformation source, depending on whether ηc is lower or higher than ~1019 Pa s, respectively. The subsequent surface recovery in period VI requires an increase in the inflation rate for any case of ηc. The volume of magma accumulated since the 1914 eruption (ΔV) is predicted to be ~0.6–0.8 km3 in 2020. The estimated inflation/deflation rate of the deformation source, in comparison with the observed volumetric eruption rate, reveals that a significant eruption occurs only when ΔV is ~0.4 km3 or more. However, even if ΔV is beyond the critical value, the eruptive activity does not depend on ΔV. The temporal inflation rate inferred in this study gives an opportunity to discuss eruptive dynamics in relation to the observed eruptive activity, such as a quantitative relationship between magma supply rate into, and discharge rate from, a deformation source.