[S-VC31] Mechanism of volcanic eruptions

[SVC31-11] Crystallization model regarding relationship between magma supply rate and CSD during the historical eruptions of Sakurajima volcano

★Invited Papers

*Atsushi Toramaru¹ (1.Department of Earth and Planetary Sciences, Faculty of Sciences, Kyushu University)

Keywords:Sakurajima, crystal size distribution, magma supply rate, crystallization model

The historical eruptions of Sakurajima volcano, Bunmei, An-ei, Taisho eruptions, provide a fortunate opportunity to theoretically understand how the magmas behave in the plumbing system during several hundred years, because the time and volume of each eruption has been constrained satisfactorily by geological methods together with petrological data. Yamashita and Toramaru (2020) revealed that the geological magma discharge rates (Qgeol) are correlated with intercepts and slopes of log-linear crystal size distributions (CSDs) of plagioclase phenocrysts with high temperature origin in those lavas. After reexamination taking into account the effect of mixing ratio of high temperature magmas to low temperature magmas on CSD values, it is found that only the slope is corelated with Q_geol, that is, Q_geol is proportional to the square of the slope: Q_geol ~ |slope|². In this talk, I propose the model to explain this relationship. In the case of crystallization in a closed-system, the slope of log-linear CSD is inversely proportional to the product of the crystal growth rate G and growth time t_c: |slope| ~ (G*t_c)^-1. In order to explain the correlation between slopes of CSDs and cooling rates in the experimental results by Pupier et al (2008), G must be proportional to the square root of cooling rate: G ~ |dT/dt|^1/2. I assume a simple plumbing system consisting of a shallow magma chamber, the lower conduit from mantle, and the upper conduit to the surface. The magma temperature in the lower conduit follows the surrounding country rock with constant geotherm. The plagioclase phenocrysts crystallize by nucleation and growth during the ascent in the lower conduit. If the conduit radius has been kept constant during 500 years, |dT/dt| of the magma is proportional to the ascent velocity V, that is, supply rate Q_m: |dT/dt| ~ Q_m. Thus, the growth rate is proportional to the square root of ascent velocity: G ~ V^1/2 ~ Q_m^1/2. The growth time is inversely proportional to the ascent velocity: tc ~ V^-1 ~ Q_m^-1. Consequently the slope is proportional to ascent velocity or supply rate : |slope| ~Q_m^1/2. From this, magma supply rate is proportional to the square of slope of CSD: Q_m ~ |slope|². The coincidence between this relation and the observational fact Q_geol ~ |slope|² highly suggests that the mass balance in the magma chamber holds for several hundred years, that is, volumes of supplied magmas are withdrawn by the eruptions.