This paper outlines methods for determining a bubble size distribution (BSD) and the moments of the BSD function in vesiculated clasts produced by volcanic eruptions. It reports the results of applications of the methods to 11 natural samples and discusses the implications for quantitative estimates of eruption processes. The analysis is based on a quantitative morphological (stereological) method for 2-dimensional imaging of cross-sections of samples. One method determines, with some assumptions, the complete shape of the BSD function from the chord lengths cut by bubbles. The other determines the 1st, 2nd and 3rd moments of distribution functions by measurement of the number of bubbles per unit area, the surface area per unit volume, and the volume fraction of bubbles. Comparison of procedures and results of these two distinct methods shows that the latter yields rather more reliable results than the former, though the results coincide in absolute and relative magnitudes. Results of the analysis for vesiculated rocks from eleven subPlinian to Plinian eruptions show some interesting systematic correlations both between moments of the BSD and between a moment and the eruption column height or the SiO2 content of magma. These correlations are successfully interpreted in terms of the nucleation and growth processes of bubbles in ascending magmas. This suggests that bubble coalescence does not predominate in sub-Plinian to Plinian explosive eruptions. The moment-moment correlations put constraints on the style of the nucleation and growth process of bubbles. The scaling argument suggests that a single nucleation event and subsequent growth with any kind of bubble interaction under continuous depressurization, which leads to an intermediate growth law between the diffusional growth (Rm ∝ t 2 3) at a constant depressurization rate and the Ostwald ripening (Rm ∝ t 1 3) under a constant pressure, where Rm and t are the mean radius of bubble and the effective time of diffusion respectively, occurred in the eruptions. It is emphasized that the BSD in vesiculated rocks from terrestrial volcanoes can be used to estimate quantitatively eruption processes such as the initial saturation pressure and magma ascent velocity in a volcanic conduit.
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