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Fig. 9 | Earth, Planets and Space

Fig. 9

From: Quantitative relationship between plume emission and multiple deflations after the 2014 phreatic eruption at Ontake volcano, Japan

Fig. 9

Calculated ρβ values for the shallow reservoir. Plots are made for each of two end members of \(\beta_{\text{c}}\): a \(\beta_{\text{c}}\) = 1.4 × 10−8 Pa−1 (\(V\) = 107 m3) and at b \(\beta_{c}\) = 1.4 × 10−9 Pa−1 (\(V\) = 108 m3) (see also Additional file 1: Text S2). ρβ are computed as a function of S, (0.0 ≤ S ≤ 1.0) at each pressure. Details of these parameters setting are described in Additional file 1: Text S1. Solid and open symbols correspond to two-phase and single-phase state, respectively. Solid circles and triangles correspond to host rock porosity \(\phi\) = 0.1 and 0.5 in the two-phase state, respectively. Red and blue symbols correspond to conditions of lithostatic and hydrostatic pressure at the 500-m depth, respectively. A black dashed line shows an upper limit value of \(\rho \beta\), which is derived from observations. Gray-shaded area indicates possible range of allowable ρβ values, within which even calculated values with pressure drop should range

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