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Fig. 5 | Earth, Planets and Space

Fig. 5

From: Combined approach to estimate the depth of the magma surface in a shallow conduit at Aso volcano, Japan

Fig. 5

2-D PDFs of two estimated unknown parameters. These unknowns are the depth of the magma–air interface and the sound velocity inside the vent. a–d PDFs assuming four frustum pipe radii (\(a_\text {c}=\) 35, 46, 58, and 71 m, respectively). The results generally indicate that large PDF values are distributed at shallower depths (<200 m) and over wide sound velocity ranges. e Summed PDFs of these four results. The four PDF values are multiplied by the weighting coefficient of each shape, as determined from the observed PDF of \(f_\text {1}/f_\text {0}\) (Fig. 2b) at the time of summation. The total PDF value in the region surrounded by a white line is equivalent to half the whole area. This region is at a depth of 40–200 m and a sound velocity of 300–680 m/s. The thin gray line is the estimated range from the previous study using only the time delay of arrivals (Ishii et al. 2019)

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