Fig. 9

Re-estimated 2-D PDF distribution of the estimated magma–air interface depth and sound velocity. The total PDF value in the region surrounded by a black line is equivalent to half the whole area. This region is at a depth of 40–200 m and a sound velocity of 300–780 m/s. The thin gray line shows the estimated range from the previous study using only the time delay of arrivals (Ishii et al. 2019). The dashed gray line is the estimated range of Fig. 5e. The pattern of this PDF distribution is very similar to that in Fig. 5e