Fig. 1

a The black circles represent the peak amplitude of the observed air pressures relative to the distances between the barometers and the Tongan volcano. The red line is the regression line of the peak amplitude developed by applying the attenuation relationship \(h_{{\text{A}}} = h_{0} R^{ - 0.5}\), where \(h_{0}\) is assumed to be 132 hPa, and \(R\) is the distance from the source. b The black and red lines display the observed and simulated air pressures in Japan. The green bars indicate the peak amplitude estimated by the regression. The station locations are shown in Additional file 1: Fig. S1