Based on the barometric data that recorded by the seismic monitoring network in Chinese Mainland, the primary infrasonic periods and relative arrival times of 462 stations are obtained with the aid of Meyer's wavelet decomposition, Welch's periodogram spectrum estimation and waveform cross-correlation, etc. By extracting the seismic Rayleigh waves of two IRIS stations in the South Paci c and comparing them with the synthetic seismograms, the time of the rst two large volcanic eruptions and the largest volcanic eruption are credibly deduced, and then the travel times and propagation speeds of the primary infrasonic waves are obtained. In order to further explain the subsequent confused infrasound phases on pressure, a series of numerical simulations with the acousticgravity wave propagation equation are successfully applied to yield highly similar waves corresponding to the barometric records, which indicates that the eruption source contains more than 10 events in an hour. From the above analysis, major conclusions are obtained as followings: (1) the primary pressure disturbance of the Tonga volcano eruption appears to be a simple bulge; however, it is in fact a complex wave composed of multiple eruptions. Its largest eruption is about 13 minutes later than the rst large eruption of the very day. (2) Besides the tropospheric propagation, a clear infrasonic phase that propagates in the stratosphere is also observed in some stations, and its amplitude is about a fth of the primary infrasound. The waves propagating in the stratosphere may have been apparently delayed because of travelling against the westerly wind. (3) The group velocity of the primary infrasound wave from the troposphere is about 308m/s. Its average period is 70 minutes, and its wavelength is about 1300km. Its arrival deviation at each station is negatively correlated with the difference of the near-surface air temperature between North China and South China. However it is challenging to accurately estimate the parameters of the subsequent waves propagating in the stratosphere or along the other side of the Earth due to their low SNR, even though it would be roughly estimated that the speed of the propagation in the stratosphere is only about 225m/s. (4) The phenomenon that there are much smaller periods and later arrivals at the stations within 200km around Beijing may be related to the signi cant cooling with 12℃ change, which appears from Ulantoba, Outer Mongolia, to Beijing and begins from the noon of January 15 in Beijing time.