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Based on the barometric data recorded by the seismic monitoring network on the Chinese mainland, Lamb wave 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. By extracting the seismic Rayleigh waves of two seismic stations in the South Pacific and comparing them with the synthetic seismograms, the occurrence time of the first two large volcanic eruptions and the largest volcanic eruption are credibly deduced, and then the travel times and propagation speeds of the Lamb waves are obtained. In order to further explain the attributes of the pressure disturbance associated with the complex acoustic gravity wave (AGW) phases on pressure, a series of numerical simulations with the QSSP program are applied to yield highly similar waves corresponding to the barometric records, which indicates that the eruption source may contain more than 10 sub-events within an hour. According to our detailed analyses, major conclusions are obtained as follows: (1) Although the primary pressure disturbance of the Tonga volcanic eruption appears to be a simple bulge, it is in fact a complex wave composed of multiple eruptions. The largest eruption occurred about 13 min after the first large eruption. (2) In addition to the propagation of the traditional Lamb mode, the Pekeris mode phase that propagates with a lower speed is also observed in some stations, and its amplitude is about a fifth of the Lamb wave. The Pekeris waves may have been more significantly delayed as they traveled against the westerly wind due to their much shorter periods and lower velocities. (3) The group velocity of the Lamb wave is about 308 m/s. Its average period is 70 min, and the wavelength is about 1300 km. The arrival time deviation at each station is negatively correlated with the difference in the near-surface air temperature between North and South China. However, accurately estimating the parameters of the Pekeris waves or the antipodal Lamb waves is challenging due to their low signal-to-noise ratio (SNR), even though the horizontal propagation speed of the Pekeris wave toward China is estimated to be approximately 225 m/s. (4) Much shorter periods and later arrivals at the stations within 200 km of Beijing may be related to the significant cooling (i.e. 12 °C temperature drop), which occurred from Ulantoba, Outer Mongolia, to Beijing beginning at noon on January 15 (Beijing time). [ABSTRACT FROM AUTHOR]