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Tsunamis generated by the Hunga Tonga–Hunga Ha'apai volcanic eruption on January 15, 2022 were recorded on ocean bottom pressure and tide gauges around the Pacific Ocean, earlier than the expected arrival times calculated by tsunami propagation speed. Atmospheric waves from the eruption were also recorded globally with propagation speeds of ~ 310 m/s (Lamb wave) and 200–250 m/s (Pekeris wave). Previous studies have suggested that these propagating atmospheric waves caused at least the initial part of the observed tsunami. We simulated the tsunamis generated by the propagation of the Lamb and Pekeris waves by adding concentric atmospheric pressure changes. The concentric sources are parameterized by their propagation speeds, initial atmospheric wave amplitudes that decay with the distance, and a rise time. For the Lamb wave, inversions of the observed tsunami waveforms at 14 U.S. and nine New Zealand DART stations indicate the start of the positive rise at 4:16 UTC, the peak amplitude of 383 hPa, and the propagation speed of 310 m/s, assuming a rise time of 10 min. The later phases of the observed tsunami waveforms can be better reproduced by adding another propagating concentric wave (Pekeris wave) with a negative amplitude (− 50 hPa) and propagation speeds of 200–250 m/s. The DART records around the Pacific indicate that the Pekeris wave speed is faster toward the northwest and slightly slower toward the northeast. The synthetic waveforms roughly reproduced the far-field tsunami waveforms recorded at tide gauge stations, including the later phases, suggesting that the large amplitude in the later phase may be due to the coupling of the Pekeris wave and the tsunami, as well as resonance around tide gauge stations. [ABSTRACT FROM AUTHOR]