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On 15 January 2022, a large eruption of the Hunga Tonga-Hunga Ha'apai volcano in Tonga triggered globally observed tsunami waves. While the first arrival in the observed wave trains is now widely known to be related to the atmospheric Lamb wave generated by the eruption, large later phases, whose amplitudes were comparable to the first ones, were also recorded. In this study, we estimated the source of the later phases based on the Vespa analysis and proposed a new numerical scheme to reproduce them. The Vespa analysis estimates the arrival time and incident angle of each signal by a slant-stack process using its theoretical traveltime. The Vespa analysis revealed that small atmospheric waves excited the large later tsunamis. For the numerical experiments, we used two types of synthetic methods: finite difference method and normal mode theory. We found that both a good atmospheric wave model and bathymetric effect were important to generate the atmospheric-induced tsunamis corresponding to the later phases. A hybrid method calculating tsunamis by the finite difference method with the atmospheric waves by the normal mode theory as the input successfully reproduced the observed records, particularly in amplitude over the entire records. [ABSTRACT FROM AUTHOR]

SUMMARY: The 15 January 2022 eruption of the Hunga–Tunga volcano generated a Lamb pressure wave propagating all over the globe and triggering a tsunami throughout the planet. A first atmospheric wave arrived 16 hr after the eruption on the French Mediterranean coasts and propagated southward. A second one originating from Africa was observed 4 hr later with an attenuated amplitude. The first wave can be roughly defined either by a N wave or a sinusoid signal with a period close to 50 min and an amplitude of 130 Pa. In the Mediterranean Sea, the tsunami was recorded by almost all standard coastal tide gauges or pressure gauges. The French tide gauge stations recorded water waves with amplitudes ranging from a few centimetres to 10 cm and with periods ranging from 10 min to 1 hr. Numerical simulation of the tsunami is performed by the operational code Taitoko for different atmospheric sources. Non-linear shallow water equations are solved by a finite-difference method, using the nested multigrid approach. The tsunami is generated by calculating analytically the atmospheric pressure gradient in the momentum equations. Comparisons of time-series between numerical solutions and records are satisfactory for most tide-gauges along the French Mediterranean coast. Sensitivity analysis on the atmospheric source and on the resolution is performed. For most tide-gauge stations, numerical results show that the wave forms depend first on local resonance phenomena. [ABSTRACT FROM AUTHOR]