The violent eruption of the Hunga (Tonga) submarine volcano on 15 January 2022 caused a 58 km-heigh ash plume, catastrophic tsunami, and significant global seismic and infrasound waves. However, the physical mechanism underpinning its multiple-explosive events remains unclear, and its resolvability relies on the seismic waveform source inversion. The studies of two different point-source models, the seismic moment tensor (MT) and the single force (SF), have been performed separately for this eruption, which, interestingly, can explain the seismic data adequately. Here, we use a joint inversion of MT and SF to unravel a composite source of an explosive MT and a significant upward force for the first major explosive event. Regarding the direction and magnitude, we propose that the upward force is likely a rebound force in response to the pressure drop on the seafloor because the water body above the volcano was abruptly uplifted by the shallow underwater explosion.

Determining the seismic moment tensors (MT) from the observed waveforms, known as full-waveform seismic MT inversion, remains challenging for small to moderate-size earthquakes at regional scales. Firstly, there is an intrinsic difficulty due to a tradeoff between the isotropic (ISO) and compensated linear vector dipole (CLVD) components of MT that impedes resolving shallow explosive sources, e.g., underground nuclear explosions. It is caused by the similarity of long-period waveforms radiated by ISO and CLVD at regional distances. Secondly, regional scales usually bear complex geologic structures; thus, inaccurate knowledge of Earth’s structure should be considered a theoretical error in the MT inversion. However, this has been a challenging problem. So far, only the uncertainty of the 1D Earth model (1D structural error), apart from data errors, has been explored in the source studies. Here, we utilize a hierarchical Bayesian MT inversion to address the above problems. Our approach takes advantage of affine-invariant ensemble samplers to explore the ISO-CLVD tradeoff space thoroughly and effectively. Furthermore, we invert for station-specific time shifts to treat the structural errors along specific source-station paths (2D structural errors). We present synthetic experiments demonstrating the method’s advantage in resolving the ISO components. The application to nuclear explosions conducted by the Democratic People’s Republic of Korea (DPRK) shows highly similar source mechanisms, dominated by a high ISO, significant CLVD components, and a small DC component. The recovered station-specific time shifts from the nuclear explosions present a consistent pattern, which agrees well with the geological setting surrounding the event location.