The 2022 Hunga Tonga-Hunga Ha'apai Volcanic Earthquake’s Source Mechanism Revealed Through a Hierarchical Bayesian Treatment of Moment Tensor and Single-Force

Inferring the seismic source mechanisms of small-to-medium-size earthquakes from the observed waveforms via inverse methods remains challenging. Firstly, a more generalized source representation is required to include a broader range of seismic sources. A seismic moment tensor (MT) is widely used to parameterize a seismic point source by assuming no net torque. However, there are well-documented seismic sources for which net torques are significant, and single force (SF) components are necessary to describe the physics of the problem, e.g., landslides and volcanic and glacier earthquakes. Secondly, the inter-parameter correlation, e.g., the tradeoffs between the MT’s isotropic and compensated-linear-vector-dipole components for shallow explosive events and the MT and SF components at all depths, can be significant. Therefore, there is imperative for advanced sampling algorithms to explore the parameter space thoroughly and effectively. Thirdly, a complete uncertainty treatment should consider theory error primarily due to the imperfection of Earth's structure (referred to as structural error) apart from data noise. To date, the uncertainty of the 1D Earth model (1D structural error) has been investigated and proven indispensable in source studies. A rigorous uncertainty estimate can improve the resolvability of source parameters, but its implementation has been challenging.

We propose a joint point-source MT and SF inversion within the hierarchical Bayesian framework to address the abovementioned set of challenges in treating the 2022 Hunga Tonga-Hunga Ha'apai event. MT and SF are combined to represent a broader range of sources in the waveform inversion. Our approach takes advantage of affine-invariant ensemble samplers to explore the parameter 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). After comprehensive synthetic experiments to demonstrate the feasibility of our approach, we focus on physics-based scenarios for the 2022 Hunga Tonga-Hunga Ha'apai volcanic earthquake. More specifically, we analyze the non-double-couple character and the role of SF in the source mechanism. Our approach provides further insights into this particular earthquake and a platform for future studies of seismic events in various geological environments.