A Joint Point-source Moment Tensor and a Single Force Inversion Within Hierarchical Bayesian Inference for Revealing the Source Mechanism of Underground Nuclear Explosions

A seismic moment tensor (MT) consisting of 6 independent components is widely used to parameterise 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., the collapse of cavities, landslides, and glacier earthquakes. Therefore, combining MT and SF components can explore a broader range of source representation in seismic source inversion. In addition, rigorous uncertainty estimate has been a leading-edge topic in seismic source inversion. A complete uncertainty treatment should consider both data noise involved in the acquisition process and theoretical error primarily due to imperfect knowledge of Earth structure. Recent advancements jointly treating data noise and theoretical errors have been made for the MT representation within the hierarchical Bayesian framework, where noise is treated as a free parameter. However, to our best knowledge, a decomposition of the seismic source to MT and SF, including a rigorous treatment of uncertainty, remains an unaddressed problem. Here, we propose a joint inversion scheme of MT and SF within the hierarchical Bayesian framework that accounts for both data and structural (theory) uncertainties. Several carefully designed synthetic experiments modelling underground explosions demonstrate the feasibility of this method. Our current focus is on practical applications. We are hopeful that our approach will provide further insights into the physics of seismic sources for underground nuclear explosions, thus helping verify compliance with the CTBT.