Coseismic slip distribution inversion by least squares: A Bayesian method for uncertainty-constrained regularization

The study investigates the least squares coseismic slip distribution inversion problem combined with the Bayesian method for determining the regularization factor. In response to the significant time consumption of the Bayesian method in coseismic slip distribution inversion, the neglect of uncertainty in earthquake studies by the least squares method, and the issue that using L-curve, U-curve, and EI-curve to determine the regularization factor only provides numerical point estimates, a method is proposed that combines the Bayesian method with least squares coseismic slip inversion. The task of determining the regularization factor is assigned to the Markov Chain Monte Carlo (MCMC) method under the Bayesian framework, while the final slip distribution inversion is performed using least squares. The proposed method was verified using the February 6, 2016, Meinong earthquake and demonstrated its superiority in correspondence with the fault geometry parameter inversion of the Meinong earthquake. The inversion results show that the maximum slip of the Meinong earthquake was 0.54 m, the average slip angle was 44.94°, the seismic moment was 5.26 × 10¹⁸ N·m and the moment magnitude was M_W6.45. This method takes into account the uncertainties in earthquake studies and helps provide new insights into post-seismic deformation mechanisms. Moreover, in the future, the inherent advantages of the Bayesian method can be expanded by incorporating specific geophysical factors of each earthquake into the prior information constraints for the regularization factor.