The research on Bayesian inference for geophysical inversion

Based on statistical theory, the Bayesian inversion method adopts the posterior probability distribution to evaluate the model parameters under the constraints of prior information and observation data. Compared to deterministic inversion theory, Bayesian inference is beneficial to quantitative evaluation of inversion uncertainty by the model parameter marginal probability distribution, maximum a posterior estimation (MAP), mean model estimation and correlation coefficient, which accurately reflects the constraint ability of observation data and prior information on model parameters. We systematically summarized the application of the Bayesian inference in geophysical inversion and proposed the basic flowchart to realize Bayesian model evaluation. Firstly, the Bayesian theory is simply introduced. The prior information probability distribution, the likelihood function formula, and the construction of the posterior probability equation are explained in detail. Secondly, the implementation process of Bayesian inversion is discussed in detail. As for model parameter updates, the concepts of fixed and trans-dimensional inversion with the hyperparameter optimization are discussed. In terms of inversion methods, the Markov Chain Monte Carlo (MCMC) sampling methods of fixed and trans-dimensional inversion are highlighted. In consideration of model parameter evaluation, the calculation of Bayesian statistical parameters under different conditions is introduced. Then the specific measures to improve the sampling efficiency of Bayesian inversion are discussed. Finally, the application of Bayesian inference in geophysical inversion is summarized.