Bayesian inversion of airborne EM data with spatial correlation prior information

Bayesian inversion of electromagnetic data can obtain key information on the uncertainty of subsurface resistivity. However, due to its high computational cost, Bayesian inversion is largely limited to 1D resistivity models. In this study, a fast Bayesian inversion method is implemented by introducing the spatial correlation as prior information. The information entropy theory of continuous functions is introduced to quantify the degrees of freedom of the parameters of the spatial correlation prior model. The analysis shows that the degrees of freedom of model parameters is significantly smaller than the number of model parameters when spatial correlation prior information is introduced. The inversion results of 2D synthetic models and field dataset show that considering the spatial correlation prior information, hundreds of thousands of MCMC sampling steps are needed to enable the inversion of up to thousands of model parameters. This result provides a possible idea for future Bayesian inversion of complex 3D models.