Iterative Prior Resampling and rejection sampling to improve 1D geophysical imaging based on Bayesian Evidential Learning (BEL1D)

The non-uniqueness of the solution of inverse geophysical problem has been recognized for a long-time. Although stochastic inversion methods have been developed, deterministic inversion using subsequent regularization are still more widely applied. This is likely due to their efficiency and robustness, compared to the computationally expensive and sometimes difficult to tune to convergence stochastic methods. Recently, Bayesian Evidential Learning 1D imaging has been presented to the community as a viable tool for the efficient stochastic 1D imaging of the subsurface based on geophysical data. The method has been proven to be as fast, or sometimes even faster, than deterministic solution. However, the method has a significant drawback when dealing with large prior uncertainty, as often encountered in geophysical surveys: it tends to overestimate the uncertainty range. In this paper, we provide an efficient way to overcome this limitation through Iterative Prior Resampling (IPR) followed by rejection sampling. IPR adds the posterior distribution calculated at a former iteration to the prior distribution in a subsequent iteration. This allows to sharpen the learning phase of the algorithm and improve the estimation of the final posterior distribution, while rejection sampling eliminates models not fitting the data. In this contribution, we demonstrate that this new approach allows BEL1D to converge towards the true posterior distribution. We also analyze the convergence behavior of the algorithm and derive guidelines for its application. We apply the approach for the interpretation of surface waves dispersion curves, but the approach can be generalized to other geophysical methods.