Improving Bayesian Evidential Learning 1D imaging (BEL1D) accuracy through iterative prior resampling

Bayesian Evidential Learning 1D Imaging (BEL1D) has been recently introduced as a new computationally efficient tool for the interpretation of 1D geophysical datasets in a Bayesian framework. Applications have already been demonstrated for Surface Nuclear Magnetic Resonance (SNMR) data and surface waves dispersion curves. The case of SNMR is particularly relevant in hydrogeophysics, as it directly sounds the water content of the subsurface. BEL1D relies on the constitution of statistical relationships in a reduced dimension space between model parameters and simulated data using prior model samples that replicate the field experiment. In BEL1D, this relationship is deduced through Canonical Correlation Analysis (CCA). When using large prior distributions, CCA may lead to numerous poorly correlated distributions for higher dimensions. Those poorly correlated distributions are resulting in a low reduction of uncertainty on some parameters, even if the experiment is supposed to be sensitive to them. This phenomenon is related to the aggregation of multiple parameters in the same dimension, hence the possible aggregation of sensitive and insensitive parameters. However, arbitrarily reducing the extent of the prior will lead to biased estimations. To overcome this impediment, we introduce an iterative procedure, using the posterior model space of the previous iteration as prior model of the current iteration. This approach frequently reveals higher correlations between the datasets and the model parameters, while still using large unbiased priors. It enables BEL1D to produce better estimations of the posterior probability density functions of the model parameters. Nonetheless, iterating on BEL1D presents several challenges related to the presence of insensitive parameters, that will always mitigate the capacity to reduce at once the uncertainty on the whole set of parameters describing the models. On noise-free synthetic datasets, this method leads to near-exact estimation of the sensitive parameters after few (two to three) iterations. On noisy datasets, the resulting distributions bear some uncertainty, arising directly from the presence of noise, but to a lesser extent than the non-iterative approach.. The procedure remains more computationally efficient than McMC.