Efficient uncertainty quantification in FDEM inversion using an adjusted Bayesian information criterion

Abstract Frequency-domain electromagnetic (FDEM) inversion is non-unique. The resulting inversion represents only one preferred solution under the chosen parameterization and regularization. Bayesian approaches characterize such uncertainty but often require millions of forward evaluations. This study develops a framework for layer-count assessment and model-averaged uncertainty quantification using an effective-degrees-of-freedom-adjusted Bayesian information criterion (EDF-BIC). EDF-BIC replaces the nominal parameter count with the effective degrees of freedom so that the penalty reflects the data-fitting flexibility retained after regularization. Criterion differences among evaluated candidate layer counts are converted into relative-support weights. Layer-count model averaging (LCMA), combined with a Laplace approximation, propagates candidate-conditional parameter uncertainty and uncertainty among layer counts into the resistivity structure. For the five-layer U05 model, the EDF adjustment increased the weighted mean layer count from 4.06 to 5.15 and reduced the low-layer-count preference of nominal BIC. In the G02 and G05 experiments, EDF-BIC support varied spatially near layer pinch-outs, disappearing layers, and interface variations, while between-model uncertainty was concentrated in transition zones. Across 50 noise realizations with the candidate sets, error model, and regularization fixed, mean empirical coverage of the P10–P90 intervals was 87.57% for G02 and 83.66% for G05. Application to the Yemaquan L52 and L53 field data recovered consistent principal electrical structures, whereas interface positions and geometries were more sensitive to layer-count choice. EDF calculation and uncertainty analysis added less than 1% to candidate-inversion time. The framework provides a computationally tractable approach to layer-count assessment and uncertainty propagation.