Probability-Perturbation McMC for 3D Bayesian TDEM Inversion with Unknown Covariance Parameters

Zhuo Liu , Zhen Yin, Jonas Kloeckner, Jack Muir, Jef Caers

We present a hierarchical Bayesian inversion framework for large-scale 3D time-domain electromagnetic (TDEM) data that jointly infers the subsurface conductivity field and the parameters controlling a Gaussian process (GP) covariance function, requiring minimal assumptions about subsurface spatial structure. The framework addresses two fundamental bottlenecks in 3D probabilistic inversion: the curse of dimensionality in high-dimensional model space, resolved through GP parameterization that encodes spatial continuity in a compact set of hyperparameters; and the prohibitive cost of repeated forward evaluations, resolved through a 3D surrogate that replaces the PDE-based solver during McMC sampling. Posterior sampling is performed via the Probability Perturbation Method (PPM) within a Metropolis-Hastings algorithm augmented with delayed rejection and adaptive annealing, which together balance global exploration and local posterior refinement. Prior falsification through Principal Components Analysis (PCA) ensures the training ensemble covers the data-consistent region of model space before inversion begins. We validate the framework on synthetic experiments of increasing complexity and demonstrate its application to field TDEM data from a greenfield Ni-Cu-Co sulfide exploration target in the Midcontinent Rift system. The surrogate reduces the per-iteration forward cost by a factor of approximately 10,000 relative to the full PDE solver, making 50,000-iteration 3D McMC chains tractable on a single workstation. The resulting posterior ensemble enables full 3D uncertainty quantification, interpretable GP-parameter recovery, and loss-based false-positive screening of subsurface anomalies.