Adaptive Geological Model Parameterization Using Reversible Jump MCMC

Uncertainty quantification is a key component of geological modeling for mining, exploration, and civil engineering. While uncertainty estimation workflows for implicit structural modeling and inversion are well established for fixed parameter spaces, they require the number of model parameters to be defined a priori. This assumption is often unjustified and subjected to bias, as the number of geological layers or phases is commonly unknown, leading to models that are either overly complex or overly simplistic. Trans-dimensional Markov chain Monte Carlo methods provide a powerful framework for model selection by favoring parsimonious representations in settings with high uncertainty. In particular, Reversible Jump Markov chain Monte Carlo (RJ-MCMC) has recently gained attention for solving inverse problems with variable dimensionality. In this study, we investigate the applicability of RJ-MCMC to parameters governing geological interpolation functions. By automatically inferring the optimal number of parameters, the method reduces reliance on subjective user choices. We generate synthetic geophysical data from simple structural models to establish ground truth and perform geophysical inversion (gravity) by updating ensembles of prior structural models. This probabilistic framework enables likelihood-based model evaluation and supports further inference as new data become available. Generated candidates can be grouped to identify model archetypes that fit the data, while parsimony is maintained.