| Markov chain Monte Carlo (MCMC) techniques have attracted wide attention in geophysical estimation of hydrogeological properties due to their ability to recover multiple, equally probable solutions that enable uncertainty assessment. Standard MCMC methods, however, become computationally intractable in high dimensional problems. This research has developed a MCMC method that operates in the reduced-dimensional space, thereby enabling the estimation of a small number of inversion parameters while incorporating knowledge of the physics of the target process. First, we generate training images (TIs) from Monte Carlo simulation of the hydrologic process of interest. We then used proper orthogonal decomposition (POD) to extract a small number of optimal basis vectors that capture most of the variability in the TIs, leading to dimensionality reduction. The basis vectors were subsequently used to constrain the inversion problem to reconstruct the target field. We demonstrate the performance of the algorithm with synthetic electrical resistivity imaging of unimodal and bimodal solute plumes. The unimodal plume was consistent with the hypothesis underlying the generation of the TIs whereas bimodality in the target plume morphology was not theorized. The same set of TIs were, however, employed in both reconstructions. We achieved 90% reduction in the dimensionality of the MCMC problem while being able to retrieve multiple plausible results for uncertainty analysis. Additionally, although bimodality was not captured in the prior conceptualization, the algorithm was able to flexibly adapt towards the geophysical data to yield reasonable results. |
