Hydrogeological process-based constraint for high-resolution proxy-modeling in hydrogeophysics

Abstract:

The classic advection-dispersion transport model fails to reproduce observed solute migration in highly heterogeneous aquifers. Advancing understanding of transport in highly heterogeneous aquifers requires in-situ observation of small-scale transport behavior, which demands fine-scale spatial discretization of the estimation problem. Geophysics presents a unique opportunity to non(minimally)-invasively observe in-situ small-scale transport features. The geophysical estimation problem involves two-step computations, the forward and inverse computations, with several computations of the full-physics forward problem that can become computationally prohibitive and intractable in high-dimensional problems. Moreover, we typically compute both the forward and inverse problems on the same grid (dimensionality), which imposes an implicit constraint on the dimensionality of the model that can be recovered. We present a novel process-based proxy-modeling strategy that decouples the dimensionalities of the forward and inverse problems into two different levels of approximations. Specifically, the method performs: 1) the forward computations on a coarser spatial discretization compared to the full-dimensionality of the desired hydrogeological model, and 2) the inverse computations proceed in the reduced-dimensionality space, which allows the estimation of a small number of model parameters to predict the high-dimensional target model.

We demonstrate the method with a numerical electrical resistivity imaging of a high-resolution 3D solute plume with increasing dimensionality of the forward computations. We compare our proxy-approximations with corresponding tomograms obtained from the standard Tikhonov (ST) inversion. We achieved 94.7-99.7% and over 99.8% truncations in the dimensionalities of the forward and inverse problems, respectively. All our proxy-approximations out-performed the tomograms obtained from the ST inversions. The ability of our method to accurately recover the high-resolution target even on a very coarse spatial discretization of the forward problem demonstrates the potential of the presented proxy-approximation strategy to recover high-resolution hydrogeological models at a significantly reduced computational overhead.