Physically based regularization of hydrogeophysical inverse problems for improved imaging of process‐driven systems

[1] We introduce a new strategy for integrating hydrologic process information as a constraint within hydrogeophysical imaging problems. The approach uses a basis-constrained inversion where basis vectors are tuned to the hydrologic problem of interest. Tuning is achieved using proper orthogonal decomposition (POD) to extract an optimal basis from synthetic training data generated by Monte Carlo simulations representative of hydrologic processes at a site. A synthetic case study illustrates that the approach performs well relative to other common inversion strategies for imaging a solute plume using an electrical resistivity survey, even when the initial conceptualization of hydrologic processes is incorrect. In two synthetic case studies, we found that the POD approach was able to significantly improve imaging of the plume by reducing the root mean square error of the concentration estimates by a factor of two. More importantly, the POD approach was able to better capture the bimodal nature of the plume in the second case study, even though the prior conceptual model for the POD basis was for a single plume. The ability of the POD inversion to improve concentration estimates exemplifies the importance of integrating process information within geophysical imaging problems. In contrast, the ability to capture the bimodality of the plume in the second example indicates the flexibility of the technique to move away from this prior process constraint when it is inconsistent with the observed ERI data.