Inversion of hydrogeological and time-lapsed GPR data for flow parameters

Methods for estimating hydraulic properties are in great demand for modeling fluid flow and contaminant transport in the shallow subsurface. Estimates of flow parameters (such as permeability, porosity and parameters defining water retention curves) are typically obtained through the inversion of hydrogeological data (e.g., water saturation and capillary pressure measurements). However, ill-posedness and non-uniqueness often arise in such inverse problems making the solutions elusive. Incorporating additional types of data, such as from geophysical methods, is one way to improve the situation. Ground-penetrating radar (GPR) in particular has proven to be sensitive to subsurface fluid flow processes (e.g., changes in water saturation) though some uncertainty exists in interpreting GPR images. In the present work, an inverse technique is presented that uses time-lapsed GPR measurements along with transient hydrogeological data. Specifically, a maximum a posteriori (MAP) formulation, based on the Bayesian approach to parameter uncertainty, is chosen for its ability to incorporate prior information into the solution; this general framework can be simplified to other commonly used inverse problem formulations. Through a synthetic case study, numerical modeling of GPR and variably saturated flow allows for exploration of the benefits offered by inclusion of GPR data in estimation of flow parameters