Uniqueness and stability analysis of hydrogeophysical inversion for time-lapse ground-penetrating radar estimates of shallow soil hydraulic properties

Precise measurement of soil hydraulic properties at field scales is one of the prerequisites to simulate subsurface flow and transport processes, which is crucial in many research and engineering areas. In our study, we numerically analyze uniqueness and stability for integrated hydrogeophysical inversion of time-lapse, off-ground ground-penetrating radar (GPR) data in estimating the unsaturated soil hydraulic properties. In the inversion, hydrodynamic modeling based on the one-dimensional (1-D) Richards equation is used to physically constrain a full-waveform radar electromagnetic model. Synthetic GPR data, in terms of 3-D multilayered media Green's functions, were generated for three different textured soils (coarse, medium, and fine) and assuming different infiltration events. Inversion was performed iteratively to estimate three key soil hydraulic parameters (α, n, and K_s) of the Mualem-van Genuchten model using the global multilevel coordinate search optimization algorithm. For the coarse- and medium-textured soils, inversions converged to the actual solution for all scenarios. For the fine soil, estimation errors occurred, mainly because of the higher attenuation of the electromagnetic waves in such a soil (high electric conductivity). The procedure appeared to be generally stable with respect to possible errors in the hydrodynamic and petrophysical model parameterization. However, we found that particular attention should be given to an accurate estimation of the saturated water content and infiltration flux for real field applications. The results from our numerical experiments suggest that, in theory, the proposed method is promising for the noninvasive identification of the shallow soil hydraulic properties at the field scale with a high spatial resolution.