Sequential and coupled inversion of time-lapse borehole GPR measurements for vadose zone model parameterization

Abstract

A profound understanding of the infiltration dynamics into the vadose zone is crucial to our capacity to link surface and subsurface processes for the description of the hydrologic cycle. A key to establish reliable models describing the infiltration process is the knowledge of the soil hydraulic parameters. A promising approach to estimate soil hydraulic parameters is inverse modeling based on dynamic changes in soil water content (SWC). In this context, ground penetrating radar (GPR) has been recognized as a powerful geophysical technique in vadose zone hydrogeophysics, because SWC is strongly related to the soil bulk permittivity that can be precisely determined by GPR. The aim of this thesis is to investigate the feasibility of using time-lapse GPR measurements obtained during infiltration events for vadose zone characterization with a special focus on the estimation of soil hydraulic parameters. <br /> A prerequisite for estimating soil hydraulic parameters based on GPR measurements obtained during infiltration events is that the GPR measurements should reliably reflect the transient SWC dynamics during and after infiltration events. To verify this, a 4-day infiltration experiment was performed at the rhizotron facility in Selhausen, Germany. SWC information at 0.2, 0.4, 0.6, 0.8, and 1.2 m depths were obtained by zero-offset profiling (ZOP) measurements from horizontal borehole GPR. Unfortunately, SWC information for the top 0.1 m of soil obtained by ZOP measurements was not reliable due to the strong interference between direct and refracted waves. To solve this problem, surface GPR measurements were additionally conducted. Dispersive guided waves were observed in the 500 MHz surface GPR data because the infiltration event generated electromagnetic waveguides in the top soil layer. This allowed to obtain SWC information of the top 0.1 m soil layer through dispersion analysis of the dispersive surface GPR data. By combining surface and horizontal borehole GPR measurements, the vertical SWC profiles (0 - 1.2 m) and dynamics were successfully represented during and after infiltration events. Additionally, it was found that the GPR-derived SWC corresponded well with independently measured SWC estimates obtained with time domain reflectometry (TDR) and the known amount of water applied in the infiltration events. <br /> In a next step, the performance of sequential and coupled inversion strategies for estimating hydraulic parameters from horizontal borehole GPR measurements during infiltration events was investigated. For this, a synthetic modelling study was performed first. The sequential inversion was based on measured SWC profiles obtained from the GPR travel times of the direct wave based on the straight-wave approximation and modelled SWC profiles obtained with HYDRUS-1D. Due to interpretation errors near the infiltration front and the soil surface associated with the straight-wave approximation, the sequential inversion scheme inaccurately estimated the soil hydraulic parameters in the synthetic modelling study. On the other hand, the coupled inversion scheme relied on the measured GPR travel time information and the simulated GPR travel times obtained by coupling HYDRUS-1D with a forward model describing GPR wave propagation (gprMax3D). As the interpretation errors from the straight-wave approximation were avoided, the coupled inversion scheme obtained accurate estimates of the soil hydraulic parameters in the synthetic modelling study. The coupled inversion approach was also applied to the actual horizontal borehole GPR measurements obtained during the 4-day infiltration experiment at the rhizotron facility, where it also provided plausible estimates of the hydraulic parameters. <br /> Finally, a synthetic modelling study was conducted to evaluate the potential advantages and shortcomings of coupled full waveform inversion (CFWI) of horizontal borehole GPR measurements for estimating soil hydraulic parameters and layer thickness for a 2-layer soil profile. Here, CFWI uses the full GPR waveform instead of the first arrival time, which is expected to provide additional information for parameter estimation. The results of the CFWI were compared to the coupled inversion of GPR travel times, as well as sequential inversion using SWCs from GPR travel times. A workflow of the CFWI was proposed and an efficient synthetic infiltration experiment was designed. The results for the synthetic experiment showed that CFWI allowed to accurately estimate layer thickness for a 2-layered soil profile in addition to the soil hydraulic parameters, because CFWI used additional information contained in reflected waves from the layer boundary. Moreover, the hydraulic parameter estimates from the coupled inversion of travel times exhibited a slight deviation from the true values and a relatively larger uncertainty in the hydraulic conductivity and retention functions. In contrast, the soil hydraulic parameters estimated by CFWI showed considerably smaller uncertainty and better matched with the known water retention and hydraulic conductivity curves. However, there are still several remaining challenges for the application of CFWI to measured GPR data. First, an effective approach for source wavelet estimation from measured ZOP data needs to be developed. Second, a sophisticated hydrological model combining the simulations of water flow and solute transport needs to be considered for CFWI to better estimate the electrical conductivity distributions during the infiltration process. Finally, the accuracy and especially the efficiency of the current GPR forward modelling method needs to be improved to enable CFWI for actual GPR data. <br /> In conclusion, the combined use of surface and horizontal borehole GPR measurements was able to provide accurate information on the spatiotemporal SWC variation induced by infiltration. This allowed the use of sequential and coupled inversion approaches to obtain estimates of soil hydraulic parameters. It was found that coupled inversion outperforms sequential inversion for the estimation of the soil hydraulic parameter from time-lapse horizontal borehole GPR data if strong SWC gradients occurred during the infiltration events. In addition, it was shown that CFWI has several additional advantages over the coupled inversion of GPR travel time data, and thus could become a promising approach for characterizing soil hydraulic properties at the field scale after resolving several remaining challenges.