Full-waveform inversion of surface ground penetrating radar data and coupled hydrogeophysical inversion for soil hydraulic property estimation

Non-invasive electromagnetic methods are increasingly applied for a wide range of applications in geophysical engineering, infrastructure characterization and environmental and hydrological studies. A variety of geophysical techniques are routinely used to estimate medium properties, monitor shallow soil conditions and provide valuable estimates of soil water content and the soil hydraulic parameters needed for the understanding of the highly dynamic hydrological processes in the subsurface. Traditionally, estimates of the soil water content are obtained using the subsurface permittivity and conductivity in combination with petrophysical relationships such as the Complex Refractive Index Model (CRIM) or empirical relationships such as Topp's equation and Archie's law. Here, especially surface ground penetrating radar (GPR) is a technique that enables a quick and effective mapping of the subsurface dielectric permittivity. Although GPR has the potential to return permittivities and conductivities for the same sensing volume at the field scale, estimates of the conductivity based on conventional ray-based techniques that only use part of the measured data and simplified approximations of the reality contain relatively large errors. Full-waveform inversion (FWI) overcomes these limitations by using an accurate forward modeling and inverts significant parts of the measured data to return reliable quantitative estimates of both permittivity and conductivity. In this work, we introduce a novel full-waveform inversion scheme that is able to reliably estimate permittivity and conductivity values from surface GPR data. It is based on a frequency-domain solution of Maxwell’s equations including far-, intermediate- and near-fields assuming a three-dimensional, horizontally layered model of the subsurface, and requires a starting model of the subsurface properties as well as the estimation of a source wavelet. Although the full-waveform inversion is relatively independent of the permittivity starting model, inaccuracies in the conductivity starting model result in erroneous effective wavelet amplitudes and therefore in erroneous inversion results, since the conductivity and wavelet amplitudes are coupled. Therefore, the permittivity and conductivity are updated simultaneously with the phase and amplitude of the source wavelet. Here, optimizing the medium properties and reducing the misfit is carried out using a gradient free approach. This novel FWI is applied the analysis of ground waves and reflected waves. In the case of synthetic single layered and waveguide data, where the starting model differs significantly from the true model parameter, we were able to reconstruct the obtained model properties and the effective source wavelet. For measured waveguide data, different starting values returned the same quantitative medium properties and a data-driven effective source wavelet.