Quantitative conductivity and permittivity estimation using full-waveform inversion of on-ground GPR data

Abstract

Conventional ray-based techniques for analyzing common-midpoint (CMP) ground-penetrating radar (GPR) data use part of the measured data and simplified approximations of the reality to return qualitative results with limited spatial resolution. Whereas these methods can give reliable values for the permittivity of the subsurface by employing only the phase information, the far-field approximations used to estimate the conductivity of the ground are not valid for near-surface on-ground GPR, such that the estimated conductivity values are not representative for the area of investigation. Full-waveform inversion overcomes these limitations by using an accurate forward modeling and inverts significant parts of the measured data to return reliable quantitative estimates of permittivity and conductivity. Here, we developed a full-waveform inversion scheme that uses a 3D frequency-domain solution of Maxwell’s equations for a horizontally layered subsurface. Although a straightforward 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, because the conductivity and wavelet amplitudes are coupled. Therefore, the permittivity and conductivity are updated together with the phase and the amplitude of the source wavelet with a gradient-free optimization approach. This novel full-waveform inversion is applied to synthetic and measured CMP data. 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 wavelet and quantitative permittivities and conductivities. This novel approach enables the quantitative estimation of permittivity and conductivity for the same sensing volume and enables an improved characterization for a wide range of applications.

Soil hydraulic material properties and subsurface architecture from time-lapse GPR

“…10) also show that both the permittivity and the thickness of the gravel layer can be estimated 25 reliably with the presented evaluation method using travel time and amplitude information of a single channel. Evaluation methods that merely exploit the signal travel time (e.g., Gerhards et al, 2008), require additional measurements to achieve this goal.…”

“…At the beginning of the experiment, the simulated wavelet is too broad for reflection (V) whereas it is too narrow for the reflection (VII). This indicates that (i) the assumption of a constant direct electric conductivity in the whole architecture is suboptimal 25 and that (ii) the direct electric conductivity can be assessed with GPR measurements.…”

“…These parameter sets serve as initial parameters for the simulated annealing algorithm which is sequentially coupled with the Levenberg-Marquardt algorithm. We show that this procedure allows to accurately estimate the subsurface architecture and the associated effective 25 hydraulic material properties for synthetic and measurement data.…”

“…Many full waveform inversion approaches directly use the resulting Green's function (e.g., Lambot et al, 2009;Busch et al, 2012;Jadoon et al, 2012) in the cost function. Using the full antenna signal may lead to many local minima prohibiting a reliable identification of the global minimum (e.g., ford et al, 2014).…”

Soil hydraulic material properties and layered architecture from time-lapse GPR

“…On-ground measurements (e.g., Buchner et al, 2012;Busch et al, 2012;Léger et al, 2015) offer the most flexible approach. They have the disadvantage, however, that the antenna characteristics are influenced by the coupling to the ground.…”