2.5D crosshole GPR full-waveform inversion with synthetic and measured data

Abstract

<jats:p> Full-waveform inversion (FWI) of cross-borehole ground-penetrating radar (GPR) data is a technique with the potential to investigate subsurface structures. Typical FWI applications transform 3D measurements into a 2D domain via an asymptotic 3D to 2D data transformation, widely known as a Bleistein filter. Despite the broad use of such a transformation, it requires some assumptions that make it prone to errors. Although the existence of the errors is known, previous studies have failed to quantify the inaccuracies introduced on permittivity and electrical conductivity estimation. Based on a comparison of 3D and 2D modeling, errors could reach up to 30% of the original amplitudes in layered structures with high-contrast zones. These inaccuracies can significantly affect the performance of crosshole GPR FWI in estimating permittivity and especially electrical conductivity. We have addressed these potential inaccuracies by introducing a novel 2.5D crosshole GPR FWI that uses a 3D finite-difference time-domain forward solver (gprMax3D). This allows us to model GPR data in 3D, whereas carrying out FWI in the 2D plane. Synthetic results showed that 2.5D crosshole GPR FWI outperformed 2D FWI by achieving higher resolution and lower average errors for permittivity and conductivity models. The average model errors in the whole domain were reduced by approximately 2% for permittivity and conductivity, whereas zone-specific errors in high-contrast layers were reduced by approximately 20%. We verified our approach using crosshole 2.5D FWI measured data, and the results showed good agreement with previous 2D FWI results and geologic studies. Moreover, we analyzed various approaches and found an adequate trade-off between computational complexity and accuracy of the results, i.e., reducing the computational effort while maintaining the superior performance of our 2.5D FWI scheme. </jats:p>

Accounting for Modeling Errors in Linear Inversion of Crosshole Ground‐Penetrating Radar Amplitude Data: Detecting Sand in Clayey Till

“…(b) The geometrical spreading of the energy. In 3D the correction factor is 1/ L , whereas synthetic 2D data is corrected with $$1/\sqrt{L}$$ (Mozaffari et al., 2020); and (c) the antenna gain effect, A 0 , which is a scaling factor that accounts for the transmitter strength (B. Zhou & Fullagar, 2001). A 0 is typically unknown, but we assume that it is constant for our survey, consistent with Holliger et al.…”

“…(2010) and Mozaffari et al. (2020) has been used extensively. Klotzsche, Vereecken, and Van Der Kruk (2019) provides a comprehensive overview of the method and its applications.…”

Detection of Tracer Plumes Using Full‐Waveform Inversion of Time‐Lapse Ground Penetrating Radar Data: A Numerical Study in a High‐Resolution Aquifer Model

“…Mozaffari et al. (2020) demonstrated that this transformation mainly affects late arrival amplitudes of the measured data in the presence of high contrast layers, which results in a difference of approximately 2% between 2.5D and 2D FWI results for both ε r and σ b . A similar behavior can be seen in our tests.…”

“…As a result, only 3D GPR FWI and to a lesser extent 2.5D, which consider the 3D medium and plume heterogeneity, can minimize such errors. Although a 2.5D FWI method in the time domain exists (Mozaffari et al., 2020), to analyze a high number of data sets is currently not feasible due to the high computation costs, as just for a single forward run it is 10 times larger than for a 2D forward run.…”

Fractal-Constrained Crosshole/Borehole-to-Surface Full-Waveform Inversion for Hydrogeological Applications Using Ground-Penetrating Radar

“…In particular, source deconvolution [31], [32] and using the ratio of two electromagnetic field parameters [33] have been successfully applied for removing the effects of the unknown source wavelet. Moreover, in an effort to reduce the computational requirements, 2.5D forward solvers and 2D to 3D transformations have been proposed in order to replace costly 3D simulations [34]. Furthermore, the presence of numerous local minimal in the optimization space has been tackled via ray-based initial models [16], using global optimizers [35], [36], and by gradually increasing the selected bandwidth as the optimization progresses [37].…”