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

Abstract

Mapping high permeability sand occurrences in clayey till is fundamental for protecting the underlying drinking water resources. Crosshole ground penetrating radar (GPR) amplitude data have the potential to differentiate between sand and clay, and can provide 2D subsurface models with a decimeter‐scale resolution. We develop a probabilistic straight‐ray‐based inversion scheme, where we account for the forward modeling error arising from choosing a straight‐ray forward solver. The forward modeling error is described by a Gaussian probability distribution and included in the total noise model by addition of covariance models. Due to the linear formulation, we are able to decouple the inversion of traveltime and amplitude data and obtain results fast. We evaluate the approach through a synthetic study, where synthetic traveltime and amplitude data are inverted to obtain slowness and attenuation tomograms using several noise model scenarios. We find that accounting for the forward modeling error is fundamental to successfully obtain tomograms without artifacts. This is especially the case for inversion of amplitude data since the structure of the noise model for the forward modeling error is significantly different from the other data error models. Overall, inversion of field data confirms the results from the synthetic study; however, amplitude inversion performs slightly better than traveltime inversion. We are able to characterize a 0.4–0.6 m thick sand layer as well as internal variations in the clayey till matching observed geological information from borehole logs and excavation.

High‐Resolution Geological Information from Crosshole Ground Penetrating Radar in Clayey Tills

“…Prior to inversion, the measured MOG amplitude data were corrected for geometrical spreading of the energy, radiation patterns of the antenna and the antenna gain effect, . See, for example, Holliger et al (2001) and Jensen et al (2022a) for details on amplitude corrections. Traveltime data were time‐zero corrected using the time‐zero correction factor, , estimated from the acquired calibration lines.…”

“…We use a probabilistic linear inversion with a geostatistical Gaussian prior model included and we account for the forward modeling errors arising from choosing a linear scheme. The method is described in detail by Jensen et al (2022a). The obtained tomograms presented here are the mean of all the equally likely subsurface representations that are consistent with the a priori information and the data.…”

“…The EM wave velocity can be related to the dielectric permittivity of the subsurface, which can be translated to subsurface water content (e.g., Huisman et al 2003). The attenuation of the EM wave provides additional information on the bulk electrical conductivity, which is different for sand and clay (e.g., Reynolds 2011), and crosshole GPR hence has the potential to distinguish between sandy and clayey features between boreholes (Looms et al 2018; Jensen et al 2022a). GPR is minimally‐invasive and can be used in already existing boreholes, and can therefore be integrated in any ongoing site investigation.…”

“…Crosshole GPR has been used for a wide range of applications, such as monitoring infiltration using time‐lapse tracer studies (e.g., Hubbard et al 2001; Chang et al 2006; Gueting et al 2017), characterizing subsurface moisture content (e.g., Alumbaugh et al 2002), and for characterizing porosities in aquifers (e.g., Klotzsche et al 2013; Zhou et al 2020). Until recently, GPR was not applied in clay tills due to the attenuation of the signal, but Looms et al (2018) and Svendsen et al (2023) showed that GPR can be used in these environments, given sufficiently short borehole separation up to 5 to 7 m. Furthermore, Jensen et al (2022a), recently developed a linear inversion algorithm that allows for fast interpretation of both GPR traveltime and amplitude data, which makes the method attractive for use as part of contaminated site investigations.…”

Crosshole Ground‐Penetrating Radar in Clay‐Rich Quaternary Deposits: Toward Characterization of High‐Loss Media

“…Once the radar response has been quantified using radar wave attributes, the two important material properties, radar wave velocity, and attenuation can be estimated. The assumptions regarding the EM wave propagation path has a large impact on both velocity (Hansen et al., 2014) and attenuation estimation (Jensen et al., 2022). The simplest assumption regarding the travel path of the EM wave is the straight ray approximation.…”