Estimation of the lateral correlation structure of subsurface water content from surface‐based ground‐penetrating radar reflection images

Abstract

[1] Over the past decade, significant interest has been expressed in relating the spatial statistics of surface-based reflection ground-penetrating radar (GPR) data to those of the imaged subsurface volume. A primary motivation for this work is that changes in the radar wave velocity, which largely control the character of the observed data, are expected to be related to corresponding changes in subsurface water content. Although previous work has indeed indicated that the spatial statistics of GPR images are linked to those of the water content distribution of the probed region, a viable method for quantitatively analyzing the GPR data and solving the corresponding inverse problem has not yet been presented. Here we address this issue by first deriving a relationship between the 2-D autocorrelation of a water content distribution and that of the corresponding GPR reflection image. We then show how a Bayesian inversion strategy based on Markov chain Monte Carlo sampling can be used to estimate the posterior distribution of subsurface correlation model parameters that are consistent with the GPR data. Our results indicate that if the underlying assumptions are valid and we possess adequate prior knowledge regarding the water content distribution, in particular its vertical variability, this methodology allows not only for the reliable recovery of lateral correlation model parameters but also for estimates of parameter uncertainties. In the case where prior knowledge regarding the vertical variability of water content is not available, the results show that the methodology still reliably recovers the aspect ratio of the heterogeneity.Citation: Irving, J., R. Knight, and K. Holliger (2009), Estimation of the lateral correlation structure of subsurface water content from surface-based ground-penetrating radar reflection images, Water Resour. Res., 45, W12404,

Geostatistical inversion of seismic and ground‐penetrating radar reflection images: What can we actually resolve?

“…Note that, despite its conceptual simplicity, the PRS model given by equations (1) and (2) has been found to provide remarkably accurate and realistic approximations of the images obtained by depthmigrating full-waveform simulations of seismic or GPR reflection data [e.g., Irving et al, 2009Irving et al, , 2010Scholer et al, 2010].…”

“…However, such work has either been largely empirical or methodologically inadequate, and a rigorous means of linking the statistical properties of depth-imaged reflection data to the geostatistical properties of velocity has only recently been presented. Irving et al [2009Irving et al [ , 2010 describe the corresponding methodology and provide a comprehensive review of previous work on this topic. With the availability of this method and the development of an effective inversion approach, however, have come some surprising and somewhat enigmatic observations.…”

Surface and borehole ground-penetrating-radar developments

“…Tomographic and full-waveform inversion methods have been developed as a general tool for inverting GPR scattering data for a variety of applications, including subsurface water-content estimation ͑Bradford et al, Irving et al, 2009;Crocco et al, 2010;Minet et al, 2010͒ as well as methods using properties of waveguides for inverting near-surface properties ͑Arcone et al, Strobbia and Cassiani, 2007;van der Kruk et al, 2007;van der Kruk et al, 2009͒. Multioffset data have been used in AVO inversion to estimate thin-bed properties ͑e.g., Deparis and Garambois, 2009͒.…”

Estimation of the 3D correlation structure of an alluvial aquifer from surface‐based multi‐frequency ground‐penetrating radar reflection data

“…Rea and Knight ; Oldenborger, Knoll and Barrash ; Knight, Tercier and Irving ; Dafflon, Tronicke and Holliger ; Knight et al . ; Irving, Knight and Holliger ; Irving and Holliger ; Irving, Scholer and Holliger ). Rea and Knight () compared the correlation structure of an outcrop image with that of the corresponding GPR data and found good overall agreement.…”

“…Irving et al . () were the first to present a physically and mathematically consistent model relating the 2D spatial autocorrelation of the subsurface water‐content distribution to that of the corresponding GPR data, taking into account the effects of antenna frequency. Based on this model, they proposed a Bayesian Markov chain Monte Carlo (MCMC) inversion approach to estimate the subsurface horizontal correlation statistics from the GPR reflection data.…”