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.