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Estimation of the lateral correlation structure of subsurface water content from surface‐based ground‐penetrating radar reflection images
Author(s) -
Irving James,
Knight Rosemary,
Holliger Klaus
Publication year - 2009
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2008wr007471
Subject(s) - ground penetrating radar , radar , markov chain monte carlo , reflection (computer programming) , monte carlo method , inversion (geology) , posterior probability , bayesian probability , autocorrelation , geology , sampling (signal processing) , soil science , statistics , remote sensing , mathematics , computer science , optics , seismology , physics , telecommunications , tectonics , programming language , detector
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.