Accounting for Correlated Data Errors during Inversion of Cross-Borehole Ground Penetrating Radar Data

Least-squares tomographic inversion of cross-borehole ground penetrating radar (GPR) data was used to estimate the radar wave velocity distribution in the upper ∼10 m of the vadose zone at a field site in northern Zealand, Denmark. The radar wave velocities were transformed to values of water saturation and formed a basis for hydrologic studies of flow characteristics of the vadose zone. Cross-borehole GPR data are likely to be contaminated by correlated data errors that may give rise to significant artifacts in the inverse estimate of the velocity distribution if they are not properly accounted for during the inversion process. We analyzed two sources of correlated data errors (unknown cavities and small-scale clay-enriched zones close to the borehole walls), which we assumed to play a significant role in the cross-borehole GPR data sets collected at our field site. The correlated errors may be accounted for by specification of data error covariance matrices, which are included as a priori knowledge in the inverse operator used in the tomographic algorithm. The study indicates that proper accounting for correlated data errors significantly suppresses the effects of these data errors and results in trustworthy inverse estimates of the radar wave velocities between the boreholes. Suppression of the influence of the correlated data errors is a necessity for obtaining realistic hydrologic models of the vadose zone. Using popular inverse methods that disregard the data error correlation properties can lead to severe artifacts in the inverse model estimate and, therefore, can lead to incorrect hydrologic interpretations. Our findings are based on both synthetic tests and a real data example.