Accounting for modeling errors in linear inversion of cross-borehole georadar amplitude data - exemplified for detection of sand lenses in clayey till.

Heterogeneous glacial sediments dominate the geology of large parts of the Northern Hemisphere. This complex geology makes it a challenging task to delineate the pathway of contaminated water to the underlying groundwater reservoirs. The migration pathway occurs predominantly within the sand structures in the otherwise low-permeable clay matrix. Cross-borehole ground penetrating radar is a minimally invasive method that has been proven successful in identifying and characterizing sand occurrences in clayey till.

Previous studies indicate, that cross-borehole radar amplitude data can delineate sand lenses in clayey till better than travel time data. However, linear inversion of amplitude data is typically unsuccessful since the obtained attenuation tomograms are contaminated with artifacts, that arises from the simplified parameterization in the inverse problem. A quantification of this modeling error associated with an approximate linear inversion scheme, can be obtained following the methodology proposed in earlier studies.

In this study, a probabilistic linear inversion scheme of cross-borehole GPR amplitude data is proposed, where geostatistical prior information is included, and the forward modeling error that arises from using a straight-ray forward model as opposed to a full waveform forward model is accounted for statistically. The forward modeling error is quantified by inferring a Gaussian probability distribution, with mean, d_T , and covariance, C_T , from a sample of the modeling error. The error mean and covariance matrix is included in the posterior probability distribution to the linear inverse problem.

First, a synthetic study is designed as a proof-of-concept of the inversion scheme. Secondly, the developed inversion scheme is tested on field data from a gravel pit west of Copenhagen, Denmark. Preliminary results indicate, that a sand layer of 0.5 m can be successfully identified and characterized by linear inversion of amplitude data. By accounting for the forward modeling error, the artifacts that typically contaminate attenuation tomograms are eliminated.