2-D joint structural inversion of cross-hole electrical resistance and ground penetrating radar data

We present a joint structural inversion algorithm for cross-hole electrical resistance tomography (ERT) and cross-hole radar travel time tomography (RTT) that encourages coincident sharp changes on a smoothly varying background in the two models. The proposed approach is based on the combination of two iterative soft-thresholding inversion algorithms in parallel manner where the structural information is exchanged at each iteration. Iterative thresholding algorithm allows to obtain a sparse wavelet representation of the model (blocky model) by applying a thresholding operator to the wavelet coefficients of model obtained through a Gauss–Newton iteration. The structural information is introduced in the inversion system using the smoothness weighting matrices that control boundary cells and the thresholds that are estimated by maximizing a structural similarity criterion, which is a function of the two (ERT and RTT) models. A Canny edge detector is implemented to extract the structural information. The detected edges serve to build a weighting matrix that is used to alter the smoothness matrix constraint. To validate our methodology and its implementation, tests were performed on three synthetic models. The results show that the parameters estimated by our joint inversion approach are more consistent than those from individual inversions and another joint inversion algorithm. In addition, our approach appears to be robust in high noise level conditions. Finally, the proposed algorithm was applied for vadose zone characterisation in a sandstone aquifer. It achieves results that are consistent with hydrogeological information and geophysical logs available at the site. The results were also compared in terms of structural similarities to models obtained by a joint structural inversion algorithm with a cross-gradient constraint. Based on this comparison and hydrogeologic information, we conclude that the proposed algorithm allows to the RTT and ERT models to be dissimilar in the areas where the data are incompatible.

► 2-D joint structural inversion of cross-hole electrical resistance and ground penetrating radar data.
► Exchange of structural information using weighting matrix.
► L1-norm penalty in the wavelet domain.
► Vadose zone characterisation in a sandstone aquifer.