2-D COOPERATIVE CROSS-HOLE ERT AND FULL-WAVEFORM GPR INVERSION

Abstract

Full-waveform inversion (FWI) of cross-hole ground penetrating data allows a better resolution in comparison to ray-based tomography. The inverse problem is solved using local optimization algorithms that can converge to local minimum depending on the selection of starting model, nonlinearity of the problem, lack of low frequencies, presence of noise, and approximate modeling of the wave-physics complexity. In this work, multiscale FWI strategy is combined cooperatively with electrical resistivity tomography (ERT) to mitigate the nonlinearity and ill-posedness of FWI, and to improve the ERT resolution. In the FWI, the gradient of the misfit function is generally dominated by the high frequencies. This behavior can potentially be the cause of convergence into local minima, as the determination of the high frequencies depends in turn on the accuracy of the low frequencies. The proposed multiscale FWI reduces the number of model parameters and yields low frequencies in the model space using a regularization method that consists of imposing an L1-norm penalty in the wavelet domain. The minimization of the L1-norm penalty is carried out using an accelerated iterative soft thresholding algorithm. As wavelet transforms provide estimates of the local frequency content of the conductivity or permittivity images, the thresholds are used to control the frequency content in the model space. Generally, a high threshold value is chosen for the 20th first iterations in order to enhance the update of the low frequencies. Then the soft thresholding step tries to find the best thresholds to maximize the structural similarities between conductivity and permittivity images. The initial velocity model for FWI is built from first-arrival traveltime tomography, whereas the ERT current inversion model is used as FWI conductivity starting model. The conductivity model resulting from FWI is then introduced as reference model in ERT inverse problem using hierarchical Bayesian approach. To validate our methodology and its implementation, two synthetic models were created. Experiments demonstrate that the proposed approach improves the spatial resolution and convergence properties in comparison to classical FWI. This work is an extension to full-waveform inversion of a previously published work (Bouchedda et al., 2012).