Tackling the non-linearity problem in GPR waveform inversion

Crosshole radar tomography is a non-invasive tool used in diverse geological, hydrogeological and engineering investigations. Conventional tomograms provided by standard ray-based techniques have limited resolution. Higher resolution radar tomograms can be derived by using full-waveform inversion schemes. However, despite the theoretical improvement in resolution, convergence problems can arise in the application of full-waveform schemes due to the ill-posed nature of the inverse problem and the high non-linearity of the relationship between the model parameters and the scattered fields (i.e. the forward problem). We present here a new inversion scheme that starts with a low-pass filtered version of the radargrams and progressively expands the frequency bandwidth as the iterations proceed, thus reducing the likelihood of the inversion getting trapped in a local minimum. The benefits over standard full-waveform time- domain inversion are demonstrated by means of three synthetic examples.