Taming the non-linearity problem in GPR full-waveform inversion for high contrast media

We present a new algorithm for the inversion of full-waveform ground-penetrating radar (GPR) data. It is designed to tame the non-linearity issue that afflicts inverse scattering problems, especially in high contrast media. We first investigate the limitations of current full-waveform time-domain inversion schemes for GPR data and then introduce a much-improved approach based on a combined frequency-time-domain analysis. We show by means of several synthetic tests and theoretical considerations that local minima trapping (common in full bandwidth time-domain inversion) can be avoided by starting the inversion with only the low frequency content of the data. Resolution associated with the high frequencies can then be achieved by progressively expanding to wider bandwidths as the iterations proceed. Although based on a frequency analysis of the data, the new method is entirely implemented by means of a time-domain forward solver, thus combining the benefits of both frequency-domain (low frequency inversion conveys stability and avoids convergence to a local minimum; whereas high frequency inversion conveys resolution) and time-domain methods (simplicity of interpretation and recognition of events; ready availability of FDTD simulation tools).

Research Highlights
► Non-linearity afflicts inverse problems especially in high contrast media.
► Low frequency data inversion is stable but can only map coarse structures.
► High frequency data inversion is unstable but can map sub-wavelength structures.
► Most time-domain schemes invert full bandwidth data since the first iteration.
► The new inverse scheme combines benefits/avoid issues by progressive band-expansion.