SVD Analysis of Full Wave Inversion

Full-wave inversion (FWI) is an imaging approach in which we find thequantitative subsurface parameters (such as the dielectric permittivity) whichwould best fit the recorded GPR data. This optimisation problem isnonlinear and ill-posed, and there have been numerous successes inapplying FWI to GPR data. The dominant propertiesof the FWI inversion process can be observed in the Jacobian matrix ofpartial derivatives of the forward map for each acquisition system. Here, weuse singular value decomposition (SVD) as a tool to analyse the Jacobian, to help us understand what a given acquisition system is capable of imaging.We believe FWI could have great benefits in anti-personnel landmine detection,primarily because the additional quantitative information gained could help toreduce the rate of false positives. For humanitarian de-mining thereis a need to produce cheaper hand-portable GPR equipment. We therefore askwhether a small array is suitable for FWI, if taking more measurements can compensate for a lack of multi-offset data, using singular value decomposition as a tool to guide ouranswer.