SVD analysis of GPR full-wave inversion

Full-wave inversion (FWI) is an imaging approach in which we find the quantitative subsurface parameters (such as the dielectric permittivity) which would best fit the recorded GPR data. This optimisation problem is nonlinear and ill-posed, and there have been numerous successes in applying FWI to GPR data. The dominant properties of the FWI inversion process can be observed in the Jacobian matrix of partial derivatives of the forward map for each acquisition system. Here, we use 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 to reduce the rate of false positives. For humanitarian de-mining there is a need to produce cheaper hand-portable GPR equipment.We therefore ask whether 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 our answer.