On sensitivity, and a Hessian approximation for full-wave inversion of GPR data

Francis Watson (Dstl)

Frank Adams 1,

The scattering of electromagnetic waves by a set of small, sufficiently separated inclusions can be described by an asymptotic approximation given in terms of the ‘polarisation tensors’ of each inclusion.  Each polarisation tensor is a function of the shape of the inclusion and its material contrast to the background medium, but not its position.  Such an approximation gives us an understanding of sensitivity in the inverse scattering problem which includes the non-linear effects of material contrast to the background medium.  We contrast this idea of sensitivity to the more typical understanding in which the Fréchet derivative is regarded synonymously as the sensitivity, and use it to derive a novel Hessian approximation for the full-wave inversion problem of ground-penetrating radar.

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