In ground-penetrating radar electromagnetic waves are emitted into the ground, where they are scattered by objects in the subsurface, and the reflections then recorded at some receiving antennae. The task of imaging the subsurface is to understand what distribution of objects could give rise to the recorded data: a non-linear inverse problem. This is difficult not only due to the non-linearity of the problem, but also an inexact knowledge of the wave speed in the soil due to inhomogeneities (the background medium itself needs to be resolved!), insensitivity in the data to some objects or distributions, and noise in the data. These features are common to many inverse and imaging problems.
The current standard of imaging methods often make a single scattering approximation, and a homogeneous background medium, under which a direct solution can be constructed to the imaging problem. Such assumptions may not account for many features in the data, and in a highly cluttered environment (for example) the resulting image may be very hard to interpret. Instead, one can attempt to solve the imaging problem by posing it as Full Wave Inversion. That is to solve the non-linear optimisation problem of finding the parameters describing the subsurface which would best reproduce the observed data and incorporate a prior information about the solution.
We give an overview of the method, which is now well developed for 2D imaging but there are as yet no published results in 3D (until this talk!) We also discuss some novel contributions made to 3D FWI during my PhD, and how the method may be applicable to landmine detection.