Wavefield inversion of objects in stratified environments. From backpropagation schemes to full solutions.
Résumé
This review contribution is concerned with the characterization of passive, complex objects from the observation of their interaction with wavefields generated by known active sources (wavefield inversion) in a particular scattering geometry where the data on which to base the inversion are gathered only from limited angles (aspect-limited data). Indeed, the configuration tackled here is restricted to the case of a penetrable or impenetrable, cylindrical or 3-D bounded object which is embedded in a plane-layered host medium, the sources of the probing waves and the receivers of the scattered waves both being placed on the same side of a particular interface and the object being located on the other side or deeper in the stratified host. At the extreme, this configuration may be reduced to a homogeneous host, the object being illuminated and seen from the same side (reflection-mode). We do not consider every such inversion in depth but point out the main results obtained these last few years in electromagnetics - with due reference to prominent contributions in acoustics. Let us stress that even though the above geometry can be thought of as being rather specific, there exist numerous applications of interest in a variety of domains, including - but not being limited to - the evaluation of cracks, voids or inclusions in a host structure, the detection, location and identification of man-made or natural objects buried near the surface of the earth or placed in shallow water, and the characterization and synthesis of artificial materials where inhomogeneities are distributed in a given layer. And beyond such applications, independently of the nature - elastic or electromagnetic, diffusive or propagative, transient or time-harmonic - of the wavefield, there exists a number of theoretical, numerical and experimental challenges to be faced when developing effective inversion tools in this geometry. This paper draws most of its material from references in the open literature from about 1992 'til mid-1995 but a number of older contributions are included for completeness. Citations are made to research works carried out on the subject by the authors of this review and colleagues and they are used to provide a starting point in terms of the derivation of the wavefield formulations and of many of their inversions. Particular attention is given to finding a common background to such works while keeping aside details of the inversion algorithms' derivation.