Large-Wavenumber Fourier Imaging

In Chapter 1 we discussed the historical aspects of migration. In that context, migration was viewed as the back propagation of the recorded data to its “correct” position on the image. This view was modified in Chapter 2 and 3, where we encouraged the reader to view this process as being the solution of an inverse problem. In this chapter, we will examine the imaging problem from yet another perspective, that of band- or aperture-limited Fourier transforms. In doing so, we show that there are solid mathematical reasons for choosing to invert for reflectivity. We will also see why extracting smooth information using migration-like techniques will not be easy. (Readers who wish to immediately see the methods of Chapter 3 extended to the problem of inverting seismic data collected with nonzero source-receiver offset in a variable-wavespeed medium, may skip directly to Chapters 5 and 6, and return to this chapter later.)