Chapter 5: Duality
We mentioned in Chapter 1 that all map and image transformation procedures discussed in this book rely on two basic geometric concepts: the Huygens surface (also called the diffraction-traveltime surface or the maximum-convexity surface) and the isochron (also called the aplanat, aplanatic, or equal-traveltime surface). In this chapter, we elaborate further on the common properties and the mutual relationship of these two fundamental surfaces, as well as on their relationship to the 3D reflection-traveltime surface and the 3D target reflector. We always assume a fixed measurement configuration as discussed in the “Measurement configurations” section of Chapter 2. Thus, all traveltime surfaces considered here are functions of a 2D vector parameter ?, rather than of the complete set of source and receiver coordinates xS and xG.