Two and one‐half dimensional Born inversion with an arbitrary reference

Multidimensional inversion algorithms are presented for both prestack and poststack data gathered on a single line. These algorithms both image the subsurface (i.e., give a migrated section) and, given relative true amplitude data, estimate reflection strength or impedance on each reflector. The algorithms are “two and one‐half dimensional” (2.5-D) in that they incorporate three‐dimensional (3-D) wave propagation in a medium which varies in only two dimensions. The use of 3-D sources does not entail any computational penalty, and it avoids the serious degradation of amplitude incurred by using the 2-D wave equation. Our methods are based on the linearized inversion theory associated with the “Born inversion.” Thus, we assume that the sound speed profile is well approximated by a given background velocity, plus a perturbation. It is this perturbation that we seek to reconstruct. We are able to treat the case of an arbitrary continuous background profile. However, the cost of implementation increases as one...