Inversion in Heterogeneous Media

In Chapter 3, we created our first inversion formulas for the three-dimensional inverse-scattering imaging problem. We formulated the problem for the special case of data collected with a zero-offset recording geometry, and assumed a constant-background wavespeed. The formulas we derived yielded a bandlimited representation of the singular function of a reflector surface scaled by the normal-incidence reflection coefficient of the reflector—the reflectivity function—β(x). These formulas were further shown to correspond to the classic Fourier transform—based migration formula created by Stolt [1978] and the Kirchhoff-based formula created by Schneider [1978], with the latter deduced from the former.