In Chapter , I present a formal development of wave-equation datuming operators based on the concept of adjoint operators. I compare Kirchhoff, phase shift, and finite difference formulations both mathematically and by means of synthetic examples. In this development I present a generalized framework that links all three of the wave-equation datuming formulations. This allows me to compare their individual strengths and weaknesses, and provides an understanding of exactly how wave-equation datuming transforms data and how it differs from migration. The synthetic examples demonstrate the utility of datuming in unraveling topographic distortions and provide a practical comparison of how the different methods behave in terms of dip resolution, artifacts, and efficiency.
I conclude that Kirchhoff datuming is the best suited method for my applications because it offers the most efficient and accurate method of performing large extrapolation steps in variable velocity media. It is also readily extendible to three-dimensional applications.