Offset plane wave propagation in laterally varying media

The offset plane wave equation, which is obtained from a Radon transformation of the scalar wave equation in midpoint-offset coordinates, provides a convenient framework for developing efficient amplitude preserving migrations. The Radon transformation results in additional amplitude terms that must be accounted for in downward continuation and migration. These terms include an obliquity factor and point source correction resulting from the Radon transform over offset, and transmission terms to account for the transport equation in variable velocity media. These terms can be expressed in exact form in the spectral domain for vertically varying media. For laterally varying media, we currently use a phase-shift plus interpolation framework for the amplitude terms, and a Taylor's series expansion of the velocity field over offset to provide an approximate solution to the offset plane wave equation. Phase shift and finite difference migrations based on this framework produce images on standard models that are comparable to prestack Kirchhoff and shot record migrations.