The dips need to be measured along the horizon, making the problem non-linear. A Gauss-Newton approach can be used with linearizing about the current estimated horizon volume. Again following the approach of (), we
} ,where the subscript k denotes the iteration number.
Two different approaches can be used for the linearized step (equation 5) The most efficient is to solve the problem a direct inverse in Fourier domain Lomask (2003). When space-domain weighting or model restriction () is needed, a space-domain conjugate gradient approach is warranted.
In general we deal with 2-D angle or offset gathers. The standard approach is to solve a 2-D flattening problem where is a function of time/depth and offset. We revert to a 2-D gradient operator, and solve each CMP/CRP gather independently.