Non-linear estimation of vertical delays with a quasi-Newton method

Antoine Guitton, Jesse Lomask, and Sergey Fomel

antoine@sep.stanford.edu, lomask@sep.stanford.edu, sergey.fomel@beg.utexas.edu

ABSTRACT

A local dip (or step out) between two adjacent traces embeds the necessary information to go from one reflection on one trace to the same reflection on the next. In more dimensions, i.e., 3-D, the same result is obtained between distant traces by integrating the local dips in all directions, thus obtaining relative delay maps useful for (1) automatic full-volume picking and (2) automatic flattening of horizons. The estimation of these maps from local dips is a non-linear process. In this paper, this problem is solved with a quasi-Newton technique for 2-D slices and 3-D cubes. Furthermore, the estimation of the relative delays is done globally in a least-squares sense for all reflectors at once. Synthetic and field data examples illustrate the ability of the algorithm to flatten horizon according to their geological time. As a natural extension of our algorithm, any horizon can also be picked automatically at no additional cost.