Introduction

Velocity estimation, especially in 3-D, is one of the most important and difficult problems in exploration seismology. When the media is complex, a common solution is to linearize the non-linear tomography problem around an initial velocity estimate Etgen (1990); Stork and Clayton (1991); van Trier (1990). This linearization can potentially cause convergence problems. In previous papers Clapp and Biondi (1998, 1999a, 2000), I introduced a new way to approach this linearized inverse problem. Following the methodology introduced in Biondi et al. (1997), I reformulated the tomography operator from the depth domain to the tau domain. I showed how in the tau domain our linearized operator is less affected by velocity errors therefore we are back projecting velocity changes to more accurate locations Clapp and Biondi (1999b).

A major weakness of tomography is that it has a large null space and how we fill that null space has a major effect on both conversion speed and model quality. Velocity estimates derived from tomography tend to be blobby and not geologically plausible. To create more geologically reasonable velocity models, I regularize the tomography estimation problem with a steering filter Clapp et al. (1997); Clapp (2000). A steering filter is a space-varying operator composed of small plane-wave annihilators oriented along predefined dip directions derived from early migration results or other a priori information sources.

All these previous papers dealt with the 2-D velocity estimation problem. In this paper, I extend into 3-D the previously introduced concepts and apply my tomography method to a North Sea dataset provided by Elf Aquitaine. I begin by showing how the tau tomography operator can be formulated in 3-D. I then introduce the 3-D dataset and show residual moveout remaining in the common reflection point (CRP) gathers from the initial migration. Next I show how I built the 3-D steering filter operator for the dataset. I conclude by showing the results of applying my tomography methodology onto the dataset and comparing and contrasting the migration results.