Introduction

For the exploration geophysicist, velocity is the key component in creating accurate images of the earth. Velocity is important in almost all phases of processing. It is used implicitly or explicitly in Normal Moveout (NMO), multiple attenuation, Dip Moveout (DMO) and migration. Velocity and the explorationist's final product, the earth image, play an important part in the work of other geoscientists. On an active oil field, seismic imaging helps target wells and monitor fluid flow (). It provides rock physicists with reservoir properties, and geostatisticians and reservoir engineers with constraints for their simulations ().

With the wrong velocity, seismic events do not focus and reflectors are mispositioned. Without an accurate velocity, wells will never tie with the seismic data and directional drilling becomes much more difficult. Without an accurate velocity, seismic data could easily hinder rather than help the rock physicist (), geostatistician, and reservoir engineer.

Obtaining an accurate velocity estimate is one of the most difficult problems in geophysics. Velocity estimation is a nonlinear, under-determined problem. The first step in all velocity estimation schemes is to make assumptions about subsurface properties. The most basic assumption is the one used by NMO, a horizontally stratified earth. A less stringent assumption, flat reflectors, was made by (). When the assumptions that the methods are based on are inaccurate, they fail to give satisfactory results. When this happens we are often forced to the family of methods which are generally referred to as `tomography'.