Velocity Model Estimation for Depth Imaging; a Little Theory and a Lot of Practice
Authors: Etgen J.T. 
Published: October 2008

Abstract
Creating accurate images of subsurface structure in depth requires processing algorithms that honor the physics of wavepropagation and velocity models that accurately predict the traveltimes of seismic waves. Prestack depth migration algorithms have advanced in theory and in practice to the point where they are useful in making accurate images of complex subsurface geometries through complex velocity structures. The theory behind velocity estimation techniques has also evolved rapidly in the past few years. Although many of the theoretical issues are resolved, there still exist many practical difficulties in estimating velocity models for prestack depth migration. Some of these issues are human interface issues. Some reflect a deeper problem, that we don't understand how to reconcile traveltime derived velocities with geology.

Introduction
Seismic data are recorded wavefields, functions of space and time. In the past, processed data were left in time and even interpreted in time. Velocity information was only needed in a qualitative sense. Instead of being a model of the Earth, velocity models were processing parameters, derived from the data and were supposed to represent (loosely) averages of the "true" Earth velocity model. Of course the whole idea behind the seismic experiment is to produce an image of the Earth in depth. But the transformation of seismic data into an image of the Earth in depth was expensive, error prone, and therefore forced to remain qualitative for several reasons. First, seismic data were often collected along 2-D lines; the insufficient spatial density of data made it impossible to resolve details of 3-D complex structure. This often made it impossible to tell if a structural image / velocity model was correct. Second, due to both theoretical and practical reasons, processing technology was not advanced enough to extract quantitative velocity estimates from seismic data or use that velocity information to create accurate images. In the present, 3-D seismic data acquisition is preferred over 2-D acquisition, and seismic processing technology, particularly prestack depth migration, has advanced sufficiently to make quantitatively-accurate images of subsurface structure. Although 3-D prestack depth migration embodies the correct physics to convert seismic wavefields into images of subsurface structure, an accurate velocity model is needed. Now that industry has the ability to make accurate images there is a greater demand on our ability to estimate good seismic velocity models.

Velocity Estimation: Another Kind of Seismic Interpretation
Seismic data is often visually "pleasing" because it looks like geology. Much of the task of traditional seismic interpretation is carried out by our eyes and brains without effort. We have preconceived notions of how the structural and stratigraphic boundaries in the Earth should look. When we look at seismic data, we are looking at a picture of these boundaries. The picture may be distorted, but in some sense it is a direct image. We get no such direct image of the velocity in the subsurface. The best measure of velocity we get is the traveltime of seismic waves initiated at the surface and reflected from subsurface structure, at best an indirect measure. Furthermore, since we don't actually know the positions of those reflectors, we have less constraint on the travel paths of seismic waves in a reflection experiment than we do in a VSP or cross well experiment.