Stable Determination of Internal Velocities in Complex Structure Using Tomographic Migration Velocity Analyses
Authors: Stork C. 
Published: October 2008

Abstract
Velocity variations that exist in areas of complex structure significantly distort seismic wave propagation. To properly image reflectors in complex structure, these effects from the velocity variations must be accounted for. The migration doesn't work since it assumes a Iocally invariant velocity. Depth migration is needed since it can handle the complicated wave field effects of non-constant local velocity. Depth migration in complex structure using the correct velocity field enables the image to be optimally stacked and positioned at the correct depth.
Although the field of depth migration is advancing at a fast pace, it has limited impact in the search for oil because it rarely produces images or depth structures superior to those of conventional methods. This failure results from the difficulty of determining the velocity field for the depth migration.
A form of depth migration velocity analysis is needed to produce an accurate interval velocity field. Migration velocity analysis extends many of the concepts of stacking semblance analysis to complex structure. Like stacking semblance analysis, migration velocity analysis will be a key interpretive step in the processing flow. Unlike stacking semblance analysis, the considerable geologic knowledge of the interpreter can significantly help migration velocity analysis. With the increasing speed of computers and the development of interactive systems, the processor or interpreter will soon have the capability to perform migration velocity analysis in KE office. Depth migration velocity analysis is the key to making depth migration work better on complex structures and help us find previously hidden traps.

Introduction
Reflection tomography is art inversion method that adjusts a velocity and reflector depth model "to be consistent with the pre-stack time data. This tomography approach minimizes the misfit of the data and model in the prc-migrated domain. Generally, the data are represented by the travel times of reflection events which has made the technique problematic and unpopular.
Techniques generally known as "migration velocity analysis" have a similar objective but use the postmigrated domain. For a variety of practical reasons, this post-migrated domain has advantages over the premigrated domain. With slight modifications, the reflection tomography approach can be implemented in the postmigrated domain. In the domain, a model is determined by optimizing the consistency of imaged reflection events on what has been called a "CRP gather".
Extending reflection tomography to the post-migrated domain allows much of the knowledge developed for migration velocity analysis to be coupled with that of reflection tomography. As a result many of the practical techniques developed for migration velocity analysis can be used to improve the robustness and efficiency of reflection tomography. Similarly, much of the reflection tomography work done on analysis and solution of the linear system can be applied to post-migrated domain optimization.
The simplest implementation of tomography is a travel time inversion that is referred to as reflection tomography (Bishop et al (1985), Williamson (1986& 1990), Bording et al (1987), Scales (1987) Kettnett et al (1988)Y Farm & Madariaga (1988), Dyer& Worthington (1988), and Stork & Clayton (1991).