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), % (cite Oz)  
multiple attenuation, % (cite P)
Dip Moveout (DMO)% (cite Hale)
and migration. % (cite ff).
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 image helps target wells and  monitor
fluid flow \cite{Lumley.sepphd.91}.
It  provides rock physicists with reservoir properties,
and geostatisticians and reservoir engineers constraints for their simulations
\cite{mao}.
\par
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  \cite{Claerbout.sep.100.jon1}, 
geostatistician, and reservoir engineer.
\par
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 
\longcite{Toldi.sepphd.43}.
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'.
\par


%And without an accurate velocity model, seismic data
%It  provides rock physicists with reservoir properties and 
%geostatisticians and reservoir engineers constraints for their simulations.



%These accurate 
%Without a good knowledge of 
%Without a good knowledge of the velocity, the geophysicist can either
%miss  prospects because of poor imaging, or be fooled into thinking
%velocity created artifacts represent actual targets.

%All of these uses rely heavily on an accurate velocity model.
%Without a good knowledge of the velocity, the explorationist can either
%miss  prospects because of poor imaging, or be fooled into thinking 
%velocity created artifacts represent actual targets. 
%Without an accurate
%velocity,  wells  will never tie with the seismic data and direction
%drilling is useless. And without an accurate velocity model, seismic data



%In todays integrated world reflection seismic data is no longer exclusively
%the tool of the explorationist.
%%transition
%On an active oil field seismic data helps target wells and  monitor
%fluid flow.
%It  provides rock physicists with reservoir properties and 
%geostatisticians and reservoir engineers constraints for their simulations.
%All of these uses rely heavily on an accurate velocity model.
%Without a good knowledge of the velocity, the explorationist can either
%miss  prospects because of poor imaging, or be fooled into thinking 
%velocity created artifacts represent actual targets. 
%Without an accurate
%velocity,  wells  will never tie with the seismic data and direction
%drilling is useless. 
%And without an accurate velocity model, seismic data
%is more likely to hinder rather than help the rock physicist, geostatistician,
%and reservoir engineer.
%\par
%As oil targets become more complicated 
%velocity 
%becomes even more important
%and often make the difference between success and failure.
%\par
%In addition to 
%In the integrated environment we have additional constraints. The velocity
%model that we 
%
%\par
%In this dissertation I present a new method to create a velocity model
%that both focuses data and is geologically reasonable.
%
%
