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Wave equation migration methods  are quickly becoming the
standard for high-end imaging.
These methods are more effective in handling complex
wave behavior than traditional Kirchhoff methods \cite{SEG.WEwkshop.2001}.
The downside of these methods, specifically ones
based upon the one-way wave equation, are that they are generally
more expensive than Kirchoff methods and are only accurate for
$v(z)$ media.  To overcome the latter weakness extensions such
as phase screen \cite{rousseau.seg.98}, split-step \cite{GEO55.04.04100421}, and Fourier Finite Difference (FFD) 
\cite{ristow.geo.94}
have been introduced. These
methods generally rely on downward continuing
the wave-field with multiple reference velocities and then
applying an approximate correction to the wavefield
for the true velocity. The larger the deviation of
the reference from the true velocity the less accurately
the wavefield will be modeled.
The trade-off is
that the cost of migration increases almost proportionally
with the number of reference velocities. 
Many different methods are currently employed to select the
reference velocities, each with varying levels of success, 
dependent on the input velocity.
\par
Electrical engineers and image processors face similar problems.
In speech compression  it is  important 
to accurately describe a signal in as few bytes as possible. In image processing
it is often important to reduce the number of colors in image with
as little loss in image quality as possible. These problems
have led to the field known as  quantization.
One family  of method often employed is based on Lloyd's method \cite{lloyd}, 
an iterative
technique that allows for variable rate quantization.
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\par
In this paper I propose  a new method for selecting reference
velocities based on a generalized Lloyd's method.   I show
that the method is effective in choosing appropriate  reference
velocities for a large variety of models. On two  synthetics
I demonstrate that it produces a higher quality image with fewer reference velocities.



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