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Geophysical model building springs from
a variety of related formulas ranging from inversion to back projection.
When the number of unknowns is huge,
as when we seek an image of the earth's reflectivity,
then using the conjugate operator
(also known as back projection or migration)
is always a possible starting technique.
The conjugate operator can generally be improved
by any transformation that pushes it towards a unitary operator.
*Unitary operators play an important role in imaging practice
but they do not have an obvious place in geophysical inversion theory.*
Here I review some examples
and point to our need to better understand
how to find ``preconditioning operators.''

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Stanford Exploration Project

11/17/1997