Velocity Analysis by Iterative Prestack Depth Migration: A Proposal
, by John T. Etgen

In areas of complex structure, velocity analysis and imaging
are interrelated. Knowledge of the interval velocities
is required to image the subsurface properly. However, the interval
velocities are not usually known in advance. An estimate of the subsurface
structure can improve the estimate of the interval
velocities and lead to a better
image of the geologic structure.
This
suggests an iterative approach to the imaging and velocity
analysis problem in complicated structure.
If the problem is posed in an optimization framework,
iterative prestack depth migration can provide an interval velocity
model
that best images the subsurface.
I propose an algorithm to do this.
Prestack migration (like CMP stacking), is more affected by the
low wavenumbers of the interval
velocity model than high wavenumbers.
Low wavenumber components of the interval velocity field
control gross timing and positioning of events. When forming an image of
the subsurface,
it is most important to estimate the lowest wavenumber components
of the interval velocity first. This will give a properly focused and
positioned image.
With this in mind, I propose approximating
interval velocity models with a set of smooth basis functions.
This results in far fewer parameters to be optimized than if the velocity
were allowed to be independent at many thousands of points.
Most importantly, the interval velocity model will be in terms of more
easily resolved parameters.