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The aim of velocity analysis is to get the
velocity analysis panel with the best possible resolution. Ideally a hyperbola
in a CMP gather should be mapped onto a point in a velocity analysis panel.
The operator of summation along hyperbolas does not give this
resolution.
If we find such an operator that transforms a point in a
velocity space into a hyperbola in an offset space, then by solving
the equation

| |
(1) |

we obtain
a velocity analysis panel with improved resolution (Thorson, 1984, Thorson and Claerbout, 1985).
Those authors use stochastic inversion for solving this problem
with a projected gradient descent algorithm.
In this paper, I solve the equation (1) using a conjugate gradient
method for minimizing .Even sampling in the slowness squared (sloth) domain is used.
I finally compare various ways of sampling in the velocity domain.

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Stanford Exploration Project

1/13/1998