Introduction

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 $\bf L$ that transforms a point in a velocity space into a hyperbola in an offset space, then by solving the equation  

$$\bold L \bold u = \bold d$$ (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 ${\Vert \bold L \bold u - \bold d \Vert}^2$.Even sampling in the slowness squared (sloth) domain is used. I finally compare various ways of sampling in the velocity domain.