Several papers presented at the last SEG Convention in Houston by Schneider, Backus et al have shown how important and fruitful it was to obtain a continuous knowledge of the velocity functions and they have solved their problem by a Dynamic Correlation Analysis. Our purpose is to introduce here a method based on the best summation of a set of traces instead of the best correlation.Practically, this approach has several advantages:1) Two traces only can be correlated at each step whereas the summation can bear on any number of them;2) Optimizing the summation is actually what we are looking for since, at the long end, the success of the improvement is evaluated from the compositing of several traces either weighted or not.On the other hand, an advantage of correlation is the possibility of adding correlations obtained at several places in a same neighbourhood in order to improve the results. With the summation method this is feasible only when dips are inexistent: we shall see that the difficulty due to the dip effect can be turned around.The basic principle of the method can be summed up as follows: traces relating to a same reflection point are considered; several composites are made, each after applying different move out corrections ranging widely around an estimated adequate velocity function. At each time coordinate, the best adapted velocity function, i.e. the one that yields the best phase relation between reflected events, corresponds to the composite trace the average amplitude of which is the largest.This way, the velocity function corresponding to primary reflections as well as those corresponding to multiple reflections can be established accurately.Some examples are shown.