1. Process to determine locally the shape of geological horizons, in which there is constructed a continuous function S ij,k (t) by interpolation or approximation of the discrete seismic traces of a three-dimensional seismic matrix, said S ij,k (t)'s function being designated as a “continous local seismic trace”, comprising the following steps: a). using as optimum offset of two adjacent continuous local seismic traces, the value of offset rendering maximal their correlation function, with optimal offset not being necessarily a whole multiple of the vertical sampling interval; b). taking as conditional neighborhood of a “central” continuous local seismic trace S ij,k (t) the sub-neighborhood consisting in adjacent traces S pq,k (t) corresponding to optimum offsets h ij,pq,k associated with correlations R ij,pq,k (h ij,pq,k ) greater than a predetermined threshold comprised between 0 and 1; c). defining for each continuous local seismic trace S pq,k (t) of the conditional neighborhood, a value of residual relative to said “central” continuous local seismic trace S ij,k (t) comprising parametric coefficients; d). determining the parametric coefficients a ij,k and b ij,k by minimization of a set of residuals on the conditional neighborhood.