Due to the limited resolution of seismic reflection data in imaging near vertical structures, structural models can have significant uncertainties related to fault geometries and position. These uncertainties can be reduced by performing a history matching analysis on a large number of structural models generated stochastically. This work investigates about the integration of vertical seismic profiling data as another way to constrain and reduce such uncertainties. Because travel-times are not sufficiently sensitive to fault geometry perturbations and because we cannot model amplitudes accurately, we rely on phase distortion of seismograms as they propagate through the faulted models. To extract instantaneous phase information from seismograms, we used the empirical mode decomposition algorithm. This approach offers several advantageous properties compared to computing the instantaneous phase by analytic signal transformation. An instantaneous phase misfit was then defined as the L2 norm of two instantaneous phase functions. A numerical experiment was carried out in which 60 fault networks were generated stochastically from a single 3D interpretation of multiple cross sections; the 60 models were then ranked from the most similar up to the most dissimilar from a randomly chosen reference model. Results show that the proposed misfit can successfully constrain fault geometry