Characterization of fault displacement is difficult, yet consequential for understanding fault transmissibilities or enhancing quality of structural models. In this work, we propose to study the uncertainty about the transverse component of the fault throw vector, to optimize its direction. Each fault block of a horizon is unfolded separately without taking faults into account, in order to separate the effects of unfolding and unfaulting in horizon deformations. Then, using a sequential Monte-Carlo sampling, several fault displacement models can be generated, to therefore select a set of best models of fault displacements. The proposed method perturbs the links across fault gaps on a horizon so as to make the transverse displacement variable. For each new displacement field, the horizon is restored, and deformation analysis is used to assess the likelihood of the fault displacement. The Monte-Carlo sampling technique being reputably slow, this optimization problem is solved locally for all faults, to obtain a set of possible models efficiently.