Building a stochastic structural 3D geocellular model for a reservoir in a new field is a challenge because of insufficient well data. Structural heterogeneity due to folding, faulting and/or associated erosional unconformities may not be completely captured by low resolution seismic and limited well data. This could lead to significant structural uncertainty. Hence, quantification of uncertainty capturing structural heterogeneity requires a comprehensive methodology incorporating seismic interpretation, well data and tectonic information. Experimental discrepancies between predicted and measured depths of horizons in newly drilled wells reveal strong drift, which require a nonstationary model. The physical way to create such nonstationary model is by using numerical paleo-geomechanical deformation algorithms to reconstruct the folding phenomena (e.g., finite elements). Such proposition requires a thorough understanding of rock parameters, and boundary conditions. Another plausible alternative is to use nonstationary geostatistics, because it does not require boundary conditions, or rock deformation parameters. Nevertheless, representing finite differences of order-k, which are required for geostatistical modeling, may be unachievable with insufficient well data. After revisiting the theoretical aspects of the problem, this paper shows a fast approach to quantify the structural uncertainty range for the depth of horizons accounting for spatial drift. The approach is illustrated with an example for a real clastic reservoir.