Stochastic Structural Modeling

A consistent stochastic model for faults and horizons is described. The faults are represented as a parametric invertible deformation operator. The faults may truncate each other. The horizons are modeled as correlated Gaussian fields and are represented in a grid. Petrophysical variables may be modeled in a reservoir before faulting in order to describe the juxtaposition effect of the faulting. It is possible to condition the realization on petrophysics, horizons, and fault plane observations in wells in addition to seismic data. The transmissibility in the fault plane may also be included in the model. Four different methods to integrate the fault and horizon models in a common model is described. The method is illustrated on an example from a real petroleum field with 18 interpreted faults that are handled stochastically.