Conditioned Simulations of Random Velocity Fields

In petroleum exploration and production, it is essential to have good estimations of the uncertainties on the reserves. Uncertainties on the velocity model used during the data processing are of major importance in this estimation. The generation of several velocity fields gives access to a quantified estimation of the uncertainties due to the velocity model inversion. The use of statistical methods helps in generating several important, equiprobable velocity fields, matching all the available velocity information. This paper presents an efficient simulation algorithm to generate instantaneous velocity fields, constrained by the distribution of values measured at the wells, and calibrated by the stacking velocities, taken as root-mean-square velocities. The simulations also match the covariance model given for the instantaneous velocity fields. The method is developed in a simple one-layer case with constant velocity, and then extended to more realistic situations. Finally, a real data application is shown, using data provided by ENI–Agip Division, and the efficiency of the proposed simulation method is discussed.