Accounting for Estimation Optimality Criteria in Simulated Annealing

This paper presents both estimation and simulation as optimization problems that differ in the optimization criteria, minimization of a local expected loss for estimation and reproduction of global statistics (semivariogram, histogram) for simulation. An intermediate approach is proposed whereby an initial random image is gradually modified using simulated annealing so as to better match both local and global constraints. The relative weights of the different constraints in the objective function allow the user to strike a balance between smoothness of the estimated map and reproduction of spatial variability by simulated maps. The procedure is illustrated using a synthetic dataset. The proposed approach is shown to enhance the influence of observations on neighboring simulated values, hence the final realizations appear to be "better conditioned" to the sample information. It also produces maps that are more accurate (smaller prediction error) than stochastic simulation ignoring local constraints, but not as accurate as E-type estimation. Flow simulation results show that accounting for local constraints yields, on average, smaller errors in production forecast than a smooth estimated map or a simulated map that reproduces only the histogram and semivariogram. The approach thus reduces the risk associated with the use of a single realization for forecasting and planning.