Calibration of random fields by FFTMA-SA

Abstract

A new algorithm is presented aiming to generate realizations calibrated to desired or observed field response functions. The Fast Fourier Transform Moving Average - simulated annealing algorithm (FFTMA-SA) combines the FFTMA method of simulation and the simulated annealing (SA) method for calibration. SA is performed on the uncorrelated random numbers used within the FFTMA algorithm, keeping by construction the field covariance function unchanged. Hard data exact conditioning by kriging is easily introduced into the algorithm main loop. An interesting advantage of FFTMA-SA is the capability to perturb the field locally or globally, simultaneously on any desired number of points. We therefore introduce a decreasing schedule on the number of points to perturb mimicking the cooling schedule of the temperature parameter in SA. Two cases studies are presented. The first one is a spatially asymmetric synthetic field where FFTMA-SA is shown to better reproduce the spatial asymmetry than calibrated realizations obtained either by classical SA or by FFTMA combined with gradual deformation. The second example is the Walker Lake data where regularized row and columns facies proportions are imposed. It is shown that few iterations (100) of FFTMA-SA are enough to reproduce the main characteristics of the proportion curves. Increasing the number of iterations only reduces rather uniformly the variability of realization proportions. The same data is used to illustrate the local calibration capability of the method with a local data assimilation example. The proposed algorithm offers a simple and flexible tool for calibration. It is easily adaptable for any moving average method of simulation.