Revisited Formulation and Applications of FFT Moving Average
Résumé
The fast Fourier transform-moving average (FFT-MA) is an efficient method for the generation of geostatistical simulations. The method relies on the calculation of a filter operator based on the covariance function of interest and the convolution of the filter with a white noise, to generate multiple realizations of spatially correlated variables. In this work, a revisited mathematical formulation of the FFT-MA method, with the exact expression of the filter, is presented. The proposed derivation of the filter is based on the Wiener–Khinchin theorem and the application of the Fourier transform in a discrete domain. In the specific case of white noise, the proposed formulation leads to the same expression of the traditional algorithm. However, the method can be applied to other types of noise. The proposed technique allows the calculation of a specific filter that imposes an exact covariance function on the noise. Therefore, the experimental covariance function is exactly equal to the theoretical one, which is not the case for many common simulation techniques due to the limited sample size. Applications of the FFT-MA method to synthetic and real data sets, including exact interpolation, hard data conditioning and correlated simulations from cross-correlated noises, are also presented.