Improvement of Fourier-based unconditional and conditional simulations forband limited fractal (von Karman) statistical models

We evaluate the performance and statistical accuracy of the fast Fourier tr ansform method for unconditional and conditional simulation. The method is applied under difficult but realistic circumstances of a large field (1001 by 1001 points) with abundant conditioning criteria and a band limited, ani sotropic, fractal-based statistical characterization (the von Karman model) . The simple Fourier unconditional simulation is conducted by Fourier trans form of the amplitude spectrum model, sampled on a discrete grid, multiplie d by a random phase spectrum. Although computationally efficient, this meth od failed to adequately match the intended statistical model at small scale s because of sinc-function convolution. Attempts to alleviate this problem through the "covariance" method (computing the amplitude spectrum by taking the square root of the discrete Fourier transform of the covariance functi on) created artifacts and spurious high wavenumber content. A modified Four ier method, consisting of pre-aliasing the wavenumber spectrum, satisfactor ily remedies sine smoothing. Conditional simulations using Fourier-based me thods require several processing stages, including a smooth interpolation o f the differential between conditioning data and an unconditional simulatio n. Although kriging is the ideal method for this step, it can take prohibit ively long where the number of conditions is large. Here we develop a fast, approximate kriging methodology, consisting of coarse kriging followed by faster methods of interpolation. Though less accurate than full kriging, th is fast kriging does not produce visually evident artifacts or adversely af fect the a posteriori statistics of the Fourier conditional simulation.