FLEXIBLE SPECTRAL METHODS FOR THE GENERATION OF RANDOM-FIELDS WITH POWER-LAW SEMIVARIOGRAMS

Random field generators serve as a tool to model heterogeneous media f or applications in hydrocarbon recovery and groundwater flow. Random f ields with a power-law variogram structure, also termed fractional Bro wnian motion (fBm) fields, are of interest to study scale dependent he terogeneity effects on one-phase and two-phase flow. We show that such fields generated by the spectral method and the Inverse Fast Fourier Transform (IFFT) have an incorrect variogram structure and variance. T o illustrate this we derive the prefactor of the fBm spectral density function, which is required to generate the fBm fields. We propose a n ew method to generate fBm fields that introduces weighting functions i nto the spectral method. It leads to a flexible and efficient algorith m. The flexibility permits an optimal choice of summation points (that is points in frequency space at which the weighting function is calcu lated) specific for the autocovariance structure of the field. As an i llustration of the method, comparisons between estimated and expected statistics of fields with an exponential variogram and of fBm fields a re presented. For power-law semivariograms, the proposed spectral meth od with a cylindrical distribution of the summation points gives optim al results.