Geostatistical conditional fractal simulation with irregularly spaced data

Using the model of fractional Brownian motion a method is given for carrying out conditional simulations on a sparse irregularly spaced data set. The method, on an average, maintains not only the fractal co-dimension but also the histogram, mean, variance and spatial correlation of a two-dimensional random field. The method can be implemented in the same way as either sequential Gaussian simulation or LU decomposition and does not require the use of spectral functions. A sequential Gaussian example is given using the widely published Berea sandstone data set.