In this paper, a comparative performance evaluation of geostatistical,
spectral, and fractal methods is made for short-scale variability
prediction. The algorithms compared are: sequential Gaussian simulation
method; a random fractal algorithm based on the generalised stochastic
subdivision method; and a spectral simulation approach adopted for direct
multi-dimensional simulation. The data for this study have been obtained
from a mined out coal property. As this property was being mined, a
7315 m by 7315 m (24000 ft by 24000 ft) coal block was extensively
sampled at an approximate spacing of 107 m (350 ft) and the 60-ton
samples were analysed for sulphur in the 1.50 float gravity fraction. This
data set is used here with the three methods to generate the simulated
realisations, which are analysed for semivariogram reproduction and for
simulation errors. Although all three methods converge to the true
semivariogram in an average sense, the coefficient of variation of the
average semivariogram for the Fourier integral method is minimum. The
realisations generated by the sequential Gaussian method have minimum
mean simulation error. The choice of a simulation method based on
variability reproduction and simulation errors remains difficult.