Direct sequential simulation with histogram reproduction: A comparison of algorithms

Sequential simulation is a widely used technique applied in geostatistics to generate realisations that reproduce properties such as the mean, variance and semivariogram. Sequential Gaussian simulation requires the original variable to be transformed to a standard normal distribution before implementing variography, kriging and simulation procedures. Direct sequential simulation allows one to perform the simulation using the original variable rather than in normal score space. The shape of the local probability distribution from which simulated values are drawn is generally unknown and this results in direct simulation not being able to guarantee reproduction of the target histogram; only the Gaussian distribution ensures reproduction of the target distribution, and most geostatistical data sets are not normally distributed. This problem can be overcome by defining the shape of the local probability distribution through the use of constrained optimisation algorithms or by using the target normal-score transformation. We investigate two non-parametric approaches based on the minimisation of an objective function subject to a set of linear constraints, and an alternative approach that creates a lookup table using Gaussian transformation. These approaches allow the variography, kriging and simulation to be performed using original data values and result in the reproduction of both the histogram and semivariogram, within statistical fluctuations. The programs for the algorithms are written in Fortran 90 and follow the GSLIB format. Routines for constrained optimisation have been incorporated.