A Practical Comparison between Gaussian and Direct Sequential Simulation Algorithms using a ۳D Porosity Dataset

The geo-statistical simulation algorithms for continuous spatial variables have been used widely in order to generate the statistically-honored models. There are two main algorithms doing the continuous variable simulation, Sequential Gaussian Simulation (SGS) and Direct Sequential Simulation (DSS). The main advantage of the DSS algorithm against the SGS algorithm is that in the DSS algorithm no Gaussian transformation of the original data is made. In this work, these two simulation algorithms are explained, and their applications to a ۳D spatial dataset are deeply investigated. The dataset consists of the porosity values of ۱۶ vertical wells extracted from an actual cube obtained by a seismic inversion process. One well data is excluded from the simulation process for the blind well test. Comparison between the histograms show that the histogram reproduction is slightly better for the SGS algorithm, although the population reproductions are the same for both SGS and DSS results. The DSS algorithm reproduce the mean of input data closer to the mean of well data compared to that of the SGS algorithm. Considering one realization from each simulation algorithm, the RMS error corresponding to all simulated cells against the real values is approximately equal for both algorithms. On the other hand, the error show a slightly less value when the mean of ۱۰۰ realizations of the DSS result is considered.

Keywords:

Geostatistics , Sequential Gaussian Simulation , Direct Sequential Simulation , Variogram , Porosity