direct sequential simulation

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 3D spatial dataset are deeply investigated. The dataset consists of the porosity values of 16 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 100 realizations of the DSS result is considered.

Stochastic seismic inversion is a family of inversion algorithms in which the inverse solution was carried out using geostatistical simulation. In this work, a new 3D stochastic seismic inversion was developed in the MATLAB programming software. The proposed inversion algorithm is an iterative procedure that uses the principle of cross-over genetic algorithms as the global optimization technique.
The model perturbation towards the objective function is performed recurring to direct sequential simulation and co-simulation. This new algorithm was applied to a synthetic dataset with and without noise. The results obtained for the inverted impedance were satisfactory in both cases. In addition, a real dataset was chosen to be applied by the algorithm. Good results were achieved regarding the real dataset. For the purpose of validation, blind well tests were done for both the synthetic and real datasets. The results obtained showed that the algorithm was able to produce inverted impedance that fairly matched the well logs. Furthermore, an uncertainty analysis was performed for both the synthetic and real datasets. The results obtained indicate that the variance of acoustic impedance is increased in areas far from the well location.