Uncertainty Assessment and Computational Cost of Conditional Sequential Simulation in 3D Modeling

Abstract

Conditional Sequential Simulation Processes takes relatively long computational time in 3D modeling problems depending on many relevant factors like: type of the conditional method used, model of the Variogram function, size of the spatial framework (grid) and obviously number of the repeated simulations. On the other hand, the uncertainty of the simulation depends on many factors; like simulation method, Variogram model, the nature of data and its distribution, the spatial grid framework etc. The present paper study both subjects: (1) the uncertainty analysis and assessment, and (2) computational cost analysis and performance.

Through this study, two well known methods in geostatistics were used, namely Conditional Sequential Gaussian Simulation (SGSim) and Conditional Sequential Indicator Simulation (SISim). In addition, two Variogram models were applied, the Spherical Variogram and the Gaussian Variogram. The theoretical background for each method has been explained briefly and their algorithmic steps have been specified. However variogram models were not discussed and one can find much information on this in the relevant literature.

For the purpose of this research, many tests were applied using real geo-referenced data freely available on the web. In more than 200 tests that were performed, some factors were fixed as they have no much effect on the final accuracy and speed, and three factors only were changed , namely; the size and structure of the 3D grid, the Variogram function and number of simulations each time.

Those tests showed that the uncertainty of results is improved when increasing the size of the grid and number of simulations, but this demands more computational time. Still, we need to answer the most relevant questions: what is the appropriate size of grid?, how many simulations required?, which Variogram model should we use?, in order to obtain the best accurate results with a minimum computational cost.

After many tests and the detailed statistical analysis of the results, the study extracted significant information for optimizing the Conditional Sequential Simulation in 3D modeling and has given clear, precise answers to the questions proposed in this research.