Stochastic modeling in geology: Determining the sufficient number of models

Abstract

Finding the optimal number of realizations to represent the model uncertainty when applying stochastic approaches is still a relevant question in geostatistics. The essence of the method is to visualize the realizations in a suitably constructed attribute space. To construct this space, the static connectivity metrics of the realizations were used. Within this framework, the creation of new realizations can be regarded as a sampling process, in which each new stochastic image is the equivalent of a new sampling point in the attribute space. The sampling process begins with the first few realizations appearing in a dispersed manner in random parts of the attribute space. The addition of more realizations causes the gradual emergence of higher point densities, which in the end, results in a point structure where most of the points are located in areas of high point densities with areas of low point densities surrounding them. High point densities represent typical realizations showing very similar connectiv...