Theory of deterministical and stochastical indicator mapping methods and their applications in reservoir characterization, case study of the Upper Miocene reservoir in the Sava Depression

Abstract

Indicator based geostatistical methods (Indicator Kriging and Sequential Indicator Simulations) are the mostly used methods for facies mapping or modelling. Although it is assumed that in facies variables should be discrete, it is possible to apply these methods on continuous variables as well. If a variable is continuous, a cumulative probability distribution function has to be created. Methodology includes a series of cut-offs. On the cumulative probability distribution function, probabilities for all cut-o s can be defined. Based on cut-offs, all the data can be divided into two groups: (1) the data which has values lower than the cut-o and (2) the data which has values higher or equal than the cut-offs. In this way, the indicator variable takes a value of 1 at all locations where the value is higher or equal than the cut-o and 0 otherwise. The larger number of cut-o s, the more precise the cumulative distribution function is. Indicator Kriging maps show the probability of certain lithofacies appearing in some location. On the other hand, stochastical realizations provide a different number of solutions for the same input data set. Those solutions can be very similar, but never identical. It is important to emphasize that all obtained solutions are equally probable. Results of Sequential Indicator Simulations are also probability maps. There are several advantages for Indicator based methods. They do not ask for a normal distributed input dataset (e.g., can be implemented for bimodal distribution), and show connectivity of the largest or smallest values. Indicator Kriging and Sequential Indicator Simulations are applied for porosity mapping of the Upper Miocene sandstone reservoir in the Sava Depression. During the Upper Miocene, sands were deposited through turbiditic currents in the deepest part of the sedimentation area, forming turbiditic channels. Such channels can be recognized on the probability map for the cut-o 19 % in Indicator Kriging as well as in Sequential Indicator Simulation maps.