Geostatistical Modeling in Nonstationary Conditions

This chapter focuses on the hypothesis of stationarity underlying traditional geostatistics, the limitations imposed by this hypothesis, and possible ways to overcome these limitations. The use of traditional geostatistics in non-stationary conditions can lead to significant modeling errors, including a systematic error in all realizations of the stochastic model. However, until recently, geological modeling packages (in oil, gas, and mining) and general-purpose geoinformation systems lacked any built-in tools for verifying stationarity. This chapter proposes a solution to the problem and introduces the tools available for checking the stationarity of the source data. In the second part of the chapter, the Amazonas method is demonstrated as the universal stochastic modeling algorithm that currently allows working with both stationary and non-stationary data, reproducing both smooth gradations and sharp boundaries in property changes. The features of the algorithm are demonstrated with various examples, followed by the comparison of the simulation results with traditional geostatistical tools. This chapter represents an exposition of the author’s research in the field of ensuring the correctness of geological modeling in non-stationary conditions conducted over more than 15 years.