Investigation of lithofacies predictability using the Shannon (information) entropy theorem: the Upper Eocene “Górka Lubartowska” amber deposit of the Siemien Formation

Abstract

A generalized workflow of scientific process requires data to be obtained, reprocessed, integrated, optionally transformed, modelled and finally interpreted in order to understand the underlying process. This procedure is affected by both objective and subjective uncertainties. In parallel with the development of geostatistics, the role of uncertainty has been widely investigated in geosciences. This has led to the introduction of new concepts, taken for example from thermodynamics, such as entropy. Predicting the subsurface is an especially thankless effort, as data are driven from spatially highly limited direct sources. The following paper provides an review of various applications of the Shannon entropy theorem in geoscience. Information entropy, initially proposed by Shannon (1948) provides an objective measure of overall system uncertainty. Significant concern has been focused on the application of Shannon entropy to provide an objective measure of joint system uncertainty and visualization of its spatial distribution. The area of extensively drilled Eocene amber-bearing deposits located in the Lubelskie voivodeship was selected as a case study to investigate the quality of prediction stochastic lithofacies models. The importance of adding secondary variables to a stochastic model is also reviewed here. Adding new data and rerunning the simulation allows assessment of its impact on the predictability of a stochastic model. The most important conclusion from the study is that the deposition of amber-bearing lithofacies occurred mostly in the northern part of the area investigated, as shown also by ongoing exploitation of the deposit.